arXiv:1001.0013v2 [astro-ph.CO] 8 Jan 2010Astronomy& Astrophysics manuscriptno.akari˙LF˙aa˙v7 c∝circlecopyrtESO 2018 October30,2018 EvolutionofInfraredLuminosityfunctionsofGalaxiesint he AKARINEP-Deepfield Revealing thecosmic star formationhistory hidden by dust⋆,⋆⋆ Tomotsugu Goto1,2,⋆⋆⋆,T.Takagi3,H.Matsuhara3,T.T.Takeuchi4,C.Pearson5,6,7, T.Wada3,T.Nakagawa3,O.Ilbert8, E.LeFloc’h9,S.Oyabu3, Y.Ohyama10,M.Malkan11, H.M.Lee12, M.G.Lee12,H.Inami3,13,14, N.Hwang2, H.Hanami15, M.Im12, K.Imai16,T.Ishigaki17,S.Serjeant7,and H.Shim12 1Institute for Astronomy, University of Hawaii,2680 Woodla wnDrive, Honolulu, HI,96822, USA e-mail:tomo@ifa.hawaii.edu 2National Astronomical Observatory, 2-21-1 Osawa,Mitaka, Tokyo, 181-8588,Japan 3Institute of Space and Astronautical Science, JapanAerosp ace Exploration Agency, Sagamihara,Kanagawa 229-8510 4Institute for Advanced Research, Nagoya University, Furo- cho, Chikusa-ku, Nagoya 464-8601 5Rutherford Appleton Laboratory, Chilton, Didcot,Oxfords hire OX110QX, UK 6Department of Physics,Universityof Lethbridge, 4401 Univ ersity Drive,Lethbridge, AlbertaT1J 1B1, Canada 7Astrophysics Group, Department of Physics, The OpenUniver sity, MiltonKeynes, MK76AA, UK 8Laboratoire d’Astrophysique de Marseille, BP8,Traverse d u Siphon, 13376 Marseille Cedex 12, France 9CEA-Saclay,Service d’Astrophysique, France 10Academia Sinica,Institute of Astronomyand Astrophysics, Taiwan 11Department of Physicsand Astronomy, UCLA,Los Angeles, CA, 90095-1547 USA 12Department of Physics& Astronomy, FPRD,Seoul National Uni versity, Shillim-Dong,Kwanak-Gu, Seoul 151-742, Korea 13Spitzer Science Center,California Institute ofTechnolog y, Pasadena, CA91125 14Department of Astronomical Science,The Graduate Universi tyfor Advanced Studies 15Physics Section,Facultyof Humanities and SocialSciences , Iwate University, Morioka, 020-8550 16TOMER&D Inc. Kawasaki, Kanagawa 2130012, Japan 17Asahikawa National College of Technology, 2-1-6 2-joShunk ohdai, Asahikawa-shi, Hokkaido 071-8142 Received September 15, 2009; accepted December 16, 2009 ABSTRACT Aims.Dust-obscured star-formation becomes much more important with increasing intensity, and increasing redshift. We aim to reveal cosmic star-formationhistoryobscured bydust usin g deep infraredobservation withthe AKARI. Methods. We construct restframe 8 µm, 12µm, and total infrared (TIR) luminosity functions (LFs) at 0.15< z <2.2using 4128 infraredsources intheAKARINEP-Deepfield.Acontinuous fil tercoverage inthemid-IRwavelength(2.4,3.2,4.1,7,9,11 , 15,18, and 24µm) by the AKARI satellite allows us to estimate restframe 8 µm and 12 µm luminosities without using a large extrapolation based ona SEDfit,which was the largestuncertainty inprevio us work. Results. Wehavefoundthatall8 µm(0.38< z <2.2),12µm(0.15< z <1.16),andTIRLFs( 0.2< z <1.6),showacontinuous andstrongevolutiontowardhigher redshift.Intermsofcos micinfraredluminositydensity( ΩIR),whichwasobtainedbyintegrating analytic fits to the LFs,we found a good agreement withprevio us work at z <1.2. We found the ΩIRevolves as ∝(1+z)4.4±1.0. Whenweseparatecontributionsto ΩIRbyLIRGsandULIRGs,wefoundmoreIRluminoussourcesareinc reasinglymoreimportant at higher redshift. Wefound that the ULIRG(LIRG)contribut ionincreases bya factor of 10(1.8) from z=0.35 toz=1.4. Keywords. galaxies: evolution, galaxies:interactions, galaxies:s tarburst, galaxies:peculiar, galaxies:formation 1. Introduction Studies of the extragalactic background suggest at least ha lf the luminous energy generated by stars has been reprocessed into the infrared(IR) by dust (Lagacheetal., 1999; Pugetet al., 1996; Franceschini,Rodighiero,&Vaccari, 2008), suggest ing that dust-obscured star formation was much more important a t higherredshiftsthantoday. ⋆This research is based on the observations with AKARI, a JAXA project withthe participationof ESA. ⋆⋆Based on data collected at Subaru Telescope, which is operat ed by the National Astronomical Observatory ofJapan. ⋆⋆⋆JSPSSPDfellowBell etal. (2005) estimate that IR luminosity density is 7 times higher than the UV luminosity density at z ∼0.7 than lo- cally. Takeuchi,Buat, &Burgarella (2005) reported that UV -to- IRluminositydensityratio, ρL(UV)/ρL(dust),evolvesfrom3.75 (z=0) to 15.1 by z=1.0 with a careful treatment of the sample selection effect, and that 70% of star formation activity is ob- scured by dust at 0.5 < z <1.2. Both works highlight the im- portance of probing cosmic star formation activity at high r ed- shift in the infrared bands. Several works found that most ex - tremestar-forming(SF) galaxies,whichareincreasinglyi mpor- tant at higher redshifts, are also more heavily obscured by d ust (Hopkinsetal., 2001; Sullivanet al., 2001; Buatet al.,200 7).2 Gotoet al.:InfraredLuminosityfunctions withthe AKARI Despite the value of infrared observations, studies of infrared galaxies by the IRAS and the ISO were re- stricted to bright sources due to the limited sensitiv- ities (Saundersetal., 1990; Rowan-Robinsonet al., 1997; Floreset al., 1999; Serjeantet al., 2004; Takeuchiet al., 2 006; Takeuchi,Yoshikawa,&Ishii, 2003), until the recent launc h of theSpitzer andtheAKARI satellites. Theirenormousimprov ed sensitivitieshaverevolutionizedthefield.Forexample: Le Floc’het al. (2005) analyzed the evolution of the total and 15µm IR luminosity functions (LFs) at 0< z <1based on the the Spitzer MIPS 24 µm data (>83µJy andR <24) in the CDF-S, and found a positive evolution in both luminosity and density, suggesting increasing importance of the LIRG a nd ULIRGpopulationsathigherredshifts. P´ erez-Gonz´ alezetal. (2005) used MIPS 24 µm observations oftheCDF-SandHDF-N( >83µJy)tofindthatthat L∗steadily increasesbyanorderofmagnitudeto z∼2,suggestingthatthe luminosity evolution is stronger than the density evolutio n. The ΩTIRscalesas(1+z)4.0±0.2fromz=0to0.8. Babbedgeet al. (2006) constructed LFs at 3.6, 4.5, 5.8, 8 and 24µm over0< z < 2using the data from the Spitzer Wide-areaInfraredExtragalactic(SWIRE)Surveyin a 6.5de g2 (S24µm>230µJy). They found a clear luminosity evolu- tion in all the bands, but the evolution is more pronounced at longer wavelength; extrapolatingfrom 24 µm, they inferred that ΩTIR∝(1+z)4.5. They constructed separate LFs for three dif- ferentgalaxySED (spectral energydistribution)typesand Type 1 AGN, finding that starburst and late-type galaxies showed strongerevolution.Comparisonof3.6and4.5 µmLFswithsemi- analytic and spectrophotometricmodelssuggested that the IMF is skewed towards higher mass star formation in more intense starbursts. Caputi etal.