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A&A manuscript no. ASTRONOMY (will be inserted by hand later) AND Your thesaurus codes are: ASTROPHYSICS 02 (12.04.2; 11.05.2; 11.06.1) Cosmological history of stars and metals R. Sadat1, B. Guiderdoni2 and J. Silk3 1 1 Observatoire deMidi-Pyrénées, 14 avenueEdouard Belin, 31400 - Toulouse, France 0 2 Institut d’Astrophysiquede Paris, 98bis Boulevard Arago, F-75014 Paris, France 0 2 3 Department of Physics, Astrophysics,1 Keble Road, Oxford OX1 3NP,England n Received ; accepted a J 6 2 Abstract. We study the evolution of stellar content and way by combining the SFR in the local universe, the re- the chemical enrichment of the universe averaged over sults of ground–based spectroscopic redshift surveys out 1 the whole population of galaxies by means of a series to z ∼1 (Lilly et al. 1996) and the results of deep photo- v of chemo–spectrophotometric models that take into ac- metricsurveysliketheHubble Deep Field(HDF)inwhich 2 count the metallicity and dust obscuration effects. We galaxiesphotometricredshifthavebeendeterminedbythe 7 4 investigate various classes of cosmic star formation rates Lyman dropout selection technique (Madau et al. 1996, 1 (CSFR) histories consistent with current estimations. We hereafter M96). The resulting cosmic star formation his- 0 areabletoreproduceavarietyofobservationalconstraints tory has been summarized in the so–called “Madau plot” 1 suchasthe emissivitiesatrest–frame0.44,25,60and100 which shows a rapid increase up to z ∼ 1 and then a 0 µm of the local universe and also the overall shape of decrease at higher z with a peak at z ∼1.5 - 2. How- / h the extragalactic background light from UV/NIR galaxy ever, one of the large uncertainties in deriving the CSFR p counts and the cosmic infrared background (CIB) from from the comoving luminosity density is dust obscura- - o DIRBE/FIRAS measurements. We find that the CIB at tion.Indeed,thefaintobjectshavebeenselectedoptically r 140 µm is crucial for discriminating between the CSFR and therefore may represent only the tip of the iceberg t s histories. The best–fit model to this constraint seems to because dust absorbs large amounts of UV–optical rest– a favour mid–infrared derived CSFR at low–z and a flat framelight,causingunderestimationoftheSFRbyalarge : v CSFRathigherz consistentwiththe mostrecentestima- factor. This factor is still a matter of debate, for exemple i X tions, although the shape of the CSFR at high redshifts Pettini et al. (1998) have estimated the extinction on the has little impactonthe FIR/submmpartofextragalactic Lyman Dropout galaxies (at z > 2) and found a factor r a background. We suggest that the bulk of the CIB energy of ∼ 3 while Meurer et al. (1997) derived for the same is produced by a population of moderately obscured nor- objects a factor as large as 15. Finally, there might exist malgalaxieslyingat0≤z ≤1.Wethenderivetheglobal a populationofstar–forminggalaxiesathigh–z whichare chemical enrichment and stellar content of the universe completely enshrouded in dust and therefore remain un- and find that this model predicts metallicities in good detected in the optical/near infrared as revealed by the agreement with the metallicity in DLAs given that some ISOCAM–HDF survey (Aussel et al. 1998, Elbaz et al. outflow of metal–enriched gas from galaxies is assumed, 1999 ). Moreover, new estimates of the the global star but it overproduces the current present–day stellar mass formation rate have been reported. The first one is de- density and NIR luminosity density. rived from the analysis of deep ISO images of the CFRS by Flores et al. (1999, hereafter F99) who revised previous star formation density by a factor of ∼ 3 upward at 0 ≤ z ≤ 1 and the second one comes from an analysis of Keywords:cosmology:diffuseradiation–galaxies:evolution–LymanBreakGalaxiesintheHDFbySteidelet al.(1999, ISM–intergalactic medium hereafterS99)whofoundahigherSFRatz ≈4thanpre- vious estimate by Madau et al. 1998 (hereafter M98) and thereforefoundnoevidenceforasignificantdeclineofthe 1. Introduction CSFR at high redshifts. The history of CSFR can also be observed by its im- print on the background radiation. The first detection in Thehistoryofthecosmicstarformationrate(CSFR) DIRBE data of the IR/submm backgroundby Puget and in the universe has been inferred in an unprecedented his collaborators (1996) at a level comparable and even Send offprint requests to: R. Sadat 2 R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals higher than the optical counterpart,suggests that a large 2.1. The stellar emission fraction of the energy of young stars is absorbed by dust and reradiated in the IR/submm. Understanding the na- Our models are based on up–dated libraries of the- tureandredshiftofthesourcesresponsiblefortheinfrared oretical stellar tracks and spectra allowing for the build- background is of great importance for galaxy evolution ing of new sets of spectrophotometric evolutionary