The Astrophysical Journal, 797:54 (30pp), 2014 December 10 doi:10.1088/0004-637X/797/1/54 C\Theta 2014. The American Astronomical Society. All rights reserved. Printed in the U.S.A. ULTRALUMINOUS INFRARED GALAXIES IN THE AKARI ALL-SKY SURVEY E. Kilerci Eser1, T. Goto2, and Y. Doi31 Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen O/, Denmark; ecekilerci@dark-cosmology.dk2 National Tsing Hua University, No. 101, Section 2, Kuang-Fu Road, Hsinchu 30013, Taiwan; tomo@phys.nthu.edu.tw3 The University of Tokyo, Komaba 3-8-1, Meguro, Tokyo 153-8902, Japan; doi@ea.c.u-tokyo.ac.jp Received 2014 January 10; accepted 2014 September 19; published 2014 November 25 ABSTRACT We present a new catalog of 118 ultraluminous infrared galaxies (ULIRGs) and one hyperluminous infrared galaxy(HLIRG) by cross-matching the AKARI all-sky survey with the Sloan Digital Sky Survey Data Release 10 (SDSS DR10) and the final data release of the Two-Degree Field Galaxy Redshift Survey. Forty of the ULIRGs and oneHLIRG are new identifications. We find that ULIRGs are interacting pair galaxies or ongoing or postmergers. This is consistent with the widely accepted view: ULIRGs are major mergers of disk galaxies. We confirm thepreviously known positive trend between the active galactic nucleus fraction and infrared luminosity. We show that ULIRGs have a large offset from the main sequence up to z \Lambda 1; their offset from the z \Lambda 2 "main sequence"is relatively smaller. We find a result consistent with the previous studies showing that, compared to local starforming SDSS galaxies of similar mass, local ULIRGs have lower oxygen abundances. We demonstrate for thefirst time that ULIRGs follow the fundamental metallicity relation (FMR). The scatter of ULIRGs around the FMR (0.09 dex-0.5 dex) is comparable to the scatter of z \Lambda 2-3 galaxies. We provide the largest local (0.050 < z <0.487) ULIRG catalog with stellar masses, star-formation rates, gas metallicities, and optical colors. Key words: galaxies: general - galaxies: interactions - galaxies: starburst - infrared: galaxies Online-only material: color figures 1. INTRODUCTION Luminous infrared galaxies (LIRGs), ultraluminous in-frared galaxies (ULIRGs), and hyperluminous infrared galaxies (HLIRGs) are defined by their high IR luminosities that are inthe 1011 L\Xi \Theta LIR < 1012 L\Xi , 1012 L\Xi \Theta LIR < 1013 L\Xi ,and 1013 L\Xi \Theta LIR ranges, respectively (see the reviews bySanders & Mirabel 1996; Lonsdale et al. 2006). The observed enormous IR luminosity is driven by the optical and ultraviolet(UV) radiation generated by intense star formation and active galactic nuclei (AGNs) that is absorbed by dust and re-emittedin the IR. ULIRGs have been considered as a transition phase from mergers to dusty quasars (Sanders et al. 1988b; Veilleuxet al. 2002) such that when gas-rich spiral galaxies merge, the molecular gas clouds channeling toward the merger nucleustrigger nuclear starbursts and AGN activity by the accretion of the available fuel onto the central supermassive black hole(SMBH). According to this scenario, the starburst phase evolves to a dust-enshrouded AGN phase, and once the gas and dust areconsumed, the system evolves to a bright QSO phase. Tidal interactions and merger processes between galaxiesplay a major role in the formation of elliptical galaxies (Toomre & Toomre 1972). In particular, the proposed scenario by Sanderset al. (1988b) motivated further investigation of the link between mergers and quasars in numerical simulations. Hydrodynami-cal simulations of mergers show that merger processes lead gas inflows toward the center that trigger starbursts and AGN ac-tivity (e.g., Springel et al. 2005). In the merger-driven galaxy evolution simulations, ULIRGs represent a contemporary star-burst and AGN phase at the beginning of rapid self-regulated SMBH growth (e.g., Di Matteo et al. 2005; Hopkins et al. 2007).ULIRGs evolve to red or elliptical-type remnants by negative feedback mechanisms (e.g., in the form of powerful winds andoutflows) that inhibit star formation and AGN activity (e.g., Hopkins et al. 2006, 2008a, 2008b, 2009). The link that emerged between ULIRGs and QSOs is sup-ported by much observational evidence. The morphological properties of ULIRGs indicate that they are interacting galaxiesin pre-, ongoing, or late-merger stages (Farrah et al. 2001; Kim et al. 2002; Veilleux et al. 2002, 2006). Compared to LIRGsthat are disk galaxies (if log( LIR/L\Xi ) < 11.5) or interactingsystems (if 11 .5 \Theta log(LIR/L\Xi ) < 12.0), ULIRGs are mostlyadvanced mergers (Veilleux et al. 2002; Ishida 2004). Their dynamical masses obtained from near-infrared (NIR) spectroscopyshow that they are major mergers of nearly equal mass galaxies (Veilleux et al. 2002; Dasyra et al. 2006a, 2006b). CO observa-tions proved that ULIRGs contain the required cold molecular gas for central starbursts (Downes & Solomon 1998). In addi-tion, their mid-infrared (MIR) images show that MIR emission is generated in a region of diameter \Lambda 1 kpc (Soifer et al. 2000).At least \Lambda 70% of 164 local ( z \Theta 0.35) ULIRGs harbor anAGN (Nardini et al. 2010). The coexistence of a starburst and an AGN show that both energy sources contribute to the to-tal IR luminosity. The AGN fraction and the strength of the AGN emission increases with IR luminosity; high-luminosityULIRGs (log( LIR/L\Xi ) > 12.5) and HLIRGs have a larger AGNcontribution than do lower luminosity IR galaxies (Veilleux et al. 1995, 1999b, 2002, 2009; Genzel et al. 1998; Goto 2005;Imanishi 2009; Nardini et al. 2010). ULIRGs show starburstand AGN-driven powerful outflows (e.g., Heckman et al. 2000;Rupke et al. 2002, 2005; Rupke & Veilleux 2011, 2013; Spoon et al. 2013; Veilleux et al. 2013, and references therein) that areconsistent with the negative feedback mechanisms expected for their evolution.The significance of ULIRGs in galaxy evolution is not limited to the local (z < 0.3) universe because at high redshift (z >1)they are more numerous and have a substantial contribution to the total IR luminosity density (Le Floc'h et al. 2005; Caputiet al. 2007) compared to local ULIRGs (Soifer & Neugebauer 1991; Kim & Sanders 1998). There is a significant population of 1 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi ULIRGs beyond z \Lambda 1 (e.g., Goto et al. 2011b). An importantquestion is the powering mechanism of these sources: are they powered by interaction-induced nuclear starbursts or AGN, orare they normal or undisturbed star-forming galaxies? The key properties that would answer this question are morphologies,spectral energy distributions (SEDs), and the extent of starforming regions. Observations have shown that ULIRGs athigh redshift (1.5 < z < 3.0) are mostly (\Lambda 47%) mergers orinteracting galaxies, but this sample also includes noninteracting disks, spheroids, and irregular galaxies (Kartaltepe et al. 2012).Beyond z > 2, the morphological properties of submillimetergalaxies (SMGs) are consistent with mergers and interacting systems (e.g., Tacconi et al. 2008). The morphologies ofhighz samples show that mergers or interactions are takingplace in these systems, and even a comparison of z \Lambda 2 and z \Lambda 1 samples indicates a hint of a morphological evolution suchthat z \Lambda 1 samples have slightly more mergers and interactinggalaxies (Kartaltepe et al. 2012). The SEDs of high-redshift ULIRGs are different from those of local ones. For example,they exhibit prominent polycyclic aromatic hydrocarbon (PAH) features more similar to those of local, lower IR luminosity(10.0 \Theta log( LIR/L\Xi ) < 11.0) star-forming galaxies (SFGs)than those of local ULIRGs (e.g., Farrah et al. 2008; Takagi et al. 2010). Because PAH emission indicates ongoing starformation, observations support the idea that highz ULIRGs arestarburst dominated. A similar conclusion is also achieved by the X-ray studies of high-z ULIRGs (e.g., Johnson et al. 2013).The size of the star-forming regions of highz ULIRGs arelarger than those of local ULIRGs with similar LIR (Rujopakarnet al. 2011). This suggests that in these galaxies star formation does not occur in merger nuclei, but instead it is distributedgalaxy-wide. The similarities of star-forming regions of highzULIRGs and local quiescent SFGs point to a different origin than merger-induced star formation (Rujopakarn et al. 2011).Although the evolution of ULIRGs is not fully understood yet, the observations provide evidence for changing propertieswith redshift. Understanding the role of ULIRGs in galaxy evolutionthrough cosmic time requires extensive studies and comparison of local and high-z samples. Local ULIRGs establish a basis forunderstanding the nature of ULIRGs, the origin of their extreme luminosities, and the interplay between star formation and AGNactivity in the nearby mergers. Therefore, it is important to have a large local sample and to master its overall properties.The great majority of local ULIRGs are discovered with the InfraRed Astronomy Satellite (IRAS). IRAS performed an all-skyscan in four IR bands centered at 12 um, 25 um, 60 um, and100 um. The IRAS Bright Galaxy Survey (BGS) catalog (Soiferet al. 1987) includes 10 ULIRGs selected on the basis of 60 umflux, F(60 um). This catalog was replaced by the IRAS RevisedBright Galaxy Sample (Sanders et al. 2003), which provided more accurate infrared luminosities and increased the numberof ULIRGs to 21. The IRAS 2 Jy (Strauss et al. 1992) and 1.2 Jy (Fisher et al. 1995) redshift surveys identified new ULIRGs.Sanders et al. (1988a) showed that ULIRGs with warmcolors (F(25 um)/F(60 um) > 0.2) have Seyfert-like spectra, andtherefore ULIRGs were separated into warm AGN-hosting and coldstar formation dominated systems. An analysis of the BGSsample showed that the F(60 um)/F(100 um) color increaseswith higher LIR (Soifer & Neugebauer 1991). A widely studiedlarge sample of local ULIRGs is the IRAS 1 Jy sample (Kim et al. 1998). This is a complete flux-limited sample at 60 um that iscomposed of 118 ULIRGs identified from the IRAS Faint Source Catalog (FSC; Moshir et al. 1992) and a dedicated redshiftsurvey (Kim et al. 1998). Because previous studies (Soifer & Neugebauer 1991; Strauss et al. 1992) showed that F(60 um)/F(100 um) color increases with higher LIR and that ULIRGcolors are in the range of -0.2 < F(60 um)/F(100 um) < 0.13,the IRAS 1 Jy sample ULIRGs were selected based on their warm colors (F(60 um)/F(100 um) > 0.3) (Kim et al. 1998). Withother redshift surveys such as the QDOT all-sky IRAS galaxy redshift survey (Lawrence et al. 1999), the IRAS Point SourceCatalog Redshift survey (Saunders et al. 2000), and the FIRST /IRAS radio-far-IR sample (Stanford et al. 2000), the number of IRAS ULIRGs increased. Large galaxy redshift surveyslike the Sloan Digital Sky Survey (SDSS; York et al. 2000) and the Two-Degree Field Galaxy Redshift Survey (2dFGRS;Colless et al. 2001) provide the redshifts of millions of galaxies. In particular, the SDSS made it possible to study the opticalproperties of a large sample of IR galaxies. Goto (2005) crosscorrelated the IRAS FSC with the SDSS Data Release 3 (DR3;Abazajian et al. 2005) spectroscopic catalog and identified 178 ULIRGs. Pasquali et al. (2005) cross-correlated the SDSS DR2(Abazajian et al. 2004) with the IRAS FSC and investigated the IR properties of local AGNs and star-forming galaxies.Cao et al. (2006) cross-correlated the IRAS FSC and the Point Source Catalog (PSC) with the SDSS DR2 and identified asmall sample of ULIRGs. Hwang et al. (2007) identified 324 ULIRGs, including 190 new discoveries, by cross-correlatingIRAS FSC with SDSS DR4 (Adelman-McCarthy et al. 2006), 2dFGRS, and the second data release of the 6dF Galaxy Survey(Jones et al. 2004). Hou et al. (2009) cross-correlated the IRAS FSC with the SDSS DR6 (Adelman-McCarthy et al. 2008) andidentified 308 ULIRGs. The largest all-sky IR survey after IRAS was completed by theJapanese IR satellite launched in 2006, AKARI (Murakami et al. 2007), which scanned almost all of the sky in 9 um, 18 um,65 um, 90 um, 140 um, and 160 um bands. The resolutionand sensitivity of AKARI is better than those of IRAS: the point-spread function (PSF) of AKARI is \Lambda 39\Pi \Pi (for the 90 umband), and the PSF of IRAS is \Lambda 4\Pi (for the 100 um band); at18 um AKARI is 10 times more sensitive. Another advantageof AKARI is that it has a wider and longer wavelength coverage than IRAS. In particular, the 140 um and 160 um bands are veryimportant in order to measure the peak of the dust emission near 100 um and therefore obtain more accurate IR luminosity.Goto et al. (2011b) matched IRAS IR sources with SDSS DR7 (Abazajian et al. 2009) galaxies and measured the local IRluminosity function. In this study, Goto et al. (2011b) identified ULIRGs among AKARI sources, but they did not provide adetailed catalog of these sources. In this work, we search for ULIRGs and HLIRGs in the AKARI all-sky survey. We cross-correlate the AKARI all-sky survey with 2dFGRS and the largest SDSS spectroscopic redshift catalog DR 10 (Ahn et al. 2014).In addition to the redshift information, the SDSS has a rich view of optical properties of the sources in this database. Theoptical images, spectra, colors, and value-added catalogs with emission-line properties provided by SDSS D10 give us anopportunity to investigate the morphologies, colors, stellar mass, and metallicities of the local ULIRGs identified in the AKARIall-sky survey. We provide the first catalog of ULIRGs identified in the AKARI all-sky survey.This paper has the following structure. We introduce the data to identify ULIRGs/HLIRGs and our final sample in Section 2.Our results are presented in Section 3. In Section 4, we discuss our results. This work is summarized in Section 5. Throughout 2 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi this work, we adopt a cosmology with H0 = 70 km s-1 Mpc-1,\Omega \Lambda = 0.7, and \Omega m = 0.3. 2. IDENTIFICATION OF ULTRALUMINOUS ANDHYPERLUMINOUS INFRARED GALAXIES IN THE AKARI ALL-SKY SURVEY 2.1. The Samples 2.1.1. The AKARI All-sky Survey Catalogs The AKARI all-sky survey provides two catalogs of theIR sources across more than \Lambda 97% of the whole sky with fluxes centered on two mid-IR and four far-IR bands. TheAKARI /IRC all-sky survey point source catalog version 14includes 870,973 IR sources with fluxes in the 9 um and18 um mid-IR bands. The AKARI/FIS all-sky survey brightsource catalog version 15 (Yamamura et al. 2010) contains 427,071 sources detected at 90 um with flux measurementsin the 65 um 90 um 140 um and 160 um FIR bands. Inparticular, the 140 um and 160 um fluxes are very important inconstraining the FIR SED peak and measuring LIR.In order to have a single AKARI /FIS/IRC catalog with bothFIR and mid-IR fluxes, we cross-match the IR sources in the AKARI/FIS all-sky survey bright source catalog with theAKARI /IRC all-sky survey point source catalog within a radiusof 20\Pi \Pi . The resulting AKARI /FIS/IRC catalog contains 24,701sources based on 90 um detections.To measure the IR luminosity, we obtain the spectroscopic redshifts of the IR galaxies from their optical counterparts.We cross-correlate the AKARI /FIS/IRC catalog with the largeoptical redshift catalogs as described in the following. 2.1.2. The AKARI-SDSS DR10 Sample The SDSS is the largest ground-based survey that provides aunique photometric and spectroscopic database of stars, galaxies, and quasars. The SDSS is a red magnitude limited r < 17.7survey over 14,555 deg2 of the sky. We have downloaded the SDSS DR 10 (Ahn et al. 2014) catalogs photoObj6 andspecObj3 to extract both photometric and spectroscopic information. The photoObj catalog includes all photometric infor-mation from previous data releases, and the specObj catalog includes new spectra from the Baryon Oscillation SpectroscopicSurvey7 (BOSS). We combined the two catalogs by matching OBJID in photoObj to "BESTOBJID" in specObj to obtain afull SDSS catalog of 2,745,602 sources with spectroscopic and photometric information.The AKARI /FIS/IRC catalog is cross-matched with the fullSDSS catalog. The astrometric precision of SDSS (\Lambda 0 .\Pi \Pi 1 atr = 19 mag Pier et al. 2003) is much better than that of AKARI (\Lambda 4.\Pi \Pi 8 Yamamura et al. 2010). We follow Goto et al.(2011b) and select matching radii as 20\Pi \Pi because this radius is large enough to contain different emission regions (e.g., IR andoptical) in a single galaxy; it is also small enough to not allow too many optical chance identifications that are not physicallyrelated to the IR source. Although we pick 20\Pi \Pi to be inclusive and not miss any real association, in order to eliminate anymisassociation later, we check the positional overlap of the IR 4 http://www.ir.isas.jaxa.jp/AKARI/Observation/PSC/Public/RN/AKARIIRC_PSC_V1_RN.pdf5 http://www.ir.isas.jaxa.jp/AKARI/Observation/PSC/Public/RN/AKARI-FIS_BSC_V1_RN.pdf 6 http://www.sdss3.org/dr10/spectro/spectro_access.php 7 http://www.sdss3.org/surveys/boss.php and the optical emission from each ULIRG candidate by eye.We avoid any duplicated matches, i.e., each IR galaxy is allowed to match only one SDSS counterpart. We obtain 6,468 matchesof AKARI-SDSS sources. Among those we removed the sources that were classified as stars in the specObj catalog. This resultedin a AKARI SDSS sample of 6,373 galaxies. For the IR sources in this sample we adopt the SDSS spectroscopic redshifts. 2.1.3. The AKARI-2dFGRS Sample The 2dFGRS (Colless et al. 2001) measured redshifts of245,951 galaxies within a bj < 19.45 limit. The median redshiftof this survey is z \Lambda 0.1 (Colless 2004). We use the finaldata release of the 2dFGRS, the catalog of best spectroscopic observations.8 We cross-match the AKARI/FIS/IRC catalogwith the 2dFGRS catalog with a matching radius of 20\Pi \Pi . We obtain a AKARI-2dFGRS sample of 954 galaxies withspectroscopic redshifts from 2dFGRS. 