(2007)estimatedrestframe8 µmLFsofgalaxies over 0.08deg2in the GOODS fields based on Spitzer 24 µm (> 80µJy) atz=1 and 2. They found a continuousand strong posi- tiveluminosityevolutionfrom z=0toz=1,andto z=2.However, theyalsofoundthatthenumberdensityofstar-forminggala xies withνL8µm ν>1010.5L⊙(AGNs are excluded.) increases by a factor of 20 from z=0 to 1, but decreases by half from z=1 to 2 mainlyduetothe decreaseofLIRGs. Magnelliet al. (2009) investigated restframe 15 µm, 35µm and total infrared (TIR) LFs using deep 70 µm observations (∼300µJy) in the Spitzer GOODS and FIDEL (Far Infrared Deep Extragalactic Legacy Survey) fields (0.22 deg2in total) atz <1.3. They stacked 70 µm flux at the positions of 24 µm sources when sources are not detected in 70 µm. They found no changeintheshapeoftheLFs,butfoundapureluminosityevo - lutionproportionalto(1+z)3.6±0.5,andthatLIRGsandULIRGs have increased by a factor of 40 and 100 in number density by z∼1. Also, see Daiet al. (2009) for 3.6-8.0 µm LFs based on the IRACphotometryintheNOAODeepWide-FieldSurveyBootes field. However, most of the Spitzer work relied on a large extrapolation from 24 µm flux to estimate the 8, 12 µm or TIR luminosity. Consequently, Spitzer results heavily de- pended on the assumed IR SED library (Dale&Helou, 2002; Lagache,Dole,&Puget, 2003; Chary& Elbaz, 2001). Indeed many authors pointed out that the largest uncertainty in the se previous IR LFs came from SED models, especially when one computesTIRluminositysolelyfromobserved24 µmflux(e.g., see Fig.5ofCaputiet al.,2007). AKARI, the first Japanese IR dedicated satellite, has con- tinuous filter coverage across the mid-IR wavelengths, thus , al-Fig.1. Photometric redshift estimates with LePhare (Ilbertet al., 2006; Arnoutset al., 2007; Ilbertet al., 200 9) for spectroscopically observed galaxies with Keck/DEIMOS (Takagi et al. in prep.). Red squares show objects where AGN templates were better fit. Errors of the photoz is∆z 1+z=0.036 for z≤0.8, but becomes worse at z >0.8to be∆z 1+z=0.10 due mainlyto therelativelyshallownear-IRdata. lows us to estimate MIR (mid-infrared)-luminositywithout us- ing a large k-correction based on the SED models, eliminating thelargestuncertaintyinpreviouswork.Bytakingadvanta geof this, we present the restframe 8, 12 µm and TIR LFs using the AKARI NEP-Deepdatainthiswork. Restframe 8 µm luminosity in particular is of primary rele- vance for star-forming galaxies, as it includes polycyclic aro- matic hydrocarbon (PAH) emission. PAH molecules charac- terize star-forming regions (Desert,Boulanger,&Puget, 1 990), and the associated emission lines between 3.3 and 17 µm dom- inate the SED of star-forming galaxies with a main bump lo- cated around 7.7 µm. Restframe 8 µm luminosities have been confirmed to be good indicators of knots of star formation (Calzetti etal., 2005) and of the overall star formation act ivity of star forming galaxies (Wuet al., 2005). At z=0.375, 0.875, 1.25 and 2, the restframe 8 µm is covered by the AKARI S11, L15,L18WandL24filters. We present the restframe 8 µm LFs at theseredshiftsatSection3.1. Restframe 12 µm luminosity functions have also been studied extensively (Rush,Malkan,& Spinoglio, 1993; P´ erez-Gonz´ alezet al., 2005). At z=0.25, 0.5 and 1, the restframe12 µmiscoveredbytheAKARI L15,L18WandL24 filters. We present the restframe 12 µm LFs at these redshifts in Section3.3. We also estimate TIR LFs through the SED fit using all the mid-IR bands of the AKARI. The results are presented in Section3.5. Unless otherwise stated, we adopt a cosmology with (h,Ωm,ΩΛ) = (0.7,0.3,0.7)(Komatsuet al., 2008). 2. Data & Analysis 2.1. Multi-wavelength data inthe AKARI NEP Deepfield AKARI, the Japanese infraredsatellite (Murakamiet al., 20 07), performed deep imaging in the North Ecliptic Region (NEP) from 2-24 µm, with 14 pointings in each field over 0.4 deg2(Matsuharaet al., 2006, 2007; Wada et al., 2008). DueGotoet al.:InfraredLuminosityfunctions withthe AKARI 3 Fig.2.Photometricredshiftdistribution. Fig.3.8µmluminositydistributionsofsamplesusedtocompute restframe 8 µm LFs. From low redshift, 533, 466, 236 and 59 galaxiesarein eachredshiftbin. to the solar synchronous orbit of the AKARI, the NEP is the only AKARI field with very deep imaging at these wavelengths. The 5 σsensitivity in the AKARI IR filters (N2,N3,N4,S7,S9W,S11,L15,L18WandL24) are 14.2, 11.0, 8.0, 48, 58, 71, 117, 121 and 275 µJy (Wada etal., 2008). These filters provide us with a unique continuous wavelength coverage at 2-24 µm, where there is a gap between the Spitzer IRAC and MIPS, and the ISO LW2andLW3. Please consult Wada etal. (2007, 2008); Pearsonet al. (2009a,b) for data ve ri- ficationandcompletenessestimateatthesefluxes.ThePSFsi zes are 4.4, 5.1, and 5.4” in 2−4,7−11,15−24µm bands. The depths of near-IR bands are limited by source confusion, but thoseofmid-IRbandsarebyskynoise.In analyzingthese observations,we first combinedthe three images of the MIR channels, i.e. MIR-S( S7,S9W, andS11) and MIR-L( L15,L18WandL24), in order to obtain two high- quality images. In the resulting MIR-S and MIR-L images, the residual sky has been reduced significantly, which helps to o b- tain more reliable source catalogues. For both the MIR-S and MIR-Lchannels,we use SExtractorforthecombinedimagesto determineinitialsourcepositions. We follow Takagietal. (2007) procedures for photometry and band-merging of IRC sources. But this time, to maximize the number of MIR sources, we made two IRC band-merged catalogues based on the combined MIR-S and MIR-L images, andthenconcatenatedthese catalogues,eliminatingdupli cates. Intheband-mergingprocess,thesourcecentroidineachIRC