Evolution of Infrared Luminosity functions of Galaxies in the AKARI NEP-Deep field: Revealing the cosmic star formation history hidden by dust

0.44 MB·English

by  Tomotsugu Goto

Astronomy&Astrophysicsmanuscriptno.akari˙LF˙aa˙v7 (cid:13)c ESO2010
January8,2010
Evolution of Infrared Luminosity functions of Galaxies in the
AKARI NEP-Deep field
⋆ ⋆⋆
Revealing the cosmic star formation history hidden by dust ,
TomotsuguGoto1,2,⋆⋆⋆,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,
12 16 17 7 12
M.Im ,K.Imai ,T.Ishigaki ,S.Serjeant ,andH.Shim
0 1 InstituteforAstronomy,UniversityofHawaii,2680WoodlawnDrive,Honolulu,HI,96822,USA
1
e-mail:[email protected]
0 2 NationalAstronomicalObservatory,2-21-1Osawa,Mitaka,Tokyo,181-8588,Japan
2 3 InstituteofSpaceandAstronauticalScience,JapanAerospaceExplorationAgency,Sagamihara,Kanagawa229-8510
n 4 InstituteforAdvancedResearch,NagoyaUniversity,Furo-cho,Chikusa-ku,Nagoya464-8601
a 5 RutherfordAppletonLaboratory,Chilton,Didcot,OxfordshireOX110QX,UK
J 6 DepartmentofPhysics,UniversityofLethbridge,4401UniversityDrive,Lethbridge,AlbertaT1J1B1,Canada
7 AstrophysicsGroup,DepartmentofPhysics,TheOpenUniversity,MiltonKeynes,MK76AA,UK
8
8 Laboratoired’AstrophysiquedeMarseille,BP8,TraverseduSiphon,13376MarseilleCedex12,France

9 CEA-Saclay,Serviced’Astrophysique,France
]
O 10 AcademiaSinica,InstituteofAstronomyandAstrophysics,Taiwan
11 DepartmentofPhysicsandAstronomy,UCLA,LosAngeles,CA,90095-1547USA
C
12 DepartmentofPhysics&Astronomy,FPRD,SeoulNationalUniversity,Shillim-Dong,Kwanak-Gu,Seoul151-742,Korea
h. 13 SpitzerScienceCenter,CaliforniaInstituteofTechnology,Pasadena,CA91125
p 14 DepartmentofAstronomicalScience,TheGraduateUniversityforAdvancedStudies
- 15 PhysicsSection,FacultyofHumanitiesandSocialSciences,IwateUniversity,Morioka,020-8550
o 16 TOMER&DInc.Kawasaki,Kanagawa2130012,Japan
r 17 AsahikawaNationalCollegeofTechnology,2-1-62-joShunkohdai,Asahikawa-shi,Hokkaido071-8142
t
s
a ReceivedSeptember15,2009;acceptedDecember16,2009
[
ABSTRACT
2
v Aims. Dust-obscured star-formation becomes much more important with increasing intensity, and increasing redshift. We aim to
3 revealcosmicstar-formationhistoryobscuredbydustusingdeepinfraredobservationwiththeAKARI.
1 Methods.Weconstructrestframe8µm,12µm,andtotalinfrared(TIR)luminosityfunctions(LFs)at0.15 < z < 2.2using4128
0 infraredsourcesintheAKARINEP-Deepfield.Acontinuousfiltercoverageinthemid-IRwavelength(2.4,3.2,4.1,7,9,11,15,18,
0 and24µm)bytheAKARIsatelliteallowsustoestimaterestframe8µmand12µmluminositieswithoutusingalargeextrapolation
1. basedonaSEDfit,whichwasthelargestuncertaintyinpreviouswork.
0 Results. Wehavefoundthatall8µm(0.38<z<2.2),12µm(0.15<z<1.16),andTIRLFs(0.2<z<1.6),showacontinuous
0 andstrongevolutiontowardhigherredshift.Intermsofcosmicinfraredluminositydensity(ΩIR),whichwasobtainedbyintegrating
1 analyticfitstotheLFs,wefoundagoodagreementwithpreviousworkatz <1.2.WefoundtheΩIR evolvesas∝(1+z)4.4±1.0.
: WhenweseparatecontributionstoΩIRbyLIRGsandULIRGs,wefoundmoreIRluminoussourcesareincreasinglymoreimportant
v athigherredshift.WefoundthattheULIRG(LIRG)contributionincreasesbyafactorof10(1.8)fromz=0.35toz=1.4.
i
X Keywords. galaxies:evolution,galaxies:interactions,galaxies:starburst,galaxies:peculiar,galaxies:formation
r
a
1. Introduction Belletal. (2005) estimate that IR luminosity density is 7
times higher than the UV luminosity density at z∼0.7 than lo-
Studies of the extragalactic background suggest at least half
cally.Takeuchi,Buat,&Burgarella(2005)reportedthatUV-to-
the luminous energy generated by stars has been reprocessed
IRluminositydensityratio,ρ /ρ ,evolvesfrom3.75
intotheinfrared(IR)bydust(Lagacheetal.,1999;Pugetetal., L(UV) L(dust)
(z=0) to 15.1 by z=1.0 with a careful treatment of the sample
1996; Franceschini,Rodighiero,&Vaccari, 2008), suggesting
selection effect, and that 70% of star formation activity is ob-
that dust-obscuredstar formation was much more importantat
scured by dust at 0.5< z <1.2. Both works highlight the im-
higherredshiftsthantoday.
portanceof probingcosmic star formationactivity at high red-
shift in the infrared bands. Several works found that most ex-
⋆ Thisresearch isbased on theobservations withAKARI,aJAXA
tremestar-forming(SF)galaxies,whichareincreasinglyimpor-
projectwiththeparticipationofESA.
tantathigherredshifts,are also moreheavilyobscuredbydust
⋆⋆ BasedondatacollectedatSubaruTelescope,whichisoperatedby
(Hopkinsetal.,2001;Sullivanetal.,2001;Buatetal.,2007).
theNationalAstronomicalObservatoryofJapan.
⋆⋆⋆ JSPSSPDfellow
2 Gotoetal.:InfraredLuminosityfunctionswiththeAKARI
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-Robinsonetal., 1997;
Floresetal., 1999; Serjeantetal., 2004; Takeuchietal., 2006;
Takeuchi,Yoshikawa,&Ishii, 2003), until the recent launch of
theSpitzerandtheAKARIsatellites.Theirenormousimproved
sensitivitieshaverevolutionizedthefield.Forexample:
LeFloc’hetal. (2005) analyzed the evolution of the total
and 15µm IR luminosity functions (LFs) at 0 < z < 1 based
onthe the Spitzer MIPS24µmdata (> 83µJyand R < 24)in
the CDF-S, and found a positive evolution in both luminosity
anddensity,suggestingincreasingimportanceoftheLIRGand
ULIRGpopulationsathigherredshifts.