mod- studies.Severaldeepsurveyshavebeenundertakeninthe els that take into account the effect of metallicity. These submm wavelengths range at 450 and 850 µm with the models use the Geneva group stellar evolutionary tracks SCUBA Bolometer Array and ISO satellite (at 175 µm), (Schalleretal.1992,Schaereretal.1993a,b)forfivemetal- in order to resolve this background (Kawara et al. 1997, licities Z =0.001, 0.004, 0.008, 0.02, 0.04. The main stel- Barger et al. 1998,Hughes et al. 1998, Eales et al. 1999). lar evolution phases include all the important stages ex- Recent advances in high resolution spectroscopy of high cept for low mass stars (less than 1.7 M⊙) those tracks redshift systems like damped Lyα systems (DLAs), has stop at the Giant Branch tip. We thus use the more re- provided us with precious information on early phases of cent track evolution of low mass stars which go from the chemical enrichment (Pettini et al. 1997, hereafter P97) Zero–main sequence up to the end of EAGB for only two andneutralgascontentofthe universe(Storrie-Lombardi metallicities Z = 0.02 and Z = 0.001 (Charbonnel et etal.1996)castingsomelightonthecosmicchemicalevo- al. 1996). For the other metallicities we simply interpo- lution. The aimof this paper is to explorethe predictions late between the available Geneva tracks. Choosing the that models of stellar evolution self–consistently coupled Geneva group tracks allows the use of the Z–dependent withchemicalevolutioncodewouldmakeonthemetaland stellar yields of Maeder (1992) which insures the con- stellar enrichment history of the universe. Briefly, given sistency when coupling spectrophotometric and chemical the cosmic star formation history we calculate the unat- evolutions.Forthe stellarspectraweusetheoreticalspec- tenuatedspectralluminositydensityatdifferentredshifts. tra by Kurucz (1992), with the advantage that it avoids Adoptingamodelofdustabsorptionwethencomputethe theuseofthetransformationsofbolometricluminositylog attenuated comoving luminosity density at different red- Lbol to magnitude MV, of log Teff to Spectral Type, and shiftsandwavelengthswhichisthencomparedtoavailable to luminosity classes, which are rather uncertain for the observations.Combiningthis withthe extragalacticback- hottest ones. For the coldest stars (K and M–type stars) ground will allow us to constrain the models. Predictions with T ≤ 3750 K we prefer to use models from Bessell onthecosmicchemicalenrichmentandonthestellarcon- et al. (1989, 1991a,b) for M Giants (for various Z) and tent of the universe are then derived. from Brett (1995a,b) for M dwarfs, with a single metal- This paper is organized as follow: section 2 describes the licity Z=0.02. The initial helium content of the gas from models and the inputs we used. In section 3, we discuss which stars form is computed with an initial He fraction our models predictions in the light of availablephotomet- Y =0.24 and assuming ∆Y/∆Z =3. ric constraints, such as the comoving luminosity densities from UV/vis to FIR and the cosmic infrared background 2.2. Modelling the Cosmic Chemical Evolution radiation (CIB). In section 4 we derive the chemical enrichment history of the universe and its stellar content. A model of chemical evolution allows the abundance Throughout the paper we use a value of the Hubble con- stantH =50kms−1Mpc−1,adensityparameterΩ =1 evolution in the ISM and the abundance distribution in 0 0 stars by solving a simple set of equations (Tinsley 1980). and Ω =0. Λ Forapopulationofgalaxies,the chemicalevolutionequa- tions can be expressed in terms of comoving densities of 2. The models stars, neutral gas and heavy–elementsΩg, Ω∗, ΩZ in unit of the critical mass density ρc =7×1010 M⊙ Mpc−3 : Inthisworkwestudytheglobalpropertiesofgalaxies dZΩ averaged in large comoving volumes. We are in particu- dt g =−ZΩ˙∗+Ω˙Z −Ω˙Zout (1) lar interested in the stellar and heavy element content of the universe that our models would predict using avail- Z isthemeanabundanceoftheISMofgalaxiesdefinedby able observational constraints. This is based on chemo– the ratio ΩZ/Ωg. Ω˙Zout is the comoving rate of outflowing spectrophotometricmodelsthatfollowinaself–consistent metal–enriched gas out of galaxies. In the case of closed– way the evolution of stars, dust and metals. These mod- box models this term vanishes. els are based on stellar population synthesis code which We use the Z–dependent yields of M92 with moderate is coupled to simple chemical evolution models and dust mass loss for massive stars. For intermediate stars we use absorption. The basic ingredients of our models are de- the Renzini and Voli (1981) yields. We do not make the scribedbellow (more details can be found in Devriendt et assumptionofinstantaneousrecyclingbutwetrackmetals al. 2000,hereafter DGS) ejected by stars at each timestep and let new stars form outoftheenrichedgas,assuminginstantaneousmixingof the metals. R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals 3 2.3. Dust spectra