Simulations of the cosmic infrared and submillimeter background for future large surveys: I. Presentation and first application to Herschel/SPIRE and Planck/HFI
aa r X i v : . [ a s t r o - ph ] J a n Astronomy & Astrophysi s manus ript no. 8188 (cid:13) λ ≥ µm ) is thereli emission of the formation and evolution of galaxies.The (cid:28)rst observational eviden e of this ba kground wasreported by Puget et al. (1996) and then on(cid:28)rmed byHauser et al. (1998) and Fixsen et al. (1998). The dis- overy of a surprisingly high amount of energy in theCIB has shown the importan e of studying its sour esto understand how the bulk of stars was formed in theUniverse. Deep osmologi al surveys have been arriedout thanks to ISO (see Genzel & Cesarsky, 2000; Elbaz,2005, for reviews) mainly at 15 µm with ISOCAM (e.g.Elbaz et al., 2002); at 90 and 170 µm with ISOPHOT(e.g. Dole et al., 2001); to SPITZER at 24, 70, and160 µm (e.g. Papovi h et al., 2004; Dole et al., 2004)and to ground-based instruments su h as SCUBA (e.g.Holland et al., 1998) and MAMBO (e.g. Bertoldi et al.,2000) at 850 and 1300 µm , respe tively. These surveyshave allowed for a better understanding of the CIB andits sour es (see Laga he et al., 2005, for a general review).Some of the results in lude: the energy of the CIB isdominated by starbursts although AGN (a tive gala ti nu leus) ontribute too, and the dominant ontributors tothe energy output are the LIRGs (luminous IR galaxies) atSend o(cid:27)print requests to: N. Fernandez-Conde, G. Laga he z ∼ and ULIRGs (ultra luminous IR galaxies) at z ∼ − .Determination of the CIB by the COBE satellitehas been hindered by the a ura y of subtra ting theforeground by only providing just upper limits at 12, 25,and 60 µm (Hauser et al., 1998), lower limit has beenderived at 24 µm by Papovi h et al. (2004) as well as the ontribution of 24 µm galaxies to the ba kground at 70 and160 µm (Dole et al., 2006). The ontribution of the galaxiesdown to 60 µJy at 24 µm is at least 79% of the 24 µm ba kground, and 80% of the 70 and 160 µm ba kground.For longer wavelengths, re ent studies have investigatedthe ontribution of populations sele ted in the near-IR tothe far-infrared ba kground (FIRB, λ > µm ): 3.6 µm sele ted sour es to the 850 µm ba kground (Wang et al.,2006) and 8 µm and 24 µm sele ted sour es to the 850 µm and 450 µm ba kgrounds (Dye et al., 2006). Similarstudies with Plan k and Hers hel will provide even moreeviden e of the nature of the FIRB sour es.Studying orrelations in the spatial distribution of IRgalaxies as a fun tion of redshift is an essential observation(parallel to the studies of individual high-redshift, infrared,luminous galaxies), to understand the underlying s enarioand physi s of galaxy formation and evolution. A (cid:28)rst studyhas been done using the 850 µ m galaxies (Blain et al.,2004). Although the number of sour es is quite small, they N. Fernandez-Conde: Simulations of the osmi IR and submm ba kground(cid:28)nd eviden e that submillimiter galaxies are linked to theformation of massive galaxies in dense environments des-tined to be ome ri h lusters. This has now been dire tlysupported by the dete tion of the lustering of high-redshift24 µ m sele ted ULIRGs and HyperLIRGs (Farrah et al.,2006; Maglio hetti et al., 2007). Studying orrelationswith individual IR galaxies is very hard due to either high onfusion noises, instrumental noises, or small (cid:28)elds ofobservation. It has been shown that the IR-ba kgroundanisotropies ould provide information on the orrelationbetween the sour es of the CIB and dark matter for large-s ale stru tures (Knox et al., 2001; Haiman & Knox, 2000,hereafter HK) and on the large-s ale stru ture evolution.First studies at long wavelengths have only dete ted theshot-noise omponent of the (cid:29)u tuations: Laga he & Puget(2000) at 170 µm , Matsuhara et al. (2000) at 90 and 170 µm , Miville-Des hênes et al. (2001) at 60 and 100 µm .Laga he et al. (2007) and Grossan & Smoot (2007) re-port (cid:28)rst dete tions of the orrelated omponent usingSpitzer/MIPS data at 160 µm . Laga he et al. (2007)measured a linear bias b ∼ . .Future observations by Hers hel and Plan k will allowus to probe the lustering of IR and submm galaxies.Nevertheless these experiments will be limited, the onfu-sion and instrumental noises will hinder dete tions of faintindividual galaxies. Clustering thus has to be analysed inthe ba kground (cid:29)u tuations (e.g. Negrello et al., 2007).The need for a prior understanding of what ould be doneby these experiments has motivated us to develop a set ofrealisti simulations of the IR and sub-mm sky.In Se t. 2 we present the model on whi h are basedour simulations. In Se t. 3 we dis uss how the simulationsare done and present a set of simulated sky maps andtheir orresponding atalogs. Di(cid:27)erent atalogs are reatedfor 3 di(cid:27)erent levels of orrelation between the IR galaxyemissivity and the dark-matter (cid:29)u tuation density (cid:28)eld(strong, medium, and no orrelation). For ea h of these atalogs, we an reate maps of the sky at any given IRwavelength and simulate how di(cid:27)erent instruments willsee them. We fo us in this paper on Plan k/HFI