THE ASTROPHYSICAL JOURNAL, 556 :562È581, 2001 August 1 V( 2001. The American Astronomical Society. All rights reserved. Printed in U.S.A.

INTERPRETING THE COSMIC INFRARED BACKGROUND: CONSTRAINTS ON THE EVOLUTION OFTHE DUST-ENSHROUDED STAR FORMATION RATE

R. CHARY1 AND D. ELBAZ1,2,3Received 2001 January 21 ; accepted 2001 April 5

ABSTRACTThe mid-infrared local luminosity function is evolved with redshift to Ðt the spectrum of the cosmic

infrared background (CIRB) at j [ 5 km and the galaxy counts from various surveys at mid-infrared,far-infrared, and submillimeter wavelengths. A variety of evolutionary models provide satisfactory Ðts tothe CIRB and the number counts. The degeneracy in the range of models cannot be broken by currentobservations. However, the di†erent evolutionary models yield approximately the same comovingnumber density of infrared luminous galaxies as a function of redshift. Since the spectrum of the cosmicbackground at j [ 200 km is quite sensitive to the evolution at high redshift, i.e., z[ 1, all models thatÐt the counts require a Ñattening at zD 0.8 to avoid overproducing the CIRB. About 80% of the 140 kmCIRB is produced at 0\ z\ 1.5, while only about 30% of the 850 km background is produced withinthe same redshift range. The nature of the evolution is then translated into a measure of the dust-enshrouded star formation rate (SFR) density as a function of redshift and compared with estimates fromrest-frame optical/ultraviolet surveys. The dust-enshrouded SFR density appears to peak at z\ 0.8^ 0.1,much sooner than previously thought, with a value of yr~1 Mpc~3, and remains almost0.25~0.1`0.12 M

_constant up to zD 2. At least 70% of this star formation takes place in infrared luminous galaxies withThe long-wavelength observations that constrain our evolutionary models do not strong-L IR[ 1011 L

_.

ly trace the evolution at z[ 2 and a drop-o† in the dust-enshrouded SFR density is consistent with boththe CIRB spectrum and the number counts. However, a comparison with the infrared luminosity func-tion derived from extinction-corrected rest-frame optical/ultraviolet observations of the Lyman breakgalaxy population at zD 3 suggests that the almost Ñat comoving SFR density seen between redshifts of0.8 and 2 extends up to a redshift of zD 4.Subject headings : di†use radiation È galaxies : evolution È infrared : galaxiesOn-line material : color Ðgures

1. INTRODUCTION

The extragalactic background light (EBL) in the infrared,also referred to as the cosmic infrared background (CIRB),is a record of the emission, absorption, and reradiation ofphotons integrated over the cosmic history. It provides avaluable constraint on theories of galaxy formation andevolution. The EBL at near-infrared wavelengths is due toredshifted radiation from stars. At mid-infrared (MIR)wavelengths, the background is due to redshifted emissionfrom dust that consists of the polycyclic aromatic hydrocar-bon (PAH) features and very small grains (VSGs) tran-siently heated to T D 200 K in individual galaxies. Atfar-infrared (FIR) wavelengths, the dominant contributor isthought to be cold dust (T D 20 K) that is heated by theambient interstellar radiation Ðeld in galaxies. The recentdetection of this background at 2.2, 3.5, 140, and 240 kmusing COBE DIRBE data and in the 125È2000 km rangeusing COBE FIRAS measurements by various groups(Puget et al. 1996 ; Dwek & Arendt 1998 ; Fixsen et al. 1998 ;Hauser et al. 1998 ; Schlegel, Finkbeiner, & Davis 1998 ;Lagache et al. 1999 ; Gorjian, Wright, & Chary 2000 ;Wright & Reese 2000 ; Wright 2001) has indicated that theintensity of the optical/near-infrared background is roughly

1 Department of Astronomy and Astrophysics, University of Californiaat Santa Cruz, 477 Clark Kerr Hall, Santa Cruz, CA 95064 ;rchary=ucolick.org, elbaz=ucolick.org.

2 CEA Saclay, DAPNIA, Service dÏAstrophysique, Orme des Merisiers,91191 Gif-sur-Yvette, France.Ce� dex,

3 Physics Department, University of California at Santa Cruz, SantaCruz, CA 95064.

equal to that of the far-infrared background. This impliesthat about 50% of the integrated rest-frame optical/UVemission from stars and other objects is thermally repro-cessed by dust and radiated at mid- and far-infrared wave-lengths. Thus, star formation rates (SFRs) that are derivedfrom rest-frame optical/UV luminosities of galaxies are alower limit to the true SFR (see, e.g., Madau, Pozzetti, &Dickinson 1998 ; Meurer, Heckman, & Calzetti 1999 ;Steidel et al. 1999 ; Yan et al. 1999).

The Ðrst good evidence of this came from the IRAS skysurvey, which revealed a new population of galaxies with

km)º 1011 (see review by Sanders &L IR\ L (8È1000 L_Mirabel 1996). Those with were classiÐed asL IR º 1012 L

_ultraluminous infrared galaxies (ULIGs), while galaxieswith 1012 were classiÐed as luminousL

_[ L IRº 1011 L

_infrared galaxies (LIGs).4 These objects exhibited thelargest known SFRs of all local galaxies, but had D90% ofthe bolometric luminosity being emitted in the far-infrared(40È500 km), indicating that dust reprocessing is a signiÐ-cant parameter that needs to be considered in estimates ofstar formation in certain galaxies (see, e.g., Soifer et al.1986). However, in the local universe, the integrated bolo-metric luminosity density of ““ normal ÏÏ optically selectedgalaxies is Mpc~3, while that of infraredL Bol \ 4 ] 108 L

_luminous galaxies is D8 ] 106 Mpc~3, i.e., 50 times lessL_(Soifer et al. 1987). This seems to indicate that the contribu-

4 Previously, the term LIG was used for all objects with L IRº 1011 L_

.We use ““ infrared luminous galaxies ÏÏ when referring to both LIGs andULIGs collectively.

562

CONSTRAINTS ON DUST-ENSHROUDED SFR 563

tion from LIGs and ULIGs is sufficiently small that theyneed to be considered only as extreme cases.

Spectroscopic follow-up of the faint IRAS populationthat covered a relatively small redshift range (z\ 0.27) indi-cated that infrared luminous galaxies were more numerousin the past than they are today and may make a signiÐ-cantly larger contribution to the integrated luminositydensity than inferred from observations of the local universe(Kim & Sanders 1998). Deeper observations that tracethe far-infrared luminosity of galaxies to high redshift aredifficult since cirrus and confusion noise rapidly begin todominate.

The ISOCAM guaranteed-time extragalactic surveys inconjunction with the European Large Area ISO Survey(ELAIS) and observations of the lensing cluster Abell 2390covered a range of Ñux densities between 50 kJy and 50 mJyat 15 km (Altieri et al. 1999 ; Elbaz et al. 1999 ; Serjeant et al.2000). The di†erential counts resulting from these surveysrevealed that the counts of galaxies increase quite rapidly as

at brighter Ñux levels mJy) and then ÑattenSl~3 (Sl [ 0.4out as at fainter levels. The observed mid-infraredSl~1.6counts are an order of magnitude higher than expected ifthe local mid-infrared luminosity function was not evolvingwith redshift. This rapid increase in mid-infrared luminousgalaxies has been modeled as a (1] z)4.5 luminosity evolu-tion in the 15 km local luminosity function (LLF) by Xu(2000) and as a combination of number density and lumi-nosity evolution by Franceschini et al. (2001). This evolu-tion is much stronger than observed in the UV by Cowie,Songaila, & Barger (1999), who Ðnd that the comoving UVluminosity density evolves as (1] z)1.5 instead of the(1] z)3.9B0.75 initially proposed by Lilly et al. (1996). Fur-thermore, observations of galaxies in the local universe haveshown that the mid-infrared and infrared luminosities arewell correlated (° 2). The mid-infrared luminosity of D70%of the sources seen in the ISOCAM surveys, particularly inthe Hubble Deep FieldÈNorth and Ñanking Ðelds (HDF-N ] FF), translates to an infrared luminosity greater than1011 implying that the majority of them are LIGs andL

_,

ULIGs (Elbaz et al. 2001). At zD 0.8, the mid-infrared lumi-nosity density derived from the ISOCAM 15 km sources isD7 ] 107 Mpc~3, while the 8È1000 km luminosityL

_density adopting the mid- to far-infrared correlation seen inthe local universe is D5 ] 108 Mpc~3. In comparison,L

_at zD 0, LIGs and ULIGs contribute 106 Mpc~3 to theL_12 and 15 km luminosity density and 7.8 ] 106 Mpc~3L

_to the infrared luminosity density, as derived from the LLFof Soifer et al. (1987), Fang et al. (1998), and Xu et al.(1998). This indicates an increase by a factor of about 60between zD 0 and zD 0.8, providing further evidence foran evolution in the infrared luminosity function (IRLF)with redshift.