image has beendetermined,starting fromthe sourcepositio n in the combined images as the initial guess. If the centroid det er- mined in this way is shifted from the original position by >3′′, we reject such a source as the counterpart. We note that this band-mergingmethodisusedonlyforIRCbands. We comparedraw numbercountswith previouswork based on the same data but with different source extraction method s (Wadaet al., 2008; Pearsonet al., 2009a,b) and found a good agreement. A subregion of the NEP-Deep field was observed in the BVRi′z′-bands with the Subaru telescope (Imaiet al., 2007; Wada etal., 2008), reaching limiting magnitudes of zAB=26 in one field of view of the Suprime-Cam.We restrict our analy- sis to the data in this Suprime-Cam field (0.25 deg2), where we have enough UV-opical-NIR coverage to estimate good photo- metricredshifts.The u′-bandphotometryinthisareaisprovided by the CFHT (Serjeant et al. in prep.). The same field was also observed with the KPNO2m/FLAMINGOs in JandKsto the depth ofKsVega<20(Imaiet al., 2007). GALEX coveredthe entirefieldtodepthsof FUV <25andNUV < 25(Malkanet al.in prep.). In the Suprime-Cam field of the AKARI NEP-Deep field, there are a total of 4128 infrared sources down to ∼100µJy in theL18Wfilter. All magnitudesare given in AB system in this paper. For the optical identification of MIR sources, we adopt the likelihood ratio (LR) method (Sutherland&Saunders, 1992) . For the probability distribution functions of magnitude an d an- gular separation based on correct optical counterparts (an d for this purpose only), we use a subset of IRC sources, which are detected in all IRC bands. For this subset of 1100 all-band– detected sources, the optical counterparts are all visuall y in- spected and ambiguous cases are excluded. There are multipl e opticalcounterpartsfor35%ofMIRsourceswithin <3′′. Ifwe adoptedthenearestneighborapproachfortheopticalident ifica- tion,theopticalcounterpartsdiffersfromthat oftheLRme thod for20%ofthesourceswith multipleopticalcounterparts.T hus, in total we estimate that less than 15% of MIR sources suffer fromseriousproblemsofopticalidentification. 2.2. Photometric redshift estimation For these infrared sources, we have computed photomet- ric redshift using a publicly available code, LePhare1 (Ilbertet al., 2006; Arnoutsetal., 2007; Ilbertet al., 200 9). The input magnitudes are FUV,NUV (GALEX), u(CFHT), B,V,R,i′,z′(Subaru), J,andK(KPNO2m).Wesummarizethe filtersusedinTable1. 1http://www.cfht.hawaii.edu/∼arnouts/lephare.html4 Gotoet al.:InfraredLuminosityfunctions withthe AKARI Table 1.Summaryoffiltersused. Estimate Redshift Filter Photoz0.150.8. The∆z 1+zbecomes signifi- cantly larger at z >0.8, where we suffer from relative shallow- ness of our near-IR data. The rate of catastrophic failures i s 4% (∆z 1+z>0.2)amongthespectroscopicsample. In Fig.1, we compare spectroscopic redshifts from Keck/DEIMOS (Takagi et al.) and our photometric red- shift estimation. Those SEDs which are better fit with a QSO template are shown as red triangles. We remove those red triangle objects ( ∼2% of the sample) from the LFs presented below. We caution that this can only remove extreme type-1 AGNs, and thus, fainter, type-2 AGN that could be removedby X-raysoropticalspectroscopystill remainin thesample. Fig.2showsthedistributionofphotometricredshift.Thed is- tributionhasseveralpeaks,whichcorrespondstogalaxycl usters in the field (Gotoetal., 2008). We have 12% of sources that do nothaveagoodSEDfit toobtainareliablephotometricredshi ft estimation.Weapplythisphoto- zcompletenesscorrectiontothe LFs we obtain.Readers are referredto Negrelloet atal. (200 9), who estimated photometricredshifts using only the AKARI fil - terstoobtain10%accuracy. 2.3. The1/ Vmaxmethod WecomputeLFsusingthe1/ Vmaxmethod(Schmidt,1968).The advantage of the 1/ Vmaxmethod is that it allows us to compute a LF directly from data, with no parameter dependence or an assumed model. A drawback is that it assumes a homogeneous galaxy distribution, and is thus vulnerable to local over-/ under- densities(Takeuchi,Yoshikawa,&Ishii,2000). A comoving volume associated with any source of a given luminosity is defined as Vmax=Vzmax−Vzmin, wherezmin is the lower limit of the redshift bin and zmaxis the maximum redshiftat whichthe objectcouldbe seen giventhe fluxlimit of the survey, with a maximum value corresponding to the upperredshiftoftheredshiftbin.Moreprecisely, zmax= min(z maxof the bin ,zmaxfromthe flux limit) (1) We usedtheSED templates(Lagache,Dole,&Puget, 2003) for k-corrections to obtain the maximum observable redshift fro m thefluxlimit. Foreachluminositybinthen,theLFisderivedas φ=1 ∆L/summationdisplay i1 Vmax,iwi, (2) whereVmaxis a comoving volume over which the ith galaxy couldbeobserved, ∆Listhesizeoftheluminositybin(0.2dex), andwiis the completeness correction factor of the ith galaxy. WeusecompletenesscorrectionmeasuredbyWadaet al.(2008 ) for11and24 µmandPearsonet al.(2009a,b)for15and18 µm. Thiscorrectionis25%atmaximum,sincewe onlyusethesam- plewherethecompletenessisgreaterthan80%. 2.4. Monte Carlo simulation Uncertainties of the LF values stem from various factors suc h as fluctuations in the numberof sources in each luminosity bi n, the photometric redshift uncertainties, the k-correction uncer- tainties, and the flux errors. To compute these errors we per- formedMonteCarlosimulationsbycreating1000simulatedc at- alogs,whereeach catalogcontainsthesame numberof source s, but we assign each source a new redshift following a Gaussian distribution centered at the photometric redshift with the mea- sured dispersion of ∆z/(1 +z) =0.036 for z≤0.8and ∆z/(1+z) =0.10forz >0.8(Fig.1). The flux of each source is also allowed to vary accordingto the measuredflux error fo l- lowingaGaussiandistribution.For8 µmand12µmLFs,wecan ignore the errors due to the k-correction thanks to the AKARI MIR filter coverage. For TIR LFs, we have added 0.05 dex of error for uncertaintyin the SED fitting following the discus sion in Magnelliet al. (2009). We did not consider the uncertaint y on the cosmic variance here since the AKARI NEP field cov- ers a large volume and has comparable number counts to other generalfields(Imaiet al.,2007,2008).Eachredshiftbinwe use covers∼106Mpc3of volume. See Matsuharaetal. (2006) for morediscussion on the cosmic variancein the NEP field. These estimated errors are added to the Poisson errors in each LF bi n inquadrature. 