Simulations of the cosmic infrared and submillimeter background for future large surveys: I. Presentation and first application to Herschel/SPIRE and Planck/HFI

0.99 MB·English

by  N. Fernandez-Conde

(cid:13)
Astronomy & Astrophysi
s manus
ript no. 8188
ESO 2008
February 3, 2008
Simulations of the
osmi
infrared and submillimeter
ba
kground for future large surveys: I. Presentation and (cid:28)rst
appli
ation to Hers
hel/SPIRE and Plan
k/HFI
N. Fernandez-Conde, G. Laga
he, J.-L. Puget, H. Dole
8
0
Institut d'AstrophysiqueSpatiale (IAS),bâtiment121, Université Paris-Sud 11 and CNRS (UMR 8617), 91405 Orsay,
0
Fran
e e-mail:[nestor.fernandez;guilaine.laga
he;jean-loup.puget;herve.dole℄ias.u-psud.fr
2

n 6 June 2007
a
J Abstra
t

8
2 Context.The
omingPlan
kandHers
helmissionswillsurveytheskyatunpre
edentedangulars
alesandsensitivities.
Simulations are neededfor better interpretating theresults of thesurveysand for testing newmethods of, e.g., sour
e
] extra
tion and
omponentseparation.
h Aims. We present new simulations of the infrared and submillimeter
osmi
ba
kground, in
luding the
orrelation
p between infrared galaxies. The simulations were used to quantify the sour
e-dete
tion thresholds for Hers
hel/SPIRE
- and Plan
k/HFI, as well as to studythedete
tability of the
osmi
infrared ba
kground
orrelated (cid:29)u
tuations.
o
Methods. The simulations are based on an empiri
al model of IR galaxy evolution. For these
orrelations, we only
r
t in
ludedthelinear
lustering,assumingthatinfraredgalaxies arebiasedtra
ersofthedark-matter(cid:29)u
tuationdensity
s (cid:28)eld.
a
Results. We used the simulations with di(cid:27)erent bias parameters to predi
t the
onfusion noise for Hers
hel/SPIRE
[
and Plan
k/HFI and the
ompleteness levels. We also dis
uss the dete
tability of the linear
lustering in Plan
k/HFI

1 power spe
tra, in
ludingthe foreground and ba
kgrounds
omponents.
v Con
lusions. Simulated maps and
atalogs are publi
ly available online at
9 http://www.ias.u-psud.fr/irgalaxies/simulations.php.
9
Key words. infrared: galaxies (cid:21)galaxies: evolution (cid:21) (
osmology:) large-s
ale stru
ture of universe
2
4
1. z ∼1 z ∼2−3
1. INTRODUCTION andULIRGs(ultraluminousIRgalaxies)at .
0
8 λ ≥ 8µm
The
osmi
infrared ba
kground (CIB) ( ) is the
0 Determination of the CIB by the COBE satellite
reli
emission of the formation and evolution of galaxies.
:
v The (cid:28)rst observational eviden
e of this ba
kground was has been hindered by the a

ura
y of subtra
ting the
Xi reported by Puget et al. (1996) and then
on(cid:28)rmed by foregrounµdmby only providing just upper limits at 12, 25,
and 60 (Hauser et al., 1998), lower limit has been
Hauser et al. (1998) and Fixsen et al. (1998). The dis- µm
r derived at 24 by Papovi
h et al. (2004) as well as the
a
overy of a surprisingly high amount of energy in the µm

ontributionof24 galaxiestotheba
kgroundat70and
CIB has shown the importan
e of studying its sour
es µm
160 (Dole et al.,2006).The
ontributionofthegalaxies
to understand how the bulk of stars was formed in the µJy µm µm
down to 60 at 24 is at least 79% of the 24
Universe. Deep
osmologi
al surveys have been
arried µm
ba
kground, and 80% of the 70 and 160 ba
kground.
out thanks to ISO (see Genzel & Cesarsky, 2000; Elbaz,
µm For longer wavelengths, re
ent studies have investigated
2005, for reviews) mainly at 15 with ISOCAM (e.g.
µm the
ontribution of populations sele
ted in the near-IR to
Elbaz et al., 2002); at 90 and 170 with ISOPHOT λ > 200µm µm
the far-infrared ba
kground (FIRB, ): 3.6
(e.g. Dole et al., 2001); to SPITZER at 24, 70, and µm
µm sele
ted sour
es to the 850 ba
kground (Wang et al.,
160 (e.g. Papovi
h et al., 2004; Dole et al., 2004) µm µm
2006) and 8 and 24 sele
ted sour
es to the 850
and to ground-based instruments su
h as SCUBA (e.g. µm µm
and 450 ba
kgrounds (Dye et al., 2006). Similar
Holland et al., 1998) and MAMBO (e.g. Bertoldi et al.,
µm studies with Plan
k and Hers
hel will provide even more
2000) at 850 and 1300 , respe
tively. These surveys
eviden
e of the nature of the FIRB sour
es.
have allowed for a better understanding of the CIB and
its sour
es (see Laga
he et al., 2005, for a general review).
Some of the results in
lude: the energy of the CIB is Studying
orrelations in the spatial distribution of IR
dominated by starbursts although AGN (a
tive gala
ti
galaxiesasafun
tionofredshift isanessentialobservation
nu
leus)
ontribute too, and the dominant
ontributors to (paralleltothestudiesofindividualhigh-redshift,infrared,
theenergyoutput arethe LIRGs(luminousIRgalaxies)at luminous galaxies), to understand the underlying s
enario
andphysi
sofgalaxyformationandevolution.A(cid:28)rststudy
µ
has been done using the 850 m galaxies (Blain et al.,
Send o(cid:27)print requests to: N. Fernandez-Conde, G. Laga
he 2004). Although the number of sour
esis quite small, they
2 N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground
(cid:28)nd eviden
e that submillimiter galaxies are linked to the analysis methods. The requirement was to build the
formation of massive galaxies in dense environments des- simplest model of the luminosity fun
tion (LF) evolution
tined to be
ome ri
h
lusters. This has now been dire
tly with redshift, with the lowest number of parameters, but
supportedbythedete
tionofthe
lusteringofhigh-redshift a