Similar deep surveys have been conducted at 850 kmusing the Submillimeter Common-User Bolometer Array(SCUBA) instrument on the James Clerk Maxwell Tele-scope (Hughes et al. 1998 ; Barger, Cowie, & Sanders 1999 ;Blain et al. 1999a ; Eales et al. 2000). The large beam size(14A FWHM) and the negative k-correction in this wave-length regime make identiÐcation of the optical counter-parts and thereby the redshift distribution of the sourcesvery difficult. High-resolution radio interferometric obser-vations and the use of 450 km/850 km Ñux ratios havehelped somewhat to localize the sources and constrain theredshifts (Hughes et al. 1998 ; Barger, Cowie, & Richards

2000). These have placed the bright mJy) sub-(Sl[ 6millimeter sources at zD 1È3, which has been conÐrmed bythe more extensive survey of Chapman et al. (2001). Theimplication of this is that most, if not all, of the sub-millimeter sources are extreme ULIGs with SFRs of102È103 yr~1. Furthermore, the SFR density due toM

_ULIGs must have increased by about 2 orders of magni-tude between zD 0 and zD 1È3.

Many of the LIGs and ULIGs in the local universe showmorphological signatures of interaction, and more than50% of the optical counterparts of ISOCAM HDF-N gal-axies show evidence for interactions (Mann et al. 1997).Surveys at visible wavelengths show a redshift evolution ofthe merger fraction, deÐned as the fraction of close pairs ofgalaxies, as D(1] z)3 (see, e.g., Le et al. 2000). Thus,Fevreif mergers were indeed a tracer of LIGs and ULIGs, thiswould again suggest that the bright end of the IRLF isevolving strongly. However, the faint end of the IRLF isvery poorly constrained at zD 1 since none of the long-wavelength surveys are sensitive enough to detect galaxieswith at z[ 0.5. Meurer et al. (1999) haveL IR\ 1011 L

_shown that the FIR-to-UV Ñux ratio is closely related to theUV slope for normal starbursts but that the relationshipbreaks down for ULIGs (Meurer et al. 2001). This indicatesthat the visible/near-infrared counts can potentially placeconstraints on the evolution of the faint end of the IRLF,but we postpone this discussion to the future.

In this paper, we combine data from a variety ofpublished surveys of nearby galaxies to determine the corre-lation, if any, between the luminosities at various mid- andfar-infrared wavelengths. We use these correlations to gen-erate smoothly varying spectral energy distributions (SEDs)for galaxies as a function of luminosity class. We assess theneed for luminosity and density evolution in the 15 kmluminosity function of Xu et al. (1998) and therefore the 60km luminosity function of Soifer et al. (1987) based on Ðts tothe ISOCAM 15 km, ISOPHOT 90 and 170 km, andSCUBA 850 km galaxy counts as well as the spectrum ofthe CIRB at j [ 5 km. The evolution of the mid-IR LF isthen translated to an estimate of the dust-enshrouded SFRdensity as a function of redshift and compared with SFRvalues derived from optical/near-infrared surveys. Weadopt an km s~1 Mpc~1, cos-H0\ 75 )

M\ 0.3, )" \ 0.7

mology throughout this paper unless otherwise explicitlystated.

2. LUMINOSITY CORRELATIONS IN THE INFRARED AND

TEMPLATE SPECTRAL ENERGY DISTRIBUTIONS

It can be shown that the 12 km and far-infrared lumi-nosities of galaxies in the IRAS Bright Galaxy Sample(BGS) cannot be accurately derived from their B-band lumi-nosities (Soifer et al. 1987).5 The peak-to-peak scatter in the

ratio for a Ðxed is about a factor of 20. However,LB/L IR L IRas mentioned earlier, the FIR-to-UV Ñux ratio has been

shown to be closely related to the UV slope for normalstarbursts (Meurer et al. 1999). This relationship breaksdown for the ULIGs (Meurer et al. 2001). The phenomenoncan be qualitatively explained by the fact that the UV emis-sion arises from stars that are relatively unobscured to theobserver. Regions of star formation with a large optical

5 The Zwicky magnitudes in the BGS were converted to B lumi-mZnosities using and a B-band zero point of 4260 Jy.mB\ mZ[ 0.14

564 CHARY & ELBAZ Vol. 556

depth, i.e., H II regions, could exist in the central regions ofgalaxies where almost all the UV light is reprocessed to theMIR and FIR. Thus, the regions of FIR and UV emissionwould be unrelated, especially for ULIGs. The best obser-vational evidence for this explanation can be seen in theAntennae galaxy (Mirabel et al. 1998), in which about halfthe 15 km emission seen by ISOCAM arises from regionsthat are inconspicuous at visible wavelengths. The break-down in the FIR-to-UV slope correlation for ULIGs isproblematic for the determination of the true SFR fromoptical/UV surveys since submillimeter observations usingthe SCUBA instrument indicate that ULIGs might have alarger contribution to the SFR density at high redshift. Thissuggests that it will be difficult to determine the true SFR byapplying an accurate extinction correction to the optical/UV-determined value.

Since the short-wavelength starlight and dust emissionare not closely related, an estimate of the dust-enshroudedSFR can only be derived from other tracers, such as themid-infrared and far-infrared luminosities, or by using theradioÈtoÈfar-infrared correlation shown by Condon (1992).In the mid-infrared regime, the spectra of galaxies exhibitbroad emission features at 6.2, 7.7, 8.6, 11.3, and 12.7 km,which are probably from PAHs (see review by Puget &Leger 1989). These features and their associated continuumdominate the emission at mid-infrared wavelengths short-ward of 10 km. There is, in addition, a continuum fromVSGs of size less than 10 nm, that dominates the emissionabove D10 km Boulanger, & Puget 1990 ; Laurent(De� sert,et al. 2000) except for quiescent star-forming galaxies. TheVSGs get transiently heated to temperatures of D200 K bythe ambient optical/UV continuum, which is proportionalto the star formation activity. In addition, mid-infraredmeasurements do not need large extinction correctionssince the extinction at mid-infrared wavelengths is onlyabout 1% of that at visible wavelengths (Mathis 1990). Theradio wavelengths, on the other hand, are dominated byfree-free emission from H II regions and synchrotron emis-sion from supernova remnants. Although radio obser-vations are almost confusion-limited at an 8.5 GHzsensitivity of 9 kJy obtained over the HDF (Richards et al.1998), we Ðnd that they are typically as sensitive as theISOCAM 15 km observations in that they can typicallyprobe galaxies with at zD 1. Since theL IR D 1011.4 L

_ISOCAM 15 km observations provide the primary con-straint on evolution models at z\ 1.2, we adopt as a start-ing point the local 15 km luminosity function described inXu et al. (1998) and Xu (2000). For the rest of this paper, wewill use the convention deÐned in Sanders & Mirabel(1996) :

L IR\ L (8È1000 km)

\ 1.8] 10~14] 1026(13.48L 12] 5.16L 25] 2.58L 60] L 100) (1)

L FIR \ L (40È500 km)

\ 1.6] 1.26] 10~14 ] 1026 (2.58L 60] L 100) . (2)

In the above equations, the symbol is deÐned as km)L j L l(jin units of Hz~1. and are inL_

L IR L FIR L_

.To use the mid-IR LF as a tracer of the dust-enshrouded

SFR, we Ðrst need to deÐne a calibration scale. Figures 1and 2 illustrate the accuracy with which the infrared lumi-nosity of galaxies can be derived from their mid-infrared

luminosities. Figure 1 is based on D300 galaxies from theIRAS BGS, while Figure 2 is based on published ISOCAMand ISOPHOT observations of IRAS galaxies. The datapoints with are Ðtted by a Ðrst-order poly-L IR[ 1010 L