two star layers, geometries which leads respectively to a larger and a smaller absorption (Franceschini and An- A non–negligible part of the energy released by stars dreani 1995, Andreani and Franceschini 1996). in the UV/optical wavelengths is absorbed by dust and We have also to take into account the evolution of τ V re–emitted in the IR/submm. A normal spiral such as with redshift. As already mentionned, τ is in principle V our Galaxy emits ∼ 30% of its light in the far–infrared related to the mean H–column density N and depends H (see Dwek et al. 1998 and reference therein). Taking dust on the geometrical structure of the gas. From scaling ar- obscuration into account is crucial for the census of stel- gument τ ∝ρ r we would expect that τ ∝(1+z)α V gas g V lar mass, metals and energy. Models of SEDs which cor- with α = 2. However, other factors might evolve, such rectlyconnectUV/visandIR/submmwindowsarethere- as the properties of the dust or the actual geometry of fore needed. However modelling dust extinction is not an the gas distribution within the disk so that the redshift– easy task since we have to address critical issues such as dependencemightdeviatefromthesimplescalingrelation. the dust properties, its geometrical distribution with re- Inthiscase,theslopeindexαistakenasanadjustablepa- spect to stars andits chemicalevolution.Models of SEDs rameterwhosevalueis determinedwhenconsistencywith that take into account the extinction and emission effects the HDF rest–frame UV luminosities is obtained. of dust in a consistent way have been developed by sev- Theabovemodellingofthe meanopticalthicknessisvery eralauthors(Franceschiniet al.1991,1994),Fall,Charlot crudeandprobablydoesnotreflectthecomplexityofdust and Pei (1996), Silva et al. (1998), Pei et al. (1999, here- extinction. In the following, we will use the GRV87 pre- afterPFH), butallthesemodels assumea simple relation scription in which the mean optical thickness is explic- between dust and metal abundance of the gas and do not itly relatedto the mean metallicity and to N . Following H haveadetailedmodellingofthestarlightre–processingby GRV87andFranceschiniet al.(1991)wewillassumethat dust grains. More detailed and self–consistent models of the meanface–onoptical depth of the averagegasdisk at SEDs called STARDUST have recently been developped time t and wavelength λ is given by : by DGS. Here we will follow DGS to compute the global s A Z(t) hN (t)i λ H SED from UV/vis to IR/submm wavelengths. τλ(t)=(cid:18)AV(cid:19)Z⊙(cid:18) Z⊙ (cid:19) (cid:18)2.1 1021 at cm−2(cid:19) , (4) where the mean H column density (accounting for the presence of helium) is written as: 2.3.1. Dust absorption hN (t)i≃6.8 1021g(t)f atomscm−2 . H H where g(t) is the gas fraction. A galaxy with g ≈ 0.2 has Thefirststepistocomputetheopticaldepth.Wewill < N >∼ 1.41021 atom cm−2, in good agreement with first assume a simple prescription given by: H the observational value for late–type galaxies (GRV87). τ (t)=(Aλ) τ (2) fH is a parameter which allows us to increase the H col- λ AV Z⊙ V umn density and is close to unity for normal spirals. The where(Aλ/AV)⊙istheextinctioncurveinourGalaxy(so- extinction curve here depends on the gas metallicity Z(t) larmetallicity)fromMathis et al. (1983).Inprincipleone according to power law interpolations based on the Solar should relate τ (t) to the mean H–column density which Neighbourhood and the LMC and SMC with s=1.35 for λ is proportionalto the meangas density times the gaseous λ < 2000 ˚A and s = 1.6 for λ > 2000 ˚A. The derived ex- disk scale (N (t)=M (t)/πr2 ∝ρ r ). To account for tinctioncurvesdepend stronglyonthe adoptedgeometry, H g g gas g this, we introduce a “fudge” factor τ . here we restrictedourselvesto the “slab”geometry;keep- V AsinGuiderdoniandRocca–Volmerange(1987,hereafter ing in mind that it might introduce some uncertainties in GRV87), we assume a face–on “slab” geometry distribu- theobscurationcurves.Itwouldbeinterestingtocompare tion where the gas and the stars which contribute mainly this with more detailed models of extinction curves (see todustheating aredistributedwithequalheightscalesin for example Ferrara et al. 1999) but this is beyond the the disks. Following GRV87, if τ (t) is the optical thick- scope of this present work. λ ness of the disks at wavelength λ and time t, the mean internal extinction correction (averaged over inclination Finally, the observed flux Fo∗λ is then related to the angle i) is then given by: emitted (intrinsic) flux Fλ∗ by: 1.