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dL/L∗,(L > L∗) (2)
Free parameters are: L∗(characteristic luminosity, L⊙),φ∗
(normalization, Mpc−3),αandβ(faint and bright end slopes),
respectively.ThebestﬁtvaluesforﬁeldandclusterLFsare sum-
marisedinTable1andshowninthedottedlinesinFig.1.
The bright-end slopes are not very different, but L∗of the
cluster LF is smaller than the ﬁeld by a factor of 2.4, and the
faint-endtailofclusterLF issteeperthanthatofﬁeldLF.
To further examine the difference at the faint end of the
LFs, we divide the cluster LF using the local galaxy density
(Σ5th) measuredbyKoyamaet al. (2008). Thisdensityis based
on the distance to the 5th nearest neighbor in the transverse di-
rection using all the optical photo-z members, and thus, is a
surface galaxy density. We separate LFs using similar crite ria,
logΣ5th≥2(dense),1.6≤logΣ5th<2(intermediate), and
logΣ5th<1.6(sparse), then plot LFs of each region in the4 Gotoet al.:Environemental dependence of 8 µm luminosity functions ofgalaxies atz ∼0.8
stars, circles, and squares in Fig.2. A fraction of the total vol-
umeofthe clusteris assignedto eachdensitygroupin invers ely
proportionaltothe sumof Σ3/2
5thofeachgroup.
Interestingly, the faint-end slope becomes ﬂatter and ﬂatt er
with decreasing local galaxy density. This result is consis tent
with our comparison with the ﬁeld in Fig.1. In fact, the lowes t
densityLF(squares)hasaﬂatfaint-endtailsimilartothat ofthe
ﬁeldLF.SincetheseLFsarebasedonthesamedata,changesin
the faint-end slope are not likely due to the errors in comple te-
ness correction nor calibration problems. The completenes s of
the deep and shallow regions of the cluster are measured sep-
arately. The changes in the slope is much larger than the maxi -
mumcompletenesscorrectionof25%.Wealsocheckedtheclus -
ter LFs as a function of cluster centric radius, to ﬁnd no sign iﬁ-
cantdifference,perhapsduetotheelongatedmorphologyof this
cluster. At the same time, assuming the same cluster volume,
Fig.2 shows that a possible contamination from the ﬁeld gala x-
ies to cluster LFs is only ∼0.1% in the dense region and ∼1%
eveninthe sparseregion.
It is interesting that not just the change in the scale of the
LFs, but there is a change in the L∗and the faint-end slope ( α)
of the LFs, resulting in the deﬁcit in the 10.2L⊙<logL8µm<
10.8L⊙for cluster LFs. One might imaginea change just in L∗
might explain the difference in Fig.1. However, in Fig.2, th ere
clearlyisachangein theslopeasafunctionof Σ5th.
However,interpretationis rathercomplicated;a shapeofL F
would not change if ﬁeld galaxies infall into cluster unifor mly
withoutchangingtheirstar-formationactivity.Although inclus-
ter environment,a fractionof MIR luminousgalaxiesis smal ler
than ﬁeld (Koyamaet al., 2008), uniformand instant quenchi ng
of star-formation activity of ﬁeld galaxies can only shift a LF,
butcannotaccountforachangein L∗andαoftheLFs.
Two important ﬁndings in this work are; (i) L∗is smaller
in the cluster. (ii) the faint-end slopes become steeper tow ard
higher-density regions. To explain these changes in LFs, IR -
luminousgalaxiesneedtobepreferentiallyreduced,witha rela-
tive increase of IR-faint galaxies. However, an environmen tal-
driven physical process such as the ram-pressure stripping or
galaxy-merging would quench star-formation not only in mas -
sivegalaxiesbutinlessmassivegalaxiesaswell,andthusi snot
abletoexplaintheobservedchangesinLFs.
Ontheotherhand,ithasbeenfrequentlyobservedthatmore
massive galaxies formed earlier in the Universe. This downs iz-
ing scenario also depends on the environment,in the sense th at
galaxieswith same mass are moreevolvedin higherdensityen -
vironmentsthangalaxisin less denseenvironments(Gotoet al.,
2005; Tanakaet al., 2005, 2008). Statistically, a good corr ela-
tionhasbeenfoundbetween LTIRandstellarmass(Elbazet al.,
2007). Our ﬁnding of the relative lack of IR-luminous galaxi es
in the cluster environmentmay be consistent with the downsi z-
ing scenario, where higher density regions have more evolve d
galaxies and lacks massive star-forming galaxies. In contr ast,
in lower density regions more massive galaxies are still sta r-
forming. However, since the data we have shown is in IR lumi-
nosity, to conclude on this, we need good stellar mass estima te
basedondeepernear-IRdata.
Although a speciﬁc mechanism is unclear, the steep faint-
end could also result from the enhanced star-formation in le ss
massive galaxies. In the above scenario, massive galaxies h ave
already ceased their star-formation in the cluster, but les s mas-
sive galaxiesare still formingstars. These less massive ga laxies
may stop star-formation soon to join the faint-end of the red -
sequence(Koyamaet al., 2007).Fig.3.TotalinfraredLFsofclusterRXJ1716.4 +6708atz=0.81
in the solid line, and those of the AKARI NEP deep ﬁeld in the
dashed line. Overplottedare the LFs of MS1054 from Bai et al.
(2007).
3.2. Total IRLFs
To compare the L8µmLF in Fig.1 to those in the literature, we
needtoconvert L8µmtoLTIR.Weusethethefollowingrelation
byCaputiet al.(2007);
LTIR= 1.91×(νLν8µm)1.06(±55%) (3)
Thisis better tunedfor a similar luminosityrange used here
than the originalrelationby Bavouzetetal. (2008). The con ver-
sion, however, has been the largest source of errors in estim at-
ingLTIRfromL8µm.Caputi etal.(2007)report55%ofdisper-
sion around the relation. It should be kept in mind that the re st-
frame8µm is sensitive to the star-formation activity, but at the
same time, it is where the SED models have strongest discrep-
anciesduetothecomplicatedPAHemissionlines(seeFig.12 of
Caputiet al.,2007; Gotoetal., 2010).
Theestimated LTIRcanbe,then,convertedtoSFRusingthe
followingrelationfor a Salpeter IMF, φ(m)∝m−2.35between
0.1−100M⊙(Kennicutt, 1998).