_nomial shown in equations (4)È(6). This is shown as a solidblack line in the upper panels of the Ðgure. Objects with

are not used for the Ðts. At these low lumi-L IR\ 1010 L_nosities, the fraction of the bolometric luminosity emitted in

the infrared is less than 50%; i.e., visible starlight that is notobscured by dust is dominating the radiated energy of thegalaxy. On the other hand, a signiÐcant fraction of the moreluminous objects shows disturbed morphologies, suggestinginteractions with other galaxies that would result in gas-rich systems with star formation in highly obscured regions.The lower plots in both Ðgures show the scatter in the ratioof the infrared luminosity as derived from IRAS data forthese galaxies to the infrared luminosity derived from thepolynomial Ðts. Also shown is the 1 p uncertainty in thederived infrared luminosity calculated as the range withinwhich 68% of the galaxies lie. The lowest luminosity objects

have been rejected in the lower plots.(L IR\ 109 L_

)The 6.7 km luminosities were derived from Infrared Space

Observatory (ISO) observations of D90 nearby starburst-dominated galaxies. Forty-four spiral and starburst galaxieshad photometry from ISOCAM (P. Chanial et al. 2001, inpreparation ; Roussel et al. 2001 ; Laurent et al. 2000), eightULIGs had spectra from ISOCAM circular variable Ðlter(CVF) observations (Tran et al. 2001), while 37 ULIGs hadISOPHOT mid-infrared spectra (Rigopoulou et al. 1999).Rigopoulou et al. (1999) obtained mid-infrared spectra withISOPHOT of about 60 ULIGs and about 15 low-luminosity starbursts and normal galaxies to study theemission features from the PAHs. Of the 60 ULIGs, about45 had the 7.7 km PAH feature detected with a good signal-to-noise ratio. However, the calibration and performance ofthe instrument is not very well determined. To assess thequality of the data set, we compared the ISOPHOT obser-vations on Ðve ULIGs and four low-luminosity starbursts/normal galaxies to the P. Chanial et al. (2001, inpreparation) ISOCAM LW2 observations of the same gal-axies.6 We Ðnd that for the ULIGs, the ratio of 7.7 kmline] continuum Ñux density as published in Rigopoulouet al. to the ISOCAM 6.7 km Ñux density lies in the 1.5È3.0range. In comparison, for the starbursts/normal galaxies,the ratio of 7.7 km line] continuum to the ISOCAM 6.7km Ñux density falls in the 0.2È1.6 range, a factor of 8. So,for assessing the correlation between the mid- and far-infrared luminosities, we consider the ISOCAM data onbright IRAS galaxies as well as the ULIG sample of Rigo-poulou et al. (1999), dividing the line] continuum Ñuxvalue published in the latter by 2.4 and assigning a peak-to-peak error bar of a factor of 2. This is consistent with therange of 1.5È2.7 that we Ðnd for the 7.7 kmline] continuum to the 6.7 km Ñux density ratio in theISOCAM CVF observations of Tran et al. (2001).

The 15 km and infrared luminosities of 120 IRAS gal-axies were taken from the sample of P. Chanial et al. (2001,in preparation) and the survey performed in the north eclip-tic pole region (NEPR) by Aussel et al. (2000). The NEPRsample of galaxies only has IRAS 60 km luminosities avail-able, and we have converted these to a far-infrared lumi-

6 The LW2 Ðlter is broad enough to include the 7.7 km PAH feature butis centered at 6.75 km.

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 565

FIG. 1.ÈPlots showing the relative accuracy of tracing infrared luminosities (8È1000 km) of IRAS BGS (Soifer et al. 1987) objects from the B-band (0.44km) and 12 km luminosities. The lower plots show the ratio between the true infrared luminosity and the predicted infrared luminosity derived(L IR) (SL IRT)from the B-band or 12 km luminosity using a Ðrst-order polynomial Ðtted to data points with If the infrared luminosity of all galaxies couldL IR[ 1010 L

_.

be predicted precisely from their B-band or 12 km luminosity, then all points in the lower plot would lie in a horizontal line with The lowerL IR/SL IRT \ 1.plots also show the 1 p uncertainty in the prediction of the infrared luminosities.

nosity based on a 60 kmÈtoÈfar-infrared correlation derivedby combining the IRAS BGS and the IRAS Point-SourceCatalog Redshift survey (PSCz) of Saunders et al. (2000).The far-infrared luminosity is typically about 83% of thetotal infrared luminosity, and we have applied this conver-sion to be consistent with the other plots.

Clearly, the 6.7, 12, and 15 km luminosities of galaxiestrace the infrared luminosity much better than the B-bandluminosity. The 15 kmÈtoÈIR and 12 kmÈtoÈIR corre-lations were determined from a Ðrst-order polynomial Ðttedto the data with Since the 6.7 kmÈtoÈIRL IR[ 1010 L

_.

correlation is based on di†erent data sets from CVF andbroadband photometry with ISOCAM and spectroscopyusing ISOPHOT, the polynomial Ðt for the 6.7 kmÈtoÈIRcorrelation was determined by applying a k-correction from6.7 to 15 km based on ISOCAM observations of nearbygalaxies (Fig. 3) and then using the 15 kmÈtoÈIR corre-lation. The mid-infraredÈtoÈIR correlations show a similarscatter around the correlation line, which is about a factorof 5 better than the optical-to-IR correlation.

These data sets tentatively illustrate the potential of usingthe mid-infrared as a tracer of dust-enshrouded star forma-tion, and a more homogeneous and comprehensive surveyof nearby galaxies, as will be undertaken by the Space Infra-red Telescope Facility (SIRT F ), will be required to eitherstrengthen or reject this correlation.

Kennicutt (1998) has transformed the infrared luminosityof young (age \ 108 yr) starburst galaxies to an SFR. If

we adopt the correlations shown in the previous Ðgures, wecan translate the mid-infrared luminosity of galaxies with

to an approximate estimate of the dust-L IR[ 1010 L_enshrouded SFR (o@) using the formula

o@(M_

yr~1) \ 1.71] 10~10L IR (L_

) , (3)

L IR\ 11.1~3.7`5.5 L 15 km0.998 , (4)

L IR\ 0.89~0.27`0.38 L 12 km1.094 , (5)

L IR\ 4.37~2.13`2.35 10~6 ] L 6.7 km1.62 , (6)

where all values are in units of solar luminosity. The 1 pvalues have been estimated by calculating the range ofvalues within which 68% of galaxies have their observedinfrared luminosities.

As mentioned earlier, the main observational constraintson models that trace the redshift evolution of the IRLF arethe following :

1. Di†erential counts from various surveys at mid-infrared, far-infrared, and submillimeter wavelengths.

2. The spectrum of the CIRB at j [ 5 km.

To use these constraints, it is necessary to know the lumi-nosity at di†erent wavelengths for galaxies in each lumi-nosity bin of the IRLF. This motivates the generation oftemplate spectra for objects of di†erent luminosity classes.It is useful to note that many evolutionary models that havealready been developed either use a mid-infrared template

566 CHARY & ELBAZ Vol. 556

FIG. 2.ÈPlots showing the relative accuracy of tracing infrared luminosities (8È1000 km) from the 6.7 and 15 km luminosities. The 6.7 km luminosities arefrom ISOCAM guaranteed-time surveys ( Ðlled circles ; P. Chanial et al. 2001, in preparation) and ISOPHOT 7 km spectroscopy of ULIGs (open triangles) byRigopoulou et al. (1999). Note that the Rigopoulou et al. (1999) values have been modiÐed as described in the text. Asterisks are the 6.7 km luminosities forthe starburst-dominated ULIG sample of Tran et al. (2001). Some of the extreme ULIGs might have a signiÐcant AGN contribution, which could result in adeviation from the 6.7 kmÈtoÈIR correlation derived for starbursts by decreasing the IR luminosity for a given 6.7 luminosity, as for the two brightest galaxiesin our sample. The 15 km luminosities are from the P. Chanial et al. (2001, in preparation ; Ðlled circles) and the Aussel et al. (2000 ; plus signs) sample ofgalaxies. The lower plots are similar to those in Fig. 1.

that is a very poor representation of the true PAH emissionfeatures (e.g., Rowan-Robinson 2001 ; Pearson 2001 ; Sadat,Guiderdoni, & Silk 2001) or neglect the PAH features alto-gether (Malkan & Stecker 1998, 2001). It is trivial to showthat this makes a critical di†erence in the quality of the Ðtsto the ISOCAM mid-infrared number counts and thereforea†ects the evolution parameters, particularly at z\ 1. So, itis important to have template SEDs that reproduce theobserved trend in the luminosity of local galaxies at di†er-ent wavelengths.

Using MIR, FIR, and submillimeter data from ISOCAM,IRAS, and SCUBA observations of nearby galaxies, weÐtted the observed trend between di†erent mid- and far-infrared luminosities, as shown in Figure 3. The top twopanels in the Ðgure show the ISOCAM observations at 6.7and 15 km for D50 IRAS galaxies that are described in P.Chanial et al. (2001, in preparation). The solid lines in thepanels show two Ðrst-order polynomial Ðts, one for galaxieswith 15 km luminosity less than 2 ] 109 and another forL

_more luminous galaxies. This is because the ratio betweenthe mid-infrared luminosities changes as a function of the 15km luminosity, possibly because of enhanced emission fromthe VSG component (Laurent et al. 2000). The luminositybreak corresponds to which is similar toL IRD 2 ] 1010 L

_,

the luminosity cuto† used for deriving equations (4)È(6).The panel showing the 15È60 km trend consists of datadescribed in Figure 2. The 60 kmÈtoÈFIR correlation is for

the IRAS BGS and PSCz galaxies, while the panel showingthe IR-to-FIR correlation is only for the IRAS BGS gal-axies. The last panel shows SCUBA submillimeter data onD100 IRAS galaxies (Dunne et al. 2000). In addition, thecorrelation between IRAS 25 and 100 km luminosities forgalaxies in the BGS was also determined. The solid lines forthe four lower panels utilize only a single Ðrst-order poly-nomial Ðtted to all the data points. Also shown in the panelsas triangles are the luminosities at the corresponding wave-length for the di†erent templates that were generated asdescribed below.