3. Results 3.1. 8µm LF Monochromatic 8 µm luminosity ( L8µm) is known to cor- relate well with the TIR luminosity (Babbedgeet al., 2006; Huanget al.,2007),especiallyforstar-forminggalaxiesb ecause the rest-frame 8 µm flux are dominated by prominent PAH fea- turessuchasat 6.2,7.7and8.6 µm. Since the AKARI has continuous coverage in the mid-IR wavelengthrange,therestframe8 µmluminositycanbeobtained without a large uncertainty in k-correction at a corresponding redshift and filter. For example, at z=0.375, restframe 8 µm is redshiftedinto S11filter. Similarly, L15,L18WandL24cover restframe 8 µm atz=0.875, 1.25 and 2. This continuous filter coverageisanadvantagetoAKARIdata.OftenSEDmodelsare used to extrapolate from Spitzer 24 µm flux in previous work,Gotoet al.:InfraredLuminosityfunctions withthe AKARI 5 producingasourceofthe largestuncertainty.We summarise fil- tersusedinTable1. To obtain restframe 8 µm LF, we applied a flux limit of F(S11) <70.9, F(L15) <117, F(L18W) <121.4, and F(L24)<275.8µJy atz=0.38-0.58, z=0.65-0.90, z=1.1-1.4 andz=1.8-2.2,respectively.Thesearethe5 σlimitsmeasuredin Wada etal. (2008). We exclude those galaxies whose SEDs are betterfit withQSO templates( §2). We use the completeness curve presented in Wada et al. (2008) and Pearsonet al. (2009a,b) to correct for the incom- pleteness of the detection. However, this correction is 25% at maximumsincethesampleis80%completeatthe5 σlimit.Our mainconclusionsarenotaffectedbythisincompletenessco rrec- tion. To compensatefor the increasing uncertaintyin incre asing z, we use redshift binsize of 0.38 < z <0.58, 0.65 < z <0.90, 1.1< z <1.4,and 1.8 < z <2.2.We show the L8µmdistribution in each redshift rangein Fig.3. Within each redshift bin, we use 1/Vmaxmethodto compensateforthefluxlimit ineachfilter. We show the computed restframe 8 µm LF in Fig.4. Arrows show the 8 µm luminosity correspondingto the flux limit at the central redshift in each redshift bin. Errorbarson each poi nt are basedontheMonteCarlosimulation( §2.3). For a comparison, as the green dot-dashed line, we also show the 8 µm LF of star-forming galaxies at 0< z < 0.3 by Huanget al. (2007), using the 1/ Vmaxmethod applied to the IRAC 8µm GTO data. Compared to the local LF, our 8 µm LFs showstrongevolutionin luminosity.Intherangeof 0.48< z < 2,L∗ 8µmevolvesas ∝(1+z)1.6±0.2. Detailedcomparisonwith theliteraturewill bepresentedin §4. 3.2. Bolometric IR luminosity density basedonthe 8 µm LF Constraining the star formation history of galaxies as a fun c- tion of redshift is a key to understanding galaxy formation i n the Universe. One of the primary purposes in computing IR LFs is to estimate the IR luminosity density, which in turn is a goodestimatorof thedust hiddencosmic star formationdens ity (Kennicutt, 1998). Since dust obscurationis more importan t for more actively star forming galaxies at higher redshift, and such star formationcannotbeobservedinUV light,it is importan tto obtainIR-basedestimateinordertofullyunderstandtheco smic star formationhistoryoftheUniverse. Weestimatethetotalinfraredluminositydensitybyintegr at- ingtheLFweightedbytheluminosity.First, weneedtoconve rt L8µmto the bolometric infrared luminosity. The bolometric IR luminosity of a galaxy is produced by the thermal emission of its interstellarmatter. Instar-forminggalaxies,the UV r adiation producedbyyoungstarsheatstheinterstellardust,andthe repro- cessed lightisemittedin theIR. Forthisreason,in star-fo rming galaxies,thebolometricIRluminosityisagoodestimatoro fthe current SFR (star formation rate) of the galaxy. Bavouzetet al. (2008) showed a strong correlation between L8µmand total in- frared luminosity ( LTIR) for 372 local star-forming galaxies. TheconversiongivenbyBavouzetet al.(2008)is: LTIR= 377.9×(νLν)0.83 rest8µm(±37%) (3) Caputi etal. (2007) further constrained the sample to lumi- nous, high S/N galaxies ( νL8µm ν>1010L⊙and S/N>3in all MIPS bands) in order to better match their sample, and derive d thefollowingequation.Fig.4.Restframe 8 µm LFs based on the AKARI NEP-Deep field. The blue diamons, purple triangles, red squares, and o r- ange crosses show the 8 µm LFs at 0.38< z <0.58,0.65< z <0.90,1.1< z <1.4, and1.8< z <2.2, respectively. AKARI’s MIR filters can observe restframe 8 µm at these red- shifts in a corresponding filter. Errorbars are from the Mont e Caro simulations ( §2.4). The dotted lines show analytical fits with a double-power law. Vertical arrows show the 8 µm lumi- nosity corresponding to the flux limit at the central redshif t in each redshift bin. Overplotted are Babbedgeet al. (2006) in the pink dash-dotted lines, Caputiet al. (2007) in the cyan dash - dotted lines, and Huanget al. (2007) in the green dash-dotte d lines.AGNsareexcludedfromthe sample( §2.2). LTIR= 1.91×(νLν)1.06 rest8µm(±55%) (4) Since ours is also a sample of bright galaxies, we use this equation to convert L8µmtoLTIR. Because the conversion is based on local star-forming galaxies, it is a concern if it ho lds at higher redshift or not. Bavouzetet al. (2008) checked thi s by stacking 24 µm sources at 1.3< z <2.3in the GOODS fields to find the stacked sources are consistent with the local rela - tion. They concluded that equation (3) is valid to link L8µm andLTIRat1.3< z <2.3. Takagiet al. (2010) also show that local L7.7µmvsLTIRrelation holds true for IR galaxies at z∼1 (see their Fig.10). Popeetal. (2008) showed that z∼2 sub-millimeter galaxies lie on the relation between LTIRand LPAH,7.7that has been established for local starburst galaxies. S70/S24ratios of 70 µm sources in Papovichet al. (2007) are also consistent with local SED templates. These results sug gest it isreasonabletouse equation(4) foroursample. The conversion, however, has been the largest source of er- rorinestimating LTIRfromL8µm.Bavouzetet al.