dL/L∗,(L > L∗) (2)

Free parameters are: L∗(characteristic luminosity, L⊙),φ∗

(normalization, Mpc−3),αandβ(faint and bright end slopes),

respectively.ThebestﬁtvaluesforﬁeldandclusterLFsare sum-

marisedinTable1andshowninthedottedlinesinFig.1.

The bright-end slopes are not very different, but L∗of the

cluster LF is smaller than the ﬁeld by a factor of 2.4, and the

faint-endtailofclusterLF issteeperthanthatofﬁeldLF.

To further examine the difference at the faint end of the

LFs, we divide the cluster LF using the local galaxy density

(Σ5th) measuredbyKoyamaet al. (2008). Thisdensityis based

on the distance to the 5th nearest neighbor in the transverse di-

rection using all the optical photo-z members, and thus, is a

surface galaxy density. We separate LFs using similar crite ria,

logΣ5th≥2(dense),1.6≤logΣ5th<2(intermediate), and

logΣ5th<1.6(sparse), then plot LFs of each region in the4 Gotoet al.:Environemental dependence of 8 µm luminosity functions ofgalaxies atz ∼0.8

stars, circles, and squares in Fig.2. A fraction of the total vol-

umeofthe clusteris assignedto eachdensitygroupin invers ely

proportionaltothe sumof Σ3/2

5thofeachgroup.

Interestingly, the faint-end slope becomes ﬂatter and ﬂatt er

with decreasing local galaxy density. This result is consis tent

with our comparison with the ﬁeld in Fig.1. In fact, the lowes t

densityLF(squares)hasaﬂatfaint-endtailsimilartothat ofthe

ﬁeldLF.SincetheseLFsarebasedonthesamedata,changesin

the faint-end slope are not likely due to the errors in comple te-

ness correction nor calibration problems. The completenes s of

the deep and shallow regions of the cluster are measured sep-

arately. The changes in the slope is much larger than the maxi -

mumcompletenesscorrectionof25%.Wealsocheckedtheclus -

ter LFs as a function of cluster centric radius, to ﬁnd no sign iﬁ-

cantdifference,perhapsduetotheelongatedmorphologyof this

cluster. At the same time, assuming the same cluster volume,

Fig.2 shows that a possible contamination from the ﬁeld gala x-

ies to cluster LFs is only ∼0.1% in the dense region and ∼1%

eveninthe sparseregion.