−exp(−a τ (t)/cosi) Aλ(t) = −2.5log< a τ (tλ)/λcosi >i, (3) Fo∗λ =10−0.4Aλ(t) (5) λ λ F∗ The factor a ≡ (1 − ω )1/2 takes into account the λ λ λ ThebolometricluminosityreleasedatIR/submmwave- effect of the albedo ω . This “slab” geometry is an inter- λ lengths is then given by: mediate case between the “screen” geometry, where the dust layer lies in front of the stars layer and the “sand- L (t)= F∗(t)(1−10−0.4Aλ(t))dλ. (6) wich” geometry, where the dust layer is trapped between IR Z λ 4 R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals 2.3.2. Dust emission In order to compute the IR/submm emissionspectra, oneneedstoredistributethetotalIRluminosityL over IR thewholerangeofwavelengths.Thisisachievedbyusinga dust model of the ISM. We assume the three–component (Polycyclic Aromatic Hydrocarbons, Very Small Grains and Big Grains) dust model developed by Désert et al. (1990) according to Maffei’s method (Maffei 1994) which usestheobservationalcorrelationsoftheIRASfluxratios with L . IR ThreecomponentsareconsideredinDésertetal.model spectra: – the Big grains (BG). The are made of silicates and graphiteandhavesizesbetween10nmand0.1µmand arealmostinthermalequilibrium.Theyarereasonably described by a modified blackbody ǫ B (T ) with ν ν BG emissivity ǫ =νm (where the index 1≤m≤2. ν – Polycyclicaromatichydrocarbons(PAHs).Becausethese moleculesaresmallinsize(lessthan1nm)they never Fig.1. Model spectrain theIR/submm for different total IR reachthermalequilibriumwhenexcitedbytheUV/vis radiation.Theirtemperaturefluctuatesandcanexceed luminosities ranging from 106 to1014L⊙ andan emissivity index m=1.5. theequilibriumtemperaturewhichproducesthe12µm excess and the bands at 3.3, 6.2, 7.7 and 11.3 µm. – Very small grains (VSG) with sizes between 1 and 10 nm also made of silicates and graphite.As PAHs they never reach thermal equilibrium and therefore their emissionspectrumismuchbroaderthantheblackbody spectrum at a given temperature. The temperature T of the Big Grains is given by BG the IRAS 60/100 colours provided we fix the value of the emissivity index m. The derived temperature is between 15and50K.Hereweadoptthestandardvalueofm=1.5. Modelspectrawithm=1.5seemstocoveralltherangeof observations in the submm (Guiderdoni et al. 1998). The contributions of each component is then calculated iter- atively from the 12/100, 25/100 and 60/100 ratios. The resulting spectra are computed from few µm to several mmandevolvewiththetotalIRluminosityL suchthat IR galaxies with higher L emit preferentialy at shorter λ IR (Fig. 1). Here we will adopt the model spectra of dust emissionwithtotalIRluminosity ofLIR =1010L⊙ which istypicalofnormalgalaxiesandcorrespondstoatemper- ature of BG of T ≈ 16.5 K. In spite of its limitations, BG this method is able to reproduce the FIR photometry of various individual galaxies (Maffei 1994). Fig.2. The star formation rate as function of redshifts. The curves are the different star formation histories we input in our models: (solid line), (small dashes) and (long dashes) cor- respondingtoH,L1 andL2models.Thedatapointsaretaken from M96 and F99 (filled squares): lower points and upper points respectively. Treyer et al. 1997 (empty triangle), Con- 2.4. Assumptions and inputs of the model nolly et al. 1997 (empty hexagons). At high–z, the data are from Madau et al. 1998 (open triangles) and from S99 after WechoosethreeclassesofCSFR.ThehighSFRmodel correction for extinction (crosses). (model H) choosen in order to be consistent with the R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals 5 recent estimations based on IR surveys (F99) and large model 0≤z ≤1 z ≥2 ground–basedsurveyofLyman–Breakgalaxies(S99).The lowSFRmodelsL andL areconsistentwiththeUV/optical H consistent with F99 consistent with S99 1 2 derived SFR with respectively a declining and a flat SFR L1 consistent with M96 consistent with S99 athighredshifts(seetable1).Fig.2showsthethreemod- L2 consistent with M96 consistent with M96 els of CSFR we used, together with a compilation of the Table1.DefinitionoftheclassofmodelsdescribingtheCSFR histories we input in our modelling. H model is chosen to be CSFR estimations derived from UV/vis and IR surveys. consistent withthemid–infrared CSFRinferredfrom observa- In our modelling of dust obscuration we used the HDF tionsofISO15µmselectedgalaxiesintheCFRSat0≤z≤1 rest–frame attenuated 1500 ˚A emissivity at z = 3 − 4 by F99 and with the CSFR inferred from large ground–based (from S99 for models H and L and from M96 for model 1 survey of Lyman–break galaxies by S99 and corrected for ex- L ) and the local emissivity at 100 µm to determine the 2 tinction at z >2.Models L1 and L2 both areconsistent with two adjustable parameters, τV(z =0) and α. theCSFRderivedfromtheCFRSsurveybyM96at0≤z≤1, In the case of the closed–box approximation (i.e Ω˙Zout = athigh–zmodelL1isconsistentwithS99whileL2isconsistent 0) the equations of chemical evolution (eq. 1) are solved with M98 assuming that at early times the stars form from some amount of gas whose initial gas density fraction is fixed by imposing that the present–day amount of HI gas is of the order of Ω (0)≈ 5×10−4 (as estimated by Briggs & g Rao 1993). In the case where the closed–box approximation is relaxed, we will assume for simplicity a constant outflowΩ˙Z =const.NoteherethattheISMgascontent out ofthe galaxiesisassumedto bemainly duetoneutralhy- drogengas HI; we neglectboth the ionizedand molecular