2.2. Infrared Luminosity Measurements To estimate the total IR luminosity for the galaxies inthe AKARI-SDSS and AKARI-2dFGRS samples, we perform an SED fitting using the LePhare9 (Photometric Analysisfor Redshift Estimations) code (Arnouts et al. 1999; Ilbert et al. 2006). The main function of the LePhare is to computephotometric redshifts, but it can also find the best-fitting galaxy template by a \Theta 2 fit for the given photometric magnitudesamong the input template libraries. For the AKARI-SDSS and AKARI-2dFGRS samples, we use the six AKARI bands withtheir associated uncertainties adopted from the AKARI catalogs; if the flux uncertainty is not given, we adopt 25% of themeasured flux as the uncertainty. We use the FIR SED templates of Dale & Helou (2002) as the input library. Dale & Helou(2002) provide 64 SED templates generated semiempirically to represent the IR SEDs of star-forming galaxies. Comparedto other SED models, such as the models of Chary & Elbaz (2001), these templates include FIR improvements based onISO /IRAS/SCUBA observations. However, they do not includemore sophisticated dust emission modeling as provided by Siebenmorgen & Kr"ugel (2007). Because our main focus is onmeasuring LIR, we avoid more sophisticated models and preferthe templates of Dale & Helou (2002) for the SED fitting. We fix the redshift of each galaxy and fit the FIR region of the SEDwith the AKARI broadband photometry. In the fitting procedure, k corrections are applied to the AKARI fluxes. In order to obtainthe k correction, our model flux is computed by integrating the redshifted SED model flux through AKARI's filter responsefunction. The best-fit dust templates of Dale & Helou (2002) are shown in Figure 1 (left column) for representative cases. TheAKARI /FIS name is given in the top left corner. The best-fittemplates are shown as solid magenta lines. The black filled circles are the optical (shown only for illustration purposes) andAKARI photometric fluxes; the x-axis error bars represent the wavelength range of each photometric band.As a result of the SED fitting, we obtain the total infrared luminosity integrated between 8 um and 1000 um, L8-1000 withthe maximum and minimum possible L8-1000 value based onthe flux errors. These are used to determine the upper and lower uncertainties of L8-1000.Based on the obtained L8-1000, our initial sample includes 170ULIRG and 10 HLIRG candidates: the AKARI-SDSS sample 8 http://www2.aao.gov.au/\Lambda TDFgg/ 9 http://www.cfht.hawaii.edu/\Lambda arnouts/lephare.html 3 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi Figure 1. SEDs (left), AKARI (middle), and SDSS g-r-i color combined images (right) of the four nearest ULIRGs classified as IIIa (first row), IIIb (second row), IV(third row), and IV (fourth row). The scale of the AKARI 90 um images are 165\Pi \Pi OE165\Pi \Pi . The small 5\Pi \Pi radius (colored magenta in the online version) and the large 20\Pi \Pi radius (colored green in the online version) circles mark the optical and IR sources, respectively. (A color version of this figure is available in the online journal.) has 135 ULIRG and eight HLIRG candidates, and the AKARI2dFGRS has 35 ULIRG and two HLIRG candidates. In order to have a reliable sample of ULIRGs and HLIRGs, we checkeach case to avoid any wrong identification as described in the following. 2.3. Elimination of the Mismatches The (H)ULIRG candidates in our initial sample are selectedbased on the optical spectroscopic redshifts by matching the closest optical galaxy to the AKARI source. If there is morethan one source satisfying the cross-match condition, then the 4 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi one with the smallest positional difference is considered to be amatch. Even though the positions of the optical and IR sources are close in the sky, it does not necessarily mean that the IR andoptical emissions are counterparts of the same galaxy; further care is required to make this decision.Although the optical and IR galaxies are matched within a 20\Pi \Pi radius, we visually check the positional overlap of the IRand optical emission in the AKARI images for each galaxy. For the optical counterpart we use SDSS (if available) or DigitizedSky Survey images. Examples of AKARI (middle panel) and optical (right panel) images are represented in Figure 1. TheSDSS images are gri combined color images downloaded fromthe SDSS DR10 Finding Chart Tool.10 In the AKARI images (Doi et al. 2012), the green circle represents the 20\Pi \Pi radiuslimit, whereas the optical source is marked with a 5\Pi \Pi radius magenta circle. Once we verify the positional overlap of thematched IR and optical sources, next we check whether there are any other sources overlapping with the IR source and possiblycontaminating the IR emission. Such contaminating sources can be stars or other galaxies. In particular, nearby bright galaxieslying over the IR source contribute to the observed IR emission, and therefore such cases are eliminated from the initial sample.If there is more than one overlapping optical galaxy with similar separation values within the 20\Pi \Pi radius region, the closest one isnot necessarily the true match. Because it is difficult to select the true optical counterpart for these four cases, these are eliminated.It is a concern if we are automatically removing compact groups of galaxies in these cases, but before we eliminate these weconsider the redshifts of these galaxies and check if they are in groups.Although the SDSS provides a large redshift database, not all galaxies have the spectroscopic information. Related to this, insome cases the optical source with the smallest positional difference is not included in the cross-match procedure. Therefore,the images show that instead of the true optical counterpart, some other optical galaxy with a large separation (8.\Pi \Pi 12-18.\Pi \Pi 87)is matched with the IR emission. For these cases we look at the literature (e.g., Wang & Rowan-Robinson 2009) and checkif the true optical counterpart has a spectroscopic redshift. If the redshift is not known for the "true" optical counterpart, weeliminate these cases. If the redshift is known, we adopt it for the true optical counterpart and reobtain L8-1000. Three cases(marked with an asterisk in Column 5 of Tables 1 and 2) for which 1012 L\Xi \Theta L8-1000 are kept in the sample.After we secure the optical and IR galaxy match by visual inspection, as an additional control we check the adoptedspectroscopic redshifts. For the AKARI-2dFGRS sample we require a redshift quality of \Lambda 3. This requirement led toelimination of two ULIRG and two HLIRG candidates from the AKARI-2dFGRS sample. For the AKARI-SDSS sample, wego through the SDSS spectra.11 The SDSS spectra are reduced through the spectroscopic pipeline (Bolton et al. 2012). TheSDSS pipeline determines the classification and the redshift of the spectra by applying a \Theta 2 fit with rest-frame templates ofstars, galaxies, and quasars. By looking at the SDSS spectra we eliminate the following cases from the sample: (1) the sourcesthat are classified as a galaxy but show a spectrum of a star, and (2) the spectra that show an unreliable template fit and thereforeindicate a wrong redshift. 10 http://skyserver.sdss3.org/dr10/en/tools/chart/chartinfo.aspx 11 http://dr10.sdss3.org/basicSpectra 2.4. The Final Sample Our final sample of (H)ULIRGs consists of 119 galaxies: 97are identified in the AKARI-SDSS sample and 22 are identified in the AKARI-2dFGRS sample. In order to specify the newlyidentified (H)ULIRGs in this work, we check our final sample against previously studied samples: Clements et al. (1996), Kimet al. (1998), Rowan-Robinson (2000), Hwang et al. (2007), Hou et al. (2009), and Nardini et al. (2010). Thus 40 ULIRGs andone HLIRG are newly identified in this work. The IR images of the newly identified ULIRGs and one HLIRG are availablein the Appendix (Figure A1). We divide the final sample into three subsamples: (1) new ULIRGs identified in this work, (2)known ULIRGs, and (3) new HLIRGs identified in this work. The properties of these subsamples are listed in Tables 1, 2,and 3, respectively. These tables contain the AKARI name (Column 1), the AKARI coordinates R.A. and decl. (Columns 2and 3, respectively), other name (Column 4), redshift (Column 5), total IR luminosity, LIR, (Column 6), AKARI photometricfluxes of the 65 um (F(65 um)), 90 um (F(90 um)), 140 um(F(140 um)), and 160 um (F(160 um)) bands (Columns 7, 8, 9,and 10, respectively), SDSS Petrosian r magnitude (Column 11), interaction class (IC; Column 12), reference for IC (Column 13),note related to optical images indicating if there is a star or other galaxies in the field (Column 14), and spectral classification(Column 15). Because we have only a few sources detected in the 9 um and 18 um bands, we do not list the photometric fluxesat these bands. We note that three of the new ULIRGs listed in Table 1have 65 um fluxes above 1 Jy, the flux threshold of the 1 Jysample of Kim et al. (1998), and have declination \Lambda > -40 degand galactic latitude b > 30 deg and therefore should havemade it into the 1 Jy sample. However, two of these sources (J1036317+022147 and J1125319+290316) are not observedwith IRAS. The 60 um flux of J0857505+512037 is below 1 Jy(\Lambda 0.6 Jy Moshir et al. 1992), and therefore it is not in the 1 Jy sample of Kim et al. (1998).In Table 4 we list five additional ULIRG candidates that are considered as unconfirmed cases either because their IRdetection is not significant (almost at 5 \Xi ) or the separationbetween the matched optical and IR coordinates are large (\Lambda 20\Pi \Pi ). We do not include those five sources in the final sample. 3. ANALYSIS AND RESULTS 3.1. Basic Properties of the AKARIULIRG and HLIRG Samples 3.1.1. Redshift and LIR Distributions The redshift and IR luminosity distributions of our finalsample are presented in the top and bottom panels of Figure 2, respectively. The redshift distribution covers 0.050 < z < 0.487,with a median redshift of _ z = 0.181. We have 104 ULIRGsdistributed over the 0.050 < z \Theta 0.270 range, and 14 ULIRGsare within the 0.270 < z < 0.487 range. The IR luminositydistribution of 80 ULIRGs covers the 12 .0 \Theta LIR \Theta 12.25range. The higher luminosity range of 12.25 < LIR \Theta 12.91includes 38 ULIRGs. Figure 3 shows the IR luminosity of our sample as a functionof redshift. As expected from the AKARI PSC detection limit (0.55 Jy at 90 um), LIR increases with redshift, and only thebright sources can be detected toward the higher redshifts. 5 Th eA str oph ysi cal Jou rna l,7 97: 54 (30 pp) ,20 14 De cem ber 10 Ese r,G oto ,& Do i Table 1 New ULIRG Sample Name AKARI R.A. AKARI Decl. Other Name za log(LIR/L\Xi )b F(65 um)c F(90 um)c F(140 um)c F(160 um)c rd ICe ICf Noteg Spectralh AKARI-FIS-V1 (J2000) (J2000) (Jy) (Jy) (Jy) (Jy) (mag) Ref. Class (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) J2216028+005813 22 16 02.82 +00 58 13.5 SDSS J221602.70+005811.0 0.21* 12.83+0.15-0.14 0.54 s' 0.13 0.54 s' 0.05 0.96 s' 0.63 1.14 s' 0.28 14.30 IIIa 3 u* u* u* u* u* u* J0859229+473612 08 59 22.93 +47 36 11.7 SDSS J085923.61+473610.5 0.180 12.20+0.01-0.09 u* u* u* 0.48 s' 0.06 1.95 s' 0.29 u* u* u* 14.44 IIIa 3 u* u* u* Star forming J1443444+184950 14 43 44.44 +18 49 49.7 SDSS J144344.64+184945.7 0.177 12.21+0.01-0.31 0.43 s' 0.11 0.55 s' 0.04 1.69 s' 0.53 u* u* u* 16.03 V 3 u* u* u* LINER J0857505+512037 08 57 50.48 +51 20 37.2 SDSS J085750.79+512032.6 0.366 12.89+0.07-0.02 1.12 s' 0.28 0.68 s' 0.06 1.58 s' 0.08 u* u* u* 14.40 IIIb 3 u* u* u* LINER J1106104+023458 11 06 10.37 +02 34 57.8 SDSS J110611.44+023502.2 0.283 12.23+0.06-0.06 u* u* u* 0.42 s' 0.01 1.42 s' 0.36 0.56 s' 0.14 17.17 NI 3 B Seyfert J1157412+321316 11 57 41.21 +32 13 16.4 SDSS J115741.47+321316.4 0.160 12.14+0.01-0.12 0.66 s' 0.16 0.60 s' 0.03 2.22 s' 1.21 2.23 s' 0.40 16.37 V 3 u* u* u* Star forming J1149200-030357 11 49 20.03 -03 03 57.3 SDSS J114920.04-030402.1 0.162 12.02+0.02-0.04 0.19 s' 0.05 0.42 s' 0.02 1.30 s' 0.33 2.58 s' 0.21 13.97 V,G 3 u* u* u* Star forming J0126038+022456 01 26 03.80 +02 24 55.9 SDSS J012604.62+022509.9 0.242 12.22+0.04-0.06 u* u* u* 0.63 s' 0.01 0.70 s' 0.18 u* u* u* 14.73 Tp1,G 3 u* u* u* LINER J1556089+254358 15 56 08.92 +25 43 57.8 SDSS J155609.36+254355.9 0.154 12.03+0.01-0.26 0.56 s' 0.14 0.51 s' 0.01 2.26 s' 0.57 u* u* u* 16.76 IIIa,G 3 u* u* u* Composite J0140364+260016 01 40 36.40 +26 00 15.9 SDSS J014037.36+260001.5 0.321 12.77+0.06-0.02 0.57 s' 0.14 0.56 s' 0.03 0.70 s' 0.17 2.51 s' 0.15 16.01 IIIa,G 3 u* u* u* Seyfert J1257392+080935 12 57 39.15 +08 09 35.1 SDSS J125739.33+080931.7 0.272 12.24+0.04-0.02 0.46 s' 0.12 0.51 s' 0.01 u* u* u* 0.22 s' 0.06 17.72 NI 3 u* u* u* QSO J0800007+152319 08 00 00.68 +15 23 18.7 SDSS J080000.05+152326.0 0.274 12.14+0.00-0.00 u* u* u* 0.43 s' 0.03 u* u* u* u* u* u* 14.50 V 3 A LINER\Pi J0800279+074858 08 00 27.92 +07 48 57.6 SDSS J080028.37+074915.5 0.173 12.12+0.00-0.09 0.34 s' 0.09 0.35 s' 0.09 2.29 s' 0.57 2.04 s' 0.51 13.10 V,G 3 u* u* u* LINER J0834438+334427 08 34 43.82 +33 44 27.2 SDSS J083443.56+334432.5 0.166 12.13+0.03-0.20 0.59 s' 0.15 0.65 s' 0.04 u* u* u* 2.07 s' 0.52 15.90 IIIb 3 A Composite J0823089+184234 08 23 08.91 +18 42 33.9 SDSS J082309.51+184233.4 0.425 12.57+0.43-0.03 0.45 s' 0.11 0.41 s' 0.02 u* u* u* u* u* u* 12.52 V 3 u* u* u* u* u* u* J1202527+195458 12 02 52.69 +19 54 58.4 SDSS J120252.39+195456.7 0.132 12.05+0.04-0.02 0.11 s' 0.03 0.54 s' 0.05 0.69 s' 0.10 3.43 s' 0.04 14.50 IIIb 3 u* u* u* Star forming J0912533+192701 09 12 53.33 +19 27 00.8 SDSS J091253.25+192653.9 0.233 12.11+0.09-0.04 0.17 s' 0.04 0.44 s' 0.04 0.68 s' 0.17 0.93 s' 0.23 15.49 V 3 u* u* u* Composite J0941010+143622 09 41 01.03 +14 36 22.4 SDSS J094100.81+143614.5 0.384 12.75+0.01-0.05 0.89 s' 0.22 0.77 s' 0.07 0.24 s' 0.06 0.46 s' 0.11 17.19 NI 3 B QSO J1016332+041418 10 16 33.25 +04 14 17.9 SDSS J101633.19+041422.1 0.266 12.39+0.03-0.05 0.51 s' 0.13 0.65 s' 0.10 0.91 s' 0.01 1.34 s' 0.33 14.73 IIIb 3 u* u* u* Composite J1401186-021131 14 01 18.61 -02 11 30.9 SDSS J140119.02-021126.7 0.172 12.07+0.01-0.08 0.26 s' 0.06 0.30 s' 0.08 1.85 s' 0.30 u* u* u* 15.98 IIIa 3 u* u* u* Seyfert J1258241+224113 12 58 24.10 +22 41 13.0 SDSS J125824.16+224113.6 0.208 12.07+0.05-0.04 0.97 s' 0.24 0.60 s' 0.05 1.44 s' 1.09 0.86 s' 0.21 16.62 IIIb 3 u* u* u* Composite J1036317+022147 10 36 31.66 +02 21 47.3 SDSS J103631.88+022144.1 0.050 12.06+0.03-0.04 13.32 s' 1.09 14.81 s' 0.54 10.83 s' 1.15 8.46 s' 0.74 14.75 IIIb 3 u* u* u* Composite J1050567+185316 10 50 56.73 +18 53 16.1 SDSS J105056.78+185316.9 0.219 12.60+0.03-0.06 0.67 s' 0.17 0.93 s' 0.10 3.08 s' 2.13 3.32 s' 0.45 14.91 Tp1,G 3 u* u* u* Seyfert J1111177+192259 11 11 17.72 +19 22 58.9 SDSS J111117.46+192255.0 0.225 12.60+0.03-0.06 u* u* u* 0.55 s' 0.05 0.05 s' 2.25 u* u* u* 14.56 IIIb 3 u* u* u* Star forming J1219585+051745 12 19 58.50 +05 17 44.6 SDSS J121958.11+051735.1 0.487 12.87+0.02-0.04 0.29 s' 0.07 0.82 s' 0.09 0.43 s' 0.11 u* u* u* 15.16 NI 3 A u* u* u* J1414276+605726 14 14 27.55 +60 57 25.8 SDSS J141427.98+605727.0 0.151 12.11+0.00-0.12 0.37 s' 0.09 0.63 s' 0.04 1.94 s' 0.36 2.75 s' 1.38 14.11 V 3 u* u* u* Composite J0936293+203638 09 36 29.33 +20 36 37.6 SDSS J093629.03+203620.0 0.175 12.01+0.04-0.02 0.42 s' 0.11 0.57 s' 0.09 2.05 s' 0.23 0.83 s' 0.21 14.12 IIIb 3 u* u* u* Composite J1533582+113413 15 33 58.15 +11 34 12.7 SDSS J153358.24+113415.8 0.337 12.32+0.08-0.08 0.25 s' 0.06 0.33 s' 0.04 0.46 s' 0.11 u* u* u* 15.29 V,G 3 A u* u* u* J1348483+181401 13 48 48.32 +18 14 00.9 SDSS J134848.32+181357.4 0.179 12.19+0.03-0.03 0.42 s' 0.11 0.66 s' 0.04 1.66 s' 0.03 1.17 s' 0.29 14.89 IV 3 u* u* u* Composite J1125319+290316 11 25 31.92 +29 03 16.2 SDSS J112531.90+290311.3 0.138 12.27+0.01-0.05 1.98 s' 0.14 1.84 s' 0.09 1.53 s' 0.56 u* u* u* 13.34 IV 3 u* u* u* QSO J1603043+094717 16 03 04.29 +09 47 17.5 SDSS J160304.57+094707.8 0.152 12.02+0.03-0.03 0.79 s' 0.20 0.54 s' 0.07 1.70 s' 0.01 0.36 s' 0.09 13.11 V 3 u* u* u* Star forming J1639245+303719 16 39 24.50 +30 37 19.1 SDSS J163925.01+303709.8 0.224 12.11+0.01-0.05 0.51 s' 0.13 0.51 s' 0.04 1.14 s' 0.23 0.12 s' 0.03 16.53 IIIb 3 u* u* u* u* u* u* J1050288+002806 10 50 28.80 +00 28 06.0 SDSS J105028.49+002807.7 0.216 12.38+0.13-0.08 0.53 s' 0.13 0.79 s' 0.06 1.79 s' 0.37 u* u* u* 14.77 IIIb 3 u* u* u* Composite J0928103+232521 09 28 10.29 +23 25 21.0 SDSS J092810.52+232515.8 0.197 12.07+0.08-0.04 0.09 s' 0.02 0.44 s' 0.01 1.13 s' 0.28 u* u* u* 15.40 IIIb 3 u* u* u* Star forming 6 Th eA str oph ysi cal Jou rna l,7 97: 54 (30 pp) ,20 14 De cem ber 10 Ese r,G oto ,& Do i Table 1 (Continued) Name AKARI R.A. AKARI Decl. Other Name za log(LIR/L\Xi )b F(65 um)c F(90 um)c F(140 um)c F(160 um)c rd ICe ICf Noteg Spectralh AKARI-FIS-V1 (J2000) (J2000) (Jy) (Jy) (Jy) (Jy) (mag) Ref. Class (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) J2344170+053520 23 44 17.04 +05 35 19.8 SDSS J234417.43+053533.5 0.267 12.56+0.01-0.19 0.64 s' 0.16 0.42 s' 0.06 1.29 s' 0.90 1.80 s' 0.45 15.80 IIIa 3 u* u* u* Seyfert J2353152-313234 23 53 15.20 -31 32 34.5 TGS430Z217 0.185 12.04+0.00-0.12 0.37 s' 0.09 0.23 s' 0.06 1.67 s' 0.44 2.78 s' 0.70 14.29 u* u* u* u* u* u* u* u* u* u* u* u* J1222488-040307 12 22 48.78 -04 03 07.1 TGN123Z071 0.181 12.19+0.02-0.04 0.16 s' 0.04 0.59 s' 0.10 1.68 s' 0.04 1.09 s' 0.27 15.17 u* u* u* u* u* u* u* u* u* u* u* u* J1419037-034657 14 19 03.68 -03 46 56.6 TGN145Z052 0.152 12.09+0.01-0.08 u* u* u* 0.61 s' 0.15 1.86 s' 0.66 2.49 s' 0.62 16.95 u* u* u* u* u* u* u* u* u* u* u* u* J1048019-013017 10 48 01.87 -01 30 17.4 TGN296Z061 0.167 12.09+0.07-0.07 0.49 s' 0.12 1.10 s' 0.15 1.13 s' 0.40 u* u* u* 13.53 IV 3 u* u* u* u* u* u* J1338353-041131 13 38 35.29 -04 11 31.4 TGN139Z200 0.175 12.14+0.12-0.22 0.40 s' 0.10 0.68 s' 0.29 1.77 s' 0.68 u* u* u* 15.67 u* u* u* u* u* u* u* u* u* u* u* u* Notes. a Based on SDSS optical spectra. The redshifts marked with an asterisk are adopted from Wang & Rowan-Robinson (2009) because there are no available SDSS spectra for these sources. b LIR is the total IR luminosity between 8 and 1000 um measured from the SEDs fitted to the AKARI fluxes at 65, 90, 140, and 160 um. c The AKARI flux density and the associated uncertainties are adopted from Yamamura et al. (2010). For the cases for which the flux uncertainties are not available, we adopt 25% of the measured flux as the uncertainty. d SDSS Petrosian r magnitude. e Interaction classes (IC) are described in Section 3.2. The IC listed in this table are based on combined gri SDSS images; " u* u* u* " entries in the Table indicate the lack of an SDSS image. f References: (1) Veilleux et al. (2002); (2) Hwang et al. (2007); (3) this work. g Superposition of other sources in the field: (A) star; (B) galaxy. h Classifications based on optical spectra. For the sources that are in the SDSS DR10 emissionlinesPort catalog (Thomas et al. 2013), we adopt the given BPT classifications: star forming, composite, LINER, and Seyfert. In the case of quasars (QSO), we adopt the "spectrotype" classification from the galSpecInfo catalog (see Richards et al. 2002, for the details of SDSS spectroscopic target selection). The classifications marked with a star are based on our BPT classification based on the emission-line fluxes adopted from the SDSS catalog galSpecLine7 (Tremonti et al. 2004; Brinchmann et al. 2004). 