andHers hel/SPIRE. In Se t. 4 we use the simulated maps togive predi tions for the onfusion noise, the ompleteness,and the dete tion limits for ea h of the study ases,in luding the instrumental noise. In Se t. 5 we present thepower spe tra of the CIB anisotropies for Plan k/HFI anddis uss their dete tability against the signi(cid:28) ant sour es of ontamination (shot noise, irrus, and osmi mi rowaveba kground (CMB)).Throughout the paper the osmologi al parameters wereset to h = 0 . , Ω Λ = 0 . , Ω m = 0 . . For the dark-matterlinear lustering we set the normalization to σ = 0 . µm and 1 mm. These are the spe tral energy distributionof the CIB and its (cid:29)u tuations, galaxy luminosity fun tionsand their redshift evolution, as well as the existing sour e ounts and redshift distributions.The luminosity fun tion of IR galaxies was modelled bya bimodal star-formation pro ess: one asso iated with thepassive phase of galaxy evolution (normal galaxies) andone asso iated with the starburst phase, mostly triggeredby merging and intera tions (starburst galaxies). Unlike forthe starburst galaxies, the normal galaxy ontribution tothe luminosity fun tion was onsidered mostly un hangedwith redshift. The spe tral energy distribution (SED) hanges with the luminosity of the sour e but is assumed onstant with redshift for both populations in this simplemodel.This model (cid:28)ts all the experimental data and has pre-di ted that LIRGs ( < L IR < ) dominate at z ≃ . − . and that ULIRGs/HLIRGs ( L IR > )dominate at z ≃ − the energy distribution of the CIB.One example of the agreement between the model and theobservations is shown in Fig. 2.2.1.1. Number ounts and CIB (cid:29)u tuationsTo illustrate the interest of studying the osmi ba k-ground (cid:29)u tuations in the far-IR and submm domains, weuse a simplisti approa h for the number ounts, followingLaga he & Puget (2000). The sour e number ounts an bes hemati ally represented by a power law: N ( S > S ) = N (cid:18) SS (cid:19) − α (1)where we set S to be the dete tion limit for the sour esand N the number of sour es with (cid:29)ux larger than S .In a Eu lidean Universe with uniform density of thesour es α = 1 . . In the far-IR and submm, a steeper slopeis observed with α = 2 − in the regime where negativeK- orre tion dominates. As an example, ISO observationsfound a slope of α = 2 . at 170 µm (Dole et al., 2001).Obviously, the number ounts need to (cid:29)atten for low (cid:29)uxesto ensure that the CIB remains (cid:28)nite. For the rest of thedis ussion we will assume that α = 0 for S < S ∗ . The totalintensity of the CIB omposed by all the sour es up to S max is given by: I CIB = Z S max S dNdS dS.
For the Eu lidean ase the CIB intensity is dominatedby sour es near S ∗ .Flu tuations from sour es below the dete tion limit S are given by σ = Z S S dNdS dS. . Fernandez-Conde: Simulations of the osmi IR and submm ba kground 3Figure 1. Emissivities omputed using the LDP model at(observed) 250 µm ( ontinuous line), 450 µm (long-dashedline), and 850 µm (dotted-dashed line). The emissivity fromHK at 450 µm (short-dashed line) is shown for omparison. Using dNdS given by Eq. 1 we get σ = α − α N S " − (cid:18) S ∗ S (cid:19) − α . For α > CIB (cid:29)u tuations are dominated by sour es lose to S ∗ so that the same sour es dominate both theFIRB and its (cid:29)u tuations. Therefore by studying the (cid:29)u -tuations of the FIRB, we are also studying the sour es thatform the bulk of the ontribution to the FIRB. We an he k this on lusion with the number ounts from the LDPmodel. Figure 3 shows that the same sour es dominate theba kground and the (cid:29)u tuations, but only for faint sour es(for example S . mJy). Therefore, it is ne essaryto subtra t bright sour es prior to any (cid:29)u tuation analysissin e they would otherwise dominate the (cid:29)u tuations.2.1.2. IR galaxy emissivityFor the purpose of the model we need to ompute themean IR galaxy emissivity per unit of omoving volume [ W/M pc /Hz/sr ] . It is de(cid:28)ned as j d ( ν, z ) = (1 + z ) R L bol L ν ′ = ν (1+ z ) dNdln ( L bol ) dln ( L bol ) where L is the luminosity (in W/Hz/sr ), dNdln ( L bol ) isthe omoving luminosity fun tion (in M pc − ), and ν theobserved frequen y. We ompute j d using the SEDs andluminosity fun tion from the LDP model whi h assumesthat the SED depends only on L bol . The resulting j d isdi(cid:27)erent from what is used by former approa hes (HK,Knox et al., 2001). We an see the di(cid:27)eren e between theemissivity from our model and that of HK in Fig. 1. The rude model used for the emissivities by HK gives mu hlower emissivities than ours.2.2. IR galaxy spatial distributionAny model trying to a ount for CIB (cid:29)u tuations mustdes ribe the statisti al properties of the spatial distribution Figure 2. Comparison of the observed sour e ounts (datapoints) and model predi tions ( ontinuous lines). Upper left24 µ m, Upper right 70 µ m, Lower left 160 µ m, Lower right850 µ m.Figure 3. Contributions of the sour es of (cid:29)ux S (in Jy)per Log interval of S to the ba kground (dotted line, righty axis) and (cid:29)u tuations ( ontinuous line, left y axis) at µm .of the sour es. The absen e of a ompletely