Template SEDs were generated between 0.1 and 1000 kmto reproduce the observed trend between mid-infrared andfar-infrared luminosities. To generate these templates, weused the basic Silva et al. (1998) models to reproduce theultraviolet-submillimeter SED of four prototypicalgalaxiesÈArp 220, NGC 6090, M82, and M51. These corre-spond to objects of four di†erent luminosity classesÈULIGs, LIGs, ““ starbursts ÏÏ (SBs) and ““ normal galaxies,ÏÏrespectively. ISOCAM CVF observations between 3 and 18km of these galaxies provided new data on the relativestrength of the mid-infrared features and continuum(Charmandaris et al. 1999 ; Laurent et al. 2000 ; Forster-Schreiber et al. 2001 ; Roussel et al. 2001). The mid-infraredregion of the modeled spectra were then replaced with theISOCAM observations. In addition, corrections were madefor the 17.9 km silicate feature based on observations by

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 567

FIG. 3.ÈPlot showing the data (asterisks) at di†erent wavelengths from IRAS, ISOCAM, and SCUBA surveys (Soifer et al. 1987 ; Aussel et al. 2000 ;Dunne et al. 2000 ; Saunders et al. 2000 ; P. Chanial et al. 2001, in preparation). The lines are the best-Ðt polynomial of order 1. The triangles are thecorresponding values from our template SEDs that were generated as described in the text. [See the electronic edition of the Journal for a color version of thisÐgure.]

Smith, Aitken, & Roche (1989). The four template spectrawere checked to ensure that the IRAS observed values ofthese four galaxies were reproduced. We then partitionedthe four templates into a mid-infrared (4È20 km) and far-infrared (20È1000 km) component and interpolated between

the four to generate a range of mid- and far-infrared sampletemplates of intermediate luminosity. An additional set offar-infrared templates provided by Dale et al. (2001) wereadded to the ensemble of far-infrared templates to span awider range of spectral shapes.

568 CHARY & ELBAZ Vol. 556

FIG. 4.ÈTemplate SED for objects of three di†erent infrared lumi-nosities along with the predicted luminosities at di†erent wavelengths(diamonds). The luminosities correspond to 1011, and 1010L IR\ 1012, L

_,

illustrating the SED of ULIGs, LIGs, and starbursts, respectively. Thelower plot shows the same templates, normalized at 0.44 km (B band) toshow the evolution of the spectrum as a function of infrared luminosity. Nocorrection for the UV slope has been made.

For each luminosity bin of the 15 km luminosity function,the luminosities at the following wavelengths, 6.7, 12, 25, 60,100, and 850 km, were predicted based on the polynomialÐts to the data shown in Figure 3. Of the D100 mid-infraredsample templates generated as described above, the mid-infrared template that best Ðts the predicted 6.7, 12, and 15km luminosities was selected. Similarly, the far-infraredtemplate that best Ðts the predicted 25, 60, 100, and 850 kmluminosities was selected. The luminosity of the templatesat the corresponding wavelengths was determined by inte-grating over the Ðlter curves of the instruments. Our goalwas only to generate SEDs that reproduce the observedtrend in luminosities at di†erent wavelengths. Selecting avariety of sample templates provided better Ðts to the pre-dicted luminosities than by just interpolating between thefour SEDs generated by the Silva et al. (1998) models. Thebest-Ðtting mid-infrared and far-infrared templates werethen merged together to provide the Ðnal template SED foreach luminosity bin. The red triangles in Figure 3 are theluminosities at the corresponding wavelengths from theÐnal merged template SEDs. The B-band luminosity of gal-axies in the IRAS BGS shown in Figure 1 was also used toconstrain the optical/near-infrared SED of galaxies, but, asstated before, we have not constrained the UV slope of thetemplate SEDs. The absence of a good correlation betweenthe B-band and IR luminosities implies that the optical/near-infrared part of our SEDs is highly uncertain. This isnot a major problem since we are only analyzing the dustemission in this paper. The templates for three objects withinfrared luminosities of 1010, 1011, and 1012 along withL

_

the predicted luminosities at di†erent wavelengths based onthe correlations in Figure 3 are shown in Figure 4.

3. EVOLUTION OF THE 15 km AND FAR-INFRARED LOCAL

LUMINOSITY FUNCTION

Since our intention is to use the di†erent mid- and far-infrared observational constraints to estimate the evolutionof the dust-enshrouded SFR with redshift, we use the 15 kmLLF as a tracer of dust emission in the local universe. Xu etal. (1998) and Xu (2000) derived a 15 km LLF based on acorrelation between ISOCAM mid-infrared and IRAS mid-and far-infrared data. In addition, estimates of the 12 kmLLF have been made by Rush, Malkan, & Spinoglio (1993)and Fang et al. (1998). The di†erent 12 and 15 km lumi-nosity functions are shown in Figure 5. Also shown is thepredicted 60 km LLF derived from the mid-infrared LLFusing a mid-infraredÈtoÈ60 km conversion from the poly-nomial Ðt to the observations of Aussel et al. (2000) and P.Chanial et al. (2001, in preparation) described earlier. Allthese are in good agreement with each other since theywere essentially derived from IRAS observations of nearbygalaxies.

Evolution of the luminosity function with respect to red-shift can be expressed as

((L , z) \ n(z)/(L , z) , (7)

/(L , z) \ /C Lg(z)

, 0D

, (8)

where ((L , z) is the number density of galaxies as a functionof luminosity L and redshift z. The n(z) term representsevolution in the number density of galaxies, while the /(L , z)term represents luminosity evolution. The term /(L , 0) is theLLF. We consider models where n(z) is of the form n(0)

up to a turnover redshift followed by(1] z)aD zturnD n(zturnD )up to z\ 4.5. The luminosity evolu-[(1] z)/(1 ] zturnD )]bD

tion component up to followed byg(z) \ (1 ] z)aL zturnLg(zturnL )[(1 ] z)/(1 ] zturnL )]bL.

It should be emphasized that there is considerable degen-eracy in the density and luminosity evolution of galaxies.While density evolution slides the luminosity function alongthe vertical axis, the latter slides it along the horizontal axis.However, current observations at mid- and far-infraredwavelengths detect galaxies only at the luminous end of theluminosity function, as a result of which, the two are indis-tinguishable. This is shown in Figure 6. The Ðgure alsoshows that evolving just the luminous end of the LLF, i.e.,L [ 5 ] 1010 which is similar to the model proposedL

_,

by Dole et al. (2000), would result in the same degeneracywith observations, although it would result in a somewhatunphysical break in the luminosity function.

There is an additional degeneracy induced by the fractionof the luminosity function that is evolving. Redshift mea-surements of ISOCAM 15 km sources in the HDF-N ] FFindicate that the majority of them are LIGs and ULIGs(Elbaz et al. 2001). Interestingly, when the local 60 km lumi-nosity function is compared to the Schechter function com-monly used to represent the LLF at visible wavelengths, anexcess of galaxies is seen in the 60 km LLF beyond

since the Schechter function drops fasterL 60 km[ 1011 L_at the bright end. On one hand, it seems likely that just this

excess of galaxies, most of which show morphological signa-tures of merger activity, could be evolving at high redshift.

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 569

FIG. 5.ÈVarious 12 and 60 km LLFs for km s~1 Mpc~1. In the upper plot, the black lines and symbols represent the 12 km LLF from Rush etH0\ 75al. (1993). The solid black line is the total LLF, the black dot-dashed line is the non-Seyfert contribution, the dotted line is from Seyfert 1 galaxies, and thedashed line is from Seyfert 2 galaxies. The green line and symbols are the 12 km LLF from Fang et al. (1998). The purple line and triangles are the 15 km LLFfrom Xu et al. (1998) and Xu (2000). The red line is this 15 km LLF converted to 12 km based on a k-correction derived from ISOCAM observations of 44nearby galaxies. The lower plot shows the 60 km LLF from Soifer et al. (1987) as the dashed red line, the 60 km LLF of Saunders et al. (1990) as the blacktriangles, the 12 km LLF of Fang et al. (1998) converted to 60 km using a linear 12 kmÈtoÈ60 km correlation based on IRAS BGS data as the green line, andthe Xu et al. (1998) 15 km LLF converted to 60 km as the purple line.