Pe´rez-Gonza´lezetal.(2005)usedMIPS24µmobservations
oftheCDF-SandHDF-N(>83µJy)tofindthatthatL∗steadily
increasesbyanorderofmagnitudetoz ∼2,suggestingthatthe
luminosityevolutionisstrongerthanthedensityevolution.The Fig.1. Photometric redshift estimates with LePhare
ΩTIR scalesas(1+z)4.0±0.2fromz=0to0.8. (Ilbertetal., 2006; Arnoutsetal., 2007; Ilbertetal., 2009)
Babbedgeetal. (2006) constructed LFs at 3.6, 4.5, 5.8, 8 for spectroscopically observed galaxies with Keck/DEIMOS
and 24µm over 0 < z < 2 using the data from the Spitzer (Takagi et al. in prep.). Red squares show objects where AGN
Wide-areaInfraredExtragalactic(SWIRE)Surveyina6.5deg2 templateswerebetterfit.Errorsofthephotozis ∆z =0.036for
1+z
(S24µm > 230µJy). They found a clear luminosity evolu- z ≤ 0.8, but becomes worse at z > 0.8 to be ∆z =0.10 due
tion in all the bands, but the evolution is more pronounced at 1+z
mainlytotherelativelyshallownear-IRdata.
longerwavelength;extrapolatingfrom24µm,theyinferredthat
Ω ∝(1+z)4.5. They constructed separate LFs for three dif-
TIR
ferentgalaxySED(spectralenergydistribution)typesandType lows us to estimate MIR (mid-infrared)-luminositywithoutus-
1 AGN, finding that starburst and late-type galaxies showed ing a largek-correctionbased on the SED models, eliminating
strongerevolution.Comparisonof3.6and4.5µmLFswithsemi- thelargestuncertaintyinpreviouswork.Bytakingadvantageof
analyticandspectrophotometricmodelssuggestedthattheIMF this, we present the restframe 8, 12µm and TIR LFs using the
is skewed towards higher mass star formation in more intense AKARINEP-Deepdatainthiswork.
starbursts. Restframe 8µm luminosity in particular is of primary rele-
Caputietal.(2007)estimatedrestframe8µmLFsofgalaxies vance for star-forming galaxies, as it includes polycyclic aro-
over0.08deg2 intheGOODSfieldsbasedonSpitzer24µm(> matic hydrocarbon (PAH) emission. PAH molecules charac-
80µJy)atz=1and2.Theyfoundacontinuousandstrongposi- terize star-formingregions(Desert,Boulanger,&Puget, 1990),
tiveluminosityevolutionfromz=0toz=1,andtoz=2.However, andtheassociatedemissionlinesbetween3.3and17µmdom-
theyalsofoundthatthenumberdensityofstar-forminggalaxies inate the SED of star-forming galaxies with a main bump lo-
with νL8νµm > 1010.5L⊙ (AGNsare excluded.)increasesbya cated around 7.7µm. Restframe 8µm luminosities have been
factorof20fromz=0to1,butdecreasesbyhalffromz=1to2 confirmed to be good indicators of knots of star formation
mainlyduetothedecreaseofLIRGs. (Calzettietal., 2005) and of the overall star formation activity
Magnellietal. (2009) investigated restframe 15µm, 35µm of star forming galaxies (Wuetal., 2005). At z=0.375, 0.875,
and total infrared (TIR) LFs using deep 70µm observations 1.25 and 2, the restframe 8µm is covered by the AKARI S11,
(∼300 µJy) in the Spitzer GOODS and FIDEL (Far Infrared L15,L18W andL24filters.Wepresenttherestframe8µmLFs
Deep Extragalactic Legacy Survey) fields (0.22 deg2 in total) attheseredshiftsatSection3.1.
at z < 1.3. They stacked 70µm flux at the positions of 24µm Restframe 12µm luminosity functions have also been
sourceswhensourcesarenotdetectedin70µm.Theyfoundno studied extensively (Rush,Malkan,&Spinoglio, 1993;
changeintheshapeoftheLFs,butfoundapureluminosityevo- Pe´rez-Gonza´lezetal., 2005). At z=0.25, 0.5 and 1, the
lutionproportionalto(1+z)3.6±0.5,andthatLIRGsandULIRGs restframe12µmiscoveredbytheAKARIL15,L18W andL24
haveincreasedby a factorof 40and 100in numberdensityby filters.We presenttherestframe12µmLFsattheseredshiftsin
z ∼1. Section3.3.
Also,see Daietal.(2009)for3.6-8.0µmLFsbasedonthe We also estimate TIR LFs through the SED fit using all
IRACphotometryintheNOAODeepWide-FieldSurveyBootes the mid-IR bands of the AKARI. The results are presented in
field. Section3.5.
However, most of the Spitzer work relied on a large Unless otherwise stated, we adopt a cosmology with
extrapolation from 24µm flux to estimate the 8, 12µm or (h,Ω ,Ω )=(0.7,0.3,0.7)(Komatsuetal.,2008).
m Λ
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 2. Data & Analysis
many authors pointed out that the largest uncertainty in these
2.1. Multi-wavelengthdataintheAKARINEPDeepfield
previousIR LFs came from SED models, especially when one
computesTIRluminositysolelyfromobserved24µmflux(e.g., AKARI,theJapaneseinfraredsatellite(Murakamietal.,2007),
seeFig.5ofCaputietal.,2007). performed deep imaging in the North Ecliptic Region (NEP)
AKARI, the first Japanese IR dedicated satellite, has con- from 2-24µm, with 14 pointings in each field over 0.4
tinuousfilter coverageacrossthemid-IRwavelengths,thus,al- deg2 (Matsuharaetal., 2006, 2007; Wadaetal., 2008). Due
Gotoetal.:InfraredLuminosityfunctionswiththeAKARI 3
Inanalyzingtheseobservations,wefirstcombinedthethree
images of the MIR channels, i.e. MIR-S(S7,S9W, and S11)
andMIR-L(L15,L18W andL24),inordertoobtaintwohigh-
qualityimages. In the resultingMIR-Sand MIR-L images, the
residualsky has been reducedsignificantly,which helps to ob-
tain more reliable source catalogues. For both the MIR-S and
MIR-Lchannels,weuseSExtractorforthecombinedimagesto
determineinitialsourcepositions.
We follow Takagietal. (2007) procedures for photometry
and band-mergingof 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,
andthenconcatenatedthesecatalogues,eliminatingduplicates.