7 Th eA str oph ysi cal Jou rna l,7 97: 54 (30 pp) ,20 14 De cem ber 10 Ese r,G oto ,& Do i Table 2 Known ULIRG Sample Name AKARI R.A. AKARI Decl. Other Name za log(LIR/L\Xi )b F(65 um)c F(90 um)c F(140 um)c F(160 um)c rd ICe ICf Noteg Spectralh AKARI-FIS-V1 (J2000) (J2000) (Jy) (Jy) (Jy) (Jy) (mag) Ref. Class (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) J0857064+190855 08 57 06.37 +19 08 55.4 SDSS J085706.35+190853.5 0.331 12.92+0.01-0.05 u* u* u* 0.48 s' 0.06 u* u* u* 2.56 s' 0.10 15.79 NI 3 u* u* u* QSO J1022125+241208 10 22 12.46 +24 12 07.8 SDSS J102212.64+241202.4 0.188 12.01+0.22-0.08 u* u* u* 0.59 s' 0.03 0.90 s' 2.81 u* u* u* 15.80 IV 3 u* u* u* LINER J1422313+260205 14 22 31.27 +26 02 05.2 SDSS J142231.37+260205.1 0.159 12.20+0.11-0.05 0.96 s' 0.24 1.36 s' 0.04 2.29 s' 0.43 u* u* u* 13.59 IIIa 1 u* u* u* Star forming J1231216+275524 12 31 21.57 +27 55 24.4 SDSS J123121.37+275524.0 0.212 12.33+0.01-0.09 0.52 s' 0.13 0.40 s' 0.10 1.41 s' 0.35 1.93 s' 0.48 17.35 IV 3 u* u* u* Composite J1251200+021900 12 51 20.03 +02 19 00.2 SDSS J125120.04+021902.4 0.253 12.48+0.04-0.02 1.00 s' 0.25 0.73 s' 0.04 1.86 s' 0.09 0.81 s' 0.20 15.00 V 2 u* u* u* Composite J0030089-002743 00 30 08.95 -00 27 43.5 SDSS J003009.08-002744.2 0.242* 12.46+0.03-0.03 0.37 s' 0.09 0.62 s' 0.06 1.34 s' 0.30 0.40 s' 0.10 14.56 IIIb 3 u* u* u* u* u* u* J0914140+032200 09 14 14.01 +03 22 00.4 SDSS J091413.79+032201.4 0.145 12.07+0.06-0.03 1.11 s' 0.28 1.39 s' 0.11 2.29 s' 0.51 0.86 s' 0.21 14.48 IIIa 1 u* u* u* LINER J1105377+311432 11 05 37.71 +31 14 32.3 SDSS J110537.54+311432.2 0.199 12.20+0.05-0.02 0.71 s' 0.18 0.98 s' 0.06 1.31 s' 0.33 0.59 s' 0.15 16.03 IV 1 u* u* u* Composite J0323227-075612 03 23 22.75 -07 56 12.1 SDSS J032322.87-075615.3 0.166 12.14+0.11-0.06 0.50 s' 0.12 0.91 s' 0.00 1.80 s' 0.25 u* u* u* 12.99 IV 1 u* u* u* Composite J1632212+155145 16 32 21.24 +15 51 44.8 SDSS J163221.38+155145.5 0.242 12.67+0.02-0.04 1.50 s' 0.13 1.46 s' 0.03 2.42 s' 0.48 2.75 s' 0.06 14.27 V 1 u* u* u* Composite J0148531+002857 01 48 53.10 +00 28 57.1 SDSS J014852.57+002859.8 0.280 12.30+0.26-0.04 0.70 s' 0.17 0.48 s' 0.05 0.94 s' 0.39 u* u* u* 15.49 IIIa 2 u* u* u* Composite J0159503+002340 01 59 50.28 +00 23 39.9 SDSS J015950.25+002340.9 0.163 12.43+0.01-0.04 2.01 s' 0.03 1.82 s' 0.17 2.94 s' 0.18 0.16 s' 0.04 15.63 IV 1 u* u* u* QSO J1353317+042809 13 53 31.72 +04 28 08.8 SDSS J135331.57+042805.3 0.136* 12.44+0.01-0.05 1.26 s' 0.31 1.62 s' 0.05 0.23 s' 0.06 1.61 s' 0.40 12.67 IV 1 B u* u* u* J0244173-003040 02 44 17.35 -00 30 40.3 SDSS J024417.44-003041.1 0.200 12.07+0.01-0.05 0.36 s' 0.09 0.65 s' 0.19 0.77 s' 0.19 0.86 s' 0.22 15.08 IIIa,G 2 u* u* u* QSO J1202268-012918 12 02 26.81 -01 29 18.0 SDSS J120226.76-012915.3 0.150 12.36+0.05-0.01 1.94 s' 0.39 2.54 s' 0.20 3.09 s' 0.67 1.06 s' 1.26 15.68 IV,G 3 u* u* u* Star forming\Pi J1013477+465402 10 13 47.75 +46 54 02.1 SDSS J101348.09+465359.6 0.206 12.24+0.09-0.05 0.13 s' 0.03 0.72 s' 0.05 u* u* u* u* u* u* 16.78 IV 3 u* u* u* Seyfert J0858418+104124 08 58 41.77 +10 41 24.3 SDSS J085841.77+104122.1 0.148 12.17+0.05-0.03 1.00 s' 0.25 1.55 s' 0.13 2.09 s' 0.38 2.62 s' 0.94 16.17 IV,G 1 u* u* u* Seyfert J1347336+121727 13 47 33.58 +12 17 27.4 SDSS J134733.36+121724.3 0.120 12.18+0.03-0.03 1.90 s' 0.47 1.75 s' 0.08 0.96 s' 0.24 0.97 s' 0.24 14.13 IIIb 1 u* u* u* Seyfert\Pi J0853252+252646 08 53 25.21 +25 26 45.6 SDSS J085325.07+252656.0 0.256 12.37+0.09-0.08 0.56 s' 0.14 0.68 s' 0.06 0.68 s' 4.39 1.28 s' 0.32 11.72 V 3 B QSO J0825215+383306 08 25 21.47 +38 33 05.7 SDSS J082521.65+383258.5 0.206 12.28+0.10-0.08 0.26 s' 0.06 0.59 s' 0.01 1.49 s' 0.37 u* u* u* 16.03 IIIb 2 u* u* u* Composite J0829512+384528 08 29 51.18 +38 45 27.8 SDSS J082951.39+384523.7 0.195 12.02+0.11-0.07 0.33 s' 0.08 0.53 s' 0.09 0.89 s' 0.22 u* u* u* 13.34 IIIb 2 u* u* u* Composite J1142035+005135 11 42 03.51 +00 51 35.5 SDSS J114203.41+005135.8 0.245 12.10+0.04-0.04 0.37 s' 0.09 0.45 s' 0.05 0.15 s' 0.04 0.67 s' 0.17 15.26 IV 2 u* u* u* Composite J0810595+281354 08 10 59.51 +28 13 54.1 SDSS J081059.61+281352.2 0.336 12.65+0.18-0.14 u* u* u* 0.63 s' 0.01 1.10 s' 0.28 u* u* u* 15.40 IIIb 2 u* u* u* Composite J0900252+390400 09 00 25.21 +39 03 59.8 SDSS J090025.37+390353.7 0.058 12.03+0.01-0.04 5.93 s' 0.70 5.13 s' 0.19 2.62 s' 0.91 1.43 s' 0.36 15.97 IIIb 1 u* u* u* Star forming J0830197+192040 08 30 19.74 +19 20 40.0 SDSS J083019.75+192050.0 0.186 12.03+0.12-0.07 0.49 s' 0.12 0.59 s' 0.07 u* u* u* 1.30 s' 0.33 15.02 IIIb 3 u* u* u* Star forming J1121293+112233 11 21 29.25 +11 22 33.3 SDSS J112129.00+112225.7 0.185 12.32+0.04-0.03 0.83 s' 0.21 1.07 s' 0.03 2.16 s' 0.11 u* u* u* 13.37 IIIa 2 u* u* u* Seyfert J1006038+411223 10 06 03.83 +41 12 23.4 SDSS J100603.85+411224.8 0.328 12.42+0.03-0.05 0.28 s' 0.07 0.54 s' 0.03 0.47 s' 0.12 u* u* u* 15.36 V 2 u* u* u* Star forming J0838034+505516 08 38 03.36 +50 55 16.5 SDSS J083803.61+505508.9 0.097 12.03+0.01-0.04 2.31 s' 0.04 2.00 s' 0.08 2.62 s' 0.40 u* u* u* 17.30 IV 2 u* u* u* Composite J0902489+523623 09 02 48.87 +52 36 22.6 SDSS J090248.90+523624.7 0.157 12.05+0.01-0.06 1.20 s' 0.30 0.87 s' 0.04 0.25 s' 0.06 1.56 s' 0.39 15.72 V 1 u* u* u* Composite J0847504+232113 08 47 50.37 +23 21 12.8 SDSS J084750.26+232110.9 0.152 12.01+0.09-0.08 u* u* u* 0.75 s' 0.06 1.66 s' 0.39 u* u* u* 13.62 IIIb 3 u* u* u* Star forming J1559301+380843 15 59 30.13 +38 08 42.7 SDSS J155930.40+380838.8 0.218 12.19+0.02-0.04 0.07 s' 0.02 0.58 s' 0.06 1.36 s' 0.14 2.17 s' 0.38 13.85 IV 2 u* u* u* Seyfert J1324197+053705 13 24 19.74 +05 37 05.4 SDSS J132419.89+053704.7 0.203 12.66+0.02-0.04 1.22 s' 0.30 0.89 s' 0.08 u* u* u* u* u* u* 14.68 V 1 u* u* u* QSO J1102140+380240 11 02 14.02 +38 02 40.0 SDSS J110214.00+380234.6 0.158 12.15+0.06-0.01 1.12 s' 0.28 1.32 s' 0.03 2.36 s' 0.70 0.46 s' 0.20 15.27 IIIb 1 u* u* u* Composite J1204244+192509 12 04 24.41 +19 25 08.9 SDSS J120424.54+192509.8 0.168 12.15+0.02-0.04 1.62 s' 0.41 1.24 s' 0.03 1.19 s' 0.04 0.79 s' 0.20 15.38 IV 1 u* u* u* Composite J1108513+065915 11 08 51.31 +06 59 15.1 SDSS J110851.03+065901.5 0.182 12.07+0.09-0.11 0.30 s' 0.07 0.52 s' 0.05 0.29 s' 4.55 1.68 s' 0.42 15.64 IIIa 3 B QSO J1040290+105325 10 40 29.05 +10 53 25.3 SDSS J104029.17+105318.3 0.136 12.26+0.06-0.03 2.02 s' 0.50 2.13 s' 0.13 1.46 s' 2.03 0.75 s' 0.19 14.73 IV 1 u* u* u* LINER J1207210+021702 12 07 21.03 +02 17 01.7 SDSS J120721.45+021657.8 0.222 12.09+0.04-0.04 1.32 s' 0.33 0.58 s' 0.02 0.54 s' 0.13 0.81 s' 0.20 14.36 V 2 u* u* u* Composite J1255482-033908 12 55 48.19 -03 39 08.2 SDSS J125547.83-033909.6 0.169 12.06+0.13-0.08 u* u* u* 0.73 s' 0.02 u* u* u* 1.66 s' 0.41 15.53 IV 2 A QSO J0906339+045136 09 06 33.93 +04 51 35.5 SDSS J090634.03+045127.6 0.125 12.02+0.06-0.04 1.62 s' 0.40 1.64 s' 0.07 2.94 s' 1.55 2.43 s' 0.61 13.68 IV 1 u* u* u* Composite J1153144+131432 11 53 14.39 +13 14 32.1 SDSS J115314.23+131427.9 0.127 12.26+0.05-0.02 2.37 s' 0.16 2.57 s' 0.14 2.76 s' 0.55 1.03 s' 1.03 13.50 IV 1 u* u* u* Composite 8 Th eA str oph ysi cal Jou rna l,7 97: 54 (30 pp) ,20 14 De cem ber 10 Ese r,G oto ,& Do i Table 2 (Continued) Name AKARI R.A. AKARI Decl. Other Name za log(LIR/L\Xi )b F(65 um)c F(90 um)c F(140 um)c F(160 um)c rd ICe ICf Noteg Spectralh AKARI-FIS-V1 (J2000) (J2000) (Jy) (Jy) (Jy) (Jy) (mag) Ref. Class (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) J1202054+112813 12 02 05.41 +11 28 13.2 SDSS J120205.59+112812.2 0.194 12.19+0.05-0.03 0.07 s' 0.02 1.03 s' 0.03 u* u* u* 0.87 s' 0.22 14.85 IIIa 2 A Star forming J1006432+091726 10 06 43.16 +09 17 26.3 SDSS J100643.50+091727.5 0.171 12.10+0.07-0.01 0.79 s' 0.20 1.02 s' 0.08 1.22 s' 0.30 0.42 s' 0.10 13.72 IIIb 2 u* u* u* Composite J1052232+440849 10 52 23.24 +44 08 48.6 SDSS J105223.52+440847.6 0.092 12.06+0.03-0.03 3.39 s' 0.27 3.53 s' 0.12 4.11 s' 0.37 2.96 s' 1.01 15.33 IV 1 u* u* u* Composite J1254008+101115 12 54 00.82 +10 11 14.6 SDSS J125400.80+101112.4 0.319 12.58+0.03-0.05 0.69 s' 0.17 0.79 s' 0.05 u* u* u* 0.99 s' 0.25 12.99 V 3 u* u* u* QSO J1348397+581854 13 48 39.66 +58 18 54.1 SDSS J134840.08+581852.0 0.158 12.12+0.03-0.04 0.53 s' 0.13 1.36 s' 0.03 0.93 s' 0.23 1.26 s' 0.63 15.08 IIIb 1 u* u* u* Composite J1015153+272717 10 15 15.33 +27 27 17.1 SDSS J101515.35+272717.1 0.210 12.09+0.03-0.04 0.84 s' 0.21 0.64 s' 0.02 0.86 s' 0.21 0.74 s' 0.18 13.88 V 3 u* u* u* Composite J1356100+290538 13 56 09.98 +29 05 38.0 SDSS J135609.99+290535.1 0.109 12.04+0.02-0.05 1.70 s' 0.43 1.78 s' 0.05 2.72 s' 0.56 0.26 s' 0.07 14.21 IIIb 1 u* u* u* Composite J1502320+142132 15 02 31.95 +14 21 32.4 SDSS J150231.96+142135.3 0.162 12.12+0.04-0.03 0.26 s' 0.06 1.69 s' 0.08 2.37 s' 0.28 0.77 s' 0.19 15.15 Tp1 1 u* u* u* Composite J1336237+391733 13 36 23.74 +39 17 32.5 SDSS J133624.06+391731.1 0.179 12.37+0.06-0.06 1.38 s' 0.34 1.03 s' 0.06 2.58 s' 0.36 2.74 s' 1.36 16.01 IV,G 1 u* u* u* QSO J1141215+405951 11 41 21.52 +40 59 51.3 SDSS J114122.03+405950.3 0.149 12.01+0.18-0.04 0.58 s' 0.14 1.08 s' 0.05 1.57 s' 0.61 u* u* u* 15.66 V 1 u* u* u* Composite J1433271+281157 14 33 27.14 +28 11 57.0 SDSS J143327.52+281159.9 0.175 12.12+0.16-0.07 0.46 s' 0.11 0.83 s' 0.05 1.64 s' 0.41 u* u* u* 13.94 IIIb 3 u* u* u* Seyfert J1450544+350835 14 50 54.40 +35 08 34.7 SDSS J145054.16+350837.9 0.206 12.34+0.11-0.14 0.34 s' 0.08 0.72 s' 0.07 1.81 s' 0.90 u* u* u* 14.35 V 3 u* u* u* Composite J1406380+010258 14 06 37.97 +01 02 58.1 SDSS J140638.20+010254.6 0.236 12.35+0.01-0.05 0.99 s' 0.25 0.74 s' 0.09 0.18 s' 0.05 u* u* u* 16.03 IV 2 u* u* u* Composite J1522382+333135 15 22 38.17 +33 31 35.4 SDSS J152238.10+333135.9 0.125 12.03+0.01-0.05 0.91 s' 0.23 1.26 s' 0.04 1.22 s' 0.25 u* u* u* 17.23 IV 1 u* u* u* Composite\Pi J1505390+574305 15 05 39.04 +57 43 04.6 SDSS J150539.55+574307.1 0.151 12.02+0.02-0.08 1.14 s' 0.28 0.87 s' 0.05 1.61 s' 0.97 0.73 s' 2.51 14.70 IIIb 1 u* u* u* Star forming J1441041+532011 14 41 04.11 +53 20 10.8 SDSS J144104.38+532008.7 0.105 12.03+0.01-0.04 2.03 s' 0.45 1.78 s' 0.13 1.77 s' 0.41 0.91 s' 2.13 16.49 Tp1 1 u* u* u* LINER\Pi J1706529+382010 17 06 52.87 +38 20 09.9 SDSS J170653.27+382007.1 0.168 12.15+0.02-0.04 0.79 s' 0.20 0.96 s' 0.02 1.68 s' 0.75 0.19 s' 0.05 15.16 IIIa,G 2 A LINER J1649140+342510 16 49 14.01 +34 25 09.8 SDSS J164914.09+342513.2 0.113 12.07+0.08-0.01 2.28 s' 0.36 2.24 s' 0.08 2.69 s' 0.95 1.96 s' 3.66 15.55 IIIb 1 u* u* u* Star forming J0823127+275140 08 23 12.66 +27 51 39.6 SDSS J082312.61+275139.8 0.168 12.07+0.03-0.03 0.53 s' 0.13 1.04 s' 0.02 0.96 s' 0.24 1.26 s' 0.32 18.30 IV 1 u* u* u* Star forming J1213460+024844 12 13 45.99 +02 48 43.8 SDSS J121346.11+024841.5 0.073 12.25+0.03-0.03 7.10 s' 0.51 8.69 s' 0.31 6.17 s' 0.36 3.90 s' 1.32 15.42 IIIb 1 u* u* u* Composite J1346511+074720 13 46 51.09 +07 47 20.0 SDSS J134651.09+074719.0 0.135 12.09+0.06-0.02 1.71 s' 0.43 1.49 s' 0.10 2.25 s' 0.86 0.61 s' 0.15 16.68 Tp1,G 1 u* u* u* Composite J2257246-262120 22 57 24.65 -26 21 20.5 TGS123Z162 0.164 12.16+0.05-0.06 1.27 s' 0.32 1.17 s' 0.17 1.53 s' 1.17 1.68 s' 0.11 15.22 IIIa 2 u* u* u* u* u* u* J2223286-270006 22 23 28.57 -27 00 05.7 TGS178Z172 0.131 12.19+0.05-0.02 1.87 s' 0.08 1.90 s' 0.09 2.90 s' 0.87 1.06 s' 0.26 12.70 IIIb 1 u* u* u* u* u* u* J1132417-053940 11 32 41.68 -05 39 40.2 TGN111Z322 0.230 12.18+0.07-0.05 0.44 s' 0.11 0.64 s' 0.02 0.81 s' 0.20 u* u* u* 14.46 IV 2 u* u* u* u* u* u* J0238167-322036 02 38 16.66 -32 20 36.3 TGS465Z105 0.198 12.31+0.02-0.03 1.08 s' 0.27 0.95 s' 0.11 1.66 s' 0.10 2.33 s' 0.58 13.90 V 2 u* u* u* u* u* u* J0238126-473813 02 38 12.64 -47 38 12.9 TGS875Z072 0.098 12.07+0.02-0.03 2.76 s' 0.32 3.24 s' 0.09 3.99 s' 0.42 2.34 s' 0.66 14.53 V 2 u* u* u* u* u* u* J0237297-461544 02 37 29.66 -46 15 44.4 TGS875Z471 0.206 12.37+0.06-0.06 0.90 s' 0.56 1.13 s' 0.07 1.04 s' 1.04 1.99 s' 0.50 15.94 V 2 u* u* u* u* u* u* J0048064-284820 00 48 06.37 -28 48 20.0 TGS288Z046 0.110 12.12+0.04-0.02 2.56 s' 0.64 2.48 s' 0.16 4.08 s' 0.36 u* u* u* 16.85 IIIa 1 u* u* u* u* u* u* J0112165-273819 01 12 16.49 -27 38 18.8 TGS213Z002 0.222 12.37+0.01-0.24 0.43 s' 0.11 0.45 s' 0.04 0.83 s' 0.99 1.79 s' 0.45 15.05 IIIa 2 u* u* u* u* u* u* J0138061-324519 01 38 06.14 -32 45 18.6 TGS509Z038 0.198 12.12+0.08-0.02 1.23 s' 0.31 0.75 s' 0.07 0.89 s' 0.22 0.40 s' 0.10 16.99 V 2 u* u* u* u* u* u* J0302108-270725 03 02 10.82 -27 07 24.7 TGS238Z241 0.221 12.42+0.06-0.03 0.98 s' 0.24 1.22 s' 0.15 1.07 s' 0.27 0.42 s' 0.11 15.98 IV 2 u* u* u* u* u* u* J0118266-253607 01 18 26.61 -25 36 06.8 TGS147Z020 0.237 12.12+0.04-0.03 0.67 s' 0.17 0.54 s' 0.03 0.50 s' 0.13 0.59 s' 0.15 16.32 V 2 u* u* u* u* u* u* J0152042-285116 01 52 04.20 -28 51 16.5 TGS302Z057 0.184 12.06+0.06-0.04 0.46 s' 0.11 0.73 s' 0.06 2.14 s' 0.60 1.02 s' 0.26 15.63 IIIa 2 u* u* u* u* u* u* J0159138-292436 01 59 13.82 -29 24 36.1 TGS304Z128 0.140 12.06+0.08-0.02 2.16 s' 0.40 1.36 s' 0.05 1.61 s' 0.36 0.63 s' 0.16 16.72 IV 1 u* u* u* u* u* u* J1329391-034654 13 29 39.11 -03 46 53.7 TGN137Z043 0.222 12.19+0.33-0.00 0.58 s' 0.14 0.75 s' 0.06 u* u* u* 2.49 s' 3.85 16.39 IV 2 u* u* u* u* u* u* J1112034-025414 11 12 03.36 -02 54 13.8 TGN232Z018 0.106 12.14+0.07-0.02 2.55 s' 0.39 2.93 s' 0.26 1.47 s' 0.28 u* u* u* 14.31 IV 1 u* u* u* u* u* u* J2307212-343838 23 07 21.24 -34 38 38.4 TGS538Z137 0.208 12.22+0.04-0.02 0.76 s' 0.19 0.89 s' 0.10 1.43 s' 0.36 0.34 s' 0.59 18.43 V 2 u* u* u* u* u* u* J2208493-344627 22 08 49.25 -34 46 27.4 TGS528Z076 0.174 12.21+0.05-0.14 0.80 s' 0.20 0.67 s' 0.02 1.88 s' 0.45 u* u* u* 14.93 V 2 u* u* u* u* u* u* Notes. For a, b, c, d, f, g, and h see the notes in Table 2. e See Section 3.2 for the details of the interaction classes. The IC listed in this table are mostly adopted from the references given in Column 13. 9 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi Table 3 New HLIRG Name AKARI R.A. AKARI Decl. Other Name za log(LIR/L\Xi )b F(65 um)c F(90 um)c F(140 um)c F(160 um)c rd ICe ICf Noteg Spectralh AKARI-FIS-V1 (J2000) (J2000) (Jy) (Jy) (Jy) (Jy) (mag) Ref. Class (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) J1425001+103045 14 25 00.06 +10 30 44.7 SDSS J142500.73+103043.6 0.480 13.34+0.01-0.16 0.95 s' 0.24 0.61 s' 0.06 1.97 s' 0.48 1.97 s' 0.49 18.51 V 3 u* u* u* Composite Notes. For a, b, c, d, e, f, g, and h see the notes in Table 2. 0.0 0.1 0.2 0.3 0.4 0.5 0.6Redshift (z) 0 20 40 60 80 N 12.0 12.5 13.0 13.5IR Luminosity 0 10 20 30 40 50 N Figure 2. Distributions of redshift (top) and IR luminosity, log(LIR/L\Xi ), (bottom) for the final (H)ULIRG sample. 3.1.2. FIR Color Properties of Our Sample The IR emission of the so-called normal star-forming galaxies(that are not dominated by AGN activity) is mostly due to the thermal radiation from dust grains heated by star formation.The "normal" star-forming galaxies detected by IRAS showed a clear trend of decreasing 60- to 100-um flux ratios, F(60 um)/F(100 um), with increasing 12- to 25-um flux ratios, F(12 um)/F(25 um), (Helou 1986). This trend is associated with theintensity dependence of IR colors, such that "warm" colors (greater F(60 um)/F(100 um) values) are related to active starformation with high IR luminosities (Helou 1986). Dale et al. (2001) construct single-parameter dust mod-els of normal star-forming galaxies based on the F(60 um)/F(100 um) color and the intensity of the interstellar radiationfield, U. They characterize the overall IR SED as a power-law distribution of dust mass over U such that dM(U ) \Lambda U -\Sigma dU ,where \Sigma is the exponent of the power-law distribution. Dale &Helou (2002) provide 64 SED models for a wide range of U or equivalently IRAS F(60 um)/F(100 um) color (between -0.54and 0.21) and \Sigma values (0.0625 \Theta \Sigma \Theta 4.0). In Section 2.2 0.0 0.1 0.2 0.3 0.4 0.5Redshift 12.0 12.5 13.0 13.5 log(L IR Figure 3. IR luminosity vs. redshift for 118 ULIRGs (open circles) and one HLIRG (filled circle) in the final sample. we measured LIR based on these models. In the following, weinvestigate the AKARI color properties of our ULIRG sample and compare the observed colors with the SED models of Dale& Helou (2002). For this investigation we use the AKARI F(9 um) andF(18 um) fluxes from the AKARI/IRC all-sky survey pointsource catalog. The F(65 um), F(90 um), F(140 um), andF(160 um) fluxes are listed in Tables 1, 2, and 3. Figure 4presents the observed AKARI color-color diagrams: (a) F(9 um)/F(18 um) versus F(18 um)/F(65 um), (b) F(18 um)/F(65 um) versus F(65 um)/F(90 um), (c) F(65 um)/F(90 um)versus F(90 um)/F(140 um), and (d) F(90 um)/F(140 um)versus F(140 um)/F(160 um). Panels (a) and (b) show onlythe two sources that are detected in all of the AKARI bands. Panels (c) and (d) include 71 sources that are detected in allAKARI FIS bands. The different symbols represent the spectral classes as listed in Tables 1, 2, and 3 (see Section 3.3): cir-cle (composite), star (star forming), square (LINER), diamond (Seyfert12), triangle (QSOs), plus (unclassified). In Panels (c)and (d) the FIR colors of different classes of galaxies are distributed over the entire color range. Therefore, AGNs or galax-ies cannot be distinguished by their FIR colors. However, this is expected because FIR is tracing star-formation activity withlow-temperature dust and is not sensitive to AGN activity. It is known that the IRAS mid-IR F(25 um)/F(60 um) color is anindicator of "warm" dust and an AGN component (F(25 um)/F(60 um) \Lambda 0.2) (e.g., Sanders et al. 1988a). Unfortunately, themajority of our ULIRG sample is not detected in the mid-IR colors, and therefore we do not have enough data to explore themid-IR color properties of our sample. The color-color diagrams in Panels (c) and (d) do notshow a clear correlation. It is important to keep in mind that the detection limits of AKARI bands affect the shape ofthe color-color diagrams. The detection limits of the AKARI FIS bands are 3.2 Jy, 0.55 Jy, 3.8 Jy, and 7.5 Jy for the 12 Seyfert galaxies are low-redshift (z \Theta 0.1), less luminous cousins of quasars (e.g., Richards et al. 2002). 