developedtheoreti al model for the distribution of the whole IRgalaxy populations makes the empiri al modelling of dif-ferent distributions for the sour es of the CIB ne essary inorder to prepare future observations. We used an empiri aldes ription for the spatial distribution of these sour es,whi h has been used to reate the simulated sky maps.The LDP model did not address the spatial distributionproblem due to the la k of onstraints at the time it wasbuilt. This is still mostly the ase at the time of writingthis work. The simulations by Dole et al. (2003) did notimplement any orrelation between IR galaxies and usedan un orrelated random distribution. However, sin e futureexperiments su h as Hers hel and Plan k will be able todete t large-s ale IR galaxy orrelations ( ℓ . ), amodel addressing this problem has be ome ne essary.Hers hel, with its high angular resolution, is expe tedto also probe orrelations between galaxies in the samedark-matter haloes but in this study this orrelation has N. Fernandez-Conde: Simulations of the osmi IR and submm ba kgroundFigure 4. Top: CIB Power spe trum with a bias b = 1 at Hers hel/SPIRE wavelengths 500 µm ( ontinuous line),350 µm (dashed line), and 250 µm (dotted-dashed line).Bottom: CIB Power spe trum with a bias b = 1 at Plan k/HFICIB wavelengths 850 µm ( ontinuous line),1380 µm (dashedline), and 2097 µm (dotted-dashed line).not been onsidered for simpli ity. We only onsider thelinear lustering i.e. IR galaxies as biased tra ers of thedark matter haloes, with a linear relation between thedark-matter density-(cid:28)eld (cid:29)u tuations and IR emissivity.We follow the pres ription from Knox et al. (2001). Theangular power spe trum that hara terises the spatial dis-tribution of the (cid:29)u tuations of the CIB an be written as C νl = Z dzr drdz a ( z )¯ j d ( ν, z ) b ( k, ν, z ) P M ( k ) | k = l/r G ( z ) . (2)In the equation several omponents an be identi(cid:28)ed,starting with a geometri al one dzr drdz a ( z ) (these terms takeall the geometri al e(cid:27)e ts into a ount), followed by thegalaxies emissivity ¯ j d ( ν, z ) already des ribed in Se t. 2.1.2,then the bias b ( k, ν, z ) , and (cid:28)nally the power spe trumof dark-matter density (cid:29)u tuations today P M ( k ) | k = l/r andthe linear theory growth fun tion G ( z ) . Finally ℓ is the an-gular multipole, in the Limber approximation k = l/r , andr the proper motion distan e. The way the power spe trumhas been obtained is developed in the following subse tions. 2.2.1. Dark-matter power spe trumThe power spe trum of the dark-matter distribution at z =0 an be written as P M ( k ) ∝ kT ( k ) (3)where T ( k, t ) is the transfer fun tion for a old dark-matter universe (Bardeen et al., 1986). The linear theorygrowth fun tion G ( z ) writes as G ( z ) = g (Ω( z ) , Ω Λ ( z )) g (Ω , Ω Λ0 )(1 + z ) (4)with g [Ω( z ) , Ω Λ ( z )] = 52 Ω( z ) × h Ω( z ) / − Ω Λ ( z )+ (cid:18) z ) (cid:19) (cid:18) Λ ( z ) (cid:19)(cid:21) − . And Ω Λ ( z ) = − Ω Ω (1+ z ) +1 − Ω , Ω( z ) = Ω (1+ z ) Ω (1+ z ) +1 − Ω b . δj d ( k, ν, z )¯ j d ( k, ν, z ) = b δρ ( k, ν, z )¯ ρ ( k, ν, z ) where j d is the emissivity of the IR galaxies per omoving unit volume, ¯ j d its mean level, and δj d its(cid:29)u tuations. Similarly, ρ is the dark matter density, ¯ ρ its mean value, and δρ is the linear-theory dark-matterdensity-(cid:28)eld (cid:29)u tuation.We have better knowledge of the bias for opti al andradio galaxies than for IR galaxies. Several studies havebeen able to measure the bias for the opti al sour es.As an example, a high bias ( b ∼ ) has been found at z ∼ for the Lyman-Break Galaxies (Steidel et al., 1998;Giavalis o et al., 1998; Adelberger et al., 1998)). It hasbeen found as well that the bias in reases with redshiftboth for the opti al (Marinoni et al., 2006) and the radio(Brand et al., 2003) populations. The opti al or radio bias ould be misleading as a (cid:28)rst guess for the bias of IRgalaxies. IRAS has measured a low bias of IR galaxiesat z ∼ (e.g. Saunders et al., 1992). Su h a low biasis expe ted sin e the starburst a tivity in the massivedark-matter haloes in the lo al universe is very small. Butwe expe t a higher IR bias at higher z , during the epo hof formation of galaxy lusters. Indeed, Laga he et al.(2007) report the (cid:28)rst measurements of the bias, b ∼ . in the CIB (cid:29)u tuations at 160 µm using Spitzer data. TheLDP model indi ates that galaxies dominating the 160 µ m anisotropies are at z ∼ . This implies that infraredgalaxies at high redshifts are biased tra ers of mass, unlike. Fernandez-Conde: Simulations of the osmi IR and submm ba kground 5Figure 5. Redshift ontributions to the angular powerspe trum dC l dz at ℓ = 1000 in µK for di(cid:27)erent wavelengths:250 µm ( ontinuous line), 350 µm (dotted line), 550 µm (dashed line), 850 µm (dotted-dashed line), and 1380 µm (long dashed line).in the lo al Universe. For an extensive review of the biasproblem see Lahav & Suto (2004).The IR bias ould have very omplex fun tionaldependen es, namely with the spatial frequen y k , theredshift z, and the radiation frequen y ν (for exampleif di(cid:27)erent populations of galaxies with di(cid:27)erent SEDshave