Intheband-mergingprocess,thesourcecentroidineachIRC
imagehasbeendetermined,startingfromthesourcepositionin
the combined images as the initial guess. If the centroid deter-
minedinthiswayisshiftedfromtheoriginalpositionby> 3′′,
we reject such a source as the counterpart. We note that this
band-mergingmethodisusedonlyforIRCbands.
Wecomparedrawnumbercountswithpreviousworkbased
on the same data but with different source extraction methods
Fig.2. Photometricredshiftdistribution. (Wadaetal., 2008; Pearsonetal., 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 (Imaietal., 2007;
Wadaetal., 2008), reaching limiting magnitudes of z =26
AB
inonefieldofviewoftheSuprime-Cam.Werestrictouranaly-
sistothedatainthisSuprime-Camfield(0.25deg2),wherewe
have enough UV-opical-NIRcoverageto estimate good photo-
metricredshifts.Theu′-bandphotometryinthisareaisprovided
bytheCFHT (Serjeantetal.inprep.).Thesamefield wasalso
observedwith the KPNO2m/FLAMINGOsin J and Ks to the
depthofKs < 20(Imaietal.,2007).GALEXcoveredthe
Vega
entirefieldtodepthsofFUV <25andNUV <25(Malkanet
al.inprep.).
In the Suprime-Cam field of the AKARI NEP-Deep field,
therearea totalof4128infraredsourcesdownto ∼100µJy in
theL18W filter.AllmagnitudesaregiveninABsysteminthis
paper.
For the opticalidentification of MIR sources, we adoptthe
likelihood ratio (LR) method (Sutherland&Saunders, 1992).
For the probabilitydistributionfunctionsof magnitudeandan-
gular separation based on correct optical counterparts (and 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–
Fig.3. 8µmluminositydistributionsofsamplesusedtocompute detected sources, the optical counterparts are all visually in-
restframe 8µm LFs. From low redshift, 533, 466, 236 and 59 spected and ambiguouscases are excluded. There are multiple
galaxiesareineachredshiftbin. opticalcounterpartsfor35%ofMIRsourceswithin<3′′.Ifwe
adoptedthenearestneighborapproachfortheopticalidentifica-
tion,theopticalcounterpartsdiffersfromthatoftheLRmethod
for20%ofthesourceswithmultipleopticalcounterparts.Thus,
to the solar synchronous orbit of the AKARI, the NEP in total we estimate that less than 15% of MIR sources suffer
is the only AKARI field with very deep imaging at these fromseriousproblemsofopticalidentification.
wavelengths. The 5 σ sensitivity in the AKARI IR filters
(N2,N3,N4,S7,S9W,S11,L15,L18W and L24) are 14.2,
2.2. Photometricredshiftestimation
11.0,8.0,48,58,71,117,121and275µJy(Wadaetal., 2008).
These filters provide us with a unique continuous wavelength
For these infrared sources, we have computed photomet-
coverage at 2-24µm, where there is a gap between the Spitzer ric redshift using a publicly available code, LePhare 1
IRAC and MIPS, and the ISO LW2 and LW3. Please consult (Ilbertetal., 2006; Arnoutsetal., 2007; Ilbertetal., 2009).
Wadaetal.(2007,2008);Pearsonetal.(2009a,b)fordataveri-
The input magnitudes are FUV,NUV(GALEX),u(CFHT),
ficationandcompletenessestimateatthesefluxes.ThePSFsizes B,V,R,i′,z′(Subaru),J,andK(KPNO2m).Wesummarizethe
are4.4,5.1,and5.4”in 2−4, 7−11,15−24µmbands.The filtersusedinTable1.
depths of near-IR bands are limited by source confusion, but
thoseofmid-IRbandsarebyskynoise. 1 http://www.cfht.hawaii.edu/∼arnouts/lephare.html
4 Gotoetal.:InfraredLuminosityfunctionswiththeAKARI
Table1.Summaryoffiltersused. redshiftoftheredshiftbin.Moreprecisely,
Estimate Redshift Filter zmax =min(zmax of thebin, zmax fromthefluxlimit) (1)
Photoz 0.15<z<2.2 FUV,NUV,u,B,V,R,i′,z,J,andK
WeusedtheSEDtemplates(Lagache,Dole,&Puget,2003)for
8µmLF 0.38<z<0.58 S11(11µm)
k-corrections to obtain the maximum observable redshift from
8µmLF 0.65<z<0.90 L15(15µm)
8µmLF 1.1<z<1.4 L18W(18µm) thefluxlimit.
8µmLF 1.8<z<2.2 L24(24µm) Foreachluminositybinthen,theLFisderivedas
12µmLF 0.15<z<0.35 L15(15µm)
12µmLF 0.38<z<0.62 L18W(18µm)
12µmLF 0.84<z<1.16 L24(24µm) 1 1
φ= w , (2)
TIRLF 0.2<z<0.5 S7,S9W,S11,L15,L18W andL24 ∆L V i
TIRLF 0.5<z<0.8 S7,S9W,S11,L15,L18W andL24 Xi max,i
TIRLF 0.8<z<1.2 S7,S9W,S11,L15,L18W andL24
where V is a comoving volume over which the ith galaxy
TIRLF 1.2<z<1.6 S7,S9W,S11,L15,L18W andL24 max
couldbeobserved,∆Listhesizeoftheluminositybin(0.2dex),
and w is the completeness correction factor of the ith galaxy.
i
WeusecompletenesscorrectionmeasuredbyWadaetal.(2008)
Among various templates and fitting parameters we tried, for11and24µmandPearsonetal.(2009a,b)for15and18µm.
wefoundthebestresultswereobtainedwiththefollowing:we Thiscorrectionis25%atmaximum,sinceweonlyusethesam-
used modified CWW (Coleman,Wu,&Weedman, 1980) and plewherethecompletenessisgreaterthan80%.