10 Th eA str oph ysi cal Jou rna l,7 97: 54 (30 pp) ,20 14 De cem ber 10 Ese r,G oto ,& Do i Table 4Unconfirmed ULIRG Candidates Name AKARI R.A. AKARI Decl. Other Name za log(LIR/L\Xi )b F(65 um)c F(90 um)c F(140 um)c F(160 um)c rd ICe ICf Noteg Spectralh AKARI-FIS-V1 (J2000) (J2000) (Jy) (Jy) (Jy) (Jy) (mag) Ref. Class (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) J0058034-025406 00 58 03.44 -02 54 05.8 SDSS J005802.70-025401.8 0.267 12.27+0.03-0.43 u* u* u* 0.21 s' 0.05 5.13 s' 1.49 u* u* u* 14.31 IIIb 3 B u* u* u* u* u* u* J1444024+000415 14 44 02.37 +00 04 15.0 SDSS J144402.86+000411.9 0.330 12.66+0.02-0.06 0.09 s' 0.02 0.23 s' 0.06 0.96 s' 0.24 3.74 s' 0.32 13.44 IIIa 3 u* u* u* u* u* u* u* u* u* J0545295-011324 05 45 29.50 -01 13 24.5 SDSS J054529.53-011318.0 0.884 12.82+0.02-0.07 0.41 s' 0.10 0.57 s' 0.20 u* u* u* 0.24 s' 0.06 12.76 NI 3 u* u* u* u* u* u* u* u* u* J1352265+020815 13 52 26.48 +02 08 14.9 SDSS J135227.76+020816.5 2.853 13.01+0.12-0.06 u* u* u* 0.39 s' 0.07 0.76 s' 0.18 3.28 s' 0.82 15.70 IIIa 3 Large separation u* u* u* u* u* u* J1716527+271405 17 16 52.73 +27 14 04.6 SDSS J171653.48+271406.2 0.539 12.21+0.09-0.11 u* u* u* 0.23 s' 0.06 1.97 s' 0.36 0.17 s' 0.04 11.74 V 3 A u* u* u* u* u* u* Notes. For a, b, c, d, e, f, g, and h see the notes in Table 2. 11 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi -1.5 -1.0 -0.5 0.0log(F(18t,m)/F(65t,m)) -1.5 -1.0 -0.5 0.0 0.5 log(F(9 t,m)/F(18 t,m)) (a) z=0.0z=0.1 z=0.2z=0.3 z=0.4z=0.5 -0.6 -0.4 -0.2 -0.0 0.2log(F(65t,m)/F(90t,m)) -1.5 -1.0 -0.5 0.0 0.5 log(F(18 t,m)/F(65 t,m)) (b) 0.0625, 0.21351.0625, 0.1046 1.4375, -0.00841.7500, -0.1596 2.0625, -0.33162.2500, -0.4151 2.8750, -0.53274.0000, -0.5425 \Xi log(F(60t,m)/F(90t,m)) -1.0 -0.5 0.0 0.5 1.0log(F(90t,m)/F(140t,m)) -1.0 -0.5 0.0 0.5 1.0 log(F(65 t,m)/F(90 t,m)) (c) QSOSeyfert LINERComposite Star FormingHLIRG Unclassified -1.0 -0.5 0.0 0.5 1.0 1.5log(F(140t,m)/F(160t,m)) -1.0 -0.5 0.0 0.5 1.0 log(F(90 t,m)/F(140 t,m)) (d) z=0 Figure 4. AKARI color-color diagrams. The top left (a) and right (b) panels show log(F (9 um)/F (18 um)) vs. log(F (18 um)/F (65 um)) and log(F (18 um)/F (65 um))vs. log( F (65 um)/F (90 um)) for the two ULIRGs detected in all of the AKARI bands. The bottom panels show log(F (65 um)/F (90 um)) vs. log(F (90 um)/F (140 um)) (c) and log(F (90 um)/F (140 um)) vs. log(F (140 um)/F (160 um)) (d) colors for 71 sources that are detected in the AKARI 65 um, 90 um, 140 um, and 160 um bands. The symbol code is given in the legend of panel (c). The colored symbols in each panel indicate the expected colors from the SEDtemplates of Dale & Helou (2002) at redshifts z = 0.0, 0.1, 0.2, 0.3, 0.4, and 0.5. The symbol codes for the redshifts are given in the legend of panel (a). We only show the expected colors for eight SED templates. Different colors represent different models; the parameters of the models are given in the legend of panel (b). 65 um, 90 um, 140 um and 160 um bands (Yamamura et al.2010), respectively. The WIDE-S filter centered at 90 um isthe broadest, and therefore it has the deepest detection limit compared to other bands. In Panel (d) the distribution of thecolors is shaped by the observational detection limits. This is mainly because 140 um is common in both axes. In the x-axis asthe 140 um flux gets brighter the log(F (140 um)/F (160 um))color moves toward the right, but at the same time in the y-axis the log(F (90 um)/F (140 um)) color moves downward. Thisbehavior creates a boundary on the top right corner of this diagram. Even if there were an intrinsic color-color correlationin Panel (d), it would be truncated on the upper right corner because of the observational limits. We expect to have a similardetection limit effect in Panel (c) because the 65 um and 140 umdetection limits are brighter than 90 um, and this may causecolors to hit the boundaries of 65 um and 140 um before thelimit of 90 um.In Figure 4, the colored symbols in each panel show the expected colors by the IR SED models of Dale & Helou(2002). We choose eight SEDs with different \Sigma and F(60 um)/F(100 um) values among the 64. The selected models have asequence in terms of \Sigma and log(F(60 um)/F(100 um)): 0.06 \Theta \Sigma \Theta 4.0 and -0.54 \Theta log(F(60 um)/F(100 um)) \Theta 0.21. Theexpected colors from the selected SEDs are shown with different colors; the \Sigma and log(F(60 um)/F(100 um)) parameters of eachmodel are given in the top corner of Panel (b). We show the colors expected from each model as a function of redshift from0 to 0.5 in order to illustrate the redshift dependence of the colors. The symbol code for z = 0.0, 0.1, 0.2, 0.3, 0.4, and0.5 is given in the legend of Panel (a). In Panels (c) and (d) the data show a large spread around the model colors. In Panel(c), the large vertical and horizontal spreads of log(F(65 um)/F(90 um)) and log(F(90 um)/F(140 um)) colors around themodels are mainly due to the limited parameter coverage of the SED models. The models cover the ranges between -0.54-0.21and -0.62-0.47 in the y- and x-axis, respectively. Therefore, the models do not overlap with the colors exceeding this range. InPanel (d), in particular the log(F(140 um)/F(160 um)) colorshave a large scatter around the models; the models cover only the -0.11-0.13 range, but the observed colors can exceed this up to1.27. We do not see a clear trend in log(F(140 um)/F(160 um))colors with redshift. Because we show the expected colors for z = 0.0-0.5, the observed scatter does not seem to be due to therange in redshift of our sample. We further discuss such outliers in color-color diagrams in Section 4.Because the AKARI log(F(65 um)/F(90 um)) color is equiv-alent to the IRAS log(F(60 um)/F(100 um)) color, it is pos-sible to compare the AKARI and IRAS color distributions of ULIRGs. Hwang et al. (2007) investigate the IRAS colors of324 ULIRGs and report a log(F(60 um)/F(100 um)) within the-0.80-0.22 range with a mean of -0.19. The ULIRGs in our sample have a slightly larger range, between -0.91-0.36, but 12 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi -0.05 0.00 0.05 0.10log(F(65t,m)/F(90t,m)) 12.0 12.5 13.0 13.5 log(L IR (a) QSOSeyfert LINERComposite Star FormingHLIRG Unclassified -0.1 0.0 0.1log(F(65t,m)/F(140t,m)) 12.0 12.5 13.0 13.5 log(L IR (b) -0.1 0.0 0.1 0.2log(F(65t,m)/F(160t,m)) 12.0 12.5 13.0 13.5 log(L IR (c) -0.2 -0.1 0.0 0.1log(F(90t,m)/F(140t,m)) 12.0 12.5 13.0 13.5 log(L IR (d) -0.2 -0.1 0.0 0.1log(F(90t,m)/F(160t,m)) 12.0 12.5 13.0 13.5 log(L IR/L (e) -0.2 -0.1 0.0 0.1 0.2log(F(140t,m)/F(160t,m)) 12.0 12.5 13.0 13.5 log(L IR (f) Figure 5. Color-luminosity diagrams of 71 (H)ULIRGs that are detected in all of the AKARI FIS bands. The symbol code is given in panel (a). still the AKARI log(F(65 um)/F(90 um)) colors overlap withthe IRAS log(F(60 um)/F(100 um)) colors. 3.1.3. FIR Colors versus IR Luminosity The IR-bright galaxies (109.5 L\Xi \Theta LIR < 1013 L\Xi ) studiedwith IRAS show a correlation between the IR colors and the IR luminosity: the log(F(12 um)/F(25 um)) color decreases, andthe log(F(60 um)/F(100 um)) color increases with increasingIR luminosity (Soifer & Neugebauer 1991). As stated in Section 3.1.3, the log(F(60 um)/F(100 um)) color is related to theintensity of the radiation field. The SED models of Dale & Helou (2002) cover a wide range of IRAS log(F(60 um)/F(100 um))colors that correlate with LIR; higher log(F(60 um)/F(100 um))colors indicate higher LIR (Dale & Helou 2002). In the following we investigate the color dependence of the IR luminositiesfor our (H)ULIRG sample. Figure 5 presents IR luminosity versus (a) log(F(65 um)/F(90 um)), (b) log(F(65 um)/F(140 um)), (c) log(F(65 um)/F(160 um)), (d) log(F(90 um)/F(140 um)), (e) log(F(90 um)/F(160 um)), and (f) log(F(140 um)/F(160 um)), for 71 sourcesthat are detected in all of the AKARI FIS bands. As noted before, because we have only very few sources detected in the 9- and18- um bands, we do not include those in this investigation.Because the observed colors change as a function of redshift and luminosity depends on redshift, we apply a k-correction tothe AKARI FIS colors shown in Figure 5. As noted before, the AKARI log(F(65 um)/F(90 um)) color issimilar to IRAS log(F(60 um)/F(100 um)) color, and therefore 13 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi we would expect a strong correlation in Panel (a). However, noneof the AKARI colors in Figure 5 show a clear dependence in LIRbetween 12.0 \Theta log( LIR/L\Xi ) < 13.3. Because the LIR range ofinterest in this study is very narrow compared to the LIR rangeprobed in previous studies (e.g., Soifer & Neugebauer 1991), it is natural not to see the previously discovered significantcolor- LIRcorrelations. The representative SED models shownin Figure 4 show a luminosity dependence with color, but the observed colors show a large scatter around the models(discussed in Sections 3.1.3 and 4). The large differences between the SED models and the observed colors weaken thecolor- LIR correlation expectation.In Figure 5, apart from the color dependence of the IR luminosity, different galaxy types do not show a significantdependence on color. 3.2. Visual Morphologies and Interaction Classes Morphological studies of local ULIRGs showed that they aremostly interacting galaxies showing tidal features or disturbed morphology (e.g., Farrah et al. 2001; Veilleux et al. 2002,2006). Surace (1998) introduced an interaction classification scheme based on the evolution sequence that merging galaxiesfollow in simulations (e.g., Mihos & Hernquist 1996). Such an interaction classification scheme is important in interpretingthe morphological properties of ULIRGs in the context of a galaxy evolution triggered by mergers. Veilleux et al. (2002)classified 117 local ULIRGs based on this scheme and showed that ULIRGs are interacting or advanced merger systems.Here we investigate the morphological properties of our sample with the aim of identifying interaction classes. Weuse the following widely preferred classification scheme that is described by Veilleux et al. (2002): 1. I: first approach. Separated galaxies with no signs ofinteraction or merging. 2. II: first contact. Overlapped disks without interaction signs. 3. III: premergers. Two nuclei separated by more than 10 kpc(a; wide binary) or less than 10 kpc (b; close binary), with interaction signs. 4. Tp1: interacting triplet system. 5. IV: merger. One nucleus with prominent tidal features. 6. V: old merger. Disturbed central morphology without cleartidal tail signs. 7. NI: noninteracting. Isolated single galaxy, no signs ofdisturbed morphology. Note that we added class N i to represent isolated singlegalaxies showing no signs of disturbed morphology. Also note that we do not subdivide class IV into two as done by Veilleuxet al. (2002) because we do not have K-band luminosities. We (two classifiers: EKE and TG) examined SDSS g-r-icolor combined images and classified only the galaxies for which SDSS images are available. For the known ULIRGs,we adopt the interaction classifications from the literature. We prefer to adopt the classifications mainly from Veilleux et al.(2002) and Hwang et al. (2007). The interaction classifications of the galaxies in our sample are given in Column 12 ofTables 1-3. The references for the interaction classes are given in Column 13 of Tables 1-3. In additional to the above interactionclassification, we also note whether the galaxies are in a group with (G). We define groups as galaxy systems with more thantwo members with similar colors. We note that our group definition is subjective, and the group classification given in this 0 10 20 30 40 0 10 20 30 40 Fraction (%) IIIa IIIb IV V Tp1 0.0 < z < 0.27 Figure 6. Distribution of the interaction classes for 100 ULIRGs within a 0.0 < z < 0.27 limit. Interaction classes are described in Section 3.2. The fraction of the late or old mergers that are classified as IV or V is 52%. Error bars representthe 1 \Xi Poisson errors (Gehrels 1986). work is only for guidance. The SDSS images showing examplesof different interaction classes are represented in Figure 1. As shown in Figure 3, luminosity is correlated with distance,and it becomes more difficult to identify the morphological details for more distant sources. To avoid uncertainties ininteraction classifications due to the distances, in the following analysis we focus on a redshift-limited sample of 100 ULIRGs.For comparison purposes, we apply a redshift cut of z = 0.27;this is the limit of the Veilleux et al. (2002) ULIRG sample. The distribution of interaction classes of 100 ULIRGs is shownin Figure 6. This figure presents the percentage of different interaction classes. There are no ULIRGs classified as I and II,so they are not in an early interaction phase. The fraction of triplets (Tp1) in our sample is very small (5%). The fractionof binary systems showing strong interaction features (IIIa and IIIb) is 43%. Most of the ULIRGs (52%) are single-nucleusgalaxies classified as IV and V, indicating a late- or postmerger phase. Veilleux et al. (2002) study 117 ULIRGs from the IRAS1 Jy sample (Kim et al. 1998) and report 56% of the sample as single-nucleus systems at a late merger stage. The fractionof such systems (IV or V) in our sample is 52%, and this is a result consistent with Veilleux et al. (2002). In our morphologysubsample, 35 of the 100 ULIRGs are also part of the sample of 117 ULIRGs studied by Veilleux et al. (2002), and thereforeour results can be considered as independent from those derived by Veilleux et al. (2002). We also find 11% of the ULIRGs tobe in a group environment. In Figure 7 we show the fraction of ULIRGs in differentinteraction classes as a function of IR luminosity. We divide IR luminosities into three bins (12.0 \Theta log(LIR) < 12.25,12.25 \Theta log( LIR) < 12.5, and 12.5 \Theta log(LIR)); the numberof sources in each bin is 73, 22, and 5, respectively. This figure shows a hint of a negative trend for premergers (IIIa and IIIb).The fraction of galaxies classified as IIIa and IIIb decreases from the first bin to the second, but IIIa galaxies increase in thehighest LIR bin. The fraction of mergers (IV) increases fromthe first bin to the second, but it decreases in the third bin. The fraction of old mergers (V) appears to be almost constant withluminosity. The fraction of triplets is constant in the first two bins, but it increases in the third bin. The fraction in the highestluminosity bin is highly uncertain because of the very small 14 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 12.0 12.2 12.4 12.6 12.8 13.0log(L IR 0 20 40 60 80 100 Fraction (%) 0.0 < z < 0.27IIIaIIIb IVV Tp1 Figure 7. Fraction of interaction classes per IR luminosity for 100 ULIRGs within a z < 0.27 limit. The x-axis error bars represent the range of the IRluminosity bins (12 .0 \Theta LIR < 12.25, 12.25 \Theta LIR < 12.5, 12.5 \Theta LIR < 13.0). The y-axis error bars represent the 1\Xi confidence limits of the Poisson errors on the counts given by Gehrels (1986). (A color version of this figure is available in the online journal.) number of sources. Therefore, we consider the trends, includingthe highest luminosity bin, to be unreliable. If we only take into account the first two luminosity bins, then it is clear thatthe fraction of premergers has a negative trend and the mergers have a positive trend with increasing luminosity. This is a resultconsistent with Veilleux et al. (2002), who find a positive trend in the fraction of advanced mergers and IR luminosity.The morphological properties of our sample confirm that ULIRGs are mostly either in premerger two-galaxy systems orsingle galaxies in the late or postmerger phase. This is a picture consistent with the general idea that ULIRGs are triggered bystrong interactions between galaxies. 