1001.0013.txt

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
Photoz0.15<z<2.2FUV,NUV ,u,B,V,R,i′,z,J, andK
8µm LF 0.38 <z<0.58 S11(11 µm)
8µm LF 0.65 <z<0.90 L15(15 µm)
8µm LF 1.1 <z<1.4 L18W (18 µm)
8µm LF 1.8 <z<2.2 L24(24 µm)
12µm LF 0.15 <z<0.35 L15(15 µm)
12µm LF 0.38 <z<0.62 L18W (18 µm)
12µm LF 0.84 <z<1.16 L24(24 µm)
TIRLF 0.2 <z<0.5S7,S9W,S11,L15,L18WandL24
TIRLF 0.5 <z<0.8S7,S9W,S11,L15,L18WandL24
TIRLF 0.8 <z<1.2S7,S9W,S11,L15,L18WandL24
TIRLF 1.2 <z<1.6S7,S9W,S11,L15,L18WandL24
Among various templates and fitting parameters we tried,
we found the best results were obtained with the following: w e
used modified CWW (Coleman,Wu,& Weedman, 1980) and
QSO templates.TheseCWW templatesareinterpolatedandad-
justed to better match VVDS spectra (Arnoutsetal., 2007). W e
included strong emission lines in computing colors. We used
the Calzetti extinction law. More details in training LePhare
isgiveninIlbertet al.(2006).
The resulting photometric redshift estimates agree reason -
ably well with 293 galaxies ( R <24) with spectroscopic red-
shifts taken with Keck/DEIMOS in the NEP field (Takagi et al.
inprep.).Themeasurederrorsonthephoto- zare∆z
1+z=0.036for
z≤0.8and∆z
1+z=0.10 for z >0.8. 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
0.38<z<0.58 8 µm (2.2+0.3
−0.1)×1010(2.1+0.3
−0.4)×10−31.75+0.01
−0.013.5+0.2
−0.4
0.65<z<0.90 8 µm (2.8+0.1
−0.1)×10102.1×10−31.75 3.5
1.1<z<1.4 8 µm (3.3+0.2
−0.2)×10102.1×10−31.75 3.5
1.8<z<2.2 8 µm (8.2+1.2
−1.8)×10102.1×10−31.75 3.5
0.15<z<0.35 12 µm (6.8+0.1
−0.1)×109(4.2+0.7
−0.6)×10−31.20+0.01
−0.022.9+0.4
−0.2
0.38<z<0.62 12 µm (11.7+0.3
−0.5)×1094.2×10−31.20 2.9
0.84<z<1.16 12 µm (14+2
−3)×1094.2×10−31.20 2.9
0.2<z<0.5 Total (1.2+0.1
−0.2)×1011(5.6+1.5
−0.2)×10−41.8+0.1
−0.43.0+1.0
−1.0
0.5<z<0.8 Total (2.4+1.8
−1.6)×10115.6×10−41.8 3.0
0.8<z<1.2 Total (3.9+2.3
−2.2)×10115.6×10−41.8 3.0
1.2<z<1.6 Total (14+1
−2)×10115.6×10−41.8 3.0
Fig.7.12µm luminosity distributions of samples used to com-
puterestframe12 µmLFs. Fromlowredshift,335,573,and213
galaxiesarein eachredshiftbin.
Targeted redshifts are z=0.25, 0.5 and 1 where L15,L18W
andL24filterscovertherestframe12 µm,respectively.Wesum-
marise the filters used in Table 1. Methodology is the same as
for the 8µm LF; we used the sample to the 5 σlimit, corrected
for the completeness, then used the 1/ Vmaxmethod to com-
pute LF in each redshift bin. The histogram of L12µmdistri-
bution is presented in Fig.7. The resulting 12 µm LF is shown
in Fig.8. Compared with Rush,Malkan,& Spinoglio (1993)’s
z=0 LF based on IRAS Faint Source Catalog, the 12 µm LFs
show steady evolution with increasing redshift. In the rang e of
0.25< z <1,L∗
12µmevolvesas ∝(1+z)1.5±0.4.
3.4. Bolometric IR luminosity density basedonthe 12 µm
LF
12µm is one of the most frequentlyused monochromaticfluxes
to estimate LTIR. The total infrared luminosity is computed
from theL12µmusing the conversionin Chary& Elbaz (2001);
P´ erez-Gonz´ alezet al.(2005).
logLTIR= log(0.89+0.38
−0.27)+1.094logL12µm (8)Fig.8.Restframe 12 µm LFs based on the AKARI NEP-Deep
field.Thebluediamonds,purpletriangles,andredsquaress how
the 12µm LFs at 0.15< z <0.35,0.38< z <0.62, and
0.84< z <1.16, respectively. Vertical arrows show the 12 µm
luminosity corresponding to the flux limit at the central red -
shift in each redshift bin. Overplotted are P´ erez-Gonz´ al ezet al.
(2005) at z=0.3,0.5 and 0.9 in the cyan dash-dotted lines, and
Rush,Malkan,& Spinoglio (1993) at z=0 in the green dash-
dottedlines. AGNsareexcludedfromthesample( §2.2).
Takeuchietal. (2005) independently estimated the relatio n
tobe
logLTIR= 1.02+0.972logL12µm, (9)
which we also use to check our conversion. As both au-
thors state, these conversions contain an error of factor of 2-3.
Therefore, we should avoid conclusions that could be affect ed
bysucherrors.
Then the 12 µm LF is weighted by the LTIRand integrated
to obtain TIR density. Errors are estimated by varying the fit
within 1σof uncertainty in LFs, and errors in converting from
L12µmtoLTIRareadded.Thelatter isbyfarthe largestsource
of uncertainty. Best fit parameters are presented in Table 2. In
Fig.10,we showtotal luminositydensitybasedonthe12 µmLF8 Gotoet al.:InfraredLuminosityfunctions withthe AKARI
Fig.9.Evolution of 12 µm IR luminosity density computed by
integratingthe12 µmLFsinFig.8.
Fig.10. TIR luminosity density computed by integrating the
12µmLFsin Fig.8.
presented in Fig.8. The results show a rapid increase of ΩIR,
agreeing with previous work (LeFloc’hetal., 2005) within t he
errors.
We also integrate monochromatic L12µmover the LFs
(without converting to LTIR) to derive the evolution of to-
tal12µmmonochromatic luminosity density, Ω12µm. The re-
sults are shown in Fig.9, which shows a strong evolution of
Ω12µm∝(1 +z)1.4±1.4. It is interesting to compare this to
Ω8µm∝(1 +z)1.9±0.7obtained in §3.2. Although errors are
significantonbothestimates, Ω12µmandΩ8µmshowa possibly
differentevolution,suggestingthatthecosmicinfrareds pectrum
changesits SED shape.Whetherthisisdueto evolutionindus t,
or dusty AGN contribution is an interesting subject for futu re
work.Fig.11.An example of the SED fit. The red dashed line shows
thebest-fitSEDfortheUV-optical-NIRSED,mainlytoestima te
photometricredshift.Thebluesolidlineshowsthebest-fit model
fortheIRSEDat λ >6µm,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.
This research is based on the observations with AKARI, a
JAXA projectwiththe participationofESA.
Theauthorswishtorecognizeandacknowledgetheverysig-
nificant cultural role and reverence that the summit of Mauna
Kea has always had within the indigenous Hawaiian commu-
nity. We are most fortunate to have the opportunity to conduc t
observationsfromthissacredmountain.
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