(2008)them- selvesquote37%ofuncertainty,andthatCaputietal.(2007 )re- port 55% of dispersion around the relation. It should be kept in mind that the restframe 8µm is sensitive to the star-formation activity, but at the same time, it is where the SED models have strongest discrepancies due to the complicated PAH emissio n lines. A detailed comparison of different conversions is pr e- sented in Fig.12 of Caputiet al. (2007), who reported factor of ∼5ofdifferencesamongvariousmodels.6 Gotoet al.:InfraredLuminosityfunctions withthe AKARI Then the 8 µm LF is weighted by the LTIRand integrated to obtain TIR density. For integration, we first fit an ana- lytical function to the LFs. In the literature, IR LFs were fit better by a double-power law (Babbedgeet al., 2006) or a double-exponential (Saunderset al., 1990; Pozziet al., 2 004; Takeuchiet al., 2006; Le Floc’het al., 2005) than a Schechte r function, which declines too suddenlly at the high luminosi ty, underestimating the number of bright galaxies. In this work , we fit the 8 µm LFs using a double-powerlaw (Babbedgeet al., 2006)asshownbelow. Φ(L)dL/L∗= Φ∗/parenleftbiggL L∗/parenrightbigg1−α dL/L∗,(L < L∗) (5) Φ(L)dL/L∗= Φ∗/parenleftbiggL L∗/parenrightbigg1−β dL/L∗,(L > L∗) (6) First, the double-powerlaw is fitted to the lowest redshift L F at 0.38< z <0.58 to determine the normalization( Φ∗) and slopes (α,β).Forhigherredshiftswedonothaveenoughstatisticstosi - multaneouslyfit 4parameters( Φ∗,L∗,α,andβ).Therefore,we fixedtheslopesandnormalizationat the localvaluesandvar ied onlyL∗atforthehigher-redshiftLFs.Fixingthefaint-endslope isacommonprocedurewiththedepthofcurrentIRsatellites ur- veys (Babbedgeet al., 2006; Caputi etal., 2007). The strong er evolution in luminosity than in density found by previous wo rk (P´ erez-Gonz´ alezet al., 2005; LeFloc’het al., 2005) also justi- fies this parametrization. Best fit parameters are presented in Table2.Oncethebest-fitparametersarefound,weintegrate the doublepowerlawoutsidetheluminosityrangeinwhichwehav e data to obtain estimate of the total infrared luminosity den sity, ΩTIR. The resulting total luminosity density ( ΩIR) is shown in Fig.5 as a function of redshift. Errors are estimated by vary ing thefit within1 σofuncertaintyin LFs, thenerrorsin conversion fromL8µmtoLTIRare added. The latter is by far the larger source of uncertainty. Simply switching from equation (3) ( or- ange dashed line) to (4) (red solid line) produces a ∼50% dif- ference. Cyan dashed lines show results from LeFloc’het al. (2005) for a comparision. The lowest redshift point was cor- rectedfollowingMagnellietal. (2009). We also show the evolution of monochromatic 8 µm lumi- nosity (L8µm), which is obtained by integrating the fits, but without converting to LTIRin Fig.6. The Ω8µmevolves as ∝(1+z)1.9±0.7. The SFR and LTIRare related by the following equation for a Salpeter IMF, φ(m)∝m−2.35between0.1−100M⊙ (Kennicutt,1998). SFR(M⊙yr−1) = 1.72×10−10LTIR(L⊙) (7) The right ticks of Fig.5 shows the star formation density scale,convertedfrom ΩIRusingtheaboveequation. In Fig.5, ΩIRmonotonically increases toward higher z. Comparedwith z=0,ΩIRis∼10timeslargerat z=1.Theevolu- tionbetween z=0.5andz=1.2isalittleflatter,butthisisperhaps duetoamoreirregularshapeofLFsat0.65 < z <0.90,andthus, wedonotconsideritsignificant.Theresultsobtainedherea gree with previous work (e.g., Le Floc’het al., 2005) within the e r- rors. We compare the results with previous work in more detai l in§4.Fig.5.Evolution of TIR luminosity density computed by inte- grating the 8 µm LFs in Fig.4.The red solid lines use the con- version in equation (4). The orange dashed lines use equatio n (3).ResultsfromLeFloc’hetal.(2005)areshownwiththecy an dottedlines. Fig.6.Evolution of 8 µm IR luminosity density computed by integrating the 8 µm LFs in Fig.4. The lowest redshift point is fromHuanget al.(2007). 3.3. 12µm LF In this subsection we estimate restframe 12 µm LFs based on the AKARI NEP-Deep data. 12 µm luminosity ( L12µm) has been well studied through ISO and IRAS, and known to correlate closely with TIR luminosity (Spinoglioetal., 19 95; P´ erez-Gonz´ alezet al.,2005). As was the case for the 8 µm LF, it is advantageous that AKARI’s continuous filters in the mid-IR allow us to estimate restframe 12 µm luminosity without much extrapolation based onSEDmodels.Gotoet al.:InfraredLuminosityfunctions withthe AKARI 7 Table 2.Best fit parametersfor8,12 µmandTIRLFs Redshift λ L∗(L⊙)Φ∗(Mpc−3dex−1)α β 0.386µm,toestimate LTIR. 3.5. TIRLF AKARI’scontinuousmid-IRcoverageisalsosuperiorforSED - fitting to estimate LTIR, since for star-forming galaxies, the mid-IR part of the IR SED is dominated by the PAH emissions whichreflectthe SFR ofgalaxies,andthus,correlateswell w ith LTIR, which is also a good indicator of the galaxy SFR. The AKARI’scontinuousMIRcoveragehelpsustoestimate LTIR. After photometric redshifts are estimated using the UV- optical-NIRphotometry,we fix the redshift at the photo- z,then use the same LePhare code to fit the infrared part of the SED to estimate TIR luminosity. We used Lagache,Dole,&Puget (2003)’s SED templates to fit the photometryusing the AKARI bands at >6µm (S7,S9W,S11,L15,L18WandL24). We showanexampleoftheSEDfitinFig.11,wherethereddashed and blue solid lines show the best-fit SEDs for the UV-optical - NIR and IR SED at λ >6µm, respectively. The obtained total infraredluminosity( LTIR) is shown as a functionofredshift in Fig.12,withspectroscopicgalaxiesinlargetriangles.Th efigure shows that the AKARI can detect LIRGs ( LTIR>1011L⊙) up toz=1 and ULIRGs ( LTIR>1012L⊙) toz=2. We also checkedthatusingdifferentSEDmodels(Chary& Elbaz,2001 ; Dale& Helou,2002) doesnotchangeouressentialresults. Galaxies in the targeted redshift range are best sampled in the 18µm band due to the wide bandpass of the L18Wfilter (Matsuharaet al., 2006). In fact, in a single-band detectio n, the 18µm image returns the largest number of sources. Therefore, we applied the 1/ Vmaxmethod using the detection limit at L18W. We also checked that using the