3.3. Spectral Classification of Our Sample The power sources of ULIRGs are high rates of star formationand AGN activity (e.g., Nardini et al. 2010). The traces of the dominant power source can be detected in optical spectra.The properties of the emission lines provide a practical tool for uncovering the source of the ionization producing thoselines. To identify the spectral classes of the ULIRGs in our sample, we make use of the available SDSS catalogs providingsuch a classification. The SDSS spectroscopic pipeline classifies objects as broad-line AGNs/quasars, galaxies, or stars. We adoptthis classification to identify the quasars in our sample. Thomas et al. (2013) investigate the emission line propertiesof SDSS sources that are already classified as "galaxies" through the pipeline. They apply Baldwin-Phillips-Terlevich (BPT)diagnostics (Baldwin et al. 1981) based on [O iii] /H\Upsilon and[N ii] /H\Sigma emission line ratios to classify sources into Seyfert,low-ionization nuclear emission region (LINER), SFG, and star-forming/AGN composite. Thomas et al. (2013) use theempirical separation between AGNs and star-forming galaxies according to Kauffmann et al. (2003a), and they use theseparation line defined by Schawinski et al. (2007) to select LINERs. We adopt the spectral classification given by Thomaset al. (2013) for the ULIRGs included in their galaxy sample. Some of the ULIRGs in our sample are not included in the 0 10 20 30 40 50 0 10 20 30 40 50 Fra ctio n (% ) Composite Star Forming LINER AGN Figure 8. Distribution of spectral classes of 89 ULIRGs for which the SDSS spectra are available. Error bars represent the same quantity as in Figure 6. sample of Thomas et al. (2013). These are mostly AGNs,but a few sources are classified as broad-line AGN starbursts by the spectroscopic pipeline. To classify such sources, weadopt the available line flux measurements in the SDSS database (see the footnotes of Table 1 for the SDSS references) anduse a similar line diagnostic diagram as described by Thomas et al. (2013). The spectral classes are listed in Column 15of Tables 1-3. The spectral classes marked with a star were obtained in this work.The distribution of the spectral classes is shown in Figure 8; it represents only 89 source ULIRGs for which SDSS spectraare available. The fraction of purely star-forming galaxies is 19%. The fraction of composite galaxies in our sample is 44%.The fraction of LINERs in our sample is 11%. The LINERs are thought to be powered by AGNs (e.g., Nagar et al. 2005);however, other power sources can also produce LINER-like emission (e.g., Maoz et al. 1998; Sarzi et al. 2010). Becausethere is a debate whether LINERs are low-luminosity AGNs or a separate class of objects, to be conservative in this work weseparate LINERs from AGNs. The fraction of AGN (QSOs and Seyferts) ULIRGs in our sample is 26%.Most of the ULIRGs in our sample are classified as composite galaxies. It is important to note that these are SFGs, possiblywith a hidden AGN component. To be conservative, we do not include composites to AGNs. Because both LINERs andcomposites may harbor an AGN, the given AGN fraction is only a lower limit.Figure 9 shows the fraction of ULIRGs in different spectral classes as a function of IR luminosity. We use the same LIR binsas in Figure 7. Each bin include 61 (12.0 \Theta log( LIR) < 12.25),18 (12.25 \Theta log( LIR) < 12.5), and 10 (12.5 \Theta log(LIR)) sources.The fraction of AGNs grows with increasing LIR. Star-forminggalaxies show an opposite trend: their fraction decreases with increasing LIR. This is consistent with the results of previousstudies, which showed that the fraction of AGNs in IR galaxies increases with higher IR luminosity (Veilleux et al. 1995; Kimet al. 1998; Goto 2005). The LINERs tend to be constant in each luminosity bin. Composites also tend to be almost constant in thefirst two bins, but they show a dramatic decrease in the highest luminosity bin. Again, because the LINERs and compositesmay have an AGN contribution that is hidden in the optical wavelengths, the AGN fractions in each luminosity bin representthe lower limit. However, the trends seen in Figure 9 still agree 15 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 12.0 12.2 12.4 12.6 12.8 13.0 log(LIR 0 20 40 60 80 100 120 Fraction (%) LINERAGN CompositeStar forming Figure 9. Spectral class fraction per IR luminosity bins for 89 ULIRGs. See the caption of Figure 7 for the error bars. (A color version of this figure is available in the online journal.) with the known correlation between the AGN fraction and IRluminosity. Some 28 of the 89 ULIRGs in our optical spectral type subsample are also part of the 1 Jy sample of Veilleux et al.(1995, 1999a). Because \Lambda 31% is a small fraction, our results are mostly independent of those derived for the 1 Jy sample. 3.4. Stellar Masses, Star-formation Rates, Metallicities,and Optical Colors of ULIRGs The ULIRGs are very special galaxies that are selectedaccording to their enormous IR luminosity, which means a rich dust content. Dust has an important role in galaxy growth andevolution because it is directly linked to star formation and metals in the interstellar medium (ISM). The interplay betweenthe dust and stellar content with the star-formation rate (SFR) controls the galaxy evolution. For normal SFGs, this is evidentfrom the observed correlations between these parameters. Stellar mass (Mstar) and SFR tightly correlate within a 0 < z < 3range, and normal star-forming galaxies lie on the so-called main sequence (e.g., Noeske et al. 2007; Elbaz et al. 2007;Santini et al. 2009; Rodighiero et al. 2011; Tadaki et al. 2013). Stellar mass also strongly correlates with the metallicity (Z):massive galaxies show a higher metallicity than the less massive systems. The Mstar-Z relationship is confirmed for normal star-forming galaxies in the local universe ( z \Lambda 0.15) (Tremontiet al. 2004). Although there is not a strong relation between SFR and Z, metallicity is a function of SFR and Mstar in the Mstar-Z-SFR plane (Lara-L'opez et al. 2010; Mannucci et al.2010). Recently, Santini et al. (2014) showed that there is a tight correlation between the dust mass and SFR, and theyintroduce a fundamental relation between gas fraction, Mstar,and SFR. These relationships provide a basis for understanding the evolution of normal SFGs. The ULIRGs do not belongto this galaxy category, and in order to explore their place in galaxy evolution, we need to compare them with normal star-forming galaxies. In the following, we investigate the position of ULIRGs in Mstar- SFR, Mstar-Z relationships and in thecolor-magnitude diagram (CMD). Below we briefly outline the SDSS data used in this investigation.The available SDSS photometric and spectral data allow us to obtain stellar masses, metallicities, and optical colors of ULIRGs in our sample. The SDSS DR10 (see Ahn et al. 2014)provides stellar masses, emission-line fluxes, stellar and gas kinematics, and velocity dispersion derived spectra of galaxiesobserved by the BOSS. Following the spectroscopic pipeline (Bolton et al. 2012), the objects classified as a galaxy with areliable redshift are studied by several groups. "The Portsmouth" group derives photometric stellar mass estimates (Maraston et al.2013) and measure emission-line fluxes (Thomas et al. 2013). Maraston et al. (2013) estimate stellar masses through SEDfitting of stellar population models to u, g, r, i, and z magnitudes.They use both passive (Maraston et al. 2009) and star-forming templates (Maraston 2005) with Salpeter (1955) and Kroupa(2001) initial mass functions (IMF). Maraston et al. (2013) use the fixed BOSS spectroscopic redshift values and do not includeinternal galaxy reddening in the SED fitting procedure. The Wisconsin group also derives stellar masses via full spectralfitting (Chen et al. 2012). They use models based on stellar population models of Bruzual & Charlot (2003) with a Kroupa(2001) IMF. Chen et al. (2012) and Maraston et al. (2013) use different stellar population models based on different galaxystar-formation histories, reddening, and IMF assumptions. The stellar masses given by Maraston et al. (2013) are \Lambda 0.2 dexsmaller than the masses estimated by Chen et al. (2012), and for high signal-to-noise spectra, the results from both of the methodsagree well (Chen et al. 2012). Because spectral data quality is an issue, in this work we prefer to adopt the stellar masses givenby Maraston et al. (2013); however, this preference does not change the results of this work. Maraston et al. (2013) obtainstellar masses for active and passive stellar population models. Because ULIRGs are actively SFGs, we adopt the stellar massesfrom the stellarMassPortStarforming13 catalog. These are listed in Table 5. The magnitudes used in the stellar mass estimatesinclude contributions from star formation but also possible AGN contamination. The errors associated with the stellar masses arediscussed in Section 4.5. Thomas et al. (2013) fit stellar population synthesis modelsof Maraston & Str"omb"ack (2011) and Gaussian emission-line templates to the spectra by using the Gas and Absorption LineFitting (GANDALF) code of Sarzi et al. (2006). This code accounts for the diffuse dust on the spectral shape accordingto the Calzetti (2001) obscuration curve. Thomas et al. (2013) correct for the diffuse dust extinction and provide dereddenedemission-line fluxes (this includes Galactic extinction). In the following analysis we adopt the emission-line fluxes from theSDSS emissionlinesPort'3catalog. 3.4.1. Star-formation Rate and Stellar Mass The IR luminosity measured from the SEDs (Section 2.2)between 8 um-1000 um is the obscured emission from youngstars that is re-emitted by dust, so it can be converted to SFR. We use Equation (4) given by Kennicutt (1998) to estimatethe SFR based on LIR, SFR(IR). This conversion assumes aSalpeter (1955) IMF and that LIR is generated by recent starformation and re-emitted by dust. Even in the case of AGN we expect this assumption to still be valid to infer SFR(IR) becauseULIRGs on average have an AGN contribution from 5.0% to 40.0% AGN (e.g., Genzel et al. 1998; Veilleux et al. 2009), butthey are mostly powered by star formation. Therefore we note that the SFR(IR) values of the AGN, LINERS, and compositesmay have on average \Lambda 40.0% AGN contamination and may be 13 http://www.sdss3.org/dr10/spectro/galaxy_portsmouth.php 16 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi Table 5 Stellar Masses, Star-formation Rates, Oxygen Abundances, Optical Colors, and Absolute Magnitudes AKARI-FIS-V1 Name IRAS Name log(Mstar(M\Xi )) SFR(IR) SFR(H\Sigma ) 12+log(O/H) u0.1-r0.1 M0.1r (M\Xi yr-1) (M\Xi yr-1) (mag) (mag) (1) (2) (3) (4) (5) (6) (7) (8) J2216028+005813 F22134+0043 u* u* u* 1153463320 u* u* u* u* u* u* u* u* u* J0859229+473612 F08559+4748 10.740.100.06 275249 371010 8.94 s' 0.08 2.92 s' 0.12 -21.41 s' 0.01 J1443444+184950 F14414+1902 10.340.080.02 28110141 141919 u* u* u* 2.47 s' 0.12 -21.07 s' 0.01 J0857505+512037 F08542+5132 10.960.030.04 132524761 778787 u* u* u* 2.23 s' 0.43 -21.35 s' 0.01 J1106104+023458 u* u* u* 11.140.030.03 2924639 78686 u* u* u* 2.59 s' 0.29 -21.77 s' 0.01 J1157412+321316 F11550+3233 10.580.030.08 238157 622222 8.79 s' 0.10 1.45 s' 0.02 -21.70 s' 0.01 J1149200-030357 F11467-0247 u* u* u* 1781016 u* u* u* u* u* u* 1.72 s' 0.03 -21.29 s' 0.01 J0126038+022456 F01234+0209 10.880.400.08 2883134 000 u* u* u* 3.18 s' 0.48 -21.06 s' 0.01 J1556089+254358 F15540+2552 10.470.060.13 183583 351414 8.89 s' 0.11 2.19 s' 0.06 -21.08 s' 0.01 J0140364+260016 F01378+2545 11.030.180.32 102115252 u* u* u* u* u* u* 1.61 s' 0.67 -21.40 s' 0.02 J1257392+080935 F12551+0825 u* u* u* 2973211 u* u* u* u* u* u* 0.43 s' 0.01 -22.52 s' 0.01 J0800007+152319 u* u* u* u* u* u* 23730 u* u* u* u* u* u* 1.34 s' 0.06 -21.40 s' 0.01 J0800279+074858 u* u* u* 11.260.010.34 228342 044 u* u* u* 3.06 s' 0.17 -21.11 s' 0.01 J0834438+334427 F08315+3354 10.420.170.02 2311786 694242 u* u* u* 2.27 s' 0.08 -21.30 s' 0.01 J0823089+184234 u* u* u* 10.630.010.12 634106844 u* u* u* u* u* u* 1.77 s' 0.15 -21.45 s' 0.01 J1202527+195458 F12002+2011 10.580.020.30 193176 511111 8.92 s' 0.08 1.89 s' 0.03 -21.06 s' 0.01 J0912533+192701 u* u* u* 10.710.170.04 2224920 191414 8.63 s' 0.28 2.87 s' 0.19 -22.04 s' 0.01 J0941010+143622 F09382+1449 u* u* u* 96832101 u* u* u* u* u* u* 1.37 s' 0.06 -22.29 s' 0.01 J1016332+041418 F10139+0429 10.400.320.01 4233144 382121 8.40 s' 0.22 1.93 s' 0.09 -21.37 s' 0.01 J1401186-021131 u* u* u* 10.800.010.25 201435 633 u* u* u* 2.01 s' 0.06 -21.98 s' 0.01 J1258241+224113 u* u* u* 10.090.060.04 2012516 171414 8.59 s' 0.23 2.77 s' 0.65 -19.93 s' 0.02 J1036317+022147 u* u* u* 9.980.150.23 1961214 722 8.69 s' 0.12 1.68 s' 0.01 -20.43 s' 0.01 J1050567+185316 F10482+1909 10.400.140.07 6785680 1548383 u* u* u* 2.49 s' 0.11 -21.23 s' 0.01 J1111177+192259 u* u* u* 10.270.120.14 243236 4288 8.83 s' 0.15 0.98 s' 0.03 -21.62 s' 0.01 J1219585+051745 u* u* u* 10.880.450.09 12777494 u* u* u* u* u* u* 2.52 s' 1.19 -21.66 s' 0.01 J1414276+605726 F14129+6111 10.160.060.06 220051 2899 8.69 s' 0.10 1.07 s' 0.02 -20.69 s' 0.01 J0936293+203638 F09336+2049 10.600.010.15 177168 291111 9.00 s' 0.23 2.44 s' 0.09 -21.34 s' 0.01 J1533582+113413 u* u* u* 11.340.040.32 3577867 u* u* u* u* u* u* 2.11 s' 0.41 -22.18 s' 0.01 J1348483+181401 F13464+1828 10.160.080.07 2641817 391818 8.78 s' 0.84 2.75 s' 0.30 -19.73 s' 0.02 J1125319+290316 u* u* u* u* u* u* 3201032 u* u* u* u* u* u* 1.96 s' 0.03 -21.24 s' 0.01 J1603043+094717 F16006+0955 10.510.180.02 1811410 572121 u* u* u* 2.37 s' 0.06 -21.54 s' 0.01 J1639245+303719 F16374+3043 u* u* u* 223525 u* u* u* u* u* u* 1.69 s' 0.08 -21.64 s' 0.01 J1050288+002806 u* u* u* 10.260.010.22 41614866 632626 8.74 s' 0.13 1.31 s' 0.04 -21.58 s' 0.01 J0928103+232521 u* u* u* 10.010.320.03 2024418 1055 9.06 s' 0.09 2.18 s' 0.17 -20.18 s' 0.02 J2344170+053520 F23417+0518 11.610.090.11 62514218 43275275 u* u* u* 4.00 s' 1.64 -22.39 s' 0.01 J2353152-313234 u* u* u* u* u* u* 186043 u* u* u* u* u* u* u* u* u* J1222488-040307 u* u* u* u* u* u* 2692016 u* u* u* u* u* u* u* u* u* J1419037-034657 u* u* u* u* u* u* 213364 u* u* u* u* u* u* u* u* u* J1048019-013017 u* u* u* u* u* u* 2102940 u* u* u* u* u* u* u* u* u* J1338353-041131 u* u* u* u* u* u* 2397695 u* u* u* u* u* u* u* u* u* J0857064+190855 F08542+1920 u* u* u* 142534139 u* u* u* u* u* u* 0.16 s' 0.01 -23.15 s' 0.01 J1022125+241208 F10194+2427 10.780.030.09 17611327 u* u* u* u* u* u* 2.39 s' 0.07 -21.91 s' 0.01 J1422313+260205 F14202+2615 10.310.360.06 2748330 2988 8.68 s' 0.09 1.15 s' 0.02 -21.47 s' 0.01 J1231216+275524 F12288+2811 10.580.150.04 367669 755 8.54 s' 0.24 2.44 s' 0.09 -21.92 s' 0.01 J1251200+021900 F12487+0235 10.600.240.01 5215618 676740 8.40 s' 0.32 1.67 s' 0.04 -22.24 s' 0.01 J0030089-002743 F00275-0044 u* u* u* 4963428 u* u* u* u* u* u* u* u* u* J0914140+032200 F09116+0334 10.560.060.01 2002811 374303303 u* u* u* 2.21 s' 0.03 -21.92 s' 0.01 J1105377+311432 F11028+3130 9.970.060.04 2723313 311 u* u* u* 1.90 s' 0.10 -20.72 s' 0.01 J0323227-075612 F03209-0806 10.410.120.03 2356627 371010 8.75 s' 1.21 1.37 s' 0.03 -21.51 s' 0.01 J1632212+155145 F16300+1558 10.650.010.17 8023860 433636 8.69 s' 0.21 1.75 s' 0.06 -22.07 s' 0.01 J0148531+002857 F01462+0014 10.470.030.24 34028429 743737 u* u* u* 1.33 s' 0.04 -21.72 s' 0.01 J0159503+002340 F01572+0009 u* u* u* 4671541 u* u* u* u* u* u* u* u* u* J1353317+042809 F13509+0442 u* u* u* 473479 u* u* u* u* u* u* u* u* u* 17 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi Table 5 (Continued) AKARI-FIS-V1 Name IRAS Name log(Mstar(M\Xi )) SFR(IR) SFR(H\Sigma ) 12+log(O/H) u0.1-r0.1 M0.1r (M\Xi yr-1) (M\Xi yr-1) (mag) (mag) (1) (2) (3) (4) (5) (6) (7) (8) J0244173-003040 F02417-0043 u* u* u* 202620 u* u* u* u* u* u* u* u* u* J1202268-012918 F11598-0112 u* u* u* 394516 u* u* u* u* u* u* u* u* u* J1013477+465402 F10107+4708 10.170.300.05 3026831 u* u* u* u* u* u* 1.98 s' 0.13 -20.91 s' 0.01 J0858418+104124 F08559+1053 10.670.060.04 2542914 u* u* u* u* u* u* 2.18 s' 0.03 -21.91 s' 0.01 J1347336+121727 F13451+1232 u* u* u* 2591815 u* u* u* u* u* u* u* u* u* J0853252+252646 F08504+2538 u* u* u* 4059168 u* u* u* u* u* u* u* u* u* J0825215+383306 F08220+3842 10.650.060.01 3298757 261818 8.64 s' 0.20 2.68 s' 0.11 -21.70 s' 0.01 J0829512+384528 F08266+3855 9.660.020.05 1805127 261919 8.40 s' 0.27 2.11 s' 0.25 -19.45 s' 0.02 J1142035+005135 F11394+0108 10.160.210.07 2142219 754343 u* u* u* 1.08 s' 0.03 -21.63 s' 0.01 J0810595+281354 F08079+2822 10.280.360.01 775415212 361919 8.06 s' 0.26 1.23 s' 0.06 -21.43 s' 0.01 J0900252+390400 F08572+3915 9.420.040.02 186616 522 8.63 s' 0.14 1.84 s' 0.03 -19.40 s' 0.01 J0830197+192040 F08274+1930 10.240.160.07 1866028 1855 8.89 s' 0.07 1.00 s' 0.03 -21.03 s' 0.01 J1121293+112233 F11188+1138 10.460.010.01 3613920 812727 u* u* u* 1.67 s' 0.03 -21.97 s' 0.01 J1006038+411223 F10030+4126 10.180.190.01 4553550 664040 8.56 s' 0.27 1.38 s' 0.07 -21.46 s' 0.01 J0838034+505516 F08344+5105 9.960.080.01 186616 1855 8.63 s' 0.19 1.94 s' 0.03 -20.48 s' 0.01 J0902489+523623 F08591+5248 10.570.010.11 195625 351212 u* u* u* 2.15 s' 0.04 -21.68 s' 0.01 J0847504+232113 F08449+2332 10.230.170.06 1764229 3688 8.81 s' 0.07 1.06 s' 0.02 -20.88 s' 0.01 J1559301+380843 F15577+3816 10.700.010.05 2681623 231010 u* u* u* 1.89 s' 0.08 -21.56 s' 0.01 J1324197+053705 F13218+0552 u* u* u* 7954260 u* u* u* u* u* u* u* u* u* J1102140+380240 F10594+3818 10.470.120.04 245406 451313 8.89 s' 0.30 1.45 s' 0.02 -21.50 s' 0.01 J1204244+192509 F12018+1941 10.150.020.04 2421118 653535 7.62 s' 0.37 1.90 s' 0.05 -21.30 s' 0.01 J1108513+065915 F11062+0715 u* u* u* 2004543 u* u* u* u* u* u* u* u* u* J1040290+105325 F10378+1108 10.350.180.01 3114317 431414 u* u* u* 2.21 s' 0.05 -21.35 s' 0.01 J1207210+021702 F12047+0233 10.200.240.11 2112016 481818 8.89 s' 0.10 1.00 s' 0.03 -21.50 s' 0.01 J1255482-033908 F12532-0322 u* u* u* 1956933 u* u* u* u* u* u* u* u* u* J0906339+045136 F09039+0503 10.450.010.33 1812914 361414 8.22 s' 0.20 1.82 s' 0.04 -20.82 s' 0.01 J1153144+131432 F11506+1331 10.080.050.01 3113711 4728.28 8.40 s' 0.28 2.17 s' 0.07 -20.51 s' 0.01 J1202054+112813 F11595+1144 10.170.500.01 2683014 712525 8.75 s' 0.17 1.22 s' 0.02 -21.61 s' 0.01 J1006432+091726 F10040+0932 10.340.120.03 2183611 261515 8.75 s' 0.15 1.55 s' 0.04 -21.06 s' 0.01 J1052232+440849 F10494+4424 10.220.040.03 1961410 2055 8.37 s' 0.16 2.52 s' 0.06 -20.45 s' 0.01 J1254008+101115 F12514+1027 u* u* u* 6595075 u* u* u* u* u* u* u* u* u* J1348397+581854 F13469+5833 10.460.060.13 2241616 1366 8.77 s' 0.40 2.23 s' 0.07 -21.02 s' 0.01 J1015153+272717 F10124+2742 10.360.320.01 2131719 491919 8.45 s' 0.16 1.91 s' 0.06 -21.26 s' 0.01 J1356100+290538 F13539+2920 11.000.060.10 190718 391414 u* u* u* 3.09 s' 0.11 -20.41 s' 0.01 J1502320+142132 F15001+1433 10.440.070.01 2252015 712828 8.38 s' 0.21 2.07 s' 0.04 -21.58 s' 0.01 J1336237+391733 F13342+3932 u* u* u* 4056647 u* u* u* u* u* u* u* u* u* J1141215+405951 F11387+4116 10.450.060.02 1749313 705555 8.14 s' 1.22 2.47 s' 0.06 -21.08 s' 0.01 J1433271+281157 F14312+2825 10.720.010.06 22710231 833232 u* u* u* 2.23 s' 0.05 -21.79 s' 0.01 J1450544+350835 F14488+3521 10.860.070.02 379115103 1835757 8.79 