QSOtemplates.TheseCWWtemplatesareinterpolatedandad-
justedtobettermatchVVDSspectra(Arnoutsetal.,2007).We
2.4. MonteCarlosimulation
included strong emission lines in computing colors. We used
the Calzetti extinction law. More details in training LePhare Uncertainties of the LF values stem from various factors such
isgiveninIlbertetal.(2006). asfluctuationsinthenumberofsourcesineachluminositybin,
The resulting photometric redshift estimates agree reason- the photometric redshift uncertainties, the k-correction uncer-
ably well with 293 galaxies (R < 24) with spectroscopic red- tainties, and the flux errors. To compute these errors we per-
shiftstakenwithKeck/DEIMOSintheNEPfield(Takagietal. formedMonteCarlosimulationsbycreating1000simulatedcat-
inprep.).Themeasurederrorsonthephoto-zare ∆z =0.036for alogs,whereeachcatalogcontainsthesamenumberofsources,
1+z
z ≤ 0.8 and ∆z =0.10forz > 0.8. The ∆z becomessignifi- butwe assign each sourcea new redshiftfollowinga Gaussian
1+z 1+z distribution centered at the photometric redshift with the mea-
cantlylargeratz > 0.8,wherewesufferfromrelativeshallow-
nessofournear-IRdata.Therateofcatastrophicfailuresis4% sured dispersion of ∆z/(1 + z) =0.036 for z ≤ 0.8 and
(∆z >0.2)amongthespectroscopicsample. ∆z/(1+z)=0.10forz > 0.8(Fig.1).Thefluxofeachsource
1+z isalsoallowedtovaryaccordingtothemeasuredfluxerrorfol-
In Fig.1, we compare spectroscopic redshifts from
lowingaGaussiandistribution.For8µmand12µmLFs,wecan
Keck/DEIMOS (Takagi et al.) and our photometric red-
ignore the errors due to the k-correctionthanks to the AKARI
shift estimation. Those SEDs which are better fit with a QSO
MIR filter coverage. For TIR LFs, we have added 0.05 dex of
template are shown as red triangles. We remove those red
errorforuncertaintyintheSEDfittingfollowingthediscussion
triangle objects (∼2% of the sample) from the LFs presented
in Magnellietal. (2009). We did not consider the uncertainty
below. We caution that this can only remove extreme type-1
on the cosmic variance here since the AKARI NEP field cov-
AGNs,andthus,fainter,type-2AGNthatcouldberemovedby
ersa largevolumeand hascomparablenumbercountsto other
X-raysoropticalspectroscopystillremaininthesample.
generalfields(Imaietal.,2007,2008).Eachredshiftbinweuse
Fig.2showsthedistributionofphotometricredshift.Thedis-
covers∼ 106 Mpc3 ofvolume.SeeMatsuharaetal. (2006) for
tributionhasseveralpeaks,whichcorrespondstogalaxyclusters
morediscussiononthecosmicvarianceintheNEPfield.These
inthefield(Gotoetal.,2008).Wehave12%ofsourcesthatdo
estimatederrorsareaddedto thePoissonerrorsineachLFbin
nothaveagoodSEDfittoobtainareliablephotometricredshift
inquadrature.
estimation.Weapplythisphoto-zcompletenesscorrectiontothe
LFsweobtain.ReadersarereferredtoNegrelloetatal.(2009),
whoestimatedphotometricredshiftsusingonlytheAKARIfil- 3. Results
terstoobtain10%accuracy.
3.1. 8µmLF
2.3. The1/Vmax method Monochromatic 8µm luminosity (L8µm) is known to cor-
relate well with the TIR luminosity (Babbedgeetal., 2006;
WecomputeLFsusingthe1/V method(Schmidt,1968).The Huangetal.,2007),especiallyforstar-forminggalaxiesbecause
max
advantageofthe1/Vmax methodisthatitallowsustocompute the rest-frame8µm flux are dominatedby prominentPAH fea-
a LF directly from data, with no parameter dependence or an turessuchasat6.2,7.7and8.6µm.
assumedmodel.A drawbackis thatitassumesa homogeneous Since the AKARI has continuous coverage in the mid-IR
galaxydistribution,andis thusvulnerableto localover-/under- wavelengthrange,therestframe8µmluminositycanbeobtained
densities(Takeuchi,Yoshikawa,&Ishii,2000). without a large uncertainty in k-correction at a corresponding
A comoving volume associated with any source of a given redshift and filter. For example, at z=0.375, restframe 8µm is
luminosity is defined as V = V − V , where z redshiftedintoS11filter.Similarly,L15,L18W andL24cover
max zmax zmin min
is the lower limit of the redshiftbin and z is the maximum restframe 8µm at z=0.875, 1.25 and 2. This continuous filter
max
redshiftatwhichtheobjectcouldbeseengiventhefluxlimitof coverageisanadvantagetoAKARIdata.OftenSEDmodelsare
the survey, with a maximum value corresponding to the upper used to extrapolate from Spitzer 24µm flux in previous work,
Gotoetal.:InfraredLuminosityfunctionswiththeAKARI 5
producingasourceofthelargestuncertainty.Wesummarisefil-
tersusedinTable1.
To obtain restframe 8µm LF, we applied a flux limit
of F(S11)<70.9, F(L15)<117, F(L18W)<121.4, and
F(L24)<275.8 µJy at z=0.38-0.58, z=0.65-0.90, z=1.1-1.4
andz=1.8-2.2,respectively.Thesearethe5σlimitsmeasuredin
Wadaetal. (2008).We excludethosegalaxieswhoseSEDsare
betterfitwithQSOtemplates(§2).
We use the completeness curve presented in Wadaetal.
(2008) and Pearsonetal. (2009a,b) to correct for the incom-
pleteness of the detection. However, this correction is 25% at
maximumsincethesampleis80%completeatthe5σlimit.Our
mainconclusionsarenotaffectedbythisincompletenesscorrec-
tion.Tocompensatefortheincreasinguncertaintyinincreasing
z, we use redshift binsize of 0.38< z <0.58, 0.65< z <0.90,
1.1<z <1.4,and1.8<z <2.2.WeshowtheL distribution
8µm
ineachredshiftrangeinFig.3.Withineachredshiftbin,weuse
1/V methodtocompensateforthefluxlimitineachfilter.
max
We showthecomputedrestframe8µmLFinFig.4.Arrows
showthe8µmluminositycorrespondingto thefluxlimitatthe
centralredshiftineachredshiftbin.Errorbarsoneachpointare Fig.4. Restframe 8µm LFs based on the AKARI NEP-Deep
basedontheMonteCarlosimulation(§2.3). field. The blue diamons, purple triangles, red squares, and or-
For a comparison, as the green dot-dashed line, we also ange crosses show the 8µm LFs at 0.38 < z < 0.58,0.65 <
show the 8µm LF of star-forming galaxies at 0 < z < 0.3 z < 0.90,1.1 < z < 1.4, and 1.8 < z < 2.2, respectively.
byHuangetal.(2007),usingthe1/V methodappliedtothe AKARI’s MIR filters can observe restframe 8µm at these red-
max
IRAC8µmGTOdata.ComparedtothelocalLF,our8µmLFs shifts in a corresponding filter. Errorbars are from the Monte
showstrongevolutioninluminosity.Intherangeof0.48<z < Caro simulations (§2.4). The dotted lines show analytical fits
2,L∗ evolvesas∝(1+z)1.6±0.2.Detailedcomparisonwith with a double-powerlaw. Vertical arrows show the 8µm lumi-
8µm
theliteraturewillbepresentedin§4. nosity correspondingto the flux limit at the central redshift in
eachredshiftbin.OverplottedareBabbedgeetal.(2006)inthe
pink dash-dotted lines, Caputietal. (2007) in the cyan dash-
3.2. BolometricIRluminositydensitybasedonthe8µm
dotted lines, and Huangetal. (2007) in the green dash-dotted
LF
lines.AGNsareexcludedfromthesample(§2.2).