ounting for all statisti
al observational data between 5
µ µm
24 m sele
ted ULIRGs and HyperLIRGs (Farrah et al., and 1 mm. These are the spe
tral energy distribution
2006; Maglio

hetti et al., 2007). Studying
orrelations oftheCIBandits(cid:29)u
tuations,galaxyluminosityfun
tions
with individual IR galaxies is very hard due to either high and their redshift evolution, as well as the existing sour
e

onfusion noises, instrumental noises, or small (cid:28)elds of
ounts and redshift distributions.
observation. It has been shown that the IR-ba
kground
anisotropies
ould provide information on the
orrelation Theluminosityfun
tionofIRgalaxieswasmodelledby
between the sour
es of the CIB and dark matter for large- a bimodal star-formation pro
ess: one asso
iated with the
s
alestru
tures (Knox et al., 2001; Haiman & Knox, 2000, passive phase of galaxy evolution (normal galaxies) and
hereafter HK) and on the large-s
ale stru
ture evolution. one asso
iated with the starburst phase, mostly triggered
First studies at long wavelengths have only dete
ted the bymergingandintera
tions(starburstgalaxies).Unlikefor
shot-noise
omponentofthe(cid:29)u
tuations:Laga
he & Puget the starburst galaxies, the normal galaxy
ontribution to
µm
(2000) at 170 , Matsuhara et al. (2000) at 90 and 170 the luminosity fun
tion was
onsidered mostly un
hanged
µm µm
, Miville-Des
hênes et al. (2001) at 60 and 100 . with redshift. The spe
tral energy distribution (SED)
Laga
he et al. (2007) and Grossan & Smoot (2007) re-
hanges with the luminosity of the sour
e but is assumed
port (cid:28)rst dete
tions of the
orrelated
omponent using
onstant with redshift for both populations in this simple
µm
Spitzer/MIPS data at 160 . Laga
he et al. (2007) model.
b∼1.7
measured a linear bias .
This model (cid:28)ts all1t0h11e e<xpeLrimen<tal1d01a2ta and has pre-
IR
Future observations by Hers
hel and Plan
k will allow dzi
≃ted0.5th−at1.L5IRGs ( )Ldomi>nat1e01a2t
IR
us to probe the
lustering of IR and submm galaxies. and that ULIRGs/HLIRGs ( )
z ≃ 2−3
Nevertheless these experiments will be limited, the
onfu- dominate at the energy distribution of the CIB.
sion and instrumental noises will hinder dete
tions of faint One example of the agreement between the model and the
individual galaxies. Clustering thus has to be analysed in observations is shown in Fig. 2.
the ba
kground (cid:29)u
tuations (e.g. Negrello et al., 2007).
The need for a prior understanding of what
ould be done
2.1.1. Number
ounts and CIB (cid:29)u
tuations
by these experiments has motivated us to develop a set of
realisti
simulations of the IR and sub-mm sky. To illustrate the interest of studying the
osmi
ba
k-
ground (cid:29)u
tuations in the far-IR and submm domains, we
In Se
t. 2 we present the model on whi
h are based use a simplisti
approa
h for the number
ounts, following
our simulations. In Se
t. 3 we dis
uss how the simulations Laga
he & Puget(2000).Thesour
enumber
ounts
anbe
are done and present a set of simulated sky maps and s
hemati
ally represented by a power law:
their
orresponding
atalogs.Di(cid:27)erent
atalogsare
reated −α
S
for 3 di(cid:27)erent levels of
orrelation between the IR galaxy N(S >S )=N
0 0
S (1)
emissivity and the dark-matter (cid:29)u
tuation density (cid:28)eld (cid:18) 0(cid:19)
(strong, medium, and no
orrelation). For ea
h of these
S

atalogs, we
an
reate maps of the sky at any given IR whereweset 0 tobethedete
tionlimitforthesour
es
N S
wavelength and simulate how di(cid:27)erent instruments will and 0 the number of sour
es with (cid:29)ux larger than 0.
see them. We fo
us in this paper on Plan
k/HFI and
Hers
hel/SPIRE. In Se
t. 4 we use the simulated maps to In a Eu
lidean Universe with uniform density of the
α=1.5
give predi
tions for the
onfusion noise, the
ompleteness, sour
es . In the far-IR and submm, a steeper slope
α = 2−3
and the dete
tion limits for ea
h of the study
ases, is observed with in the regime where negative
in
luding the instrumental noise. In Se
t. 5 we present the K-
orre
tion dominates. As an example, ISO observations
α = 2.2 µm
power spe
tra of the CIB anisotropies for Plan
k/HFI and found a slope of at 170 (Dole et al., 2001).
dis
usstheir dete
tability againstthe signi(cid:28)
antsour
esof Obviously,thenumber
ountsneedto(cid:29)attenforlow(cid:29)uxes

ontamination (shot noise,
irrus, and
osmi
mi
rowave to ensure that the CIB remainαs =(cid:28)n0ite. FSor<thSe∗rest of the
ba
kground (CMB)). dis
ussionwewill assumethat for . The total
S
max
intensityoftheCIB
omposedbyallthesour
esupto
Thrhou=gh0o.7u1t,tΩhep=ap0e.7r,tΩhe
=osm0.o2l7ogi
alparameterswere is given by:
Λ m
set to . For theσ8da=rk0-.m8atter Smax dN
linear
lustering we set the normalization to . I = S dS.
CIB
dS
Z0
2. THE MODEL For the Eu
liSd∗ean
ase the CIB intensity is dominated
by sour
es near .
2.1. Galaxies' empiri
al evolution model
S
0
The model of IR galaxies used for the simula- Flu
tuations from sour
es below the dete
tion limit
tions is from Laga
he et al. (2003), revisited in are given by
Laga
he et al. (2004) (cid:21) hereafter the LDP model, see S0 dN
http://www.ias.u-psud.fr/irgalaxies/model.php. This σ2 = S2 dS.
dS
modelisa(cid:29)exibletoolforplanningsurveysanddeveloping Z0
N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground 3
Figure1. Emisµsimvities
omputed using thµemLDP model at Figure2.Comparisonofthe observedsour
e
ounts(data
(observed)250µm (
ontinuousline), 450 (long-dashed poiµnts)andmodelpredµi
tions(
ontinuouslµines).Upper left
line),and85µ0m (dotted-dashedline).Theemissivityfrom 24 µm, Upper right 70 m, Lower left 160 m, Lower right
HKat 450 (short-dashedline) isshownfor
omparison 850 m.
.
dN
Using dS given by Eq. 1 we get
α S∗ 2−α
σ2 = N S2 1− .
2−α 0 0 S
" (cid:18) 0(cid:19) #
α > 2
For S∗ CIB (cid:29)u
tuations are dominated by sour
es