s' 0.15 1.55 s' 0.02 -22.33 s' 0.01 J1406380+010258 F14041+0117 10.110.180.01 3871237 11228 7.79 s' 0.67 1.28 s' 0.04 -21.40 s' 0.01 J1522382+333135 F15206+3342 u* u* u* 184618 u* u* u* u* u* u* u* u* u* J1505390+574305 F15043+5754 10.450.060.08 181930 191111 8.85 s' 0.13 1.29 s' 0.03 -20.69 s' 0.01 J1441041+532011 F14394+5332 u* u* u* 186516 u* u* u* u* u* u* u* u* u* J1706529+382010 F17051+3824 10.260.010.01 2411020 1499 u* u* u* 2.17 s' 0.06 -20.94 s' 0.01 J1649140+342510 F16474+3430 9.630.320.15 201434 622 8.87 s' 0.09 1.73 s' 0.06 -19.69 s' 0.01 J0823127+275140 F08201+2801 10.380.110.20 2011612 1444 8.70 s' 0.10 1.58 s' 0.04 -21.19 s' 0.01 J1213460+024844 F12112+0305 10.280.010.01 3062321 933 8.39 s' 0.33 1.78 s' 0.03 -20.14 s' 0.01 J1346511+074720 F13443+0802 10.570.050.01 2113310 2033 8.97 s' 0.04 2.08 s' 0.03 -21.49 s' 0.01 J2257246-262120 F22546-2637 u* u* u* 2493229 u* u* u* u* u* u* u* u* u* J2223286-270006 F22206-2715 u* u* u* 2663013 u* u* u* u* u* u* u* u* u* J1132417-053940 F11300-0522 u* u* u* 1614327 u* u* u* u* u* u* u* u* u* J0238167-322036 F02361-3233 u* u* u* 3501925 u* u* u* u* u* u* u* u* u* J0238126-473813 F02364-4751 u* u* u* 2011114 u* u* u* u* u* u* u* u* u* 18 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi Table 5 (Continued) AKARI-FIS-V1 Name IRAS Name log(Mstar(M\Xi )) SFR(IR) SFR(H\Sigma ) 12+log(O/H) u0.1-r0.1 M0.1r (M\Xi yr-1) (M\Xi yr-1) (mag) (mag) (1) (2) (3) (4) (5) (6) (7) (8) J0237297-461544 F02356-4628 u* u* u* 4005953 u* u* u* u* u* u* u* u* u* J0048064-284820 F00456-2904 u* u* u* 2282311 u* u* u* u* u* u* u* u* u* J0112165-273819 F01098-2754 u* u* u* 4047170 u* u* u* u* u* u* u* u* u* J0138061-324519 F01358-3300 u* u* u* 224438 u* u* u* u* u* u* u* u* u* J0302108-270725 F03000-2719 u* u* u* 4572870 u* u* u* u* u* u* u* u* u* J0118266-253607 F01160-2551 u* u* u* 2272313 u* u* u* u* u* u* u* u* u* J0152042-285116 F01497-2906 u* u* u* 1972818 u* u* u* u* u* u* u* u* u* J0159138-292436 F01569-2939 u* u* u* 195376 u* u* u* u* u* u* u* u* u* J1329391-034654 F13270-0331 u* u* u* 2683050 u* u* u* u* u* u* u* u* u* J1112034-025414 F11095-0238 u* u* u* 2364411 u* u* u* u* u* u* u* u* u* J2307212-343838 F23046-3454 u* u* u* 2853011 u* u* u* u* u* u* u* u* u* J2208493-344627 F22058-3501 u* u* u* 2803375 u* u* u* u* u* u* u* u* u* J1425001+103045 F14225+1044 10.770.040.05 37661011151 1398080 8.64 s' 0.17 1.19 s' 0.06 -22.62 s' 0.00 Notes. (1) AKARI FIS-V1 Catalog name. (2) IRAS Faint Source Catalog name. (3) Stellar mass adopted from Maraston et al. (2013). (4) SFRs derived from IR luminosity. (5) SFRs derived from H\Sigma luminosity. (6) Oxygen abundances derived in this work. (7) u0.1-r0.1 color. (8) Absolute magnitude in the r band. 9.5 10.0 10.5 11.5 12.0log(M star 1 10 100 1000 10000 1011 1012 1013 LIR z=0 MS z=1 MS z=2 M S z=2 M S- x4 z=2 M S- x10 LINERAGN CompositeStar forming HLIRGUnclassified Figure 10. SFR(IR) vs. stellar mass for 75 ULIRGs and one HLIRG. The SFR(IR) values are derived from Equation (4) of Kennicutt (1998). The error bars of SFR(IR) represent the uncertainties propagated through LIRuncertainties. The solid line is the z = 0 "main sequence" of normal starforming galaxies; see Equation (5) of Elbaz et al. (2007). The dotted (colored blue in the online version) line is the SFR-Mstar relationship of z = 1 star-forming galaxies in the GOODS fields; see Equation (4) of Elbaz et al. (2007). The dashed (colored red in the online version) lines represent the SFR-Mstar relationship of z = 2 star-forming galaxies in the GOODS fields (Daddi et al.2007) and 4 and 10 times above this relationship. (A color version of this figure is available in the online journal.) overestimated up to 80-100% (Veilleux et al. 2009). DerivedSFR(IR) values are tabulated in Table 5. Figure 10 shows SFR versus Mstar for 75 ULIRGs and oneHLIRG, for which Mstar estimates are given by Maraston et al.(2013). The solid (black), dotted (blue), and dashed (red) lines represent the "main sequence" of normal SFGs at z \Lambda 0(Elbaz et al. 2007), z \Lambda 1 (Elbaz et al. 2007), and z \Lambda 2(Daddi et al. 2007), respectively. For comparison we also show the 4 and 10 times above the z \Lambda 2 "main sequence" (MS)relationship (top dashed lines). Local ULIRGs exhibit extremely high SFRs compared to normal SFGs with the same masses. It is evident from Figure 10 that local ULIRGs lie above the"main sequence" up to z \Lambda 2. We note that the "main sequence"relationships represent the total SFR obtained from the LIRand UV continuum, SFR(IR+UV). Because we do not include SFR from the UV continuum, SFR(UV), our SFR(IR) estimatesare lower than for SFR(IR+UV). However, the total SFR is dominated by SFR(IR), and therefore the difference betweenSFR(IR) and SFR(IR+UV) should be small. Previously, Elbaz et al. (2007) showed that (their Figure 17)Arp220 (a well-studied nearby ULIRG) exhibits a large offset both from the "main sequence" and the z \Lambda 1 relationship. Inthe same figure they also show that M82 (a starburst galaxy) lies above the local main sequence, but it is located in the1 \Xi confidence level of the z \Lambda 1 SFR-Mstar relationship. daCunha et al. (2010) also compared local ULIRGs with local starforming SDSS galaxies and showed that ULIRGs have higherSFRs. In Figure 10 we show a large local ULIRG sample, 75 ULIRGs, and one HLIRG. We find that local ULIRGs do notexhibit typical SFR for their masses even at z \Lambda 2. Comparedto the "main sequence" at z \Lambda 0, z \Lambda 1, and z \Lambda 2, on averageULIRGs have 92, 17, and 5 times higher SFRs, respectively. Local ULIRGs seem to be equally distributed around the dashedline, representing four times above the z \Lambda 2 MS. Compared tothe "main sequence" at z \Lambda 2, on average the AGNs, LINERs,and composite and star-forming ULIRGs have 3, 4, 5, and 5 times higher SFRs, respectively. We do not see a significantsystematic offset with optical spectral type. However, we note that AGNs, LINERs, and composites tend to have the highestSFR(IR), which might be a sign of the AGN contamination of LIR. We discuss the impact of SFH on stellar mass estimates inSection 4.5. The ionizing radiation of recently formed young stars pro-duces nebular lines such as H \Sigma ; hence it traces the unobscuredradiation generated by star formation. Therefore, it can be used to derive the SFR. As noted above, Thomas et al. (2013) onlycorrect for the diffuse dust extinction widely spread throughout the whole galaxy that affects the emission lines and stellarcontinuum, but they do not consider an embedded dust component local to star-forming regions that affects the emissionlines. This is mainly to avoid highly uncertain dust extinction 19 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 1 10 100SFR(H\Xi 10 100 1000 CompositeStar forming HLIRG (a) 12.0 12.5 13.0log(L IR/L 1 10 100 SFR(IR)/SFR(H \Xi ) CompositeStar forming HLIRG(b) 9.5 10.0 10.5 11.0log(M star 1 10 100 SFR(IR)/SFR(H \Xi ) CompositeStar forming HLIRG(c) Figure 11. (a) SFR(IR) vs. SFR(H\Sigma ), (b) SFR(IR)/SFR(H\Sigma ) vs. LIR, and (c) stellar mass for 55 ULIRGs and one HLIRG. In panel (a) the solid line represents theone-to-one relation. values measured from a Balmer decrement due to low signal-to-noise ratio (S /N) spectra. However, if we avoid this additionaldust extinction, we may underestimate the SFR based on H \Sigma luminosity, SFR(H \Sigma ). Therefore we use the already dereddenedemission-line fluxes (only for the diffuse dust component) given in emissionlinesPort3 catalog and obtain the Balmer decrement.The predicted H \Sigma /H\Upsilon ratio is 2.86 for 104 K (Osterbrock &Ferland 2006), and we adopt this value to estimate the local dust extinction around nebular regions and correct H\Sigma emission-lineflux for the estimated extinction. Applying this additional extinction correction typically results in a factor of 3.4 higherH \Sigma emission-line flux with large uncertainties. We applyEquation (2) given in Kennicutt (1998) to obtain SFR(H \Sigma ),as listed in Table 5. Because in the presence of an AGN H \Sigma emission represents the photoionization from the AGN, we do not obtain SFR(H\Sigma ) for AGNs and LINERs. Figure 11 showsa comparison between the SFR(IR) and SFR(H \Sigma ) values (a).Note that error bars of SFR(H \Sigma ) are dominated by the H\Sigma andH \Upsilon emission-line flux uncertainties. The SFR(IR) values aresystematically larger than the SFR(H \Sigma ) values; this differenceis between a factor of 2 and a factor of 130, and the median difference is a factor of 8. This indicates that even with the highestpossible dust extinction correction applied, the H \Sigma luminosityunderestimates SFR at least by a factor of two. Therefore, it is evident that H\Sigma is not sufficient to trace the SFR for ULIRGs,and IR observations are crucial to inferring the SFR of these galaxies. This is consistent with the fact that hydrogen recom-bination line SFR indicators are underluminous relative to the IR indicators in ULIRGs (e.g., Goldader et al. 1995; Kim et al.1998). In Figures 11(b) and (c) show that the difference between the SFR(IR) and SFR(H\Sigma ) does not depend on LIR or Mstar. In Figure 12 SFR(H\Sigma ) versus Mstar is shown. AlthoughSFR(H \Sigma ) underestimates SFR, Figure 12 shows that ULIRGsstill lie above the local main sequence. 3.4.2. Stellar Mass and Gas Metallicity Nuclear metallicities and stellar masses of normal star-forming galaxies show a well-established Mstar-Z correlation(Tremonti et al. 2004, hereafter T04). In the following, we compare the stellar masses and oxygen abundances of ULIRGswith the mass-metallicity relation of local star-forming SDSS galaxies obtained by Tremonti et al. (2004). Reliable metallicityconstraints are difficult to obtain from the broadband SED fitting applied by Maraston et al. (2013). Therefore, in order to measuremetallicity we adopt the relevant emission-line fluxes from Thomas et al. (2013). First, we apply the additional extinctioncorrection based on the Balmer decrement (see Section 3.4.1) to the adopted emission-line fluxes. Then we compute the 9.5 10.0 10.5 11.0log(M star 1 10 100 SFR(H \Xi Main Sequence CompositeStar forming HLIRG Figure 12. SFR(H\Sigma ) vs. stellar mass. The SFR(H\Sigma ) values are derived from Equation (2) of Kennicutt (1998). The error bars of SFR(H\Sigma ) are dominated bythe emission-line fluxes. The black solid line is the "main sequence" from Elbaz et al. (2007); dashed lines represent the 1\Xi width of the "main sequence". line ratio R23 = ([O ii] \Phi \Phi 3726, 3729+[O iii] \Phi \Phi 4959, 5007)/H \Upsilon . We convert R23 values to oxygen abundances, O/H, byfollowing Equation (1) of Tremonti et al. (2004). We list the derived oxygen abundances in Table 5. Note that this conversionand the R 23 line ratio are only applicable to normal star-forming galaxies, and they are not relevant for AGNs because the radiation from the AGN contributes to the line emission.Therefore we do not calculate metallicities for AGNs, and to be conservative we also exclude LINERs from this investigation.After excluding AGNs and LINERs, we are left with 48 ULIRGs and one HLIRG for which emission-line fluxes are given byThomas et al. (2013). The Mstar-Z distribution of our ULIRG sample is shownin Figure 13 (top). The error bars of the oxygen abundances represent the uncertainties associated with emission-line fluxesand additional extinction obtained from the Balmer decrement. The black solid line is the Mstar-Z relationship, Equation (3)given by Tremonti et al. (2004). The vast majority of ULIRGs (46 out of 48) have lower metallicities than that of the nor-mal star-forming SDSS galaxies at similar masses. In the bottom panel of Figure 13, the distribution of the residuals of themeasured oxygen abundances to the expected oxygen abundances from the T04 relationship is displayed. The distribu-tion of the residuals is comparable to the overplotted Gaussian distribution with standard deviation \Xi = 0.20 dex; thereforewe consider the shift of ULIRGs from the T04 relationship as 20 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 9.0 9.5 10.0 10.5 11.0log(M star 7 8 9 10 12 + log(O/H) CompositeStar forming HLIRG 0.0 0.5 1.0 1.5Metallicity(T04)- [12 + log(O/H)] measured 0 2 4 6 8 10 12 \Pi = 0.20 dexmean= 0.28 dex N Figure 13. Top: oxygen abundances vs. stellar mass for 48 ULIRGs and one HLIRG. The black solid line represents the mass-metallicity relationof the local SDSS galaxies given by Tremonti et al. (2004). Error bars of the oxygen abundances represent the uncertainties of emission-line fluxes (including the uncertainties associated with additional extinction based on theBalmer decrement) propagated through Equations (1) and (2) of Tremonti et al. (2004). Bottom: the distribution of the residuals between the measured oxygen abundances and the ones expected from the T04 relation. The overplottedGaussian function demonstrates that the residuals have a normal distribution with a few outliers. 0.20 dex. Normal star-forming SDSS galaxies exhibit a scatterbetween 0.07 dex-0.2 dex with a mean of 0.1 dex (Tremonti et al. 2004) around the stellar mass-metallicity relation. Thescatter of normal star-forming galaxies from this relationship is mostly attributed to the observational errors in the mass andmetallicity measurements (Tremonti et al. 2004). The scatter of ULIRGs (0.20 dex) is equal to the upper limit of the scatter ofnormal star-forming galaxies. The median error in metallicity measurements of ULIRGs is large, \Lambda 0.17 dex, and the medianerror in mass measurements is smaller, \Lambda 0.08 dex. If we consider the lower error bars, it is very likely that the metallicitydistribution of ULIRGs may shift to even lower values, and this may result in a larger scatter with respect to the T04 relationship.However, if we consider the upper error bars, only six ULIRGs may move above the T04 relationship, and most of the ULIRGswould still lie below this relationship. Previously, Rupke et al. (2008) showed that ULIRGs areunderabundant compared to the SFGs on the Mstar-Z relation.The position of our ULIRG sample with respect to the Mstar-Zrelationship of normal SFGs is consistent with the results of (Rupke et al. 2008). In our Mstar - Z subsample, 11 of the 48ULIRGs are also part of the 100 (U)LIRGs of Rupke et al. (2008). Because a small fraction (23%) of our sample overlapswith the sample of Rupke et al. (2008), our results are highly independent of theirs. 3.4.3. Color-Magnitude Distribution of ULIRGs The color versus magnitude distribution, the so-calledcolor-magnitude diagram, of galaxies out to z \Lambda 1 show twoseparate distributions (e.g., Hogg et al. 2003; Blanton et al. 2003; Baldry et al. 2004, 2006; Cooper et al. 2006; Muzzinet al. 2012): (1) a "red sequence" of early-type galaxies, and (2) a "blue cloud" of late-type galaxies. The red sequence galaxiesare bulge-dominated, more massive, non-star-forming, passive galaxies (e.g., Blanton et al. 2003, 2005; Hogg et al. 2003;Baldry et al. 2006; Driver et al. 2006). The blue cloud galaxies are disk-dominated, less massive, actively star-forming galaxies(e.g., Kauffmann et al. 2003b; Brinchmann et al. 2004; Wyder et al. 2007). Observations show that while the number densityof blue cloud galaxies has stayed almost constant, the red sequence galaxies have doubled from z \Lambda 1 to z \Lambda 0 (Bell et al.2004; Faber et al. 2007). This suggests that star-forming disk galaxies at z \Lambda 1 evolve to local passive galaxies. Such an evo-lution involves different physical processes that change galaxy morphology and quench star formation. As galaxies go througha transition phase from blue cloud to red sequence, they reside in the region in between, the so-called green valley.The transition of a late-type galaxy to an early type includes physical processes that are not fully understood yet. Mergers andAGN feedback are among the proposed star formation quenching mechanisms (e.g., Barnes & Hernquist 1996; Hopkins et al.2006, 2008a). Becasue ULIRGs are both merging systems and mostly host an AGN, they are good candidates for evolvinggalaxies from a blue cloud to a red sequence. In the following, we explore the location of our ULIRG sample in the CMD oflocal SDSS galaxies. For this investigation we have selected a local comparisonsample from the SDSS DR 10 database. We selected sources classified as galaxies that are brighter than rPetrosian <17.7 andhave spectroscopic redshifts within the 0.018 < z < 0.260interval ( zmedian = 0.1). We also select galaxies that havephotometric measurements in the u, g, and r bands. Our selection criterion leads to 499,953 galaxies. Throughout thisanalysis we use the Galactic extinction corrected "modelMag" measurements from the SDSS DR10 "PhotoObj" catalog. TheK-corrections are calculated using the kcorrect code v4.2of Blanton & Roweis (2007). For comparison with previous studies, we derive K-corrections for a fixed bandpass shift by z = 0.1. The absolute magnitudes and colors are denoted with M0.1r and u0.1-r0.1, respectively; these are tabulated in Table 5. Figure 14 shows the CMD, (u0.1-r0.1) versus M0.1r , of thecomparison and our ULIRG samples. The contours represent the number density of the comparison sample. The distributionof local SDSS galaxies shows two separate distributions: the red sequence and the blue cloud. We determine the color-magnituderelation of the red sequence and the blue cloud by following Baldry et al. (2004). We divide the comparison sample into16 M0.1r bins from -23.5 to -15.5; the bin size is 0.5 mag. For each M0.1r bin we fit the color distribution with a doubleGaussian and obtain the mean and variance for the red and the blue distributions. We adopt the color function and the absolutemagnitude functions given by Baldry et al. (2004) and obtain 21 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi -24 -22 -20 -18 M0.1r (mag) 0 1 2 3 4 u0 .1 -r 0.1 (mag) QSOSeyfert LINERComposite Star FormingHLIRG Unclassified Figure 14. Color-magnitude diagram for a local SDSS comparison