Constraining the star formation history of galaxies as a func-
tion of redshift is a key to understanding galaxy formation in
the Universe. One of the primary purposes in computing IR
LFs is to estimate the IR luminositydensity,whichin turnis a
L =1.91×(νL )1.06 (±55%) (4)
goodestimatorofthedusthiddencosmicstarformationdensity TIR ν rest8µm
(Kennicutt,1998).Sincedustobscurationismoreimportantfor
Since ours is also a sample of bright galaxies, we use this
moreactivelystarforminggalaxiesathigherredshift,andsuch
equation to convert L to L . Because the conversion is
starformationcannotbeobservedinUVlight,itisimportantto 8µm TIR
based on local star-forming galaxies, it is a concern if it holds
obtainIR-basedestimateinordertofullyunderstandthecosmic
athigherredshiftornot.Bavouzetetal.(2008)checkedthisby
starformationhistoryoftheUniverse.
stacking24µmsourcesat 1.3 < z < 2.3in theGOODSfields
Weestimatethetotalinfraredluminositydensitybyintegrat-
to find the stacked sources are consistent with the local rela-
ingtheLFweightedbytheluminosity.First,weneedtoconvert
tion. They concluded that equation (3) is valid to link L
L tothe bolometricinfraredluminosity.ThebolometricIR 8µm
8µm and L at 1.3 < z < 2.3. Takagietal. (2010) also show
luminosity of a galaxy is producedby the thermal emission of TIR
that local L vs L relation holds true for IR galaxies
itsinterstellarmatter.Instar-forminggalaxies,theUVradiation 7.7µm TIR
at z∼1 (see their Fig.10). Popeetal. (2008) showed that z ∼2
producedbyyoungstarsheatstheinterstellardust,andtherepro-
sub-millimeter galaxies lie on the relation between L and
cessedlightisemittedintheIR.Forthisreason,instar-forming TIR
L thathas beenestablished forlocalstarburstgalaxies.
galaxies,thebolometricIRluminosityisagoodestimatorofthe PAH,7.7
S /S ratios of 70µm sources in Papovichetal. (2007) are
currentSFR (star formationrate) of the galaxy.Bavouzetetal. 70 24
alsoconsistentwithlocalSEDtemplates.Theseresultssuggest
(2008)showedastrongcorrelationbetweenL andtotalin-
8µm itisreasonabletouseequation(4)foroursample.
frared luminosity (L ) for 372 local star-forming galaxies.
TIR Theconversion,however,hasbeenthe largestsourceofer-
TheconversiongivenbyBavouzetetal.(2008)is:
rorinestimatingL fromL .Bavouzetetal.(2008)them-
TIR 8µm
selvesquote37%ofuncertainty,andthatCaputietal.(2007)re-
port55%ofdispersionaroundtherelation.Itshouldbekeptin
LTIR =377.9×(νLν)0re.8s3t8µm(±37%) (3) mind that the restframe 8µm is sensitive to the star-formation
activity,butatthesame time,itis wherethe SED modelshave
Caputietal. (2007) furtherconstrainedthe sample to lumi- strongest discrepancies due to the complicated PAH emission
nous,highS/N galaxies(νL8νµm > 1010L⊙ andS/N> 3in all lines. A detailed comparison of different conversions is pre-
MIPSbands)inordertobettermatchtheirsample,andderived sented in Fig.12 of Caputietal. (2007), who reportedfactor of
thefollowingequation. ∼5ofdifferencesamongvariousmodels.
6 Gotoetal.:InfraredLuminosityfunctionswiththeAKARI
Then the 8µm LF is weighted by the L and integrated
TIR
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 (Babbedgeetal., 2006) or
a double-exponential(Saundersetal., 1990; Pozzietal., 2004;
Takeuchietal., 2006; LeFloc’hetal., 2005) than a Schechter
function, which declines too suddenlly at the high luminosity,
underestimating the number of bright galaxies. In this work,
wefitthe8µmLFsusingadouble-powerlaw(Babbedgeetal.,
2006)asshownbelow.
1−α
L
Φ(L)dL/L∗ =Φ∗ dL/L∗, (L<L∗) (5)
(cid:18)L∗(cid:19)
L 1−β
Φ(L)dL/L∗ =Φ∗ dL/L∗, (L>L∗) (6)
(cid:18)L∗(cid:19)
First,thedouble-powerlawisfittedtothelowestredshiftLFat
0.38< z <0.58todeterminethenormalization(Φ∗)andslopes
(α,β).Forhigherredshiftswedonothaveenoughstatisticstosi- Fig.5. EvolutionofTIRluminositydensitycomputedbyinte-
multaneouslyfit4parameters(Φ∗,L∗,α,andβ).Therefore,we grating the 8µm LFs in Fig.4.The red solid lines use the con-
fixedtheslopesandnormalizationatthelocalvaluesandvaried version in equation (4). The orange dashed lines use equation
onlyL∗atforthehigher-redshiftLFs.Fixingthefaint-endslope (3).ResultsfromLeFloc’hetal.(2005)areshownwiththecyan
isacommonprocedurewiththedepthofcurrentIRsatellitesur- dottedlines.
veys (Babbedgeetal., 2006; Caputietal., 2007). The stronger
evolutioninluminositythanindensityfoundbypreviouswork
(Pe´rez-Gonza´lezetal., 2005; LeFloc’hetal., 2005) also justi-
fies this parametrization. Best fit parameters are presented in
Table2.Oncethebest-fitparametersarefound,weintegratethe
doublepowerlawoutsidetheluminosityrangeinwhichwehave
data to obtain estimate of the total infrared luminosity density,
Ω .
TIR
The resulting total luminosity density (Ω ) is shown in
IR
Fig.5 as a functionof redshift. Errorsare estimated by varying
thefitwithin1σofuncertaintyinLFs,thenerrorsinconversion
from L to L are added. The latter is by far the larger
8µm TIR
source of uncertainty.Simply switching from equation (3) (or-
ange dashed line) to (4) (red solid line) producesa ∼50% dif-
ference. Cyan dashed lines show results from LeFloc’hetal.
(2005) for a comparision. The lowest redshift point was cor-
rectedfollowingMagnellietal.(2009).
We also show the evolution of monochromatic 8µm lumi-
nosity (L ), which is obtained by integrating the fits, but
8µm
without converting to L in Fig.6. The Ω evolves as
TIR 8µm
∝(1+z)1.9±0.7.