lose to so that the same sour
es dominate both the
FIRB and its (cid:29)u
tuations. Therefore by studying the (cid:29)u
-
tuationsoftheFIRB,wearealsostudyingthesour
esthat
form the bulk of the
ontribution to the FIRB. We
an

he
kthis
on
lusionwiththenumber
ountsfromtheLDP
model. Figure 3shows that the same sour
esdominate the
ba
kgroundand the (cid:29)u
tuations, but onlyforfaintsour
es
S . 50
850
(for example mJy). Therefore, it is ne
essary
Figure3. Contributions of the sour
es of (cid:29)ux S (in Jy)
to subtra
t bright sour
es priorto any (cid:29)u
tuation analysis
per Log interval of S to the ba
kground (dotted line, right
sin
e they would otherwise dominate the (cid:29)u
tuations.
y axis) and (cid:29)u
tuations (
ontinuous line, left y axis) at
850µm
.
2.1.2. IR galaxy emissivity
For the purpose of the model we need to
ompute the
m[We/aMn pIRc3/gHalza/xsyr]emissivity per unit of
omoving volume of the sour
es. The absen
e of a
ompletely developed
. It is de(cid:28)ned as theoreti
al model for the distribution of the whole IR
jd(ν,z)=(1+z) LbolLν′=ν(1+z)dlnd(LNbol)dln(Lbol) galaxy populations makes the empiri
al modelling of dif-
W/Hz/sr dN ferent distributions for the sour
es of the CIB ne
essaryin
where L is the lRuminosity (in ), dln(Lbol)is
Mpc−3 ν orderto preparefuture observations.Weusedan empiri
al
the
omoving luminosity fun
tionj(in ), and the des
ription for the spatial distribution of these sour
es,
d
observed frequen
y. We
ompute using the SEDs and whi
h has been used to
reate the simulated sky maps.
luminosity fun
tion from the LDP model whi
h assumes
L j
bol d
that the SED depends only on . The resulting is TheLDPmodeldidnotaddressthespatialdistribution
di(cid:27)erent from what is used by former approa
hes (HK, problem due to the la
k of
onstraints at the time it was
Knox et al., 2001). We
an see the di(cid:27)eren
e between the built. This is still mostly the
ase at the time of writing
emissivity from our model and that of HK in Fig. 1. The this work. The simulations by Dole et al. (2003) did not

rude model used for the emissivities by HK gives mu
h implement any
orrelation between IR galaxies and used
lower emissivities than ours. anun
orrelatedrandomdistribution.However,sin
efuture
experiments su
h as Hers
hel and Plan
k will be able to
ℓ . 1000
dete
t large-s
ale IR galaxy
orrelations ( ), a
model addressing this problem has be
ome ne
essary.
2.2. IR galaxy spatial distribution
Hers
hel, with its high angular resolution, is expe
ted
Any model trying to a

ount for CIB (cid:29)u
tuations must to also probe
orrelations between galaxies in the same
des
ribethestatisti
alpropertiesofthespatialdistribution dark-matter haloes but in this study this
orrelation has
4 N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground
2.2.1. Dark-matter power spe
trum
z =
Thepowerspe
trumofthedark-matterdistributionat
0

an be written as
P (k)∝kT2(k)
M
(3)
T(k,t)
where is the transfer fun
tion for a
old dark-
matter universe (Bardeen et al., 1986). The linear theory
G(z)
growth fun
tion writes as
g2(Ω(z),Ω (z))
G2(z)= Λ
g2(Ω ,Ω )(1+z)2 (4)
0 Λ0
with
5
g[Ω(z),Ω (z)] = Ω(z)× Ω(z)4/7−Ω (z)
Λ Λ
2
1h 1 −1
+ 1+ Ω(z) 1+ Ω (z) .
Λ
2 70
(cid:18) (cid:19)(cid:18) (cid:19)(cid:21)
Ω (z)= 1−Ω0 Ω(z)= Ω0(1+z)3
And Λ Ω0(1+z)3+1−Ω0, Ω0(1+z)3+1−Ω0
2.2.2. Bias Model
The bias of IR galaxiesrepresents their level of
orrelation
with the dark-matter density (cid:28)eld. It
an be expressed as
a fun
tion of the spatial s
ale, the redshift, and the wave-
lengthofobservation.Inthispaperandduetola
kofmea-
surements for the bias, we
onsider a simpli(cid:28)ed
onstant
b
bias .
b = 1 δj (k,ν,z) δρ(k,ν,z)
d
Figure4. Top: CIB Power spe
trum with a bias =b
µm j¯(k,ν,z) ρ¯(k,ν,z)
at Hers
hel/SPIRE wavelengths 500 (
ontinuous line), d
µm µm
350 (dashed line), and 250 (dottbed=-d1ashed line). j
Bottom: CIB Power spµe
mtrumwith a bias atµPmlan
k/HFI where d is the emijs¯sivity of the IR galaxiδejs per
CIB wavelengthµsm850 (
ontinuous line),1380 (dashed
omoving unit volume, d its mean level, and d its
ρ ρ¯
line), and 2097 (dotted-dashedline).
(cid:29)u
tuations. Similarly, is the dark matter density,
δρ
its mean value, and is the linear-theory dark-matter
density-(cid:28)eld (cid:29)u
tuation.
not been
onsidered for simpli
ity. We only
onsider the
linear
lustering i.e. IR galaxies as biased tra
ers of the
We have better knowledge of the bias for opti
al and
dark matter haloes, with a linear relation between the radio galaxies than for IR galaxies. Several studies have
dark-matter density-(cid:28)eld (cid:29)u
tuations and IR emissivity. been able to measure the bias for the opti
al sour
es.
b ∼ 3
As an example, a high bias ( ) has been found at
z ∼ 3
Wefollowthepres
riptionfromKnox et al.(2001).The for the Lyman-Break Galaxies (Steidel et al., 1998;
angular power spe
trum that
hara
terises the spatial dis- Giavalis
o et al., 1998; Adelberger et al., 1998)). It has
tribution of the (cid:29)u
tuations of the CIB
an be written as been found as well that the bias in
reases with redshift
dz dr both for the opti
al (Marinoni et al., 2006) and the radio
Cν = a2(z)¯j2(ν,z)b2(k,ν,z)P (k)| G2(z).
l r2 dz d M k=l/r (2) (Brand et al., 2003) populations. The opti
al or radio bias
Z
ould be misleading as a (cid:28)rst guess for the bias of IR
galaxies. IRAS has measured a low bias of IR galaxies
z ∼ 0
In the equation several
omdpzodnrean2t(sz)
an be identi(cid:28)ed, at (e.g. Saunders et al., 1992). Su
h a low bias
startingwithageometri
alone r2 dz (thesetermstake is expe
ted sin
e the starburst a
tivity in the massive
all the geometri
al¯jde((cid:27)νe,
zt)s into a