sample, 82 ULIRGs and one HLIRG. The contours represent the number densities for 10 levels. (H)ULIRGs are shown on top of the contours. The color-magnituderelations for the red sequence (the upper dashed, colored red in the online version), the blue sequence (the lower dashed, colored blue in the online version) and the green valley (the lower dashed, colored green in the online version) areshown. The solid (colored green in the online version) lines show the s'0.1 mag width of the green valley. See the text for detailed descriptions of these relations.The vertical and horizontal error bars represent the uncertainties in the model magnitude measurements. (A color version of this figure is available in the online journal.) the color-magnitude relations as (u0.1 - r0.1)red-sequence = 2.559 + (-0.045) OE (M0.1r + 20) + (-0.298) OE tanh \Theta M 0.1r - (-17.757) 2.833 \Lambda , (1) (u0.1 - r0.1)blue-cloud = 2.831 + 0.066 OE (M0.1r + 20) + (-2.180) OE tanh \Theta M 0.1 r - (-22.999) 6.786 \Lambda . (2) The upper and lower dashed lines in Figure 14 represent thered and blue sequence color-magnitude relations, respectively. To derive the color-magnitude relation of the green valley, welocate the minimum in the double Gaussian functions. We then fit a linear plus a tanh function, the same function used to fitred and blue sequence relations, to the minimums. The resulting relation of the green valley is (u0.1 - r0.1)green-valley = 2.232 + (-0.096) OE (M0.1r + 20) + (-0.131) OE tanh \Theta M 0.1 r - (-16.447) 0.492 \Lambda . (3) We choose the width of the green valley to be 0.1. The middledashed line in Figure 14 represents Equation (3); the solid lines represent the 0.1 mag width.In Figure 14 the color-magnitude distribution of 82 ULIRGs and one HLIRG in our sample is shown on top of the contoursof the comparison sample. From our ULIRG sample, 10 are in the red sequence, 6 are in the green valley, and 66 arein the blue cloud. Some 81% of the ULIRGs are located in the blue cloud, 12% are in "the red sequence," and only 7% are in the green valley. Two of the 6 (33%) ULIRGs are inthe "green valley" and host an AGN. One of the 10 (10%) ULIRGs is in the red sequence, and 16% of the ULIRGsin the blue cloud host an AGN. The fraction of the AGNhosting ULIRGs is highest in the green valley. Some 40% (33of 82) of the ULIRGs are located outside of the 90% level contour. The median absolute magnitude and the u0.1-r0.1color of our ULIRG sample are M0.1r = -21.40 s' 0.71 and u0.1 - r0.1 = 1.91 s' 0.64. The median absolute magnitudeof the comparison SDSS sample is M0.1r = -20.55 s' 1.12.Compared to the local SDSS sample, the absolute magnitudes of ULIRGs are 0.86 mag brighter. The median u0.1 - r0.1 of thecomparison sample is u0.1 - r0.1 = 2.56 s' 0.55, so ULIRGshave 0.64 mag brighter colors. Because ULIRGs are selected by their star-formation-powered IR luminosity, we expect themto be bright optical sources. So in a sense their bright optical colors are consistent with their identification criteria.Chen et al. (2010) study the color-magnitude properties of a sample of 54 ULIRGs from a IRAS 1 Jy sample (Kim et al.1998) and show that ULIRGs are mostly in the blue cloud. They also find that compared to SDSS galaxies local ULIRGs are0.2 mag bluer in g - r. Compared to Chen et al. (2010), westudy a larger ULIRG sample and find consistent results; we find very similar color-magnitude properties. The distributionof our ULIRG sample across the color-magnitude diagram is also similar to the distribution shown by Chen et al. (2010).We find a smaller fraction for the ULIRGs that lie outside of the 90% level contour. While they do not find any AGN-hosting ULIRGs in the "green valley," we find two ULIRGs. In our color-magnitude subsample, 22 of the 82 ULIRGs are alsopart of the 54 ULIRGs studied by Chen et al. (2010). Because only a small fraction (27%) of our color-magnitude subsampleoverlaps with the sample of Chen et al. (2010), our results are independent of theirs.We note that the colors of the AGN-hosting ULIRGs have a contribution from the central AGN. In principle, AGN contam-ination makes the ULIRG colors bluer, and this may shift them from the green valley to the blue cloud. However, Chen et al.(2010) show that on average removing the AGN contamination changes the color only by a small amount (0.005-0.007 mag).For their sample, only one source moved closer to the green valley, and 11 out of 12 remained close to their original positions.Chen et al. (2010) show that the lack of AGNs in the green valley is not due to AGN contamination. In our sample, three ofthe 15 AGN ULIRGs are part of the 12 AGN ULIRGs studied by Chen et al. (2010), and therefore we assume their results tobe valid for our sample. Because it is beyond the scope of this work, we do not attempt to remove the AGN contribution forthe AGN-hosting ULIRGs. 4. DISCUSSION 4.1. Infrared Luminosities The IR luminosities computed in this work highly depend onthe selected SED library of Dale & Helou (2002). Goto et al. (2011a) compare the IR luminosities computed from the SEDmodels of Chary & Elbaz (2001), Dale & Helou (2002), and Lagache et al. (2003) and quote the median offsets between themodels as 13%-24%. The listed IR luminosities in this work might have similar offsets between these models.In contrast, the SED models of Dale & Helou (2002) represent especially the IR SEDs of normal SFGs, and they are notspecifically developed for ULIRGs. For example, Rieke et al. 22 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi (2009) compare the observed SEDs of five local purely star-forming ULIRGs with a Dale & Helou (2002) template with \Sigma = 1.5 and point out that at high IR luminosities the FIRbump of their SEDs is more peaked. If the intrinsic SEDs of local ULIRGs are more peaked than in Dale & Helou (2002)SED models, then the IR luminosities computed in this work might be overestimated. However, the comparison of Rieke et al.(2009) is based on a very small sample, and a full comparison between possible ULIRG SEDs is beyond the scope of thiswork. However, Rieke et al. (2009) and our sample have one common source, IRAS 12112+0305, for which we compare theIR luminosities based on the Dale & Helou (2002) model SED and the observed SED used by Rieke et al. (2009). We findthat the IR luminosity computed from the Dale & Helou (2002) model SED is only \Lambda 5% higher than IR luminosity based on theSED template of Rieke et al. (2009). This shows that while Rieke et al. (2009) state that their SEDs are more peaked compared tothe Dale & Helou (2002) template, the difference between the IR luminosities is small. These considerations suggest that theIR luminosities presented in this work do not have a significant systematic offset. Even though the Dale & Helou (2002) modelsare not special for ULIRGs, the high number of already known ULIRGs in our sample that are identified based on these SEDtemplates indicates that the IR luminosity measurements based on the SED templates of Dale & Helou (2002) are reliable foridentifying ULIRGs. 4.2. FIR Colors In Panel (d) of Figure 4, four sources, J1639245+303719,J0159503+002340, J1356100+290538, and J1706529+382010, exhibit extreme log(F(140 um)/F(160 um)) > 0.9 colors com-pared to the models. For these cases we check the reliability of the flux measurements from the AKARI catalogs.In all of these cases, while the 90 um flux is highly reli-able, the 65 um, 140 um and 160 um flux measurementsare of low quality, and the uncertainty of the 160 um fluxis not given. In such cases we assumed the uncertainty as 25% of the given flux measurement, but it seems that theseuncertainties could be even larger. Because the 90 um fluxmeasurements are secure, we still consider the measured IR luminosities to be reliable. The SEDs of three cases,J1639245+303719, J1356100+290538, and J1706529+382010, show that their flux densities at 140 um are \Lambda 0.8 dex largerthan that of the models. The SED of J0159503+002340 also exhibits a large difference (>1 dex) between the observed andmodel flux at 160 um. We also checked five more sourceswith log(F(140 um)/F(160 um)) > 0.5: J1603043+094717,J0030089-002743, J1102140+380240, J1346511+074720, and J2307212-343838. The SEDs of J0030089-002743,J1102140+380240, J1346511+074720, and J2307212-343838 show that their flux densities at 140 um is 0.5-0.8 dex largerthan that of the models. The SED of JJ1603043+094717 also exhibits a 0.6 dex difference between the observed and model fluxat 160 um. These large differences between the observed colorsand what are expected from the SED models can be attributed to the low-quality 140 um and 160 um flux measurements.As mentioned in Section 3.1.3, the SED models cover only the log(F(140 um)/F(160 um)) color range between-0.5425-0.2135, and therefore in Panel (c) the three sources, J1202527+195458, J1559301+380843, and J1502320+142132,appear as outliers with log(F(140 um)/F(160 um)) < -0.58.The SEDs of these sources show that their 65 um fluxes are\Lambda 0.5 dex lower than that of the models. Although the quality of the 65 um flux measurements are low for these sources, itis more likely that the limited parameter range of the models is the main reason for their large deviation from the models. Ifthe intrinsic SEDs of ULIRGs are more peaked compared to the templates of Dale & Helou (2002) as shown by Rieke et al.(2009), then we might expect to have a wider distribution for the FIR colors, and this might explain the large scatter seen inPanels (c) and (d). 4.3. Interaction Classes In Section 3.2 the interaction classes of 64 sources are adoptedfrom the literature (Veilleux et al. 2002; Hwang et al. 2007), and 55 sources are classified in this work based on visualinspection. Although visual classification is a subjective method, we prefer it because of its practical application. Two classifiersindependently classified each source, and for most of the cases there was good agreement. There was a disagreement betweenthe classifiers only for a few cases that are single-nucleus systems at higher redshifts. In such systems, the identification ofthe disturbed morphologies or weak interaction signs is difficult. However, the number of such systems are only five, and mostof them are not included in our statistics because of the applied redshift limit. Even if they were included in our statistics, theywould be classified as N i instead of V, and this would only decrease the number of sources classified as old mergers. Sucha change would not change the high percentage of IV and V systems in the overall population.Wide binary (IIIa) systems have the largest uncertainties because most of the companion galaxies do not have spectroscopicredshifts. However, wide binary galaxies usually have similar colors, and they show interaction signs. Therefore the chancecoincidences are low, and the assumed physical connection is highly likely. Even if most of the IIIa systems were instead IV,the dominance of the mergers still holds. So the overall conclusion of the morphology investigation in Section 3.2, that the vastmajority of ULIRGs in the local universe are single-nucleus ongoing or old mergers, is not affected by the disagreements of theclassifiers or unconfirmed redshifts of the companion galaxies in wide binaries. 4.4. AGN Fraction of Our ULIRG Sample In Section 3.3 we investigate the optical spectral typesof the ULIRGs in our sample. The classification of starforming galaxies, composites, LINERs, and Seyferts is basedon empirical emission-line diagnostics. The ULIRGs are dustrich systems, and dust extinction at optical wavelengths ishigh. Therefore, the dusty nature of ULIRGs brings a large uncertainty to their optical emission-line diagnostics. Nardiniet al. (2010) use the rest-frame 5-8 um spectra to disentangle thecontribution of star formation and AGNs in ULIRGs. As shown by Nardini et al. (2010), optical diagnostics do not providereliable information on the presence of AGNs. They trace obscured AGNs in some LINERs and even some star-forminggalaxies. Therefore, as stated earlier, our spectral classification provides only a lower limit on the AGN fraction. This brings alarge uncertainty to the AGN fraction per LIR bin presented inFigure 9. It is very highly likely that most of the composites and LINERs may have an AGN component. If all of the LINERsand composites had an AGN contribution, then the correlation between the AGN fraction and LIR would still be valid.Assuming all of the LINERs and composites as AGNs may be an unrealistic overestimation because we would expect at least 23 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi some fraction of the low-luminosity ULIRGs to be dominatedby star formation. To investigate the hidden AGNs among such sources in our sample, we look at the result of the mid-IRdiagnostic applied by Nardini et al. (2010). In total we have 31 overlapping sources with their sample. Our main interest isthe AGN component of the star-forming galaxies, composites, and LINERs in our sample. For those sources we adopt theAGN bolometric contribution parameter given by Nardini et al. (2010) (the \Sigma bol parameter in their Table 1). Only one star-forming galaxy (J0900252+390400) in our sample seems to have a significant AGN contribution. If we consider this sourceas an AGN instead of a star-forming galaxy, this would not affect the correlation of AGNs and the anticorrelation of star-forminggalaxies with IR luminosity. Also, it would have a negligible effect on the fraction of AGNs: the fraction of AGNs wouldincrease to 26%, and the fraction of star-forming galaxies would decrease to 19%. 4.5. The Offset of ULIRGs from the Main Sequence ofStar-forming Galaxies The star-formation rate and Mstar are tightly correlated from z \Lambda 0 to z \Lambda 2; the slope is between \Lambda 0.6 and \Lambda 1.0(mostly depending on the galaxy sample), but the normalization decreases with redshift. This indicates that the overall SFRincreases from z \Lambda 0 to z \Lambda 2, and the SFGs were forming starsmore actively in the past compared to lower redshift galaxies at the same masses. The observations indicate that high-redshiftSFGs contain a larger molecular gas reservoir (e.g., Daddi et al. 2010; Tacconi et al. 2010), and therefore the star-formation rateper stellar mass is higher at z \Lambda 2; in time this reservoir isused up and results in lower SFRs at z \Lambda 0. Figure 10 clearlydemonstrates that local ULIRGs are outliers with respect to the "main sequence" of the normal SFGs up to z \Lambda 2. Local ULIRGsare already known to be outliers compared to the local "main sequence" (Elbaz et al. 2007). This is not surprising because,in the first place, ULIRGs are defined by their enormous IR luminosities powered by intense star formation, and in orderto be defined as ULIRGs they should have 172 \Theta SFR(IR) \Theta 1721. So their position on the y-axis is a pure selection effect,and we expect them to have higher SFRs than normal starforming galaxies. We note that Figure 10 includes type-2 AGNs,LINERs, and composites. As mentioned earlier, even the AGN has a contribution to LIR, and the measured IR luminositiesare mainly dominated by the FIR emission. As mentioned in Section 3.4.1, the average AGN contamination is \Lambda 40.0%(Veilleux et al. 2009), but the offset of the local ULIRGs from the "main sequence" relations from z \Lambda 0-2 is relatively largeand cannot be attributed to the AGN contribution in the SFR(IR) estimates alone.Normal starburst galaxies are also outliers off the "main sequence" at z \Lambda 0.7 (Guo et al. 2013) and at z \Lambda 2 (Rodighieroet al. 2011). Guo et al. (2013) show their best-fit main sequence and the main sequence relationships given by Elbaz et al.