di(cid:27)erent spatial distributions). However, for thesimulations, simpli(cid:28)ed guesses for the bias were used,namely a onstant bias of 1.5, 0.75, and 0.Figures 4 show the angular power spe trum C l for someHers hel and Plan k wavelengths. The power spe tra areshown for a onstant bias b = 1 . Sin e C ℓ ∝ b , the pre-di ted power spe trum s ales as b .2.3. Dis ussion and impli ations of the modelThe IR galaxy SED peaks near 80 µm . This ombineswith the Doppler shift and auses observations at di(cid:27)erentwavelengths to probe di(cid:27)erent redshifts. Figure 5 showsthe ontributions to the power spe trum at l = 1000 fordi(cid:27)erent redshifts, normalized to unity. The ontributionsto the same ℓ ome from higher redshift as wavelengthsin rease. The shorter wavelengths probe the lower redshiftsbe ause they are lose to the maximum of the SED, whilethe longer wavelengths probe the higher redshifts due tothe strong negative K- orre tion.Figures 7 and 6 show the redshift ontributions to theintensity of the CIB and to its integrated rms (cid:29)u tuationsfor Plan k/HFI and Hers hel/SPIRE, assuming sour eswith S > S det have been removed (cid:21) S det orresponds tothe sour e dete tion thresholds omputed in Se t. 4.3. Wesee that the (cid:29)u tuations and the FIRB are dominatedby sour es at the same redshift. Therefore, studying the(cid:29)u tuations at di(cid:27)erent wavelengths will allow us to studythe spatial distribution of the sour es forming the FIRB atdi(cid:27)erent redshifts. Figure 6. Redshift ontribution to the FIRB (top panels)and its (cid:29)u tuations (middle panels). Also shown are theredshift distributions of the dete ted sour es (bottom pan-els) for a typi al large Hers hel/SPIRE deep survey (seeSe t 4.3). From top to bottom: µm , µm and µm .The amount of (cid:29)u tuations that ome from sour esat redshifts lower than 0.25 for the Plan k/HFI ase at350 µm is noti eable from Fig. 7. This ontrasts withthe Hers hel/SPIRE predi tions where the bulk of thelow-z sour es ontributing to the (cid:29)u tuations in the N. Fernandez-Conde: Simulations of the osmi IR and submm ba kgroundFigure 7. Redshift ontribution to the FIRB (top panels) and its (cid:29)u tuations (bottom panels) for a Plan k simulation(dz=0.25) at µm (top-left (cid:28)gure), µm (top-right (cid:28)gure), µm (bottom-left (cid:28)gure), µm (bottom-right (cid:28)gure).The plots are for simulations with b = 1 . , whi h sets the dete tion limit (see Se t 4.3).Plan k ase are resolved. These individual dete tionswith Hers hel/SPIRE ould allow their subtra tion in thePlan k maps. A similar approa h ould be used betweenthe Hers hel 500 µm and the Plan k 550 µm hannels,although it is more marginal. Using information on the(cid:29)u tuations at shorter wavelengths to remove the low-z(cid:29)u tuations from longer wavelength maps ould be anotherapproa h to studying the (cid:29)u tuations at high redshiftsdire tly.A similar model has been developed by HK and revisitedby Knox et al. (2001). We ompare the HK and our C l pre-di tion at 850 µm in Fig. 8 (for the omparison, the samebias and σ is used). Our model is 2 times higher mainlydue to our higher predi tion for the IR galaxy emissivity.Similar results are found for other wavelengths.3. THE SIMULATIONSThe simulations were omputed by an IDL program that al ulates the dark-matter power spe trum and spreadsthe galaxies in the map a ording to their orrelation withthe dark-matter density (cid:28)eld. The CIB power spe trum is al ulated as explained in Se t. 2.To reate the maps, two assumptions were made: (cid:28)rstthat all the galaxies share the same spatial distributionindependently of their luminosities; se ond that both IRand normal galaxies share the same spatial distribution.This se ond assumption was made to avoid too manyfree parameters in the simulations, the ontributions ofboth populations being well separated in redshift thisassumption is a weak one.The pro ess for the reation of a virtual atalog an besummarised as follows. For a given wavelength, we reatethe map as a superposition of maps at di(cid:27)erent redshiftsfrom z = 0 to z = 6 . The separation in redshift sli esde orrelates the emission from very distant regions of themodelled volume of the universe. In order to do so, we di-vided the maps in sli es overing dz = 0 . . We an see thesize of these sli es for di(cid:27)erent redshifts in Table 1. Forall redshift ranges the size of the sli es is bigger than themeasured omoving orrelation lengths (for all populationsof galaxies). We then onstru t a brightness map for ea hredshift sli e by adding: 1) a onstant map with the meansurfa e brightness predi ted by the LDP model for that z . Fernandez-Conde: Simulations of the osmi IR and submm ba kground 7Figure 8. Our power spe trum at 850 µm ( ontinuous line)and that of Haiman & Knox (2000) (dashed line). The dif-feren es between both models arise from the di(cid:27)eren es inthe emissivities (see Fig. 1). The lower level of the HK powerspe trum omes from their lower emissivities. The emissivi-ties of HK are at lower z and therefore favour larger angulars ales for the power spe trum relative to our model.Table 1. Physi al size of the redshift sli e dz = 0 . (inMp ) for di(cid:27)erent z.z 1.0-1.1 2.0-2.1 3.0-3.1 4.0-4.1 R dz =0 . (Mp ) 233 139 93 67Table 2. FWHM of the PSF for di(cid:27)erent wavelengths ofobservation (in ar se onds) for all the simulated maps.Wavelengths ( µm )