ount), followed by the dark-matter haloes in the lo
al universze is very small. But
galaxiesemissivbi(tky,ν,z) alreadydes
ribed in Se
t. 2.1.2, we expe
t a higher IR bias at higher , during the epo
h
then the bias , and (cid:28)nally the PpMow(ekr)|ks=pel/
rtrum of formation of galaxy
lusters. Indeed, Laga
hbe∼et1a.l7.
of dark-matter density (cid:29)u
tuationGs2t(ozd)ay ℓ and (2007) report the (cid:28)rst measureµmments of the bias,
thelineartheorygrowthfun
tion .Finally isthean- in the CIB (cid:29)u
tuations at 160 using Spitzer data. The
k =l/r
gularmultipole, in the Limber approximation , and LDP model indi
ates that galaxies dominating the 160
µ z ∼ 1
rthepropermotiondistan
e.Thewaythepowerspe
trum m anisotropies are at . This implies that infrared
hasbeenobtainedisdevelopedinthefollowingsubse
tions. galaxiesat high redshifts arebiased tra
ersof mass, unlike
N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground 5
Figure5.dCRledshℓif=t 1
0o0n0tribuµtKio2ns to the angular power
spe
trum dz at in fordi(cid:27)erentwavelengths:
µm µm µm
250 (
ontinuous line), 350 (dotted line), 550
µm µm
(dashed line), 850 (dotted-dashed line), and 1380
(long dashed line).
in the lo
al Universe. For an extensive review of the bias
problem see Lahav & Suto (2004).
The IR bias
ould have very
omplex fun
tional
k
dependen
es, namely with the spatial frequen
y , the
ν
redshift z, and the radiation frequen
y (for example
if di(cid:27)erent populations of galaxies with di(cid:27)erent SEDs
have di(cid:27)erent spatial distributions). However, for the
simulations, simpli(cid:28)ed guesses for the bias were used,
namely a
onstant bias of 1.5, 0.75, and 0.
C
l
Figures4showtheangularpowerspe
trum forsome
Hers
hel and Plan
k wavelben=gth1s. The pCow∝erbs2pe
tra are
ℓ
shown for a
onstant bias b.2Sin
e , the pre-
di
ted power spe
trum s
ales as .
2.3. Dis
ussion and impli
ations of the model
µm
The IR galaxy SED peaks near 80 . This
ombines
with the Doppler shift and
auses observations at di(cid:27)erent
wavelengths to probe di(cid:27)erent redshifts. Figure 5 shows
l = 1000
the
ontributions to the power spe
trum at for
di(cid:27)erent redshifts, normalized to unity. The
ontributions
ℓ
to the same
ome from higher redshift as wavelengths
in
rease.Theshorterwavelengthsprobethelowerredshifts
be
ause they are
lose to the maximum of the SED, while
the longer wavelengths probe the higher redshifts due to
the strong negative K-
orre
tion.
Figure6. Redshift
ontribution to the FIRB (top panels)
and its (cid:29)u
tuations (middle panels). Also shown are the
Figures 7 and 6 show the redshift
ontributions to the
redshift distributions of the dete
ted sour
es (bottom pan-
intensity of the CIB and to its integrated rms (cid:29)u
tuations
els) for a typi
al large Hers
hel/SPIRE deep survey (see
for Plan
k/HFI and Hers
hel/SPIRE, assuming sour
es 250µm 350µm 500µm
S > Sdet Sdet Se
t4.3).Fromtoptobottom: , and .
with have been removed (cid:21)
orresponds to
the sour
e dete
tion thresholds
omputed in Se
t. 4.3. We
see that the (cid:29)u
tuations and the FIRB are dominated
by sour
es at the same redshift. Therefore, studying the The amount of (cid:29)u
tuations that
ome from sour
es
(cid:29)u
tuations at di(cid:27)erent wavelengths will allow us to study at redshifts lower than 0.25 for the Plan
k/HFI
ase at
µm
the spatialdistribution ofthe sour
esformingthe FIRB at 350 is noti
eable from Fig. 7. This
ontrasts with
di(cid:27)erent redshifts. the Hers
hel/SPIRE predi
tions where the bulk of the
low-z sour
es
ontributing to the (cid:29)u
tuations in the
6 N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground
Figure7. Redshift
ontribution to the FIRB (top panels) and its (cid:29)u
tuations (bottom panels) for a Plan
k simulation
350µm 550µm 850µm 1380µm
(dz=0.25)at (top-left(cid:28)gure), (top-right(cid:28)gure), (bottom-left(cid:28)gure), (bottom-right(cid:28)gure).
b=1.5
The plots are for simulations with , whi
h sets the dete
tion limit (see Se
t 4.3).
Plan
k
ase are resolved. These individual dete
tions
al
ulated as explained in Se
t. 2.
with Hers
hel/SPIRE
ould allow their subtra
tion in the
Plan
k maps. A siµmmilar approa
h
ould be µusmed between To
reate the maps, two assumptions were made: (cid:28)rst
the Hers
hel 500 and the Plan
k 550
hannels, that all the galaxies share the same spatial distribution
although it is more marginal. Using information on the independently of their luminosities; se
ond that both IR
(cid:29)u
tuations at shorter wavelengths to remove the low-z and normal galaxies share the same spatial distribution.
(cid:29)u
tuationsfromlongerwavelengthmaps
ouldbeanother This se
ond assumption was made to avoid too many
approa
h to studying the (cid:29)u
tuations at high redshifts free parameters in the simulations, the
ontributions of
dire
tly. both populations being well separated in redshift this
assumption is a weak one.
AsimilarmodelhasbeendevelopedbyHKandrevisited
C
l
byKnox et al.µ(2m001).We
omparetheHKandour pre- The pro
ess for the
reation of a virtual
atalog
an be
di
tion atσ850 in Fig. 8 (for the
omparison, the same summarised as follows. For a given wavelength, we
reate
8
bias and is used). Our model is 2 times higher mainly the map as a superposition of maps at di(cid:27)erent redshifts
z = 0 z = 6
due to our higher predi
tion for the IR galaxy emissivity. from to . The separation in redshift sli
es
Similar results are found for other wavelengths. de
orrelates the emission from very distant regions of the
modelled volume of the universe. In order to do so, we di-
dz =0.1
vided the maps in sli
es
overing . We
an see the
size of these sli
es for di(cid:27)erent redshifts in Table 1. For
3. THE SIMULATIONS
all redshift ranges the size of the sli
es is bigger than the
The simulations were
omputed by an IDL program that measured
omoving
orrelationlengths (forall populations