Alternatively, it is possible that a luminosity-dependentfraction that approaches 100% at of theL 60 km[ 1011 L

_LLF could be evolving. Unfortunately, the observationalconstraints on the faint end of the IRLF are limited sincethese galaxies are undetected at mid- and far-infrared wave-lengths at z[ 0.5. The correlation between mid-infraredand visible wavelengths being poor, the counts of galaxiesat visible/near-infrared wavelengths cannot be used to con-strain the distribution. However, we will investigate in afuture paper if the relationship between the FIR/UV Ñuxratio and UV slope can constrain the evolution of the faintend of the IRLF.

The principal observational constraints on the evolutionof the bright end of the luminosity function then are thefollowing :

1. The ISOCAM di†erential number counts at 15 km,especially the ““ knee ÏÏ in the counts slope at 0.4 mJy (Elbazet al. 1999).

2. The 15 km EBL, which has a lower limit from ISOcounts and an upper limit from gamma-ray observations ofa TeV Ñare in Markarian 501.

3. The redshift distribution of 15 km sources in the HDF-N ] FF, which is somewhat peaked at zD 0.8 (H. A. Ausselet al. 2001, in preparation) and indicates that 45% of gal-axies with mJy are LIGs and 20% are0.1\S15\ 0.4ULIGs, with the remaining being normal and low-luminosity starburst galaxies (Elbaz et al. 2001).

4. The spectrum of the cosmic far-infrared backgroundbetween 100 and 850 km as measured by DIRBE andFIRAS on COBE.

570 CHARY & ELBAZ Vol. 556

FIG. 6.ÈDegeneracy between luminosity and density evolution. Thetriangles are the extrapolated 60 km LLF of Soifer et al. (1987), the solidline is the resultant luminosity function at zD 1 assuming a density evolu-tion of (1 ] z)5, while the dashed line is the luminosity function at zD 1assuming a luminosity evolution of (1 ] z)2. Also shown is the typicalluminosity range of galaxies that have been detected by current long-wavelength surveys.

5. ISOPHOT 90 and 170 km counts and SCUBA 850km number counts (Efstathiou et al. 2000 ; Hughes et al.1998 ; Blain et al. 1999a ; Barger et al. 1999 ; Eales et al. 2000 ;Dole et al. 2001).

The k-correction of galaxies illustrated in Figure 7 clearlyillustrates the range of redshifts that can be studied byobservations at these wavelengths. The 850 km obser-vations are typically confusion-limited at 2 mJy. However,deeper lensed surveys or using high-resolution radio inter-ferometric data can push the detection threshold down to0.5 mJy, which is past the confusion limit. This allows thedetection of objects with out to zD 5,L IR [ 5 ] 1011 L

_which transforms to an SFR of greater than 85 yr~1.M_On the other hand, the ISO mid- and far-infrared obser-

vations are typically dominated by galaxies at z\ 1 and socan constrain the low-redshift turnover in the luminosityfunction evolution.

Figure 8 illustrates the nature of the counts if the 15 kmluminosity function remained equal to the local one at allredshifts, i.e., no evolution. The Ðrst plot shows theISOCAM 15 km di†erential counts from Elbaz et al. (1999),which include the IRAS 12 km counts converted to 15 kmby Xu (2000) and the ELAIS 15 km counts of Serjeant et al.(2000) renormalized as in Genzel & Cesarsky (2000). Theremaining plots show the ISOPHOT FIRBACK 170 kmcounts, ISOPHOT, IRAS BGS, and PSCz 90 km counts,and SCUBA 850 km integral counts. Also shown are therelative contributions from ULIGs, LIGs, and L IR \ 1011

galaxies to the counts at di†erent wavelengths.7 Clearly,L_some form of redshift evolution in the luminosity function is

required to Ðt the counts. It should be emphasized thatevolutionary models should be Ðtted to the di†erentialcounts at di†erent wavelengths since integral counts tend tosmooth over any subtle changes in the galaxy count slope.This requires that the calibration of the data from di†er-ent surveys using the same instrument be consistent andaccurate.

7 From now on, we refer to the galaxies as normal/SBL IR\ 1011 L_galaxies

The ISOPHOT 90 km data are known to su†er fromlarge calibration uncertainties that are not reÑected in theerror bars. We show in ° 3.3 that our models Ðt the 170 kmcounts but consistently overpredict the 90 km counts,although both wavelengths probe similar populations ofgalaxies at z\ 1.2. We Ðnd that an upward correction ofthe 90 km Ñux densities by 30%, which is well within thecalibration uncertainties, leads to excellent agreementbetween our models and the data. In addition, the faint-endPSCz counts are known to su†er from incompleteness(Efstathiou et al. 2000).

Any evolution of the luminosity function must have aturnover at some redshift to avoid overproducing thezturnCIRB. In theory, the turnover redshifts thezturnD (zturnL ), a

Dvalue for the slope of the density (luminosity) evolution(aL)

at and the value for can be di†er-z\ zturn, bD

(bL) z[ zturnent, implying that there are e†ectively six parameters. We,

however, consider models with since it iszturnD \ zturnLunclear why the turnover for luminosity and density evolu-tion, both of which are probably induced by galaxy inter-actions, should be di†erent. The range of values for a, b, and

selected for our models were 1¹ a ¹ 6, [3 ¹ b ¹ 0,zturnand respectively. Evolutionary models0.6¹ zturn ¹ 1.5,with pure luminosity evolution and pure density evolutionare also considered.

3.1. Constraints on Pure Density EvolutionWe Ðnd that pure density evolution of the entire lumi-

nosity function cannot reproduce the counts at all the wave-lengths. In this scenario, the 15 km counts are dominated bythe normal/SB galaxies, not by LIGs and ULIGs, which isinconsistent with observations in the HDF-N ] FF.Second, the normal/SB galaxies are unable to reproduce thebreak in the 15 km counts seen at 0.4 mJy but insteadproduce a sharp break only at mJy.Sl \ 0.2

However, density evolution models that evolve just afraction of the 15 km luminosity function, with the fractionbeing less than 5% at and approachingL 15 kmD 109 L

_100% at 15 km luminosities greater than 8] 1010 pro-L_

,vides reasonable Ðts to the data (dotted line in Fig. 14). Thebest-Ðt density evolution parameters then are a

D\ 12.0

^ 0.5 up to followed byzturnD \ 0.7^ 0.1 [0.5\bD

¹ 0(Fig. 9). The Ðrst plot shows the spectrum of the CIRB withlower limits from integrated counts of galaxies in theoptical/UV from Madau & Pozzetti (2000), measurementsin the near- and far-infrared using the DIRBE instrument(Hauser et al. 1998 ; Finkbeine, Davis, & Schlegel 1999 ;Gorjian et al. 2000 ; Wright 2001), an estimate of the far-infrared background from FIRAS (Lagache et al. 1999), andlower limits in the mid-infrared, far-infrared, and sub-millimeter from counts of individual galaxies (Elbaz et al.1999 ; Blain et al. 1999a ; Matsuhara et al. 2000). Also shownis the upper limit on the CIRB from TeV observations ofMrk 501 (Stanev & Franceschini 1998) and the cosmicmicrowave background at j [ 300 km. The remaining plotsshow the counts for this evolution model.

Models with result in a signiÐcant over-aD

[ 13.0prediction of the 170 km counts, while under-a

D\ 11.0

predicts the submillimeter counts. Changing the turnoverredshift to high redshift shifts the knee in the 15 kmzturnDdi†erential counts to fainter Ñux levels and vice versa. Theslope of the evolution at is mainly constrained byzturnD [ 0.7the spectrum of the CIRB at j [ 200 and the 850 kmcounts.

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 571

FIG. 7.ÈPredictions of Ñux densities at di†erent wavelengths as a function of redshift for objects with an infrared luminosity of 1013 (triple-dotÈdashedline), 1012 (dotted line), 1011 (dashed line) and 3 ] 1010 (dot-dashed line). The solid horizontal line is the sensitivity of the deepest unlensed observationL

_performed. The observations of lensing clusters at 15 km are sensitive down to 50 kJy, while those at 850 km are sensitive down to 0.5 mJy.

The 170, 90, and 15 km observations all probe the popu-lation of galaxies at z\ 1.2. However, in this density evolu-tion model, the 15 km counts are dominated (D90%) byLIGs and have an D5% contribution from ULIGs. In com-parison, the 170 km counts are dominated by ULIGs atredshifts between 0.5 and 1, while the 90 km counts haveroughly equal contributions from all three populations ofgalaxies. The 850 km galaxies at Ñux densities larger than 1mJy are mainly ULIGs at z[ 1, while LIGs between red-shifts of 0.6 and 2.0 dominate the counts at fainter Ñuxlevels.