The SFR and L are related by the following equation
TIR
for a Salpeter IMF, φ (m) ∝ m−2.35 between 0.1 − 100M⊙ Fig.6. Evolution of 8µm IR luminosity density computed by
(Kennicutt,1998). integrating the 8µm LFs in Fig.4. The lowest redshift point is
fromHuangetal.(2007).
SFR(M⊙yr−1)=1.72×10−10LTIR(L⊙) (7)
3.3. 12µmLF
The right ticks of Fig.5 shows the star formation density
scale,convertedfromΩIR usingtheaboveequation. In this subsection we estimate restframe 12µm LFs based
In Fig.5, Ω monotonically increases toward higher z. on the AKARI NEP-Deep data. 12µm luminosity (L )
IR 12µm
Comparedwithz=0,Ω is∼10timeslargeratz=1.Theevolu- has been well studied through ISO and IRAS, and known to
IR
tionbetweenz=0.5andz=1.2isalittleflatter,butthisisperhaps correlate closely with TIR luminosity (Spinoglioetal., 1995;
duetoamoreirregularshapeofLFsat0.65<z <0.90,andthus, Pe´rez-Gonza´lezetal.,2005).
wedonotconsideritsignificant.Theresultsobtainedhereagree As was the case for the 8µm LF, it is advantageous that
with previous work (e.g., LeFloc’hetal., 2005) within the er- AKARI’s continuousfilters in the mid-IR allow us to estimate
rors.Wecomparetheresultswithpreviousworkinmoredetail restframe 12µm luminosity without much extrapolation based
in§4. onSEDmodels.
Gotoetal.:InfraredLuminosityfunctionswiththeAKARI 7
Table2.Bestfitparametersfor8,12µmandTIRLFs
Redshift λ L∗(L⊙) Φ∗(Mpc−3dex−1) α β
0.38<z<0.58 8µm (2.2+0.3)×1010 (2.1+0.3)×10−3 1.75+0.01 3.5+0.2
−0.1 −0.4 −0.01 −0.4
0.65<z<0.90 8µm (2.8+0.1)×1010 2.1×10−3 1.75 3.5
−0.1
1.1<z<1.4 8µm (3.3+0.2)×1010 2.1×10−3 1.75 3.5
−0.2
1.8<z<2.2 8µm (8.2+1.2)×1010 2.1×10−3 1.75 3.5
−1.8
0.15<z<0.35 12µm (6.8+0.1)×109 (4.2+0.7)×10−3 1.20+0.01 2.9+0.4
−0.1 −0.6 −0.02 −0.2
0.38<z<0.62 12µm (11.7+0.3)×109 4.2×10−3 1.20 2.9
−0.5
0.84<z<1.16 12µm (14+2)×109 4.2×10−3 1.20 2.9
−3
0.2<z<0.5 Total (1.2+0.1)×1011 (5.6+1.5)×10−4 1.8+0.1 3.0+1.0
−0.2 −0.2 −0.4 −1.0
0.5<z<0.8 Total (2.4+1.8)×1011 5.6×10−4 1.8 3.0
−1.6
0.8<z<1.2 Total (3.9+2.3)×1011 5.6×10−4 1.8 3.0
−2.2
1.2<z<1.6 Total (14+1)×1011 5.6×10−4 1.8 3.0
−2
Fig.7. 12µmluminositydistributionsofsamplesusedto com- Fig.8. Restframe 12µm LFs based on the AKARI NEP-Deep
puterestframe12µmLFs.Fromlowredshift,335,573,and213 field.Thebluediamonds,purpletriangles,andredsquaresshow
galaxiesareineachredshiftbin. the 12µm LFs at 0.15 < z < 0.35,0.38 < z < 0.62, and
0.84 < z < 1.16,respectively.Verticalarrowsshowthe12µm
luminosity corresponding to the flux limit at the central red-
Targetedredshiftsarez=0.25,0.5and1whereL15,L18W shiftin eachredshiftbin.Overplottedare Pe´rez-Gonza´lezetal.
andL24filterscovertherestframe12µm,respectively.Wesum- (2005) at z=0.3,0.5 and 0.9 in the cyan dash-dotted lines, and
marise the filters used in Table 1. Methodologyis the same as
Rush,Malkan,&Spinoglio (1993) at z=0 in the green dash-
for the 8µm LF; we used the sample to the 5σ limit, corrected dottedlines.AGNsareexcludedfromthesample(§2.2).
for the completeness, then used the 1/V method to com-
max
pute LF in each redshift bin. The histogram of L distri-
12µm
bution is presented in Fig.7. The resulting 12µm LF is shown Takeuchietal. (2005) independently estimated the relation
in Fig.8. Compared with Rush,Malkan,&Spinoglio (1993)’s tobe
z=0 LF based on IRAS Faint Source Catalog, the 12µm LFs
show steady evolutionwith increasing redshift. In the range of
0.25<z <1,L∗ evolvesas∝(1+z)1.5±0.4. logL =1.02+0.972logL , (9)
12µm TIR 12µm
which we also use to check our conversion. As both au-
3.4. BolometricIRluminositydensitybasedonthe12µm
thors state, these conversionscontain an error of factor of 2-3.
LF
Therefore, we should avoid conclusions that could be affected
12µmisoneofthemostfrequentlyusedmonochromaticfluxes bysucherrors.
to estimate LTIR. The total infrared luminosity is computed Thenthe12µmLFisweightedbytheLTIR andintegrated
fromtheL usingtheconversioninChary&Elbaz(2001); to obtain TIR density. Errors are estimated by varying the fit
12µm
Pe´rez-Gonza´lezetal.(2005). within 1σ of uncertainty in LFs, and errorsin convertingfrom
L toL areadded.Thelatterisbyfarthelargestsource
12µm TIR
of uncertainty. Best fit parameters are presented in Table 2. In
logL =log(0.89+0.38)+1.094logL (8) Fig.10,weshowtotalluminositydensitybasedonthe12µmLF
TIR −0.27 12µm
8 Gotoetal.:InfraredLuminosityfunctionswiththeAKARI
Fig.11.Anexampleof theSED fit. Thered dashedline shows
thebest-fitSEDfortheUV-optical-NIRSED,mainlytoestimate
photometricredshift.Thebluesolidlineshowsthebest-fitmodel
fortheIRSEDatλ>6µm,toestimateL .
TIR
Fig.9. Evolutionof 12µmIR luminositydensitycomputedby
integratingthe12µmLFsinFig.8.