al
ulates the dark-matter power spe
trum and spreads of galaxies). We then
onstru
t a brightness map for ea
h
the galaxiesin the map a

ording to their
orrelationwith redshift sli
e by adding: 1) a
onstant map with the mean
z
the dark-matter density (cid:28)eld. The CIB power spe
trum is surfa
e brightness predi
ted by the LDP model for that
N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground 7
µm
Figure9. Plan
k maps at 550 in MJy/sr with b=0
(left) and b=1.5(right). The maps simulatea regionof the
1024
sky of 49 square degrees with pixels of 25 ar
se
.
µm
Figure8.Ourpowerspe
trumat850 (
ontinuousline)
and that of Haiman & Knox(2000) (dashed line). The dif-
feren
es between both models arise from the di(cid:27)eren
es in
theemissivities(seeFig.1).ThelowerleveloftheHKpower
spe
trum
omesfromtheirloweremissivities.Theemissivi-
tiesofHKareatlowerzandthereforefavourlargerangular
s
ales for the power spe
trum relative to our model.
dz = 0.1 µm
Table 1. Physi
al size of the redshift sli
e (in Figure10. Hers
hel maps at 500 in MJy/srwith b=0
Mp
) for di(cid:27)erent z. (left) and b=1.5(right). The maps simulatea regionof the
1024
sky of 0.3 square degrees with pixels of 2 ar
se
. The
z 1.0-1.1 2.0-2.1 3.0-3.1 4.0-4.1
Rdz=0.1 small size of the maps makes it di(cid:30)
ult to appre
iate the
(Mp
) 233 139 93 67
e(cid:27)e
t of the large-s
ale
lustering.
Table 2. FWHM of the PSF for di(cid:27)erent wavelengths of b = 0,0.75,1.5
observation (in ar
se
onds) for all the simulated maps. were used for thµemsimulations ( µm ). Examples
of maps at 500 (Hers
hel) and 550 (Plan
k) made
(µm)
Wavelengths 350 550 850 1380 2097 with b=1.5 and b=0 are shown in Figs. 9 and 10. The
Plan
kHFIFWHM ((cid:17)) 300 300 300 330 480 di(cid:27)eren
e in the spatial
orrelationsiseasilynoti
ed in the
(µm)
Wavelengths 250 350 550 Plan
k simulations. On the other hand, the smaller size of
Hers
hel SPIREFWHM ((cid:17)) 17 24 35 the Hers
hel simulations makes it more di(cid:30)
ult to see the

orrelation.
The simulated maps and their asso-
sli
e, 2) a map of the (cid:29)u
tuations for the given bias pre-
z
iated
atalogs are publi
ly available at
di
ted by our spatial distribution model for that sli
e.
z http://www.ias.u-psud.fr/irgalaxies/simulations.php.
The (cid:29)u
tuations are not
orrelated between sli
es. The
brightness map is then
onverted into (cid:29)ux map. At ea
h
luminosity, this
an be
onverted into maps of numbers of
4. NOISE AND SOURCE DETECTION
sour
es. These numbers of sour
es are then redistributed
z
into smaller sli
es (inside the 0.1 sli
e) to re(cid:28)ne the lu- The simulations
an be used to test the dete
tion
apa-
minosity/(cid:29)uxrelation.Note that all sour
eshavethe same bilities of Plan
k/HFI and Hers
hel/SPIRE. For the (cid:28)rst
underlying low frequdezn
=y s0p.1atial distribution (but not the time these simulations use an empiri
al modµel that repro-
same positions) per sli
e. The position, luminos- du
esalltheobservational
onstraintsfrom5 mto1.3mm
ity, type (normal or starburst) and redshift of all sour
es and in
lude the spatial
orrelation between the IR galax-
are stored in a
atalog. Sin
e we know these four parame- ies and the dark mattLer>de1n0s9iLty⊙(cid:28)eld for galaxies up to
ters for all the sour
es, we
an now
reate maps of the sky very low luminosities ( ). They provide a useful
at any given wavelength.To simulate the observations,the toolforpreparingfutureobservationswithPlan
k/HFIand
map is
onvolved with the point spread fun
tion (PSF) of Hers
hel/SPIRE.
the
hosen instrument.
4.1. Dete
tion of bright sour
es
For the purpose of this paper we have
reated
Plan
k/HFI mapsat 350, 550, 850, 1380and 2097mi
rons As stated previously bright sour
es dominate the power
and Hers
hel/SPIRE maps at 250, 350 and 500 mi
rons. spe
trum of the FIRB (see Fig. 3). We therefore need
A des
ription of the wavelengths and spatial resolution to subtra
t them before studying the (cid:29)u
tuations in the
of the maps are given in Table 2. Three di(cid:27)erent biases ba
kground. In this se
tion we
on
entrate on dete
ting
8 N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground
σ
thres
them in three steps: 1) wavelet (cid:28)ltering, 2) dete
tion, 3) the di(cid:27)erent modify the rate of good-to-bad dete
-
σ 2σ
thres map
measurement of the (cid:29)ux. tions. For a low dete
tion threshold ( = , i.e. for
µm
example 290 mJy/pix at Plan
k 350 for a map with
b=0 and no instrumental noise), the number of bad dete
-
(cid:21) Wavelet (cid:28)ltering: Before trying to dete
t the sour
es tions
an be
ome biggerthan that of realdete
tions. For a
σ 3σ
thres map
we perform a wavelet transform of our simulated higherdete
tion threshold ( = i.e. 440mJy/pix
µm
maps with the (cid:16)atrou(cid:17) algorithm. We remove spatial at 350 ), we(cid:28)nd thatthe gooddete
tionsdominatethe
frequen
ies that are both higher and lower than the badones,butwedonotdete
tasmanyfaintsour
es.Thus
σ
thres
FWHM of the PSF. the number of false dete
tions depends strongly on .
Fordi(cid:27)erents
ienti(cid:28)
goals,it
anbeinterestingtousedif-
σ
thres
The small-s
ale (cid:28)ltering improves the estimation of ferent . Forexample,if weareinterestedin sear
hing
the position of the sour
es when the instrumental for obje
ts at high redshifts, we
ould allow our dete
tions
noise is in
luded in the simulations. In
ontrast to the tohave25%badsour
estobeabletodete
tsomeinterest-
z