It is interesting that not just the change in the scale of the

LFs, but there is a change in the L∗and the faint-end slope ( α)

of the LFs, resulting in the deﬁcit in the 10.2L⊙<logL8µm<

10.8L⊙for cluster LFs. One might imaginea change just in L∗

might explain the difference in Fig.1. However, in Fig.2, th ere

clearlyisachangein theslopeasafunctionof Σ5th.

However,interpretationis rathercomplicated;a shapeofL F

would not change if ﬁeld galaxies infall into cluster unifor mly

withoutchangingtheirstar-formationactivity.Although inclus-

ter environment,a fractionof MIR luminousgalaxiesis smal ler

than ﬁeld (Koyamaet al., 2008), uniformand instant quenchi ng

of star-formation activity of ﬁeld galaxies can only shift a LF,

butcannotaccountforachangein L∗andαoftheLFs.

Two important ﬁndings in this work are; (i) L∗is smaller

in the cluster. (ii) the faint-end slopes become steeper tow ard

higher-density regions. To explain these changes in LFs, IR -

luminousgalaxiesneedtobepreferentiallyreduced,witha rela-

tive increase of IR-faint galaxies. However, an environmen tal-

driven physical process such as the ram-pressure stripping or

galaxy-merging would quench star-formation not only in mas -

sivegalaxiesbutinlessmassivegalaxiesaswell,andthusi snot

abletoexplaintheobservedchangesinLFs.

Ontheotherhand,ithasbeenfrequentlyobservedthatmore

massive galaxies formed earlier in the Universe. This downs iz-

ing scenario also depends on the environment,in the sense th at

galaxieswith same mass are moreevolvedin higherdensityen -

vironmentsthangalaxisin less denseenvironments(Gotoet al.,

2005; Tanakaet al., 2005, 2008). Statistically, a good corr ela-

tionhasbeenfoundbetween LTIRandstellarmass(Elbazet al.,

2007). Our ﬁnding of the relative lack of IR-luminous galaxi es

in the cluster environmentmay be consistent with the downsi z-

ing scenario, where higher density regions have more evolve d

galaxies and lacks massive star-forming galaxies. In contr ast,

in lower density regions more massive galaxies are still sta r-

forming. However, since the data we have shown is in IR lumi-

nosity, to conclude on this, we need good stellar mass estima te

basedondeepernear-IRdata.

Although a speciﬁc mechanism is unclear, the steep faint-

end could also result from the enhanced star-formation in le ss

massive galaxies. In the above scenario, massive galaxies h ave

already ceased their star-formation in the cluster, but les s mas-

sive galaxiesare still formingstars. These less massive ga laxies

may stop star-formation soon to join the faint-end of the red -

sequence(Koyamaet al., 2007).Fig.3.TotalinfraredLFsofclusterRXJ1716.4 +6708atz=0.81

in the solid line, and those of the AKARI NEP deep ﬁeld in the

dashed line. Overplottedare the LFs of MS1054 from Bai et al.

(2007).

3.2. Total IRLFs

To compare the L8µmLF in Fig.1 to those in the literature, we

needtoconvert L8µmtoLTIR.Weusethethefollowingrelation

byCaputiet al.(2007);

LTIR= 1.91×(νLν8µm)1.06(±55%) (3)

Thisis better tunedfor a similar luminosityrange used here

than the originalrelationby Bavouzetetal. (2008). The con ver-

sion, however, has been the largest source of errors in estim at-

ingLTIRfromL8µm.Caputi etal.(2007)report55%ofdisper-

sion around the relation. It should be kept in mind that the re st-

frame8µm is sensitive to the star-formation activity, but at the

same time, it is where the SED models have strongest discrep-

anciesduetothecomplicatedPAHemissionlines(seeFig.12 of

Caputiet al.,2007; Gotoetal., 2010).

Theestimated LTIRcanbe,then,convertedtoSFRusingthe

followingrelationfor a Salpeter IMF, φ(m)∝m−2.35between

0.1−100M⊙(Kennicutt, 1998).