350 550 850 1380 2097Plan k HFI FWHM ((cid:17)) 300 300 300 330 480Wavelengths ( µm )
250 350 550Hers hel SPIRE FWHM ((cid:17)) 17 24 35sli e, 2) a map of the (cid:29)u tuations for the given bias pre-di ted by our spatial distribution model for that z sli e.The (cid:29)u tuations are not orrelated between z sli es. Thebrightness map is then onverted into (cid:29)ux map. At ea hluminosity, this an be onverted into maps of numbers ofsour es. These numbers of sour es are then redistributedinto smaller z sli es (inside the 0.1 sli e) to re(cid:28)ne the lu-minosity/(cid:29)ux relation. Note that all sour es have the sameunderlying low frequen y spatial distribution (but not thesame positions) per dz = 0 . sli e. The position, luminos-ity, type (normal or starburst) and redshift of all sour esare stored in a atalog. Sin e we know these four parame-ters for all the sour es, we an now reate maps of the skyat any given wavelength. To simulate the observations, themap is onvolved with the point spread fun tion (PSF) ofthe hosen instrument.For the purpose of this paper we have reatedPlan k/HFI maps at 350, 550, 850, 1380 and 2097 mi ronsand Hers hel/SPIRE maps at 250, 350 and 500 mi rons.A des ription of the wavelengths and spatial resolutionof the maps are given in Table 2. Three di(cid:27)erent biases Figure 9. Plan k maps at 550 µm in MJy/sr with b=0(left) and b=1.5 (right). The maps simulate a region of thesky of 49 square degrees with pixels of 25 ar se .Figure 10. Hers hel maps at 500 µm in MJy/sr with b=0(left) and b=1.5 (right). The maps simulate a region of thesky of 0.3 square degrees with pixels of 2 ar se . Thesmall size of the maps makes it di(cid:30) ult to appre iate thee(cid:27)e t of the large-s ale lustering.were used for the simulations ( b = 0 , . , . ). Examplesof maps at 500 µm (Hers hel) and 550 µm µ m to 1.3 mmand in lude the spatial orrelation between the IR galax-ies and the dark matter density (cid:28)eld for galaxies up tovery low luminosities ( L > L ⊙ ). They provide a usefultool for preparing future observations with Plan k/HFI andHers hel/SPIRE.4.1. Dete tion of bright sour esAs stated previously bright sour es dominate the powerspe trum of the FIRB (see Fig. 3). We therefore needto subtra t them before studying the (cid:29)u tuations in theba kground. In this se tion we on entrate on dete ting N. Fernandez-Conde: Simulations of the osmi IR and submm ba kgroundthem in three steps: 1) wavelet (cid:28)ltering, 2) dete tion, 3)measurement of the (cid:29)ux.(cid:21) Wavelet (cid:28)ltering: Before trying to dete t the sour eswe perform a wavelet transform of our simulatedmaps with the (cid:16)atrou(cid:17) algorithm. We remove spatialfrequen ies that are both higher and lower than theFWHM of the PSF.The small-s ale (cid:28)ltering improves the estimation ofthe position of the sour es when the instrumentalnoise is in luded in the simulations. In ontrast to the onfusion noise, the instrumental noise is not orrelatedfor neighbouring pixels. This dominates errors inestimating the position of the sour es.The large-s ale (cid:28)ltering orre ts for a bias in thedete tion algorithm. The algorithm sear hes for sour esusing the absolute value of the pixel and not its valuerelative to its environment. This biases the dete tionstowards sour es in bright regions. The removal of thelarge spatial (cid:29)u tuations orre ts this e(cid:27)e t.The sele tion of spatial frequen ies to be used for thedete tion has been manually optimised for ea h mapto a hieve a maximum number of reliable dete tions.This treatment is similar to what was done in theMIPS Spitzer maps (Dole et al., 2004). A omprehen-sive study of the appli ation of the wavelet (cid:28)lteringte hnique for the sour e dete tions at long wavelengthsfor Plan k and Hers hel/SPIRE is beyond the s opeof this paper and has been fully dis ussed in e.g.López-Caniego et al. (2006).(cid:21) Dete tion algorithm: The algorithm is based on the(cid:16)(cid:28)nd(cid:17) routine of the DAOPHOT library. In the (cid:28)lteredimage the algorithm sear hes for peaks higher than a ertain threshold σ thres . It uses the PSF shape and theneighbouring pixels to analyse whether the peak is the entre of a sour e.