onfusionnoise,theinstrumentalnoiseisnot
orrelated ingsour
esathigh .Forstudiesofstatisti
alpropertiesof
for neighbouring pixels. This dominates errors in thesour
es,it wouldbene
essaryto useastrongerthresh-
σ = 3σ ∼ 10%
thres map
estimating the position of the sour
es. old. For our purpose, we used ( of
false dete
tions).
The large-s
ale (cid:28)ltering
orre
ts for a bias in the
dete
tionalgorithm.The algorithmsear
hesforsour
es
using the absolute value of the pixel and not its value 4.2. Instrumental and
onfusion noises
relative to its environment. This biases the dete
tions
Instrumental and
onfusion noises have been studied both
towards sour
es in bright regions. The removal of the
separately and in
ombination in order to quantify their
large spatial (cid:29)u
tuations
orre
ts this e(cid:27)e
t.
relative
ontribution to the total noise. The estimated
instrumental noises per beam for Plan
k and Hers
hel are
The sele
tion of spatial frequen
ies to be used for the
given in Table 3. The instrumental noise per beam for
dete
tion has been manually optimised for ea
h map
Plan
kistheaverageoneovertheskyfora1-yearmission.
to a
hieve a maximum number of reliable dete
tions.
The instrumental noise per beam for Hers
hel is typi
al of
This treatment is similar to what was done in the
large surveys. We take the sensitivity of the so-
alled level
MIPS Spitzer maps (Dole et al., 2004). A
omprehen-
5 and level 6 of the S
ien
e A
tivity Group 1 (SAG 1) of
sive study of the appli
ation of the wavelet (cid:28)ltering
the SPIRE guaranteed time team.
te
hnique for the sour
e dete
tions at long wavelengths
for Plan
k and Hers
hel/SPIRE is beyond the s
ope
of this paper and has been fully dis
ussed in e.g. We studied the standard deviation of the measured
(cid:29)uxes in random positions for di(cid:27)erent maps. These
López-Caniego et al. (2006).
maps were one of instrumental noise, three with dif-
(cid:21) Dete
tion algorithm: The algorithm is based on the ferent bias (b=0, 0.75, 1.5) but without instrumental
(cid:16)(cid:28)nd(cid:17) routine of the DAOPHOT library. In the (cid:28)ltered noise, and
omplete maps
reated by adding the map
of instrumental noise to the three sour
e maps. We
all
image the algorithm sear
hes for peaks higher than a
σ

ertain threshold thres. It uses the PSF shape and the these maps hereafter instrumental-only,
onfusion-only,
and
omplete-maps. We (cid:28)t a Gaussian to the histogram
neighbouring pixels to analyse whether the peak is the
of the (cid:29)uxes measured in these random positions and

entre of a sour
e.

onsidered the standard deviation of this Gaussian as the
best estimate of the standard deviation of the photometry
(cid:21) Flux measurement: We developed a PSF (cid:28)tting al- σ
of a sour
e and therefore of the 1 instrumental,
on-
gorithm that we used in the original map (without
(cid:28)ltering)tomeasurethe(cid:29)uxofthesour
es.Wede
ided fusion,andtotalnoise.ResultsareshowninTables4and5.
whether the dete
tions are real or false by two
riteria:
1) proximity and 2) a

ura
y (see Se
t. 4.1.1). The
onfusion noise in
reases with the bias. This e(cid:27)e
t
is noti
eable for the Plan
k observations, but not for the
Hers
hel ones be
ause of the higher Hers
hel/SPIRE an-
gular resolution. Also, for the
onsidered Hers
hel/SPIRE
4.1.1. Bad dete
tions
surveys, the instrumental noise is always greater than the
A dete
tion is
onsidered good or bad based on two
onfusion noise. For Plan
k the
orrelation e(cid:27)e
t is more

riteria: 1) proximity with the position of an input sour
e noti
eableforlongerwavelengthssin
ethey probeprogres-
and2) a