formsofthe gas(HII andH ).Thisapproximationisrea- 2 sonable at high redshifts, as measurements of gas content of Damped Lyman α systems show low ionization states (Viegas 1995) and low molecules abundances (Levshakov etal.1992,Petitjeanetal.2000).Locally,thisapproxima- tionmaynotholdsincethepresent–daylate–typegalaxies containonaverageanon–negligiblefractionofH (Young 2 & Scoville1991)whichwouldresultin a factoroftwo un- certainty on Ω or more if H contribution to the ISM gas 2 gas is more important (Pfenniger et al. 1994). We adopt a Salpeter IMF φ(m)∝m−x with x=1.35 for md ≤ m ≤ mup and md = 0.1 M⊙ and mup = 100 M⊙. Fig.3.Therest–framespectralenergydistributionSEDfrom ThisIMFhasbeenfoundtobe morereliableinreproduc- UV/vis to FIR/submm at z = 0. The data points are from ing the observed emissivities locally than the Scalo IMF Ellis et al. (1996) for 0.44 µm ; Gardner et al. (1997) for 2.2 (Lilly et al. 1996, M98). µm; and Soifer & Neugbauer (1991) for 25, 60 and 100 µm. Finally, we will suppose to a first order that the results are independent of the cosmological parameters. Discus- sion of the effect of the cosmological parameters on the 3.1. The rest–frame comoving emissivity from luminosity density can be found in (Cassé et al. 1998). UV/optical to IR/submm We are interested in the global evolution of the radi- ationfrom both the stellar andthe dust component.This 3. The results and comparison to observations can be described by the comoving luminosity density ρν asafunctionofredshiftdefinedastheenergyradiatedper unitfrequencyperunitofco–movingvolumeatredshiftz. Deepgalaxysurveyshaveallowedtheprobingofrest– The intrinsic stellar emissivity can be expressed in terms frameUV/opticaltoNIRemissivitiesofhighandlowred- of the global star formation rate Ω˙∗ shiftgalaxies.WhencombinedwiththeCIBmeasurement t ittorpyroovfisdteasrufosrwmiathtiocnr.ucial constraints on the global his- ρ∗λ =ρcZ Fλ∗(t−t′)Ω˙∗(t′)dt′ (7) 0 whereF∗(t−t′)isthestellarpopulationspectrumascom- λ puted by our population synthesis code (see DGS for details). 6 R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals The spectral luminosity density at each redshift is com- We here ignore the contribution of AGNs in heating the puted by simply summing the observed(attenuated) stel- dust. Predictions of our models for the intensity of the larradiationandthedustradiation:ρ (z)=ρ∗ (z)+ρd(z) background radiation in the optical and IR/submm 1 are ν oλ λ whereρ∗ isrelatedtotheintrinsic(unabsorbed)emissiv- showninFig.4.Theoverallspectrumseemstobewellre- oλ ity by: ρ∗ =10−0.4Aλρ∗. produced by all the models regardlessof their very differ- oλ λ We first fix the adjustable parameters of the models α ent SFR histories. In particular, the shape of the submm andτ ,by fits to the observedluminositydensity at1500 partoftheextragalacticbackgrounddoesnotdiscriminate V ˚A at z = 3−4 and the local to the local 100 µm emis- between the models, and is therefore not a very crucial sivity respectively.The best–fit solutions are obtained for probeofthestarformationhistory.Instead,the CIBdata the following values of the parameters (τ , α): (1.3, 1.4), point at 140 µm is very discriminant. Only mid–infrared V (1.2, 1.4) and (1.2, 0.8). The corresponding values of the derived CSFR at low–z (model H) is able to correctly extinction factor A varies from A = 0.45 locally to match this point while UV–derived low–z CSFR (L and V V 1 A = 2 − 2.5 at z = 3 − 4 for model H. In the case L models) , falls considerably short of the COBE detec- V 2 of model L , A is almost constant, varying from 0.45 tions at λ = 140 µm. Moreover, the CIB is less sensitive 2 V locally to 0.53 at z = 3−4. Fig. 3 shows the resulting to the CSFR shape at high–z. For example, had we cho- z =0co–movingspectralluminositydensityfromUV/vis sen a model similar to H–model at low–z but with a de- toIR/submmwavelengths,onwhicharesuperimposedthe clining SFR at high–z, we would obtain an accpetable fit data.OurmodelswithaSalpeterIMFgiveoverallgoodfit to the 140 µm data. This result suggests that the bulk tothepresent–daystellarlightfromUV/vistoIR.Except of the energy in the FIR/submm is due to moderately forthe2.2µmemissivitywhichseemstobeoverestimated obscured normal galaxies lying at low and moderate red- byH–typemodels,ourmodelsareablereproducethedata shifts (0 ≤ z ≤ 1) and not by a population of heavily ex- not only at 100 µm (which is expected since it is used as tinguished star–forming regions located at very high red- an input) but also at λ = 0.44, 2.2, 25, 60 µm, whatever shifts, as previously claimed (Blain et al. 1998, hereafter the chosenCSFRhistory.Thisresultshowsthatlocalco– B98). We also show the predicted intensity of the back- moving emissivities are not sensitive to the CSFR and ground radiation when the GRV87 prescription for the therefore are not suitable to constrain the star formation optical depth τ is used (eq. 4). As we can see there is no λ ratehistory.We alsocompute the resultingspectrallumi- strong