(cid:21) Flux measurement: We developed a PSF (cid:28)tting al-gorithm that we used in the original map (without(cid:28)ltering) to measure the (cid:29)ux of the sour es. We de idedwhether the dete tions are real or false by two riteria:1) proximity and 2) a ura y (see Se t. 4.1.1).4.1.1. Bad dete tionsA dete tion is onsidered good or bad based on two riteria: 1) proximity with the position of an input sour eand 2) a ura y of (cid:29)ux for this sour e. The former requiresthat our dete tion is loser than FWHM/5 to at least one(cid:16)neighbour(cid:17) sour e in our atalog. The latter requires thatthe di(cid:27)eren e between the (cid:29)ux of one of the (cid:16)neighbour(cid:17)sour es in the atalog and that of the dete ted sour e hasto be smaller than the onfusion and/or instrumental noise(see Tables 4 and 5). We onsider the dete tion to be goodonly if both riteria are satis(cid:28)ed.The dete tion pro ess also produ es dete tions that donot omply with these riteria. We an see in Fig. 12 how the di(cid:27)erent σ thres modify the rate of good-to-bad dete -tions. For a low dete tion threshold ( σ thres = σ map , i.e. forexample 290 mJy/pix at Plan k 350 µm for a map withb=0 and no instrumental noise), the number of bad dete -tions an be ome bigger than that of real dete tions. For ahigher dete tion threshold ( σ thres = σ map i.e. 440 mJy/pixat 350 µm ), we (cid:28)nd that the good dete tions dominate thebad ones, but we do not dete t as many faint sour es. Thusthe number of false dete tions depends strongly on σ thres .For di(cid:27)erent s ienti(cid:28) goals, it an be interesting to use dif-ferent σ thres . For example, if we are interested in sear hingfor obje ts at high redshifts, we ould allow our dete tionsto have 25% bad sour es to be able to dete t some interest-ing sour es at high z . For studies of statisti al properties ofthe sour es, it would be ne essary to use a stronger thresh-old. For our purpose, we used σ thres = 3 σ map ( ∼ offalse dete tions).4.2. Instrumental and onfusion noisesInstrumental and onfusion noises have been studied bothseparately and in ombination in order to quantify theirrelative ontribution to the total noise. The estimatedinstrumental noises per beam for Plan k and Hers hel aregiven in Table 3. The instrumental noise per beam forPlan k is the average one over the sky for a 1-year mission.The instrumental noise per beam for Hers hel is typi al oflarge surveys. We take the sensitivity of the so- alled level5 and level 6 of the S ien e A tivity Group 1 (SAG 1) ofthe SPIRE guaranteed time team.We studied the standard deviation of the measured(cid:29)uxes in random positions for di(cid:27)erent maps. Thesemaps were one of instrumental noise, three with dif-ferent bias (b=0, 0.75, 1.5) but without instrumentalnoise, and omplete maps reated by adding the mapof instrumental noise to the three sour e maps. We allthese maps hereafter instrumental-only, onfusion-only,and omplete-maps. We (cid:28)t a Gaussian to the histogramof the (cid:29)uxes measured in these random positions and onsidered the standard deviation of this Gaussian as thebest estimate of the standard deviation of the photometryof a sour e and therefore of the 1 σ instrumental, on-fusion, and total noise. Results are shown in Tables 4 and 5.The onfusion noise in reases with the bias. This e(cid:27)e tis noti eable for the Plan k observations, but not for theHers hel ones be ause of the higher Hers hel/SPIRE an-gular resolution. Also, for the onsidered Hers hel/SPIREsurveys, the instrumental noise is always greater than the onfusion noise. For Plan k the orrelation e(cid:27)e t is morenoti eable for longer wavelengths sin e they probe progres-sively higher redshifts and therefore higher dark-matterpower spe tra, as dis ussed in Se t 2.3 (see Fig. 5).The total noise σ C + I is lose to the value σ C + I = σ C + σ I (see Tables 4 and 5). For Plan k atshort wavelengths (350 µm and 550 µm ), the onfusionnoise is the dominant sour e of noise. The instrumentalnoise be omes dominant at µm for b=0 and b=0.75.For longer wavelengths, it dominates for any bias. ForHers hel the instrumental noise dominates the total noisefor both the shallow and deep surveys. The onfusion noise. Fernandez-Conde: Simulations of the osmi IR and submm ba kground 9Table 3. Simulation input instrumental noise per pixel ofsize equal to beam for Plan k and for Hers hel for a deepand a shallow survey .Wavelengths HFI ( µm )
350 550 850 1380 2097 σ Inst (mJy) 31.30 20.06 14.07 8.43 6.38Wavelengths SPIRE ( µm )
250 350 500 σ Inst
Deep (mJy) 4.5 6.1 5.3 σ Inst
Shallow (mJy) 7.8 10.5 9.2Table 4. Noise on the retrieved sour es with only instru-mental noise ( σ I ), onfusion noise ( σ C ), and total noise( σ C + I ) in mJy for Plan k/HFI.Wavelengths HFI ( µm ) 350 550 850 1380 2097 σ I σ C b=0 111.5 41.5 14.7 4.6 2.1 σ C b=0.75 124 54.3 21.3 7.7 3.5 σ C b=1.5 158 79.8 30.4 10.9 5.4 σ C + I b=0 126.7 62.3 33 17.4 13.2 σ C + I b=0.75 153.6 75.3 38.4 19 13.8 σ C + I b=1.5 188.2 95.3 46.7 21.1 14.4Table 5. Instrumental noise ( σ I ), onfusion noise ( σ C ) andtotal noise ( σ C + I ) in mJy for Hers hel/SPIRE.Wavelengths SPIRE ( µm )
250 350 500Deep σ I σ I
15 20.1 18.2 σ C b=0, 0.75, 1.5 4.6 6.5 5.5Deep σ C + I σ C + I