ura
yof(cid:29)uxforthis sour
e.The formerrequires sively higher redshifts and therefore higher dark-matter
that our dete
tion is
loser than FWHM/5 to at least one power spe
tra, as dis
ussed in Se
t 2.3 (see Fig. 5).
(cid:16)neighbour(cid:17) sour
e in our
atalog. The latter requires that σ
C+I
the di(cid:27)eren
e between the (cid:29)ux of one of the (cid:16)neighbour(cid:17) σ2 The= tσo2ta+l σn2oise is
lose to the value
sour
es in the
atalog and that of the dete
ted sour
e has C+I C I (see Tables 4 and 5). For Plan
k at
µm µm
tobesmallerthanthe
onfusionand/orinstrumentalnoise short wavelengths (350 and 550 ), the
onfusion
(see Tables4 and5). We
onsiderthe dete
tion to be good noise is the dominant sour
e of noise. The instrumental
850µm
only if both
riteria are satis(cid:28)ed. noise be
omes dominant at for b=0 and b=0.75.
For longer wavelengths, it dominates for any bias. For
The dete
tion pro
ess also produ
es dete
tions that do Hers
hel the instrumental noise dominates the total noise
not
omply with these
riteria. We
an see in Fig. 12 how forboth theshallowanddeepsurveys.The
onfusionnoise
N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground 9
Table 3. Simulation input instrumental noise per pixel of
size equal to beam for Plan
k and for Hers
hel for a deep
and a shallow survey .
(µm)
Wavelengths HFI 350 550 850 1380 2097
σInst
(mJy) 31.30 20.06 14.07 8.43 6.38
(µm)
Wavelengths SPIRE 250 350 500
σInst
σInst Deep(mJy) 4.5 6.1 5.3
Shallow (mJy) 7.8 10.5 9.2
Table 4. Noise on the retrieved sour
es with only instru-
σ σ
I C
mental noise ( ),
onfusion noise ( ), and total noise
σ
C+I
( ) in mJy for Plan
k/HFI.
µm
Wavelengths HFI( ) 350 550 850 1380 2097
σI
σC 61.3 39.2 27.8 16.7 12.5
σC b=0 111.5 41.5 14.7 4.6 2.1
σCb=0.75 124 54.3 21.3 7.7 3.5
σσCσC+C+I+IbIb==b1=0..5075 111255638..76 677259...338 333803..44 111709..49 11533...482 Fbi=gu0rea1t13.50Sµtumd.yTohfe
hoomripzloentteanlessstrafoigrhPtllainne
km/HarFkIsw80it%h
b=1.5 188.2 95.3 46.7 21.1 14.4 of
ompleteness.
σ σ
I C
Table5.Instrumentalnoise( ),
onfusionnoise( )and
σ
C+I
total noise ( ) in mJy for Hers
hel/SPIRE.
(µm)
Wavelengths SPIRE 250 350 500
σI
Deep σI 8.7 11.3 10.1
σC Shallow 15 20.1 18.2
b=0,σ0.C7+5I, 1.5 4.6 6.5 5.5
Deep σC+I 9.8 12.3 11
Shallow 16 20.8 19
Figure12. Good dete
tions (thi
k line) vs bad dete
tions
(thinline)Left:Histogramofgoodandbaddete
tionsusing
is not strongly a(cid:27)e
ted by the bias be
ause of the small σthres
small (290 mJy). Right: Histogram of good and bad
FWHM of the PSF. σthres
dete
tions using higher (440 mJy) in the same map.
Both plots have been done using a Plan
k simulated map
b=0
with .
4.3. Completeness
Table 6.Completenesslimits(inmJy)forthePlan
k/HFI
The (cid:28)rst study of the point-sour
es dete
tion limit for CI CC
maps with instrumental noise ( ),
onfusion noise ( )
Plan
k was
arried out based on a generalisation of CC+I b
and both ( ). We
onsider =0, 0.75, and 1.5.
the Wiener (cid:28)ltering method (Bou
het & Gispert, 1999).
Re
ently López-Caniego et al. (2006) used the most re
ent µm
Wavelengths HFI( ) 350 550 850 1380 2097
availabletemplates of the mi
rowavesky and extragala
ti
CI =80%
point sour
e simulations, in
luding both the radio and CCCC==808%0% b=0 253166 115774 6100.85 6270 85.06
IR galaxies, to estimate the Plan
k dete
tion limits. CC =80%b=0.75 550 239.5 88.5 30.5 15.5
Here we revisit those results with new models for IR CC+I =80%b=1.5 684 300 121 40 24
galaxies and the last noise estimates for Plan
k/HFI and CC+I =80% b=0 560 234 126 71 52
Hers
hel/SPIRE. CC+I =80%b=0.75 607 290 141 74 55
b=1.5 709 360 171 80 58.5
N
A
For the study of the
ompleteness, a number of
sour
es of equal (cid:29)ux are randomnly distributed in the
µm
maps. Ea
h sour
e is pla
ed far enough from the other to example of the
ompletness at 350 is shown in Fig.
avoidtheseadditionalsour
es
ontributingtothe
onfusion 11. Results for all wavelengths are given in Tables 6 and
noise. The dete
tion and photometry of these sour
es is 7. They are
onsistent with the instrumental,
onfusion,

arriNedoutasdes
ribedatthebeginningofthese
tion.We and total noises given in Se
t. 4.2 and the
on
lusions
G

all the number of good dete
tions that
omply with from that se
tion remain valid for the
ompleteness. For
the (cid:16)proximityC(cid:17) and (cid:16)a

ura
y(cid:17)
riteria.CThe=
omNGple×ten10es0s simulated maps in
luding both extragala
ti
sour
es and
for this (cid:29)ux F is then
al
ulated as F NA . instrumental noise, we (cid:28)nd that the 80%
ompleteness
4−5σ
The
ompleteness of the dete
tions of sour
es for a given level
oin
ide with (cid:29)ux limits around .
(cid:29)ux depends on both the instrumental noise and the

onfusion noises. The results for the
ompleteness are Taking these 80%
ompletness limits as a dete
tion
∼
averaged over 3000 individual fake sour
es per (cid:29)ux. An threshold, the predi
iton for the number of sour
es de-
10 N. Fernandez-Conde: Simulations of the
osmi
IRand submmba
kground
|b| > 30o
Table 7. Completeness limits (in mJy) for the Using the average spe
trum of the HI-
orrelated
C
I
Hers
hel/SPIRE maps with instrumental noise ( ),
on- dust emission measured using FIRAS data, we
onverted
C C µ
C C+I
fusion noise ( ), and both ( ). the 100 m power spe
tra to the Plan
k wavelengths. For
(µm) the dis
ussion, we
onsidered both the total
irrus (cid:29)u
tu-
WavelengthCsIS=PI8R0%E 250 350 500 ations and 10% residual (cid:29)u
tuations. These 10%
ould be
Deep CI =80% 33 45.9 37.9 a
hievable with Plan
k in low dust-
olumn-density regions
ShalCloCw=80% 57.3 84.2 67.3
ontaining an
illary HI data.
CC+I =80% 35 32 27.4
Deep CC+I =80% 49.8 64.4 48.4 The CMB a
ts as ba
kground noise for the CFIRB.
Shallow 70 96.5 75.5
However, the CMB angular power spe
trum is known
to an a