difference between the two prescriptions. nosity density in the case where GRV87 prescription for It is interesting to compare our result with other works. τ (t) is used and found no difference with models which PFH have made use of many observational inputs (from λ use our simple prescription (eq. 2); the two SEDs are al- QSOs absorption line surveys, optical imaging, redshift most undistinguishable. surveys,andFIRAS/DIRBEcosmicinfraredbackground) We use for the determination of dust emission a model to derive solutions for the cosmic histories of star forma- with LIR = 1010L⊙. To take into account the uncertain- tionrate.Theyfoundaglobalstarformationratewhichis ties in the FIR part of the SED, we run our models with higher than the UV–derived one, in good agreementwith a higher IR luminosity LIR ≥ 1012L⊙ which is typical of our result. Although their three solutions do not fit the the Ultra–Luminous Infrared Galaxies (ULIRGs). As ex- CIB at 140 µm, their solutions are actually significantly pected, we found that the peak emission in Far–Infrared below this data point (see their fig. 11). Our result in (100µm)isshiftedtowardshorterwavelengths,leadingto the other hand, is in disagreementwith previous worksin a poorer fit to the data. which it is claimed that the best CSFR solution is higher and flatter at high redshifts than the optically derived form (B98, Gispert et al. 2000). Note that these authors used a different approach than ours and did not use the 3.2. The Extragalactic Background Radiation point at 140 µm to discriminate between the models, as in the present work. The second observational constraint is set by the extragalactic background light (EBL). Cosmological impli- cations of the CIB on the CSFR have been discussed by severalgroups,for example M98,Dwek et al. (1998),Gis- 4. Cosmological history of metals pert et al. (2000). Here we use our models to derive the intensity of the background. The intensity I of EBL re- ν Inorderto getaconsistentpicture ofthe evolutionof sults from integrating the emission coming from various the universe,oneshouldrelatetheCSFRtothemetalen- extragalactic objects on the line of sight over the cosmic richmentoftheuniverseanditsstellarcontent.Toachieve time. this goalwe will use the CSFR model that accountfor all TheintensityI atagiventimetisgivenbythefollowing: ν 1 Recent tentative of CIB detection at 2.2 and 3.5 µm has c ∞ dt been reported by Gorjian et al. (2000), our best–fit model is I = dzρ . (8) ν 4π Z ν(1+z)(cid:12)dz(cid:12) consistent with their estimated intensity at 2.2 and 3.5 µm 0 (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) (cid:12) R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals 7 available data from UV/vis to FIR/submm wavelengths to compute the enrichment history of the universe. 4.1. Chemical enrichment of the ISM Our knowledge of chemical evolution was based on local observations(mainly the solar neighbourhood) until the outcome of high–z observations of damped Lyα systems, which allowed us to draw some conclusion about galaxy evolution in terms of the cosmic evolution of the meanmetallicity andcoolneutralgas.There aresomein- dications that these DLAs represent the progenitors of present–day galaxies, although the nature of these objects is still a matter of debate. Moreover, it is not yet clear whether the mean HI weighted metallicity derived from current observations of DLAs is representative or not of the global metal enrichment of the Universe. The picture that emerges from the DLAs observations is that i) the neutral gas content is decreasing from z ∼ 3 to the present–epoch,correspondingto the conversionofgas into stars and that ii) the metallicity is decreasing with increasingredshift,withverylowmetallicitiesathighred- shifts,whichwouldsuggestthatthesesystemsareintheir early phase of enrichment. Figure5showsthemeanabundanceofmetalsintheinter- stellarmediumZ asfunctionofredshiftscomparedto ISM the metallicity at high redshift derived from the observed abundance of Zn in damped Lyα systems (Pettini et al. 1997), which should agree if DLA and field galaxies have thesamemetalenrichment.Theuncertaintyinthedatais still large though, and no attempt has been made to correct for the observational biases which could potentially alter our interpretation of the DLAs metal abundances (Prantzos & Boissier 2000 and reference therein) but see Savaglio2000.Wefindthatintheclosed–boxassumption, our best–fit to the CIB at 140 µm model clearly fails to reproduce the data; it overpredicts the mean metallicity Fig.4. The predicted diffuse backgrounds in the optical and by a factor of ∼ 3 at 2 ≤ z ≤ 3. This is less than that FIR/submmascomparedtocurrentlimitsanddetections.The found by B98 with their submm–derived CSFR (a factor coding of the curves are same as in fig 1. Solid hexagons re- as high as 5). Our best–fit model also produces a mean sult from the faint galaxy counts at 3600 - 22000 ˚A (Pozzetti metallicityZ(0)whichis≈2timeslargerthanthemetal- et al. 1998). The empty square results from galaxy counts at licity in the local universe if we assume it to be solar. 