16 20.8 19is not strongly a(cid:27)e ted by the bias be ause of the smallFWHM of the PSF.4.3. CompletenessThe (cid:28)rst study of the point-sour es dete tion limit forPlan k was arried out based on a generalisation ofthe Wiener (cid:28)ltering method (Bou het & Gispert, 1999).Re ently López-Caniego et al. (2006) used the most re entavailable templates of the mi rowave sky and extragala ti point sour e simulations, in luding both the radio andIR galaxies, to estimate the Plan k dete tion limits.Here we revisit those results with new models for IRgalaxies and the last noise estimates for Plan k/HFI andHers hel/SPIRE.For the study of the ompleteness, a number N A ofsour es of equal (cid:29)ux are randomnly distributed in themaps. Ea h sour e is pla ed far enough from the other toavoid these additional sour es ontributing to the onfusionnoise. The dete tion and photometry of these sour es is arried out as des ribed at the beginning of the se tion. We all N G the number of good dete tions that omply withthe (cid:16)proximity(cid:17) and (cid:16)a ura y(cid:17) riteria. The ompletenessfor this (cid:29)ux C F is then al ulated as C F = N G N A × .The ompleteness of the dete tions of sour es for a given(cid:29)ux depends on both the instrumental noise and the onfusion noises. The results for the ompleteness areaveraged over ∼ b = 0 at µm . The horizontal straight line marks 80%of ompleteness.Figure 12. Good dete tions (thi k line) vs bad dete tions(thin line) Left: Histogram of good and bad dete tions usingsmall σ thres (290 mJy). Right: Histogram of good and baddete tions using higher σ thres (440 mJy) in the same map.Both plots have been done using a Plan k simulated mapwith b = 0 .Table 6. Completeness limits (in mJy) for the Plan k/HFImaps with instrumental noise ( C I ), onfusion noise ( C C )and both ( C C + I ). We onsider b =0, 0.75, and 1.5.Wavelengths HFI ( µm ) 350 550 850 1380 2097 C I = 80%
236 157 108 67 50 C C = 80% b=0 516 174 60.5 20 8.6 C C = 80% b=0.75 550 239.5 88.5 30.5 15.5 C C = 80% b=1.5 684 300 121 40 24 C C + I = 80% b=0 560 234 126 71 52 C C + I = 80% b=0.75 607 290 141 74 55 C C + I = 80% b=1.5 709 360 171 80 58.5example of the ompletness at 350 µm is shown in Fig.11. Results for all wavelengths are given in Tables 6 and7. They are onsistent with the instrumental, onfusion,and total noises given in Se t. 4.2 and the on lusionsfrom that se tion remain valid for the ompleteness. Forsimulated maps in luding both extragala ti sour es andinstrumental noise, we (cid:28)nd that the 80% ompletenesslevel oin ide with (cid:29)ux limits around − σ .Taking these 80% ompletness limits as a dete tionthreshold, the predi iton for the number of sour es de-0 N. Fernandez-Conde: Simulations of the osmi IR and submm ba kgroundTable 7. Completeness limits (in mJy) for theHers hel/SPIRE maps with instrumental noise ( C I ), on-fusion noise ( C C ), and both ( C C + I ).Wavelengths SPIRE ( µm )
250 350 500Deep C I = 80%
33 45.9 37.9Shallow C I = 80% C C = 80%
35 32 27.4Deep C C + I = 80% C C + I = 80%
70 96.5 75.5te ted dire tly by Hers hel/SPIRE for the deeper survey onsidered here is 8.3 × /sr at 250 µm , 1.1 × /sr at 350 µm , and 1.8 × /sr at 500 µm . The fra tion ofresolved CFIRB varies between 8 and 0.3% from 250 to500 µm .5. CIB (cid:29)u tuationsThe Plan k and Hers hel/SPIRE surveys allow an unpre e-dented sear h for CFIRB (cid:29)u tuations asso iated with large-s ale stru ture and galaxy lustering. Ba kground (cid:29)u tua-tions probe the physi s of galaxy lustering over an en-semble of sour es, with the bulk of the signal ontributionoriginating from sour es well below the dete tion thresh-old. Thus a omprehensive (cid:29)u tuation analysis is an es-sential omplement to the study of individually dete tedgalaxies. In this se tion, we restri t ourselves to predi tionsfor Plan k/HFI, ex luding the 143 and 100 GHz hannels.At these low frequen ies, we are dominating by the non-thermal emission of the radiosour es (cid:21) that are not in lud-ing in our model (cid:21) and the Poisson term dominates the lustering term (e.g. González-Nuevo et al., 2005). Also, weex lude the Hers hel/SPIRE ase sin e our simulations in- lude the lustering of CIB sour es in two di(cid:27)erent halos( h ), but not the lustering within the same halo ( h ). The h term dominates for ℓ & and will be a uratelymeasured by Hers hel/SPIRE. Only large-s ale surveys anput strong onstraints on the h term. Measuring the h lustering with CFIRB anisotropies is one of the goals ofPlan k/HFI.5.1. Contributors to the angular power spe trumFrom the far-IR to the millimeter, the sky is made up of theCFIRB and two other sour es of signal, the gala ti irrusand the CMB (we negle t the SZ signal). Understandingour observations of the CFIRB requires understanding the ontributions from these two omponents whi h a t for usas foreground and ba kground ontamination.The gala ti irrus a ts as foreground noise for theCFIRB. The non-white and non-Gaussian statisti al prop-erties of its emission make it a very omplex foreground omponent. The power spe trum of the IRAS 100 µm emission is hara terised by a power law Gautier et al.(e.g. 1992). Here we ompute the angular power spe trumof the dust emission following Miville-Des henes et al.