The pure density evolution model shown appears tooverpredict the contribution from LIGs (D90%) to the 15km number counts and underestimates the bright-end 850km counts. Second, many LIGs and ULIGs have been mor-phologically associated with disturbed systems. So a steepevolution in the density of objects should reÑect in anincrease of the merger fraction, which is deÐned as the frac-tion of galaxies in close pairs. Observationally, the mergerfraction when averaged over all galaxies appears to evolve

much slower with redshift, approximately as (1] z)3 (see,e.g., Le et al. 2000). It is possible, though, that theFevreLIGs and ULIGs have a merger fraction that increasesmuch more rapidly than (1 ] z)3, but this has not beenestimated since there are no clear observational signaturesof LIGs and ULIGs at visible wavelengths. Although thereis no strong observational evidence in favor of pure densityevolution of a fraction of the luminosity function, we showin Figure 14 that it does predict the same number density ofinfrared luminous galaxies at high redshift as other modelsand so cannot be entirely ruled out.

3.2. Constraints on Pure L uminosity EvolutionWe have shown above that some form of luminosity evol-

ution is required to avoid deriving large values for the slopeof the density evolution. The slope of the luminosity evolu-tion is strongly constrained by the mid-infrared numbera

Lcounts. Values of are unable to reproduce theaL\ 4.5

break of the di†erential counts seen at a 15 km Ñux densityof 0.4 mJy, while results in an overproduction ofa

L[ 5.5

572 CHARY & ELBAZ Vol. 556

FIG. 8.ÈResults for a no-evolution model with thin solid line representing the contribution from all galaxies, with the dotted line indicating ULIGs only,the dashed line indicating LIGs only, while the dot-dashed line is for normal/starburst galaxies, i.e., (This convention will be used for theL IR\ 1011 L

_remaining Ðgures as well). Clockwise from top left : (1) ISOCAM di†erential counts at 15 km. Also shown are the bright-end IRAS counts of Xu (2000), whichpotentially have a factor of 2 uncertainty associated with them. (2) SCUBA 850 km integral counts. (3) IRAS and ISOPHOT 90 km di†erential counts. (4)ISOPHOT 170 km di†erential counts (see text for references).

the counts at bright Ñux densities (Fig. 10). If the entire LLFis evolved (solid black line in Fig. 14), up toa

L\ 5.0 zturnL \

0.8 followed by the 90 km di†erential[0.5\bL¹ 0.0,

counts are overproduced, but all the other counts are repro-duced very well.

This is only partially consistent with the results of Xu(2000), who suggested that the mid-infrared counts can bemodeled by evolving the entire LLF by L (z)P (1] z)4.5 forz\ 1.5 and by L (z)\ L (0)] 2.54.5 for higher redshifts. WeÐnd that a luminosity evolution of (1 ] z)4.5 up to zD 1followed by L (z)\ L (0)] 2.04.5 overpredicts the CIRB andprovides only marginal Ðts to the mid-infrared counts at thefaint end. Extending this evolution up to severelyzturnL D 1.5overpredicts the CIRB as well as the observed faint-end 15and 850 km counts.

The main problem with pure luminosity evolution is thatthe 90 km counts at Jy are overproduced, but, asSl\ 6mentioned earlier, this can be resolved by rescaling theISOPHOT 90 km Ñux densities upward by 30%, which iswithin the calibration uncertainties of the instrument. Inaddition, the break in the 15 km di†erential counts in thisevolution model is not as sharp as observed.

As in the pure density evolution model, the counts at 15,90, and 170 km all trace galaxies at z\ 1.2, but the relativecontributions from LIGs, ULIGs, and normal/SB galaxiesdi†er, with the 90 km counts having roughly equal contri-butions from all three populations, the 170 km counts being

dominated by ULIGs, and the 15 km counts being domi-nated by LIGs and low-redshift normal/SB galaxies. Pureluminosity evolution predicts that the contribution fromnormal/SB galaxies to the 15 km counts between 0.1 and 0.4mJy is 35%, similar to that observed in the HDF-N] FF.However, the contribution from ULIGs in the same Ñuxdensity range is found to be only 6% in this model, which isa factor of 3È4 smaller than that observed.

3.3. Combination of L uminosity and Density EvolutionWe have already illustrated the degeneracy and problems

with pure luminosity and pure density evolution in the Ðtsto the number counts. As illustrated above, both of themprovide reasonable Ðts to the spectrum of the CIRB and tothe di†erential counts at three wavelengths. An additionaldegeneracy is introduced when using a combination ofluminosity and density evolution with only a fraction of theLLF evolving.

The fraction of the LLF that is evolving is deÐned as the““ dusty starburst ÏÏ population. We consider these to be gal-axies with This corresponds toL

B/L IR\ 0.5. L IRº 1010.2

All galaxies with are then evolved,L_

. L IRº 1010.2 L_while only about 5% of the galaxies with L IR\ 1010.2 L

_(““ normal ÏÏ galaxy population) are evolved, with a smoothtransition between the two (dashed line in Fig. 14). We alsoconsidered models where the dusty starburst population isdeÐned at a larger minimum luminosity but(L IR D 1011 L

_)

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 573

FIG. 9.ÈResults for the best-Ðtting pure density evolution model with only the most luminous end of the LLF evolving (dotted line in Fig. 14). Theevolutionary parameters are and The upper left plot shows the spectrum of the CIRB: triangles represent the COBE DIRBEa

D\ 12.0, b

D\ 0, zturnD \ 0.7.

results, squares with upward arrows are lower limits from integrated counts at di†erent wavelengths, the dark band is the FIRAS constraint, the hatchedregion represents upper limits from TeV gamma-ray observations of Mrk 501, the dashed line represents the cosmic microwave background, and the heavysolid line is the prediction from the model. The remaining plots are similar to Fig. 8.

were unable to Ðnd evolution parameters that could reason-ably reproduce all the data.

Our best-Ðt model using a combination of both densityand luminosity evolution for a fraction of the LLF asdeÐned above is shown in Figure 11. Almost all the countsare reproduced quite well, with the exception of the 90 kmcounts from ISOPHOT and PSCz, which all our modelsconsistently overestimate. We interpret this to be due to acalibration error in the ISOPHOT data as a result of whichthe published Ñux density values are low by D30%. Alsoshown in the Ðgure is the surface density of galaxies perredshift bin contributing to the counts at di†erent wave-lengths, as derived from the model, and the observed red-shift distribution of the ISOCAM 15 km galaxies in theHDF-N] FF (H. A. Aussel et al. 2001, in preparation). Thesize of each redshift bin is 0.2.

In the preceding three subsections, we have shown arange of models that evolve the local 15 km luminosityfunction and Ðt the observed counts at mid- and far-infraredwavelengths as well as the spectrum of the CIRB. UltradeepSIRT F observations at 24 km can potentially break thedegeneracy in these models if the counts can be determinedto an accuracy of 20% or better (Fig. 12). The range ofintegral source counts that we predict based on our threeevolutionary models (density, luminosity, and a com-bination of both) are 4.7, 3.8, and 3.7 arcmin~2 for Sl [ 120kJy and 19.8, 19.3, and 11.8 arcmin~2 for kJy.Sl[ 22

However, the integral counts can be as low as 9.1 arcmin~2at a Ñux density limit of 22 kJy for models that are at theextreme lower limit of the uncertainty in current obser-vations.

4. THE ORIGIN OF THE CIRB

4.1. Nature of the Galaxies Contributing to the CIRBIn our evolution models, we have assumed that the con-

tribution from active galactic nuclei (AGNs) to the countsand the cosmic background is insigniÐcant. Other evolu-tionary models, which assumed an AGN component,arrived at the same conclusion (Malkan & Stecker 1998 ;Rowan-Robinson 2001 ; Xu et al. 2000 ; A. Franceschini etal. 2001, in preparation). Observational evidence for thisassumption comes from deep Chandra observations of theHDF-N proper (Brandt et al. 2001), which detected eight ofthe ISOCAM 15 km sources. However, only one of these isan AGNs at zD 1, and this was already known as suchfrom observations at visible wavelengths (see discussion inElbaz et al. 2001 ; H. A. Aussel et al. 2001, in preparation). Itshould be noted that it is insufficient to have an AGN in agalaxy to violate this assumption but that the integratedinfrared light of the galaxy must be dominated by an AGNrather than by star formation. However, since the contribu-tion of dust-enshrouded AGN at high redshift, beyondISOCAM detection thresholds, is unknown, our results are

574 CHARY & ELBAZ

FIG. 10.ÈResults for the best-Ðtting pure luminosity evolution model of the entire LLF (solid black line in Fig. 14) with andaL\ 5.0, b

L\ 0, zturnL \ 0.8 ;

reduces the CIRB at j [ 200 km but slightly lowers the bright-end SCUBA counts at Ñux densities greater than 2 mJy.bL\[0.25

subject to this uncertainty. A large ([20%) contributionfrom AGNs to the source counts or the CIRB will imply aweaker redshift evolution of the luminosity function.