2000˚A(Armandetal.1994).TheEmptyhexagonisthedetec- We have therefore relaxed the closed–box approximation tionat3.5µmfromCOBE/DIRBEbyDwek&Arendt(1998). and allowed for some outflowing of metal–enriched gas The filled squares correspond to the COBE/DIRBE residuals from the galaxies. As we can see from figure 5, the agree- (Hauser 1996) only 140 µm and 240 µm signals are firm de- mentwiththedatabecomesbetterthanintheclosed–box tections(Hauseret al.1998),allotherpointsareupperlimits. models. If we further assume that the ejected metals are Empty trianglesarethe100,140and240µmestimationsfrom responsible for IGM pollution, we can use our model to Lagache et al. (2000). The Filled triangles are theestimations of the CIB at 850 and 450 µm from repsectively Blain et al. estimate the amount of metals present in the IGM. 1999) and Smail et al. (1997) updated by Ivison et al. (1999). The Empty squares are the lower limit to the background at 7 and 15 µ m from Altieri et al. ( 1999). The empty losanges are the lower limit to the 15 µm and an upper limit to the 4.2. Chemical enrichment of the IGM 0.912 µmbackgroundbyVogelet al.(1995). Thezigzag isthe COBE/FIRASresidualsdetectedbyPugetetal.(1996)andre- The detections of CIV and Si IV absorption lines in visitedbyGuiderdoniet al.(1997).Thelowerpanelshowsthe the Lyα forest as reported (Tytler et al. 1995, Songaila predicted diffuse background intensity obtained using GRV87 prescriptionofdustextinction(dottedline)ascomparedtothe 8 R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals & Cowie 1996,Songaila (1997)can potentially give us information about the early enrichment of the intergalactic medium (IGM) with metals (Gnedin & Ostriker 1997). If we assume that the IGM metal content can well be rep- resented by the metallicity inferred from Lyα clouds, we may compare our prediction of the density of metals to the observations of CIV and Si IV absorption lines in the Lyα forest. Assuming that ejected metal–enriched gas is uniformelydistributedintheintergalacticmedium,wees- timate the meanco–movingdensity of metals in the IGM by integrating Ω˙Z over the time. We find that the den- out sity ofheavy–elementsatz =0 is ΩIGM =7.7×10−5 (i.e m ρm =5.4×106M⊙ Mpc−3).Atz ≈3.2,ΩImGM ∼6×10−7 in agreement within the error bar with the data point of ΩIGM ∼8×10−7reportedbySongaila(1997).Thisresult m supports the general belief that the chemical enrichment of the IGM may be due to the outflowing of metals from galaxies,although this scenario is still a matter of debate (see Gnedin 1997 for an alternative scenario). It has been pointed out that if no differences exist be- Fig.5. Evolution with redshift of the mean comoving ISM tween field and clusters galaxies, then clusters of galaxies metallicity aspredictedbythebest–fitmodel(solidline).The can provide us with information about the chemical en- dotted line curve corresponds to the case of closed box evolu- richmenthistoryoftheuniverse(Renzini1997).Wethere- tion.Thedatapointscorrespondtothemetallicity asinferred from the DLAs Pettini et al. (1997). The point at z =0.77 is fore estimate the local IGM mean metallicity Z (0)= IGM ΩIGM/Ω andfindittobeoftheorderof10−3.Usingthe from Boissé et al. (1998). m b low value of D/H ( η ∼ 5.3) by Burles & Tytler (1998) 10 (Ω ≈ 0.077) and assuming a solar metallicty of 0.016, b this value yields to a global mean metallicity of 6% solar very important as it shows that models able to produce which is ∼ 4 times smaller than the metallicity derived enoughenergyintheFIRpartoftheCIBleadtoanexcess fromX–rayobservationsoftheintra–clustermediumICM of stars as compared to the present–day estimates. Note (∼0.25Z⊙).AssuggestedbyRenzini(1997),this cluster– thattheFIR/submmderivedCSFRofB98producevalues field difference may be due to either cluster–related pro- of Ω∗(0) at least a factor of two higher than that which cesses such as stripping or ram pressure or to a flatter our models produce; this is due to their higher CSFR at IMF in clusters relative to field galaxies. Note that if we high redshifts. The current Ω∗(0) estimate is still uncer- use the high value of D/H ≈ 10−4 (e.g. Lemoine et al. tain though. There are several sources of errors that can 1999 for a review) yielding Ωb ≈ 0.02, we would obtain a bias the inferred Ω∗(0), such as the uncertainties in the global metallicity of 0.2 solar which is close to the ICM derived luminosity functions parameters Φ∗ and L∗; on metallicity. the estimation of the contribution of starlight from low Regarding the large uncertainties in the observations and surface brightness (LSB) galaxies; in the adopted stellar the limitations of our models (a constant metal–enriched M/L ratio of disks, spheroids and irregulars. However all gasejectioniscertainlyacrudeapproximation),weshould these effects are not very important and cannot account be cautious before drawing any conclusion regarding the for the discrepancy. More exotic solutions should there- global enrichment of the universe. fore be invoked. Several solutions are possible, first it is possible that some stars (extragalactic stars, machos) are missedinthecensusofthestellarbudgetbutitisunlikely that we missed that significantly. 