L15flux limit does not change our main results. The same Lagache,Dole,&Puget (2003)’s models are also used for k-corrections necessary to compute VmaxandVmin. The redshift bins used are 0.2 < z <0.5,0.5< z <0.8,0.8< z <1.2,and 1.2 < z <1.6. A distri- butionof LTIRineachredshiftbinis showninFig.13. Theobtained LTIRLFsareshowninFig.14.Theuncertain- ties are esimated through the Monte Carlo simulations ( §2.4). For a local benchmark, we overplot Sanderset al. (2003) who derived LFs from the analytical fit to the IRAS Revised Bright Galaxy Sample, i.e., φ∝L−0.6forL < L∗andφ∝L−2.2for L > L∗withL∗= 1010.5L⊙. The TIR LFs show a strong evo- lutioncomparedtolocalLFs.At 0.25< z <1.3,L∗ TIRevolvesGotoet al.:InfraredLuminosityfunctions withthe AKARI 9 Fig.12.TIR luminosity is shown as a function of photometric redshift. The photo- zis estimated using UV-optical-NIR pho- tometry.LTIRisobtainedthroughSED fit in7-24 µm. Fig.13.AhistogramofTIRluminosity.Fromlow-redshift,144, 192, 394, and 222 galaxies are in 0.2 < z <0.5, 0.5< z <0.8, 0.8< z <1.2,and1.2 < z <1.6,respectively. as∝(1 +z)4.1±0.4. We further compare LFs to the previous workin§4. 3.6. Bolometric IR luminosity density basedonthe TIRLF Using the same methodology as in previous sections, we inte- grateLTIRLFs in Fig.14 through a double-power law fit (eq. 5 and 6). The resulting evolution of the TIR density is shown with red diamonds in Fig.15, which in in good agreement with LeFloc’hetal.(2005)withintheerrors.Errorsareestimat edby varying the fit within 1 σof uncertainty in LFs. For uncertainty intheSEDfit,weadded0.15dexoferror.Bestfitparametersar e presented in Table 2. In Fig.15, we also show the contributio ns toΩTIRfromLIRGsandULIRGswiththebluesquaresandor- ange triangles, respectively. We further discuss the evolu tion of ΩTIRin§4.Fig.14.TIRLFs.Verticallinesshowtheluminositycorrespond- ing to the flux limit at the central redshift in each redshift b in. AGNsareexcludedfromthesample( §2.2). Fig.15. TIR luminosity density (red diamonds) computed by integrating the total LF in Fig.14. The blue squares and oran ge trianglesareforLIRG andULIRGsonly. 4. Discussion 4.1. Comparison with previouswork In this section, we compare our results to previous work, esp e- ciallythosebasedontheSpitzerdata.Comparisonsarebest done inthesamewavelengths,sincetheconversionfromeither L8µm orL12µmtoLTIRinvolves the largest uncertainty. Hubble pa- rametersinthepreviousworkareconvertedto h= 0.7forcom- parison.10 Gotoet al.:InfraredLuminosityfunctions withthe AKARI 4.1.1. 8µm LFs Recently, using the Spitzer space telescope, restframe 8 µm LFs ofz∼1 galaxies have been computed in detail by Caputiet al. (2007) in the GOODS fields and by Babbedgeetal. (2006) in theSWIREfield.Inthissection,wecompareourrestframe8 µm LFs(Fig.4)tothese anddiscusspossibledifferences. In Fig.4, we overplot Caputi etal. (2007)’s LFs at z=1 and z=2inthecyandash-dottedlines.Their z=2LFisingoodagree- ment with our LF at 1.8 < z <2.2. However, their z=1 LF is larger than ours by a factor of 3-5 at logL >11.2. Note that the brightest ends( logL∼11.4)are consistent with each other to within 1 σ. They have excluded AGN using optical-to-X-ray flux ratio, and we also have excluded AGN through the optical SED fit. Therefore, especially at the faint-end, the contami na- tionfromAGN isnot likelyto be the maincauseof differences . Since Caputiet al. (2007) uses GOODS fields, cosmic variance may play a role here. The exact reason for the difference is un - known, but we point out that their ΩIRestimate at z=1 is also higherthanotherestimatesbyafactorofafew(seetheirFig .15). Once converted into LTIR, Magnelliet al. (2009) also reported Caputiet al.(2007)’s z=1LF ishigherthantheirestimatebased on 70µm by a factor of several (see their Fig.12). They con- cluded the difference is from different SED models used, sin ce their LF matched with that of Caputi etal. (2007)’s once the same SED models were used. We will compare our total LFs tothosein theliteraturebelow. Babbedgeet al. (2006) also computed restframe 8 µm LFs using the Spitzer/SWIRE data. We overplot their results at 0.25< z <0.5and0.5< z <1in Fig.4 with the pink dot- dashedlines.Inbothredshiftranges,goodagreementisfou ndat higherluminositybins( L8µm>1010.5L⊙).However,atallred- shift ranges including the ones not shown here, Babbedgeet a l. (2006) tends to show a flatter faint-end tail than ours, and a smallerφby a factor of ∼3. Although the exact reason is un- known, the deviation starts toward the fainter end, where bo th works approach the flux limits of the surveys. Therefore,pos si- blyincompletesamplingmaybeoneofthereasons.Itisalsor e- portedthat thefaint-endof IRLFsdependson theenvironmen t, in the sense that higher-density environment has steeper fa int- end tail (Gotoet al., 2010). Note that at z=1, Babbedgeet al. (2006)’s LF (pink) deviates from that by Caputiet al. (2007) (cyan) by almost a magnitude. Our 8 µm LFs are between these works. These comparisons suggest that even with the current gen- eration of satellites and state-of-the-art SED models, fac tor-of- several uncertainties still remain in estimating the 8 µm LFs at z∼1. More accurate determination has to await a larger and deeper survey by the next generation IR satellites such a s HerschelandWISE. To summarise, our 8 µm LFs are between those by Babbedgeetal.(2006)andCaputiet al.(2007),anddiscrepa ncy is by a factor of several at most. We note that both of the previ - ous works had to rely on SED models to estimate L8µmfrom the Spitzer S24µmin the MIR wavelengths where SED model- ing is difficult. Here, AKARI’s mid-IR bands are advantageou s indirectlyobservingredshiftedrestframe8 µmfluxinoneofthe AKARI’s filters, leading to more reliable measurement of 8 µm LFswithoutuncertaintyfromtheSED modeling. 4.1.2. 