ura
y of 1% or better (Plan
k-HFI web site:
http://www.plan
k.fr/). This
ombines with its well-
te
ted dire
tly by Hers×
h1e0l/5/SsPrIRE for thµemdeepe×r 1su05rv/esyr knownspe
traldependen
etoallowfora
leansubtra
tion

onsiderµemd here is ×8.1304/sr at 2µ5m0 , 1.1 of its
ontribution that in turn allows for dete
tions of
at 350 , and 1.8 at 500 . The fra
tion of Cl
the CFIRB even for wavelengths where the CMB
resolved CFIRB varies between 8 and 0.3% from 250 to
µm dominates. We
onsider for the rest of the dis
ussion a
500 .

onservative assumption, that is that the residual CMB
(cid:29)u
tuations are approximately 2%.
Theangularpowerspe
trumofIRgalaxiesis
omposed
5. CIB (cid:29)u
tuations
ofa
orrelatedand aPoissonianpart.Asdis
ussedin Se
t.
ThePlan
kandHers
hel/SPIREsurveysallowanunpre
e- 2.1, the
ontribution to the Poissonian part is dominated
dentedsear
hforCFIRB(cid:29)u
tuationsasso
iatedwithlarge- by relatively faint sour
es after subtra
ting the brightest
s
ale stru
ture and galaxy
lustering. Ba
kground (cid:29)u
tua- galaxies (see Fig. 3). We
onsider that we
an remove
tions probe the physi
s of galaxy
lustering over an en- sour
esbrighterthanour80%
ompletenessdete
tionlimit
semble of sour
es, with the bulk of the signal
ontribution (see Tables 6 and 7). For doing so, we use the te
hnique
originating from sour
es well below the dete
tion thresh- des
ribedin Se
t.4.1formeasuringthepositionand (cid:29)uxes
old. Thus a
omprehensive (cid:29)u
tuation analysis is an es- of the sour
es and on
e these are known we subtra
t a
sential
omplement to the study of individually dete
ted PSF with the measured (cid:29)ux from the map.
galaxies.Inthisse
tion,werestri
tourselvestopredi
tions
C
for Plan
k/HFI, ex
luding the 143 and 100 GHz
hannels. The
orrelated l is obtained as des
ribed in Se
t 2.1.
At these low frequen
ies, we are dominating by the non- For the relative error on the power spe
trum, we follow
thermal emissionof the radiosour
es(cid:21)that arenot in
lud- Knox (1995):
ing in our model (cid:21) and the Poisson term dominates the
δC 4π 0.5 2 0.5 Aσ2

lusteringterm(e.g.González-Nuevo et al.,2005).Also,we l = 1+ pix
ex
lude the Hers
hel/SPIRE
ase sin
e our simulations in- Cl (cid:18)A(cid:19) (cid:18)2l+1(cid:19) NClWl!

lude the
lustering of CIB sour
es in two di(cid:27)erent halos
2h 1h
(1h ),butnotthe
lusteriℓng&wi3t0h0in0thesamehalo( ).The σpix
term dominates for and will be a

urately where A is the observed area, the rms noise per
measuredbyHers
hel/SPIRE.O2hnlylarge-s
alesurveys
2ahn pixel (instrWumlental plus
onfusion), N the number of
put strong
onstraints on the term. Measuring the pixels, and theWwli=ndeo−wl2σfuB2n
tion for a map made with

lustering with CFIRB anisotropies is one of the goals of a Gaussian beam .
Plan
k/HFI.
5.1. Contributors to the angular power spe
trum 5.2. Dete
tability of CFIRB
orrelated anisotropies
C
l
Fromthefar-IRtothemillimeter,theskyismadeupofthe The study of the on di(cid:27)erent s
ales allows us to study
CFIRB and two other sour
es of signal, the gala
ti

irrus di(cid:27)erent aspe
ts of the physi
s of the environment of
and the CMB (we negle
t the SZ signal). Understanding IR galaxies (see Cooray & Sheth, 2002). Large s
ales
l < 100
our observations of the CFIRB requires understanding the ( ) give information on the
osmologi
al evolution

ontributions from these two
omponents whi
h a
t for us of primordial density (cid:29)u
tuations in the linear phase and
as foreground and ba
kground
ontamination. therefore on the
osmologi
al parameters. Intermediate
s
ales are mostly in(cid:29)uen
ed by the mass of dark halos
The gala
ti

irrus a
ts as foreground noise for the hosting sour
es, whi
h determines the bias parameter.
l > 3000
CFIRB. The non-white and non-Gaussian statisti
al prop- Small s
ales ( ) probe the distribution of sour
es
erties of its emission make it a very
omplex foreground in the dark-matter halos and therefore the non-linear
µm

omponent. The power spe
trum of the IRAS 100 evolution of the stru
tures. This non linear evolution was
emission is
hara
terised by a power law Gautier et al. not a

ounted for in our model.
(e.g. 1992). Here we
ompute the angular power spe
trum
of the dust emission following Miville-Des
henes et al. We
an see in Fig. 13 the di(cid:27)erent
ontributions to the
C C b = 1
l l
(2007). These authors analysed the statisti
al properties for Plan
k/HFI: the
orrelated CFIRB with
µ b = 3 ∆ℓ/ℓ
of the
irrus emission at 100 m using the IRAS/IRIS and with their respe
tive error bars ( =0.5),
data. We used their power spe
trum normalization and Poissonian (cid:29)u
tuations, dust, and CMB
ontributions.
µ C
l
slope (varying with the mean dust intensity at 100 m). The dust and CMB are plotted both before and after