The evolution parameters in our model are constrainedstrongly by the ISOCAM counts at z\ 1.2 and by theSCUBA counts at zD 1È3. In addition, the ISOCAMcounts are dominated by LIGs, while the SCUBA countsare dominated by ULIGs. Thus, barring a dramatic changein the ratio of LIGs to ULIGs between a redshift of 1 and 2,we conclude that our models have robustly determined theevolution of the luminous end of the LLF(L IR [ 1011 L

_)

up to zD 2. At z? 2, the best constraint comes from thespectrum of the CIRB. Since all our models that are almostÑat beyond zD 2 provide values for the CIRB that are atthe upper limit of the values observed by FIRAS, we con-clude that these models place a strong upper limit on theestimate of dust-enshrouded star formation at z[ 2.

Our models indicate that about 80% of the 140 km CIRBis produced at z\ 1.5. In comparison, 90% of the 15 kmEBL, 65% of the 240 km background, and only about 30%of the 850 km background are produced within this redshiftrange (Table 1). We also derive that ISOCAM galaxiesbrighter than 0.1 mJy contribute 14.5 nW m~2 sr~1 to the140 km EBL, while galaxies brighter than 0.05 mJy produce16.8 nW m~2 sr~1. This accounts for about 75% of the totalfar-infrared background (Table 2). In comparison, we Ðndthat the contribution from SCUBA-detected galaxiesbrighter than the confusion limit of 2 mJy at 850 km is only3.4 nW m~2 sr~1 at 140 km, while galaxies brighter than 0.5mJy produce 16.4 nW m~2 sr~1. This is because at 850 km

Ñux densities fainter than 1 mJy, the LIGs that dominatethe ISOCAM counts and produce the majority of the 140km EBL contribute signiÐcantly to the SCUBA counts. Thetotal EBL at 15 km from our model is 3.2 nW m~2 sr~1.The EBL obtained by integrating the observed ISOCAMcounts above 50 kJy is 2.4^ 0.5 nW m~2 sr~1 (Elbaz et al.2001) ; hence, as much as 73%^ 15% of the 15 km back-ground might have already been resolved by ISOCAM. Themodels indicate that ULIGs contribute 15% of the 15 kmEBL observed by ISOCAM above 0.1 mJy, LIGs about65%, and normal and low-luminosity starburst galaxies thebalance. In comparison, at 140 km, we Ðnd that ULIGscontribute 25% of the CIRB, LIGs contribute 60%, andnormal/SB galaxies the balance (Fig. 13). Thus, infraredluminous galaxies, which appear to be indistinguishablefrom normal galaxies in terms of their optical/near-infraredluminosity and which form a negligible part of the energybudget in the local universe, dominate the star formationand therefore the energy budget at redshifts zD 1È3.

4.2. Infrared L uminosity Function and the L yman BreakGalaxy Connection

The Ðrst panel of Figure 14 shows the 15 km LLF alongwith the fraction of galaxies that are evolved in the di†erentmodels. For the density evolution model, the dotted line isevolved. For the luminosity evolution model, the whole 15km LLF, shown as the solid black line, is evolved. For themodel with density ] luminosity evolution, the dashedline is evolved. In the pure density evolution anddensity ] luminosity evolution model, there is a non-

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576 CHARY & ELBAZ Vol. 556

TABLE 1

ORIGIN OF THE CIRB

lIl(nW m~2 sr~1) CONTRIBUTION FROM

WAVELENGTH z\ 1.5 GALAXIES

(km) Observed Model (%)

15 . . . . . . . . . . . . 2.4 ^ 0.5 3.2 9024 . . . . . . . . . . . . . . . 4.2 83140 . . . . . . . . . . . 25^ 7 23.1 82240 . . . . . . . . . . . 14^ 3 15.1 67850 . . . . . . . . . . . 0.5 ^ 0.2 0.63 28

evolving component with a constant comoving density thatcorresponds to the di†erence between the total LLF and theevolving component.

Although the fraction of the luminosity function that isevolving and the evolutionary parameters are signiÐcantlydi†erent in our three evolutionary scenarios, we Ðnd thatour models predict similar comoving number densities ofinfrared luminous galaxies at high redshift. This is illus-

TABLE 2

ORIGIN OF THE 140 kM EBL AS DERIVED FROM THE MODELS

ContributionSource Type (%)

ULIGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25LIGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60L IR \ 1011L

_galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

ISOCAM galaxies with Sl(15 km)[ 0.1 mJy . . . . . . . 63ISOCAM galaxies with Sl(15 km)[ 0.05 mJy . . . . . . 73SCUBA galaxies with Sl(850 km)[ 2 mJy . . . . . . . . . 15SCUBA galaxies with Sl(850 km)[ 0.5 mJy . . . . . . . . 71

FIG. 12.ÈPrediction for integral source counts seen by SIRT F at 24km for the three di†erent evolutionary models described in the text. Thedashed line is for pure density evolution, the triple-dotÈdashed line is forpure luminosity evolution, the solid line is for density ] luminosity evolu-tion, while the thin broken lines are contributions from ULIGs, LIGs, and

galaxies to the counts from the density ] luminosity evolu-L IR\ 1011 L_tion using the convention deÐned in Fig. 8. [See the electronic edition of the

Journal for a color version of this Ðgure.]

FIG. 13.ÈPlot showing the relative contribution of LIGs (dashed line),ULIGs (dotted line), and normal/starburst galaxies (dot-dashed line) to the140 km EBL as a function of redshift. Each redshift bin is 0.2.

trated in the two panels of Figure 14, which show thederived 15 km luminosity function at redshifts of 0.4 and0.8. The models also provide strong evidence for a change inthe shape of the IRLF. The comoving number density ofinfrared luminous galaxies has to increase by more than 2orders of magnitude between redshifts of 0 and 1 to Ðt theISOCAM and SCUBA counts. The faint end of the LLFcannot be enhanced by the same factor since this would leadto an overproduction of the CIRB, although these galaxieswould be below the sensitivity limit of the long-wavelengthsurveys. Lastly, as much as 85% of the far-infrared back-ground can be attributed to infrared luminous galaxies.This implies that the contribution from normal and low-luminosity starburst galaxies to the dust-(L IR \ 1011 L

_)

enshrouded SFR is relatively small. So, estimates of thetotal SFR made by applying a constant extinction correc-tion to all optical/UV selected galaxies are incorrect. Weconclude that long-wavelength surveys between 15 and 850km that probe galaxies at the luminous end of the IRLFprovide a very e†ective way of tracing the bulk of the dust-enshrouded star formation.

The connection between infrared luminous galaxies andthe Lyman break galaxy (LBG) population is intriguing.Figure 14 shows a comparison between the LBG 60 kmluminosity function at zD 3 of Adelberger & Steidel (2000,hereafter AS00), which was derived based on an extinctioncorrection to optical/UV data as a function of the UV slopeof individual galaxies, and our equivalent 60 km luminosityfunction at zD 3, which we have argued earlier is only astrong upper limit. The agreement is extremely good con-sidering that they were estimated in completely independentways. The AS00 luminosity function predicts almost thesame luminosity function as our estimate from the pureluminosity evolution model to within 50%. It is discrepantwith the luminosity functions from our other two models byas much as an order of magnitude at the faint end but onlyby a factor of 2 at the bright end. As mentioned earlier, thelong-wavelength surveys that constrain our models aremainly sensitive to the evolution of galaxies at the brightend of the luminosity function at z\ 2. We are unable toconstrain with much certainty the evolution of the faint endof the luminosity function, although we do place an upperlimit based on the observed intensity of the CIRB. Further-

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 577

FIG. 14.ÈTop left-hand panel : Local 15 km luminosity function (solid line). For pure luminosity evolution, we evolved the whole LLF; the dashed line isthe starburst component that is evolved in the density ] luminosity evolution model, and the dotted line is the luminous component that is evolved in puredensity evolution models. Top right-hand panel : Total (evolving] nonevolving) 15 km luminosity function for the three models at z\ 0.4. Bottom left-handpanel : Total 15 km luminosity function at z\ 0.8. Bottom right-hand panel : 15 km luminosity function at z\ 3 converted to 60 km and compared with the 60km LBG luminosity function (diamonds) of Adelberger & Steidel (2000). [See the electronic edition of the Journal for a color version of this Ðgure.]

more, our estimates at zD 3 are only a strong upper limit tothe number density of infrared luminous galaxies since anyfurther evolution at high redshift overproduces the CIRB atj [ 200 km, while a decay in the evolution at z[ 2 as[1] (z[ 2)]~2 is marginally consistent with both the sub-millimeter counts and the CIRB spectrum. Thus, we con-clude that optical/UV surveys that trace the LBGpopulation at z[ 3, after an extinction correction factorthat spans the 2È100 range, provide a good estimate ofdust-enshrouded star formation at high redshift. They com-plement the results of future mid- and far-infrared surveyswith SIRT F, which will be able to directly observe the dustemission of LBGs with LIG-type infrared luminosities up tozD 2.5.