(2007). These authors analysed the statisti al propertiesof the irrus emission at 100 µ m using the IRAS/IRISdata. We used their power spe trum normalization andslope (varying with the mean dust intensity at 100 µ m). Using the average | b | > o spe trum of the HI- orrelateddust emission measured using FIRAS data, we onvertedthe 100 µ C l even for wavelengths where the CMBdominates. We onsider for the rest of the dis ussion a onservative assumption, that is that the residual CMB(cid:29)u tuations are approximately 2%.The angular power spe trum of IR galaxies is omposedof a orrelated and a Poissonian part. As dis ussed in Se t.2.1, the ontribution to the Poissonian part is dominatedby relatively faint sour es after subtra ting the brightestgalaxies (see Fig. 3). We onsider that we an removesour es brighter than our 80% ompleteness dete tion limit(see Tables 6 and 7). For doing so, we use the te hniquedes ribed in Se t. 4.1 for measuring the position and (cid:29)uxesof the sour es and on e these are known we subtra t aPSF with the measured (cid:29)ux from the map.The orrelated C l is obtained as des ribed in Se t 2.1.For the relative error on the power spe trum, we followKnox (1995): δC l C l = (cid:18) πA (cid:19) . (cid:18) l + 1 (cid:19) . Aσ pix N C l W l ! where A is the observed area, σ pix the rms noise perpixel (instrumental plus onfusion), N the number ofpixels, and W l the window fun tion for a map made witha Gaussian beam W l = e − l σ B .5.2. Dete tability of CFIRB orrelated anisotropiesThe study of the C l on di(cid:27)erent s ales allows us to studydi(cid:27)erent aspe ts of the physi s of the environment ofIR galaxies (see Cooray & Sheth, 2002). Large s ales( l < ) give information on the osmologi al evolutionof primordial density (cid:29)u tuations in the linear phase andtherefore on the osmologi al parameters. Intermediates ales are mostly in(cid:29)uen ed by the mass of dark haloshosting sour es, whi h determines the bias parameter.Small s ales ( l > ) probe the distribution of sour esin the dark-matter halos and therefore the non-linearevolution of the stru tures. This non linear evolution wasnot a ounted for in our model.We an see in Fig. 13 the di(cid:27)erent ontributions to the C l for Plan k/HFI: the orrelated CFIRB C l with b = 1 and b = 3 with their respe tive error bars ( ∆ ℓ/ℓ =0.5),Poissonian (cid:29)u tuations, dust, and CMB ontributions.The dust and CMB C l are plotted both before and after. Fernandez-Conde: Simulations of the osmi IR and submm ba kground 11Figure 13. Power spe tra for Plan k of the orrelated IR galaxies with b=1 (thi k ontinuous line) and b=3 (thin ontinuous line), Poisson (cid:29)u tuations for sour es fainter than 709, 363, 171, 80 mJy at 350, 550, 850 and 1380 µm respe tively (short dashed line), dust with an HI olumn density of 1.5 at/cm and 2.7 at/cm for the 400Sq. Deg. and ∼ ∆ ℓ/ℓ =0.5.Table 8. Multipole ℓ ranges where the CFIRB orrelated anisotropies are higher than the irrus and CMB omponents.Wavelengths ( µm ) 350 550 850 1380400 Sq. Deg. b=1 < ℓ < < ℓ < < ℓ < Indete table400 Sq. Deg. b=3 < ℓ < < ℓ < < ℓ < < ℓ < < ℓ < < ℓ <
Indete table15000 Sq. Deg. b=3 < ℓ < < ℓ < < ℓ < < ℓ < ℓ ranges where the CFIRB orrelated anisotropies are higher than the residual irrus and CMB omponents (10%, and 2% respe tively).Wavelengths ( µm ) 350 550 850 1380400 Sq. Deg. b=1 < l < < l < < l < Indete table400 Sq. Deg. b=3 < l < < l < < l < < l < < l < < l < < l < Indete table15000 Sq. Deg. b=3 < l < < l < < l < < l < implementing the orre tions dis ussed above (10% and2% residuals, respe tively). For the dust we sele ted forthe estimation of the olumn density a (cid:28)eld entred on theSWIRE/ELAIS S1 (cid:28)eld. This (cid:28)eld has a very low levelof dust ontamination. For a 400 sq. deg. area entredat ( l, b ) = (311 o , − o ) , we have an average HI olumndensity of only 1.5 10 at/ m . We also take the wholesky above | b | > o ( ∼ ). The average HI olumndensity is 2.7 10 at/ m .At all wavelengths, the orrelated CFIRB C l is dom-inated by the other omponents on both very large andvery small s ales. The angular frequen ies where the C l is dominated by the galaxy orrelation depends mainlyon the wavelength, if the bias and irrus level are (cid:28)xed.On large s ales the C CF IRBl is dominated by the dust forwavelengths up to 550 µm , and for longer wavelengths itis dominated by the CMB. On small s ales the Poissonian(cid:29)u tuations dominate the power spe tra.We an see in Tables 8 and 9 the ranges for whi hCFIRB- orrelated anisotropies are dominating dependingon whether we onsider a partial subtra tion of the irrusand CMB or not. On small angular s ales (large ℓ ), therange of ℓ where the orrelated C l dominates in reaseswith the wavelength. On large angular s ales (small ℓ ), theresults depend on whether we onsider partial subtra tionof the irrus and CMB or not.Table 8 shows the ℓ ranges for where CFIRB orrelatedanisotropies are dominating when no subtra tion of thedust or CMB has been performed. At large angular s alesand wavelengths up to 850 µm the dete tability is betterfor the small map be ause of its lower N(HI) olumndensity. Without any dust ontamination orre tion, thisprevents us from taking advantage from the smaller errroron the estimation of the C l in the very large area surveysand makes both kind of observation omplementary. In lean regions of the sky, the best wavelengths for theobservation of the large s ales CFIRB anisotropies are 350 µm and 550 µm .The large-s ale dete tability drasti ally improves in the ase of partial subtra tion of the CMB and dust irrus asseen in Table 9. As dis ussed above we expe t to be able tosubtra t the dust (cid:29)u tuations and the CMB to a 10% and2% of their original level. This does not hange our abilityto measure the orrelated CFIRB C l ℓ < −5000