3.5. TIRLF
AKARI’scontinuousmid-IRcoverageisalsosuperiorforSED-
fitting to estimate L , since for star-forming galaxies, the
TIR
mid-IRpartoftheIRSEDisdominatedbythePAH emissions
whichreflecttheSFRofgalaxies,andthus,correlateswellwith
L , which is also a good indicator of the galaxy SFR. The
TIR
AKARI’scontinuousMIRcoveragehelpsustoestimateL .
TIR
After photometric redshifts are estimated using the UV-
optical-NIRphotometry,wefixtheredshiftatthephoto-z,then
usethesameLePharecodetofittheinfraredpartoftheSED
to estimate TIR luminosity. We used Lagache,Dole,&Puget
(2003)’sSEDtemplatestofitthephotometryusingtheAKARI
bands at >6µm (S7,S9W,S11,L15,L18W and L24). We
showanexampleoftheSEDfitinFig.11,wherethereddashed
and bluesolid lines show the best-fitSEDs forthe UV-optical-
NIR andIR SED at λ > 6µm, respectively.The obtainedtotal
infraredluminosity(L )isshownasafunctionofredshiftin
TIR
Fig.12,withspectroscopicgalaxiesinlargetriangles.Thefigure
shows that the AKARI can detect LIRGs (LTIR > 1011L⊙)
up to z=1 and ULIRGs (LTIR > 1012L⊙) to z=2. We also
checkedthatusingdifferentSEDmodels(Chary&Elbaz,2001;
Dale&Helou,2002)doesnotchangeouressentialresults.
Fig.10. TIR luminosity density computed by integrating the
Galaxies in the targeted redshift range are best sampled in
12µmLFsinFig.8.
the 18µm band due to the wide bandpass of the L18W filter
(Matsuharaetal., 2006).Infact,in a single-banddetection,the
18µm image returns the largest number of sources. Therefore,
presented in Fig.8. The results show a rapid increase of ΩIR, we applied the 1/Vmax method using the detection limit at
agreeingwithpreviouswork(LeFloc’hetal.,2005)withinthe L18W. We also checked that using the L15 flux limit does
errors. notchangeourmainresults.ThesameLagache,Dole,&Puget
We also integrate monochromatic L over the LFs (2003)’s models are also used for k-corrections necessary to
12µm
(without converting to L ) to derive the evolution of to- compute V and V . The redshift bins used are 0.2<
TIR max min
tal 12µm monochromatic luminosity density, Ω . The re- z <0.5,0.5< z <0.8,0.8<z <1.2,and1.2<z <1.6.Adistri-
12µm
sults are shown in Fig.9, which shows a strong evolution of butionofL ineachredshiftbinisshowninFig.13.
TIR
Ω12µm ∝ (1 + z)1.4±1.4. It is interesting to compare this to TheobtainedLTIRLFsareshowninFig.14.Theuncertain-
Ω ∝ (1+ z)1.9±0.7 obtained in §3.2. Although errors are ties are esimated through the Monte Carlo simulations (§2.4).
8µm
significantonbothestimates,Ω andΩ showapossibly For a local benchmark, we overplot Sandersetal. (2003) who
12µm 8µm
differentevolution,suggestingthatthecosmicinfraredspectrum derivedLFs fromthe analyticalfit to the IRAS Revised Bright
changesitsSEDshape.Whetherthisisduetoevolutionindust, GalaxySample,i.e.,φ ∝ L−0.6 forL < L∗ andφ ∝ L−2.2 for
or dusty AGN contribution is an interesting subject for future L > L∗ withL∗ = 1010.5L⊙.TheTIRLFsshowastrongevo-
work. lutioncomparedtolocalLFs.At0.25<z <1.3,L∗ evolves
TIR
Gotoetal.:InfraredLuminosityfunctionswiththeAKARI 9
Fig.12. TIR luminosityis shown as a functionof photometric
redshift. The photo-z is estimated using UV-optical-NIR pho-
tometry.L isobtainedthroughSEDfitin7-24µm.
TIR
Fig.14. TIRLFs.Verticallinesshowtheluminositycorrespond-
ing to the flux limit at the central redshiftin each redshift bin.
AGNsareexcludedfromthesample(§2.2).
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.
Fig.15. TIR luminosity density (red diamonds) computed by
as ∝ (1 + z)4.1±0.4. We further compare LFs to the previous
integratingthetotalLFin Fig.14. Thebluesquaresandorange
workin§4.
trianglesareforLIRGandULIRGsonly.
3.6. BolometricIRluminositydensitybasedontheTIRLF
Using the same methodology as in previous sections, we inte-
grate LTIR LFs in Fig.14 through a double-power law fit (eq. 4. Discussion
5 and 6). The resulting evolution of the TIR density is shown
with red diamondsin Fig.15, which in in goodagreementwith 4.1. Comparisonwithpreviouswork
LeFloc’hetal.(2005)withintheerrors.Errorsareestimatedby
varyingthefit within1σ of uncertaintyinLFs. Foruncertainty In thissection,we compareourresultsto previouswork,espe-
intheSEDfit,weadded0.15dexoferror.Bestfitparametersare ciallythosebasedontheSpitzerdata.Comparisonsarebestdone
presentedin Table2.InFig.15, wealso showthe contributions inthesamewavelengths,sincetheconversionfromeitherL
8µm
toΩ fromLIRGsandULIRGswiththebluesquaresandor- or L to L involvesthe largestuncertainty.Hubblepa-
TIR 12µm TIR
angetriangles,respectively.Wefurtherdiscusstheevolutionof rametersinthepreviousworkareconvertedtoh=0.7forcom-
Ω in§4. parison.
TIR
10 Gotoetal.:InfraredLuminosityfunctionswiththeAKARI
4.1.1. 8µmLFs overplottheirresults in similar redshiftrangesas the cyandot-
dashedlinesinFig.8.ConsideringbothLFshavesignificanter-
Recently,usingtheSpitzerspacetelescope,restframe8µmLFs
ror bars, these LFs are in good agreement with our LFs, and
of z ∼1galaxieshavebeen computedin detailby Caputietal.
showsignificantevolutionin the12µmLFscomparedwith the
(2007) in the GOODS fields and by Babbedgeetal. (2006) in
z=012µmLFbyRush,Malkan,&Spinoglio(1993).Theagree-
theSWIREfield.Inthissection,wecompareourrestframe8µm
ment is in a stark contrast to the comparison in 8µm LFs in
LFs(Fig.4)totheseanddiscusspossibledifferences.
§4.1.1,wherewesufferedfromdifferncesofafactorofseveral.