12 µm LFs P´ erez-Gonz´ alezet al. (2005) investigated the evolution of rest- frame12µmLFsusingthe SpitzerCDF-S andHDF-N data.Weoverplot their results in similar redshift ranges as the cya n dot- dashed lines in Fig.8. Consideringboth LFs have significant er- ror bars, these LFs are in good agreement with our LFs, and show significant evolution in the 12 µm LFs compared with the z=012µmLFbyRush,Malkan,&Spinoglio(1993).Theagree- ment is in a stark contrast to the comparison in 8 µm LFs in §4.1.1, wherewe sufferedfromdifferncesof a factor of sever al. Apossiblereasonforthisisthat12 µmissufficientlyredderthan 8µm, that it is easier to be extrapolated from S24µmin case of the Spitzer work. In fact, at z=1, both the Spitzer 24 µm band and AKARI L24observe the restframe 12 µm directly. In addi- ton, mid-IR SEDs around 12 µm are flatter than at 8 µm, where PAH emissions are prominent.Therefore,SED modelscan pre- dict the flux more accurately. In fact, this is part of the rea- sonwhyP´ erez-Gonz´ alezet al.(2005)chosetoinvestigate 12µm LFs. P´ erez-Gonz´ alezetal. (2005) used Chary&Elbaz (2001 )’s SEDtoextrapolate S24µm,andyet,theyagreewellwithAKARI results, which are derived from filters that cover the restfr ame 12µm. However, in other words, the discrepancy in 8 µm LFs highlights the fact that the SED models are perhaps still imp er- fect in the 8 µm wavelengthrange, and thus, MIR-spectroscopic data that covers wider luminosity and redshift ranges will b e necessary to refine SED models in the mid-IR. AKARI’s mid- IR slitless spectroscopy survey (Wada, 2008) may help in thi s regard. 4.1.3. TIRLFs Lastly,we compareourTIRLFs(Fig.14) withthoseinthelite r- ature.AlthoughtheTIRLFs canalso be obtainedbyconvertin g 8µmLFsor12 µmLFs,wealreadycomparedourresultsinthese wavelengths in the last subsections. Here, we compare our TI R LFstoLe Floc’het al.(2005)andMagnellietal. (2009). LeFloc’het al. (2005) obtained TIR LFs using the Spitzer CDF-S data. They have used the best-fit SED among various templatestoestimate LTIR.WeoverplottheirtotalLFsinFig.14 with the cyan dash-dotted lines. Only LFs that overlapwith o ur redshit ranges are shown. The agreement at 0.3< z <0.45 and0.6< z <0.8is reasonable, considering the error bars on bothsides.However,inallthreeredshiftranges,LeFloc’h et al. (2005)’sLFsare higherthanours,especiallyfor 1.0< z <1.2. We also overplot TIR LFs by Magnellietal. (2009), who used Spitzer 70 µm flux and Chary& Elbaz (2001)’s model to estimateLTIR.Inthetwobins(centeredon z=0.55and z=0.85; pink dash-dotted lines) which closely overlap with our reds hift bins, excellent agreement is found. We also plot Huynhet al. (2007)’s LF at 0.6< z <0.9in the navy dash-dotted lines, whichis computedfromSpitzer 70µmimagingin the GOODS- N, and this also shows very good agreement with ours. These LFs are on top of each other within the error bars, despite the fact that these measurements are from different data sets us ing differentanalyses. This means that LeFloc’hetal. (2005)’s LFs is also higher thanthatofMagnelliet al.(2009),inadditiontoours.Apos sible reasonis that both Magnelliet al. (2009) and we removedAGN (at least bright ones), whereas Le Floc’het al. (2005) inclu ded them. This also is consistent with the fact that the differen ce is larger at 1.0< z <1.2where both surveys are only sen- sitive to luminous IR galaxies, which are dominated by AGN. Another possible source of uncertainty is that Magnelliet a l. (2009) and we used a single SED library, while LeFloc’het al. (2005)pickedthebestSEDtemplateamongseverallibraries for eachgalaxy.Gotoet al.:InfraredLuminosityfunctions withthe AKARI 11 Fig.16.EvolutionofTIRluminositydensitybasedonTIRLFs(redcir cles),8µmLFs(stars),and12 µmLFs(filledtriangles).The blue open squaresand orangefilled squaresare for LIRG and UL IRGs only, also based on our LTIRLFs. Overplotteddot-dashed lines are estimates from the literature: LeFloc’het al. (20 05), Magnelliet al. (2009) , P´ erez-Gonz´ alezet al. (2005) , Caputiet al. (2007), and Babbedgeet al. (2006) are in cyan, yellow, green , navy,and pink, respectively.The purple dash-dottedline shows UV estimatebySchiminovichetal. (2005).Thepinkdashedline showsthetotalestimateofIR(TIRLF)andUV (Schiminoviche t al., 2005). 4.2. Evolution of ΩIR In this section, we compare the evolution of ΩIRas a function ofredshift.InFig.16, weplot ΩIRestimatedfromTIRLFs(red circles), 8 µm LFs (brown stars), and 12 µm LFs (pink filled tri- angles),as a functionof redshift.Estimatesbased on12 µmLFs and TIR LFs agree each other very well, while those from 8 µm LFs show a slightly higher value by a factor of a few than oth- ers. This perhaps reflects the fact that 8 µm is a more difficult part of the SED to be modeled, as we had a poorer agreement amongpapersintheliteraturein8 µmLFs.Thebright-endslope of the double-power law was 3.5+0.2 −0.4in Table 2. This is flat- ter than a Schechter fit by Babbedgeet al. (2006) and a double- exponential fit by Caputiet al. (2007). This is perhaps why we obtainedhigher ΩIRin8µm. We overplot estimates from various papers in the litera- ture(LeFloc’hetal.,2005; Babbedgeet al.,2006;Caputiet al., 2007; P´ erez-Gonz´ alezet al., 2005; Magnelliet al., 2009) in the dash-dottedlines. Our ΩIRhasverygoodagreementwith these at0< z <1.2,withalmostallthedash-dottedlineslyingwithin ourerrorbarsof ΩIRfromLTIRand12µmLFs.Thisisperhaps because an estimate of an integrated value such as ΩIRis more reliablethanthat ofLFs. Atz >1.2, ourΩIRshows a hint of continuous increase, while Caputiet al. (2007) and Babbedgeetal. (2006) observe da slight decline at z >1. However,as both authorsalso pointed out, at this high-redshift range, both the AKARI and Spitzer satellites are sensitive to onlyLIRGs and ULIRGs, and thust he extrapolationto fainterluminositiesassumesthefaint-e ndslope of the LFs, which couldbe uncertain.In addition,this work h as a poorerphoto-zestimate at z >0.8(∆z 1+z=0.10)due to the rel- atively shallow near-IR data. Several authors tried to over come thisproblembystackingundetectedsources.However,ifan un- detectedsourceisalsonotdetectedatshorterwavelengths where positions for stacking are obtained, it would not be include d in the stacking either. Next generation satellite such as Hers chel, WISE, and SPICA (Nakagawa, 2008) will determine the faint- endslopeat z >1moreprecisely. We parameterize the evolution of ΩIRusing a following function. ΩIR(z)∝(1+z)γ(10) By fitting this to the ΩIRfrom TIR LFs, we obtained γ= 4.4±1.0. This is consistent with most previous works. For example, LeFloc’hetal. (2005) obtained γ= 3.9± 0.4, P´ erez-Gonz´ alezet al. (2005) obtained γ= 4.0±0.2, Babbedgeetal. (2006) obtained γ= 4.5+0.7 −0.6, Magnelliet al. (2009) obtained γ= 3.6±0.4. The agreement was expected fromFig.16,butconfirmsastrongevolutionof ΩIR.12 Gotoet al.:InfraredLuminosityfunctions withthe AKARI Fig.17. Contribution of ΩTIRtoΩtotal= ΩUV+ ΩTIRis shownasa functionofredshift. 