4.3. Stellar content of the universe Second, contamination by AGN causes problems that are more important than we think. We know from IRAS and Our models can also provide the global evolution of SCUBA observations and recently from X–ray Chandra the stellar content. Fig. 6 shows the inferred evolution of observations(Bargeretal.2000)thatapopulationofdust the stellar content as a function of the cosmic epoch for enshrouded AGNs do exist (Sanders and Mirabel 1996). eachofthe models of CSFR . The estimate of the current However it is still unclear how important this contamina- z = 0 Ω∗(0) ∼ 0.004−0.008 comes from Briggs (1997). tionisasitisdifficulttodiscriminatebetweenapurestar- We can see that the best–fit model to the 140 µm data burst and a dusty AGN in the object identification pro- point predicts a present–day stellar mass density larger cess. Therefore, it is highly probable that a large fraction by at least a factor of two than the current value. This is ofthe CIBmaybe due to the dustenshroudedAGNpop- R. Sadat, B. Guiderdoni and J. Silk: Cosmological history of stars and metals 9 ulation. AGN contamination also complicates the deriva- the light at λ = 2.2µm. At wavelengths dominated by tion of the star formation rate history from the observed the dust emission (at λ = 25, 60 and 100 µm), we find luminositieseveninthemulti–wavelengthssurveys(asthe good agreementwith the observationsindependent of the onederivedbyF99),althoughitislesscriticalthaninthe choosen CSFR. UV wavelengths. Third,ouradoptedSalpeterIMFis responsibleforsucha •We show that the point at 140 µm is crucial for con- discrepancy.A IMF biasedagainstlow–massstars,would straining the CSFR history and seems to favour a higher reduce the number of long–lived stars and thus attenuate comoving star formation rate at low redshifts than the the discrepancy. Evidence of a shallow mass function be- UV/optically derivedone;howeverthe shape athigh red- low1M⊙ hasbeenobservedintheGalacticdisk(Gouldet shifts of the CSFR is not well constrained by the CIB al. 1996)andmorerecentlyinthe Galactic bulge(Zoccali measurements, contrary to previous claims. etal.2000).AheavilybiasedIMFhasalsobeensuggested from microlensing data (Chabrier 1999). • We suggest that the main contribution to the bulk of the CIB and more specifically to the energy at 140 µm is due to normalgalaxies, lying at low and moderate redshifts,andnottodistantanddustygalaxiesaspreviously suggested. • Concerning the history of the metal enrichment, we findthatintheframeofclosed–boxevolution,ourbest–fit model to the CIB at 140 µm overpredicts the metallicity as observed in DLAs. A better agreement is obtained in the case of a model with some outflowing metal–enriched gas. • Assuming that the ejected metal–enriched material is responsible for the IGM metallicity we derive,the IGM metal content and found it to be consistent within the error bar with the metals in the Lyα forest. However, we cannot derived conclusions regarding the IGM metal– enrichment given the large uncertainties in the data and the crudness of our metal enrichment treatment. • Our best–fit model to the CIB at λ = 140 over- Fig.6.Evolutionasafunctionofredshiftofoftheco–moving poduces the present–day stellar mass density Ω∗(0) by a factor of at least ∼2 as comparedto the currentvalue. If stellarmassdensity.Codingofthemodelsareasinfig.2.The the CIB at λ = 140 µm is correct, then this discrepancy horizontallinesdefinethedataofthetotalmassdensityofthe and the excess of light at λ = 2.2 µm could be explained stars at the present epoch as estimated by Briggs (1997) by our choice of Salpeter IMF. This would then be an indication in favour of an IMF which is biased toward massivestars,openinganewdebateontheuniversalityof the initial mass function. However,one may keepin mind 5. Conclusions that our calculations have been done under the assump- tion that the FIR/submm background is due to a stellar Wehaveusedaseriesofself–consistentchemo–spectro- component only; we neglect any contribution of AGNs in photometric models whichtake into accountthe metallic- dust heating, which is probably not true. ity and dust obscuration effects to study the global evolution of spectrophotometric properties together with the Acknowledgements. Weare very gratefull to A. Blanchard for stellar, chemical and radiation content of the galaxies av- fruitful discussions. We thank the referee A. Ferrara for his eraged over a large co–moving volume, independently of usefulcommentswhichhelpedustoimprovethecontentofthis their individual details and properties. paper. 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