In Fig.4, we overplotCaputietal. (2007)’s LFs at z=1 and Apossiblereasonforthisisthat12µmissufficientlyredderthan
z=2inthecyandash-dottedlines.Theirz=2LFisingoodagree- 8µm, that it is easier to be extrapolatedfrom S in case of
24µm
ment with our LF at 1.8< z <2.2. However, their z=1 LF is the Spitzer work. In fact, at z=1, both the Spitzer 24µm band
larger than ours by a factor of 3-5 at logL > 11.2. Note that andAKARIL24observetherestframe12µmdirectly.Inaddi-
thebrightestends(logL ∼ 11.4)areconsistentwitheachother ton, mid-IRSEDs around12µm are flatter than at 8µm, where
to within 1σ. They have excludedAGN using optical-to-X-ray PAHemissionsareprominent.Therefore,SEDmodelscanpre-
flux ratio,and we also haveexcludedAGN throughthe optical
dict the flux more accurately. In fact, this is part of the rea-
SED fit. Therefore, especially at the faint-end, the contamina-
sonwhyPe´rez-Gonza´lezetal.(2005)chosetoinvestigate12µm
tionfromAGNisnotlikelytobethemaincauseofdifferences.
LFs.Pe´rez-Gonza´lezetal.(2005)usedChary&Elbaz(2001)’s
SinceCaputietal.(2007)usesGOODSfields,cosmicvariance
SEDtoextrapolateS ,andyet,theyagreewellwithAKARI
24µm
mayplayarolehere.Theexactreasonforthedifferenceisun-
results, which are derived from filters that cover the restframe
known,but we pointout that their ΩIR estimate at z=1 is also 12µm. However, in other words, the discrepancy in 8µm LFs
higherthanotherestimatesbyafactorofafew(seetheirFig.15).
highlightsthefactthattheSEDmodelsareperhapsstillimper-
OnceconvertedintoLTIR,Magnellietal.(2009)alsoreported fectinthe8µmwavelengthrange,andthus,MIR-spectroscopic
Caputietal.(2007)’sz=1LFishigherthantheirestimatebased data that covers wider luminosity and redshift ranges will be
on 70µm by a factor of several (see their Fig.12). They con- necessary to refine SED models in the mid-IR. AKARI’s mid-
cludedthe differenceis fromdifferentSED modelsused,since
IR slitless spectroscopy survey (Wada, 2008) may help in this
their LF matched with that of Caputietal. (2007)’s once the
regard.
same SED models were used. We will compare our total LFs
tothoseintheliteraturebelow.
Babbedgeetal. (2006) also computed restframe 8µm LFs 4.1.3. TIRLFs
using the Spitzer/SWIRE data. We overplot their results at
0.25 < z < 0.5 and 0.5 < z < 1 in Fig.4 with the pink dot- Lastly,wecompareourTIRLFs(Fig.14)withthoseintheliter-
dashedlines.Inbothredshiftranges,goodagreementisfoundat ature.AlthoughtheTIRLFscanalsobeobtainedbyconverting
higherluminositybins(L8µm >1010.5L⊙).However,atallred- 8µmLFsor12µmLFs,wealreadycomparedourresultsinthese
shiftrangesincludingtheonesnotshownhere,Babbedgeetal. wavelengthsinthelastsubsections.Here,wecompareourTIR
(2006) tends to show a flatter faint-end tail than ours, and a LFstoLeFloc’hetal.(2005)andMagnellietal.(2009).
smaller φ by a factor of ∼3. Although the exact reason is un- LeFloc’hetal. (2005) obtained TIR LFs using the Spitzer
known, the deviation starts toward the fainter end, where both CDF-S data. They have used the best-fit SED among various
worksapproachthefluxlimitsofthesurveys.Therefore,possi- templatestoestimateL .WeoverplottheirtotalLFsinFig.14
TIR
blyincompletesamplingmaybeoneofthereasons.Itisalsore- withthecyandash-dottedlines.OnlyLFsthatoverlapwithour
portedthatthefaint-endofIRLFsdependsontheenvironment, redshit ranges are shown. The agreement at 0.3 < z < 0.45
in the sense that higher-density environment has steeper faint- and0.6 < z < 0.8isreasonable,consideringtheerrorbarson
end tail (Gotoetal., 2010). Note that at z=1, Babbedgeetal. bothsides.However,inallthreeredshiftranges,LeFloc’hetal.
(2006)’s LF (pink) deviates from that by Caputietal. (2007) (2005)’sLFsarehigherthanours,especiallyfor1.0<z <1.2.
(cyan)byalmostamagnitude.Our8µmLFsarebetweenthese We also overplot TIR LFs by Magnellietal. (2009), who
works. used Spitzer 70µm flux and Chary&Elbaz (2001)’s model to
These comparisonssuggest that even with the current gen- estimateL .Inthetwobins(centeredonz=0.55andz=0.85;
TIR
eration of satellites and state-of-the-artSED models, factor-of- pink dash-dottedlines) which closely overlapwith our redshift
several uncertainties still remain in estimating the 8µm LFs bins, excellent agreement is found. We also plot Huynhetal.
at z∼1. More accurate determination has to await a larger (2007)’s LF at 0.6 < z < 0.9 in the navy dash-dotted lines,
and deeper survey by the next generation IR satellites such as whichiscomputedfromSpitzer70µmimagingintheGOODS-
HerschelandWISE. N, and this also shows very good agreement with ours. These
To summarise, our 8µm LFs are between those by LFs are on top of each other within the error bars, despite the
Babbedgeetal.(2006)andCaputietal.(2007),anddiscrepancy fact that these measurementsare from differentdata sets using
isbyafactorofseveralatmost.Wenotethatbothoftheprevi- differentanalyses.
ous works had to rely on SED models to estimate L8µm from ThismeansthatLeFloc’hetal. (2005)’sLFsisalso higher
the Spitzer S24µm in the MIR wavelengthswhere SED model- thanthatofMagnellietal.(2009),inadditiontoours.Apossible
ingisdifficult.Here,AKARI’smid-IRbandsareadvantageous reasonisthatbothMagnellietal.(2009)andweremovedAGN
indirectlyobservingredshiftedrestframe8µmfluxinoneofthe (at least bright ones), whereas LeFloc’hetal. (2005) included
AKARI’sfilters, leadingtomorereliablemeasurementof8µm them. This also is consistent with the fact that the difference
LFswithoutuncertaintyfromtheSEDmodeling. is larger at 1.0 < z < 1.2 where both surveys are only sen-
sitive to luminous IR galaxies, which are dominated by AGN.
Another possible source of uncertainty is that Magnellietal.
4.1.2. 12µmLFs
(2009)andweusedasingleSEDlibrary,whileLeFloc’hetal.
Pe´rez-Gonza´lezetal. (2005) investigated the evolution of rest- (2005)pickedthebestSEDtemplateamongseverallibrariesfor
frame12µmLFsusingtheSpitzerCDF-SandHDF-Ndata.We eachgalaxy.