4.3. Differential evolution among ULIRG,LIRG,normal galaxies In Fig. 15, we also plot the contributions to ΩIRfrom LIRGs and ULIRGs (measured from TIR LFs) with the blue open squares and orange filled squares, respectively. Both LIRGs and ULIRGs show strong evolution, as has been seen for to- talΩIRin the red filled circles. Normal galaxies ( LTIR< 1011L⊙) are still dominant, but decrease their contribution to- ward higher redshifts. In contrast, ULIRGs continueto incr ease their contribution. From z=0.35 to z=1.4,ΩIRby LIRGs in- creases by a factor of ∼1.6, andΩIRby ULIRGs increases by a factor of ∼10. The physical origin of ULIRGs in the local Universe is often merger/interaction(Sanders& Mirabel, 1 996; Taniguchi&Shioya, 1998; Goto, 2005). It would be interesti ng to investigate whether the merger rate also increases in pro por- tion to the ULIRG fraction, or if different mechanisms can al so produceULIRGsathigherredshift. 4.4. Comparison tothe UVestimate We have been emphasizing the importance of IR probes of the total SFRD of the Universe. However, the IR estimates do not take into account the contribution of the unabsorbed UV ligh t produced by the young stars. Therefore, it is important to es ti- matehowsignificantthisUV contributionis. Schiminovichet al. (2005) found that the energy density measured at 1500 ˚A evolves as ∝(1+z)2.5±0.7at0< z <1 and∝(1 +z)0.5±0.4atz >1. using the GALEX data sup- plemented by the VVDS spectroscopic redshifts. We overplot their UV estimate of ρSFRwith the purple dot-dashed line in Fig.16. The UV estimate is almost a factor of 10 smaller than the IR estimate at most of the redshifts, confirming the impor - tanceofIRprobeswheninvestingtheevolutionofthetotalc os- mic star formation density. In Fig.16 we also plot total SFD ( or Ωtotal)byadding ΩUVandΩTIR,withthemagentadashedline. In Fig.17, we show the ratio of the IR contribution to the to- tal SFRD of the Universe ( ΩTIR/ΩTIR+ ΩUV) as a function of redshift. Although the errors are large, Fig.17 agrees wi thTakeuchi,Buat,& Burgarella (2005), and suggests that ΩTIR explains 70% of Ωtotalatz=0.25, and that by z=1.3, 90% of the cosmic SFD is explained by the infrared. This implies tha t ΩTIRprovidesgoodapproximationofthe Ωtotalatz >1. 5. Summary We have estimated restframe 8 µm, 12µm, and total infrared lu- minosity functions using the AKARI NEP-Deep data. Our ad- vantage over previous work is AKARI’s continuous filter cov- erage in the mid-IR wavelengths (2.4, 3.2, 4.1, 7, 9, 11, 15, 1 8, and24µm),whichallowustoestimate mid-IRluminositywith- out a large extrapolationbased on SED models, which were the largest uncertainty in previous work. Even for LTIR, the SED fitting is much more reliable due to this continuouscoverage of mid-IRfilters. Ourfindingsareasfollows: –8µm LFs show a strong and continuous evolution from z=0.35 to z=2.2. Our LFs are larger than Babbedgeet al. (2006), but smaller than Caputi etal. (2007). The differenc e perhaps stems from the different SED models, highlighting a difficulty in SED modeling at wavelengths crowded by strong PAH emissions. L∗ 8µmshows a continuous evolution asL∗ 8µm∝(1+z)1.6±0.2in therangeof 0.48< z <2. –12µm LFs show a strong and continuous evolution from z=0.15toz=1.16with L∗ 12µm∝(1+z)1.5±0.4. Thisagrees well with P´ erez-Gonz´ alezet al. (2005), including a flatte r faint-endslope. A better agreementthan with 8 µm LFs was obtained, perhaps because of smaller uncertainty in model- ing the 12 µm SED, and less extrapolationneededin Spitzer 24µmobservations. –The TIR LFs show good agreement with Magnelliet al. (2009), but are smaller than Le Floc’het al. (2005). At 0.25< z <1.3,L∗ TIRevolvesas ∝(1+z)4.1±0.4.Possible causes of the disagreement include different treatment of SEDmodelsinestimating LTIR,andAGNcontamination. –TIR densities estimated from 12 µm and TIR LFs show a strong evolution as a function of redshift, with ΩIR∝ (1 +z)4.4±1.0.ΩIR(z)also show an excellent agreement withpreviousworkat z <1.2. –We investigated the differential contribution to ΩIRby ULIRGsandLIRGs.WefoundthattheULIRG(LIRG)con- tribution increases by a factor of 10 (1.8) from z=0.35 to z=1.4, suggesting IR galaxies are more dominant source of ΩIRathigherredshift. –We estimated that ΩIRcaptures80% of the cosmic star for- mationatredshiftslessthan1,andvirtuallyallofitathig her redshift.Thusaddingtheunobscuredstarformationdetect ed at UV wavelengths would not change SFRD estimates sig- nificantly. Acknowledgments We are grateful to S.Arnouts for providing the LePhare code, and kindly helping us in using the code. We thank the anony- mousrefereeformanyinsightfulcomments,whichsignifican tly improvedthe paper. T.G. and H.I. acknowledgefinancial supportfrom the Japan Society for the Promotion of Science (JSPS) through JSPS Research Fellowships for Young Scientists. HML acknowl- edges the support from KASI through its cooperative fund in 2008. TTT has been supported by Program for Improvement of Research Environment for Young Researchers from SpecialGotoet al.:InfraredLuminosityfunctions withthe AKARI 13 CoordinationFundsforPromotingScienceandTechnology,a nd the Grant-in-Aid for the Scientific Research Fund (20740105 ) commissioned by the Ministry of Education, Culture, Sports , Science and Technology (MEXT) of Japan. TTT has been also partially supported from the Grand-in-Aid for the Global CO E Program “Quest for Fundamental Principles in the Universe: from Particles to the Solar System and the Cosmos” from the MEXT. 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