(2007) and Daddi et al. (2007) in their Figure 7, where they report starburst galaxies as outliers. Because the local ULIRGsample lies above these main sequence relationships and their galaxy sample, it can be concluded that compared to normalstarburst galaxies at z \Lambda 0.7 local ULIRGs exhibit higher SFRs.Rodighiero et al. (2011) define off-sequence galaxies (see their Figure 1) as the ones lying a factor of 10 above the z \Lambda 2SFR- Mstar relation of Daddi et al. (2007). Compared to theseextreme outliers at z \Lambda 2, as seen in Figure 10, 90% of thelocal ULIRGs have lower SFRs, and only 10% have comparable 9.5 10.0 10.5 11.0 11.5 12.0log(M star 1 10 100 1000 10000 1011 10 1013 LIR z=0 MS z=1 MS z=2 MS z=2 MS- x4 z=2 MS- x10 LINERAGN CompositeStar forming HLIRGUnclassified Figure 15. Same as Figure 10, but stellar masses are shifted by 0.5 dex. SFRs. The SMGs, often referred as high-redshift analogs oflocal ULIRGS, are also known to be outliers compared to the z \Lambda 2 SFR-Mstar relation (Tacconi et al. 2008; Daddi et al.2007, 2009; Takagi et al. 2008). Compared to massive SFGs at the same masses, SFRs of SMGs are 10 times higher (Daddiet al. 2007, but also see Michal/owski et al. 2012). As noted by Daddi et al. (2007), SMGs at z \Lambda 2 and local ULIRGshave similar properties: both are rare sources and outliers in SFR-Mstar relations. However, compared to the location ofSMGs shown by Daddi et al. (2007) (their Figure 17(b)), local ULIRGs occupy a wider Mstar range, and they are closer to the z \Lambda 2 SFR-Mstar relation.As expected, galaxies with similar IR luminosities should have similar SFRs and positions in the SFR-Mstar diagram. Inparticular, we call attention to the role of the stellar mass as the distinguishing parameter. At this point it is important toconsider the uncertainties of the stellar masses in interpreting Figure 10. The ULIRGs in our sample have moderate stellarmasses within the 9.42 < log(Mstar(M\Xi )) <11.61 range, and themedian is 10.41. We compare the adopted stellar masses from Maraston et al. (2013) with the Mstar estimates given by previousULIRG studies. Rodr'iguez Zaur'in et al. (2010) provide Mstarestimates for 36 local ULIRGs derived by performing spectral synthesis modeling on high-quality optical spectra. We havetwo sources that overlap with their sample, J0900252+390400 and J1052232+440849, and they report 1.0 dex and 0.5 dexhigher stellar masses, respectively. However, we note that J0900252+390400 is the lowest mass ULIRG in our sample,and as mentioned in Section 4.4 it has an AGN. Therefore, we consider the difference of 1 dex in Mstar for this particularobject to be an exceptional case. da Cunha et al. (2010) also provide Mstar estimates for a sample of 16 purely star-formingULIRGs based on full SED modeling, including UV to FIR wavelengths. We have one common source with this sample(J1213460+024844), and for this source the Mstar estimatesagree well; their estimate is just 0.06 dex higher than the adopted value from Maraston et al. (2013). As shown byRodr'iguez Zaur'in et al. (2010), ULIRGs contain different stellar populations (very young, young, intermediate-young, and oldstellar populations) at the same time, and their optical light is mainly dominated by the less-massive young stellar populations.Therefore, we expect the stellar mass estimates of ULIRGs to be highly dependent on the approach followed (SED orspectral fitting), the data used, and the assumed star-formation 24 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 0 200 400 600 800 1000 1200SFR(IR) 0 2 4 6 8 10 12 14 N Pre-Mergers (IIIa,IIIb)Mergers (IV) Post-Mergers (V) 0 20 40 60 80SFR(IR)/M star [Gyr-1] 0 2 4 6 8 10 N Pre-Mergers (IIIa,IIIb)Mergers (IV) Post-Mergers (V) Figure 16. SFR(IR) (top) and specific star-formation rate (SFR/Mstar) (bottom)distribution of 68 ULIRGs as a function of interaction stage. histories (SFHs). In particular, Mstar estimates of ULIRGs likecomplex galaxies from SED fitting can be very sensitive to the assumed SFHs. As shown by Michal/owski et al. (2012)and Michal/owski (2014), using multicomponent SFHs that fit young and old populations result in systematically higher stellarmasses compared to exponentially declining SFH. Therefore, it is very likely that the adopted Mstar values in this workare underestimated. Obtaining the most robust stellar mass estimates of ULIRGs is beyond the scope of this paper, butwith the available data we are able to assign an uncertainty limit. Considering the Mstar differences of two (because it isan exceptional case, we exclude J0900252+390400) ULIRGs with respect to the values reported by Rodr'iguez Zaur'in et al.(2010) and da Cunha et al. (2010), all of the adopted Mstar valuesin this work might be underestimated by 0.06 dex-0.5 dex. A natural consequent question is the effect of this underestimatein Figure 10. To be conservative, we may assume that Mstar areunderestimated by 0.5 dex. As shown in Figure 15, if we shift stellar masses by 0.5 dex, ULIRGs still exhibit a large offset fromthe z \Lambda 0 and z \Lambda 1 main sequence, but they are consistent withthe z \Lambda 2 main sequence. This shows that even the stellar massesadopted in Figure 10 are underestimated, but this does not change the main conclusion that ULIRGs are outliers compared 7.5 8.0 8.5 9.0 9.5 10.0 10.512+log(O/H) 0 5 10 15 20 N Pre-Mergers (IIIa,IIIb)Mergers (IV) Post-Mergers (V) Figure 17. Oxygen abundance distributions of 39 ULIRGs as a function of interaction stage. to the z \Lambda 0 and z \Lambda 1 main sequence. However, it indicates thattheir offset from the z \Lambda 2 "main sequence" is very likely dueto their underestimated stellar masses. Of course Figure 15 is a simple illustration and might not reflect the Mstar distribution ofULIRGs at all; thus we caution against its interpretation. 4.6. Comparison of SFRs with Observationsand Simulations of Mergers The ULIRGs are interacting systems and are mostly ongoingor late mergers, and their extreme SFRs are generally attributed to merger events. Observations support this link: the SFRs oflocal ULIRGs are consistent with the observed enhanced SFR of mergers (e.g., Ellison et al. 2008, 2013). Moreover, the role ofmerger processes in triggering the SFR is a general prediction of merger models showing that major mergers cause nuclear gasinflows (Barnes & Hernquist 1991, 1996), and these inflows generate an intense SFR that peaks around when merginggalaxies coalesce (e.g., Di Matteo et al. 2005, 2007; Springel et al. 2005; Montuori et al. 2010; Torrey et al. 2012). Mergermodels show that star-formation activity increases after the first peri-center passage and reaches its maximum level when twogalaxies coalesce. In this picture we expect to observe lower SFRs in the premerger (widely or closely separated binaries)ULIRGs compared to the ULIRGs in the coalescence phase. In order to check whether the observed SFRs of our ULIRGsample are consistent with this prediction, in the top panel of Figure 16 the SFR(IR) distribution of ULIRGs is shownas a function of interaction class (defined in Section 3.2). We find that ULIRGs do not show a systematic difference inSFR(IR) for different interaction stages. We do not find the coalescence stage to be the peak of the SFR, as suggested bygeneral merger simulations (e.g., Torrey et al. 2012). Because the SFR is correlated with stellar mass, in the bottom panelof Figure 16 we show a specific star-formation rate, sSFR (SFR(IR)/Mstar), as a function of interaction class. This panelshows a distribution similar to the top one: sSFR does not depend on the interaction stage. Of course this does not mean thatULIRGs are completely inconsistent with the merger models because we are not tracing single merger events in time assimulations do. Instead we are looking at different snapshots of merger events for different sources. Therefore, Figure 16is rather consistent with the observations Rodr'iguez Zaur'in et al. (2010) showing that ULIRGs have complex multistellarpopulations. In some ULIRGs, the SF activity triggered in 25 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 0.0 0.5 1.0 1.5 2.0 2.5log(SFR(H\Xi )) 7 8 9 10 12 + log(O/H) log(Mstar 10.1510.30 10.4510.60 10.7510.90 9.5 10.0 10.5 11.0log(M star -0.6 -0.4 -0.2 -0.0 0.2 0.4 0.6 [12 + log(O/H)] measured - [12 + log(O/H)] FMR Figure 18. Left panel: FMR (Equation (2) of Mannucci et al. 2010) for different mass bins as a function of SFR. The colored lines show the mass bin. The colored open squares show the ULIRGs in each mass bin. Right panel: metallicity residuals of ULIRGs from the FMR; the colors represent the same mass bins labeled in theleft panel. The residuals represent the median values in each bin, except for the first and the last bins, which have single measurements. precoalescence epochs is probably comparable with that of theother coalescence phase; thus we see a similar distribution for different interaction phases.Merger simulations also predict that nuclear gas inflows in the periods prior to increasing SFR epochs cause nuclearmetallicity dilution, but afterward high SFRs cause metallicity enhancement (e.g., Torrey et al. 2012), so the overall metallicitychange has a rather complex fluctuating nature as the merger progresses. In Figure 17, we show the oxygen abundancedistribution of ULIRGs as a function of merger stage. Again the three distributions (premerger, merger, and postmerger) overlapand do not show a significant difference. As discussed above, we do not probe the evolution of oxygen abundances for individualULIRGs as simulations do, so based on Figure 17 we cannot conclude any inconsistency with their predictions. However,when we compare oxygen abundances of ULIRGs with that of normal SFGs, we find that they systematically have loweroxygen abundances, and this is consistent with the predictions of the numerical simulations (e.g., Torrey et al. 2012). Similarly,interacting galaxies such as close pairs (e.g., Kewley et al. 2006; Ellison et al. 2008) do not lie on the Mstar-Z relation. Theseinteracting, merging galaxies exhibit a lower metallicity than the noninteracting normal SFGs. 4.7. ULIRGs in the Fundamental Metallicity-Mass-SFR Plane Figure 13 shows that ULIRGs have lower metallicities withrespect to the Mstar-Z relation. The possible systematic uncer-tainties discussed in Section 4.5 are relevant to Figure 13, too. However, because the Mstar-Z relation is rather flat with in-creasing stellar mass, a shift of 0.5 dex in Mstar does not changethe observed scatter of ULIRGs. Figure 10 indicates that local ULIRGs have SFRs comparablewith z \Lambda 2.0 galaxies, and it is known that z \Lambda 2.2 galaxies havelower metallicities compared to local galaxies with the same masses (Erb et al. 2006; Tadaki et al. 2013). A similar resultwas also found for even higher redshift galaxies of z = 3-4(Maiolino et al. 2008; Mannucci et al. 2009). Star-forming galaxies up to z \Lambda 2.5 follow the fundamentalmetallicity relation (FMR), a tight relation between Mstar, gasmetallicity, and SFR (Mannucci et al. 2010). This relation indicates that metallicity decreases with increasing SFR forlow Mstar, but for high Mstar it does not change with SFR.So, according to the FMR at a fixed mass we expect to have lower metallicities with increasing SFR. In order to understandif the lower metallicities of ULIRGs are due to higher SFRs, we need to check if they are on the FMR plane. We base thisinvestigation on the FMR defined by Mannucci et al. (2010) for local SDSS galaxies. Following (Mannucci et al. 2010),we divide 47 (H)ULIRGs into 11 mass bins of 0.15 dex from log(Mstar(M\Xi )) = 9.70 to 10.90. We only consider the binscontaining at least one galaxy, and this selection results in 9 mass bins. To be consistent with Mannucci et al. (2010), we use theSFR(H \Sigma ) estimates obtained in Section 3.4.1. Because ULIRGstypically have larger SFRs, we extrapolate Equation (2) of Mannucci et al. (2010) up to log SFR(H\Sigma ) = 2.4. The left panelin Figure 18 shows the local FMR (Equation (2) of Mannucci et al. 2010) for these mass bins (color coded), where open circlesshow the distribution of ULIRGs in each mass bin (color coded with respect to mass). The right panel in Figure 18 shows theresiduals between the measured metallicities of ULIRGs and FMR. These are the median values in each bin, but the firstand the last bin represent residuals of single measurements. Without considering the uncertainties, the residuals of ULIRGsfrom the FMR are between 0.09 dex-0.26 dex. This is of course larger than the dispersions of the local SDSS galaxies that are\Lambda 0.05 dex, but it indicates that local ULIRGs are consistent with the FMR. We also note that the residuals of local ULIRGs arecomparable with that of high-redshift z \Lambda 2 galaxies (Mannucciet al. 2010). If we consider the uncertainties, the largest residual is \Lambda 0.5 dex; this might indicate an inconsistency with the FMR.We used the same recipe to infer oxygen abundances and SFRs, so the offset of 0.5 dex cannot be due to metallicity or SFRmeasurements themselves. However, the largest contribution to the metallicity uncertainties comes directly from the emission-line flux uncertainties, and this point can only be addressed with higher quality data. So the large uncertainties showing\Lambda 0.5 dex residuals do not necessarily mean a real offset from the FMR. However, also note that ULIRGs are interacting rarelocal galaxies with very high SFR, and they are expected to show a large scatter around the FMR (Mannucci et al. 2010). 26 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi 4.8. ULIRGs in a Color-Magnitude Diagram In Section 3.4.3 we found that local ULIRGs are opticallybright and blue galaxies. As noted before, this is consistent with their starburst nature. However, ULIRGs are dusty galaxies,and one might expect them to have redder colors due to dust extinction. However, as suggested by Chen et al. (2010), thedust distribution in ULIRGs might not be uniform, and therefore their stellar light is not completely obscured.The low fraction of ULIRGs in the green valley, as suggested by Chen et al. (2010), indicates that ULIRGs are rapidly SFGs,and they have not yet evolved into a transition phase. The evolution tracks of ULIRGs in the color-magnitude diagramis beyond the scope of this paper; for a discussion on this topic we refer readers to Chen et al. (2010). 5. CONCLUSIONS We identified ULIRGs in the AKARI all-sky survey by cross-matching the AKARI catalogs with SDSS DR 10 and 2dFGRS. With the advantage of AKARI and the available SDSS data,we are able to investigate morphologies, stellar masses, SFRs, gas metallicities, and optical colors of a large sample of localULIRGs. We examined the SFR- Mstar, Mstar-Z, SFR-Mstar-Z,and color-magnitude relations of our local ULIRG sample. The following summarizes the main conclusions from this work. 1. A sample of 118 ULIRGs and one HLIRG with F(90 um) \Lambda 0.22 Jy have been identified in the AKARI all-sky survey. Forty of the ULIRGs and one HLIRG are newly identifiedin the AKARI all-sky survey based on the spectroscopic redshifts from SDSS DR10 and 2dFGRS. The redshift rangeof our ULIRG sample is 0.050 < z < 0.487 and the medianredshift is 0.181. 2. In the redshift (z < 0.27) limited sample of 100 ULIRGs, allshow interaction features, either between two galaxies or in a single system. Only 5% are interacting triplets, 43% of theULIRGs are two-galaxy systems with strong tidal tails or bridges, and 52% of the ULIRGs are ongoing/post mergersshowing strong tidal tails or disturbed morphology. Our results support the known picture of ULIRGs as mergers.3. Based on the adopted optical emission-line diagnostics, we confirm the known trend of increasing AGN fraction withhigher IR luminosity. 4. Compared to SFR(IR), SFR(H\Sigma ) strongly underestimatesthe SFR of local ULIRGs by a factor of \Lambda 8. This implies that IR observations provide the best estimate of SFR forhighly star-forming dusty galaxies. 5. The ULIRGs have significantly higher SFRs than do themain sequence of normal SFGs up to z \Lambda 2. Local ULIRGshave 92, 17, and 5 times higher SFRs than do the main sequence galaxies with similar mass at z \Lambda 0, z \Lambda 1, and z \Lambda 2, respectively. Most of the local ULIRGs have lowerSFRs than do the off-main sequence galaxies at z \Lambda 2.6. We find that ULIRGs have lower gas metallicities compared to the Mstar-Z relation of normal star-forming galaxies;hence we confirm previous studies. We also find that local ULIRGs follow the FMR with high dispersions between0.09 dex-0.5 dex, which is similar to that of high-redshift (z \Lambda 2-3) galaxies.7. Compared to previous studies, we investigate the color properties of a larger ULIRG sample and find that 81%of the ULIRGs are in the blue cloud, 12% are in the "red sequence," and 7% are in the green valley. The vast majorityof local ULIRGs in our sample are blue galaxies. We provide the largest local ULIRG comparison sample tofurther study the Mstar, SFRs, gas metallicities, and optical colorsof high-redshift ULIRGs. We thank the anonymous referee for many insightful com-ments. We thank Marianne Vestergaard and Jens Hjorth for their comments. The Dark Cosmology Centre is funded by the Dan-ish National Research Foundation. AKARI is a JAXA project with the participation of universities and research institutes inJapan, the European Space Agency (ESA), the IOSG (Imperial College, UK, Open University, UK, University of Sussex,UK, and University of Groningen, Netherlands) Consortium, and Seoul National University, Korea. Funding for SDSS-IIIhas been provided by the Alfred P. Sloan Foundation, the participating institutions, the National Science Foundation, and theU.S. Department of Energy Office of Science. The SDSS-III Web site is http://www.sdss3.org/. SDSS-III is managed by theAstrophysical Research Consortium for the participating institutions of the SDSS-III Collaboration, including the Universityof Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University ofFlorida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica deCanarias, the Michigan State /Notre Dame/JINA ParticipationGroup, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max PlanckInstitute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, PennsylvaniaState University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, Uni-versity of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. The digitizedsky surveys were produced at the Space Telescope Science Institute under U.S. government grant NAG W-2166. The imagesof these surveys are based on photographic data obtained using the Oschin Schmidt Telescope on Palomar Mountain andthe UK Schmidt Telescope. The plates were processed into the present compressed digital form with the permission of theseinstitutions. The National Geographic Society-Palomar Observatory Sky Atlas (POSS-I) was made by the California Instituteof Technology with grants from the National Geographic Society. The Second Palomar Observatory Sky Survey (POSS-II)was made by the California Institute of Technology with funds from the National Science Foundation, the National GeographicSociety, the Sloan Foundation, the Samuel Oschin Foundation, and the Eastman Kodak Corporation. The Oschin Schmidt Tele-scope is operated by the California Institute of Technology and Palomar Observatory. The UK Schmidt Telescope was operatedby the Royal Observatory Edinburgh, with funding from the UK Science and Engineering Research Council (later the UK Parti-cle Physics and Astronomy Research Council), until 1988 June, and thereafter by the Anglo-Australian Observatory. The blueplates of the southern Sky Atlas and its Equatorial Extension (together known as the SERC-J), as well as the Equatorial Red(ER), and the Second Epoch [red] Survey (SES) were all taken with the UK Schmidt. This research has made use of NASA'sAstrophysics Data System Bibliographic Service. APPENDIX IR IMAGES OF NEWLY IDENTIFIED SOURCES We present the IR (AKARI 90 um) images of the newlyidentified ULIRGs and one HLIRG in Figure A1. 27 The Astrophysical Journal, 797:54 (30pp), 2014 December 10 Eser, Goto, & Doi Figure A1. AKARI 90 um images of all of the newly identified ULIRGs and one HLIRG. The scale of the images is 165\Pi \Pi OE 165\Pi \Pi . 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