There is observational evidence that the LBG populationis distinct from the bright km)[ 6 mJy] sub-[Sl(850millimeter galaxies (Barger et al. 2000 ; Chapman et al.2000). This is because most of the bright 850 km galaxies areextreme ULIGs with The AS00 obser-L IR [ 1012.6 L

_.

vations detect only two of 831 galaxies above this detectionthreshold, and only 27 of their LBG sample would have asubmillimeter detection above the level of D1 mJy. Second,at zD 3, the 850 km observations would probe rest-frameD200 km emission. For a given far-infrared luminosity, the60 km luminosity shows a factor of 2È3 less scatter than the850 km luminosity among local galaxies (Fig. 3), suggestingthat the j [ 200 km spectral shape of galaxies might poten-tially have a larger scatter, which would lead to uncertainÑux estimates on a galaxy-by-galaxy basis. Lastly, we donot Ðnd any scenario in which the contribution fromULIGs is greater than 30% of the comoving SFR at zD 3.Naturally, the contribution from extreme ULIGs traced bythe bright submillimeter galaxies is even smaller. Thus,although the contribution to the SFR density from extremeULIGs is missed in observations of the LBG population,their contribution is signiÐcant only at the level of less than10%, and hence they are less important to an estimate of thehigh-redshift dust-enshrouded star formation.

FIG. 15.ÈUpper plot : Absolute maximum and minimum range of values derived from our model for the obscured SFR density in comparison to observedoptical/UV points in a km s~1 Mpc~1 and cosmology for comparison to other works. Data points are from Lilly et al. (1996). Madau et al.H0\ 50 q0\ 0.5(1996), Connolly et al. (1997), Cowie et al. (1999), Steidel et al. (1999), and Yan et al. (1999) ; (black plus signs, blue diamonds, green crosses, inverted triangles, redcrosses, and purple triangles, respectively). The dotted black line is the model of Xu et al. (2000). L ower plot : Our three models for the obscured SFR with theobserved UV points as dotted symbols and the extinction-corrected estimates from Madau et al. (1998), Meurer et al. (1999), Steidel et al. (1999), andThompson et al. (2001) as blue diamonds, open red squares, red crosses, and Ðlled red squares, respectively. Also shown is the rate derived from ISOobservations of the CFRS Ðeld (Flores et al. 1999) as Ðlled red circles and estimates from the radio and submillimeter by Barger et al. (2000) as Ðlled blacksquares. Our three evolutionary models are shown as a solid line (pure luminosity), a dashed red line (pure density), and a dashed blue line(density ] luminosity). We assign a 1 p error of 50% to our estimates of the dust-enshrouded SFR. We emphasize that our models only place a strong upperlimit on the SFR at z[ 2 and drop-o† with redshift to agree with the extinction-corrected optical/UV measurements is consistent with both the sub-millimeter counts and the CIRB spectrum.

CONSTRAINTS ON DUST-ENSHROUDED SFR 579

FIG. 16.ÈPlots showing the contribution to the dust-enshrouded SFR density from only LIGs and ULIGs as derived from our three models. Acomparison with Fig. 15 shows that the contribution from normal/SB galaxies with is relatively small at z[ 0.5, D5%È30% depending on theL IR\ 1011 L

_model. Symbols are the same as those in Fig. 15.

4.3. T he Revised Star Formation History of the UniverseHaving constrained the evolution of the mid-infrared and

thereby the far-IRLFs, we can derive the evolution of thedust-enshrouded SFR with redshift. Using the equationslisted in ° 2, our derived comoving SFR from all galaxies isshown in Figure 15, while the separate contribution from

LIGs and ULIGs is shown in Figure 16. Figure 15 alsoshows the absolute minimum and maximum range of dust-enshrouded SFR values. The maximum values are derivedfrom models that marginally overproduce the CIRB andthe counts. The minimum values are derived by using anevolutionary model that is marginally consistent with the

580 CHARY & ELBAZ Vol. 556

observations (° 4.2) and by only considering the contribu-tion from LIGs and ULIGs since those are the only galaxiesthat are directly observed at high redshift in the 15 and 850km surveys. Also shown are the SFR as inferred from directobservations at visible/UV/near-infrared wavelengths (Lillyet al. 1996 ; Madau et al. 1996 ; Connolly et al. 1997 ; Cowieet al. 1999 ; Steidel et al. 1999 ; Yan et al. 1999), SFR esti-mates obtained from extinction corrections to these obser-vations (Madau et al. 1998 ; Meurer et al. 1999 ; Steidel et al.1999 ; Thompson, Weymann, & Storrie-Lombardi 2001),and SFRs derived from ISOCAM observations of theCanada-France Redshift Survey Ðeld (Flores et al. 1999). Inaddition, lower limits to the SFR from radio measurementsand two points representing the completeness correctedsubmillimeter observations are also shown (Barger et al.2000). The 1 p uncertainty in our derived rate is about 50%and is primarily dependent on the transformation from 15km to infrared luminosities, which, as derived earlier, has a1 p of 40%, and the transformation from infrared lumi-nosities to SFR, which assumes a Salpeter initial mass func-tion (IMF) and also has an uncertainty of about 30%(Kennicutt 1998).

The dust-enshrouded SFR density peaks at a redshift of0.8^ 0.1 with a value of yr~1 Mpc~3. In a0.25~0.1`0.12 M

_(0.3, 0.7, 75) cosmology, this corresponds to 6.2 Gyr afterthe Big Bang. The dusty SFR then remains almost constantup to zD 2, which corresponds to an age of 3 Gyr beyondwhich this value provides a strong upper limit to theamount of dust obscuration. This is similar to the shape ofthe star formation history preferred by Sadat et al. (2001) intheir analysis of the CIRB. Our values are a factor of 2larger than estimates at zD 1 from Ha observations by Yanet al. (1999) and a factor of 3È7 larger than extinction-uncorrected optical/UV observations at z\ 2. The modelsare in excellent agreement with the submillimeter data cor-rected for incompleteness (Barger et al. 2000) but are higherthan the Steidel et al. (1999) extinction-corrected points.The values we derive are systematically higher than those inGispert, Lagache, & Puget (2000) but within the uncer-tainties, especially if the di†erence in the cali-L IR-to-SFRbration coefficient is factored in. Our models also indicate afaster evolution at z\ 1 than the models of Blain et al.(1999b), which is not surprising since they did not use theISOCAM data to constrain their low-redshift evolution.However, our high-redshift plateau is similar to their Anvil-10 model.

Recently, Xu et al. (2000) have developed a multip-arameter model in which the 25 km luminosity function ofShupe et al. (1998) is partitioned into three componentsÈstarburst, late-type galaxies, and AGNsÈand each com-ponent is evolved independently of the other. SpeciÐcally,they evolved the starburst population in luminosity as(1] z)4.2 and in density as (1] z)2 out to z\ 1.5. The late-type galaxy population was evolved in luminosity as(1] z)1.5, while the galaxies with AGNs evolve in lumi-nosity as (1 ] z)3.5. Beyond z\ 1.5, all the componentsdrop o† as (1 ] z)~3. Using a 25 kmÈtoÈIR luminosity con-version based on IRAS data, we have converted their evolu-tion for starburst and late-type galaxies into an SFR andcompared it with ours. This is shown as the black dottedline in the upper plot of Figure 15. We Ðnd that theirderived rates between redshifts of 1 and 2.5 are inconsistentwith our models. The motivation for this peak is not clearsince only the CIRB and the SCUBA counts place con-straints on the evolution at this redshift range and both can

be reproduced very well by an almost Ñat evolutionaryhistory at z[ 0.8 (see ° 3). However, their evolution at z\ 1agrees reasonably well with ours since both are principallyconstrained by the 15 km ISOCAM counts. Furthermore,their decline in the SFR at high redshift (z[ 2) is similar butbelow our lower limit.

By integrating our comoving SFR density over redshiftand thereby cosmic time, we can derive the density of starsand stellar remnants and compare it with the total baryondensity in the local universe. Stellar lifetimes were chosenfor solar metallicity stars (Bressan et al. 1993), while themass of remnants was chosen using the recipe of Prantzos &Silk (1999) and references therein. If a Salpeter IMF isassumed, then the model predicts a local density of baryonsof about 1.0] 109 Mpc~3, which is a factor of 2 inM

_excess of the value of (5 ^ 3)] 108 Mpc~3 estimatedM_by Fukugita, Hogan, & Peebles (1998). The model also pre-

dicts that 100% of the local stars and remnants would havebeen produced at a redshift z\ 2.0. If we instead use theshape of the IMF below 1 suggested by Gould, Bahcall,M

_& Flynn (1996), which reduces the number density of low-mass stars, then the density of stars and remnants resultingfrom the model is 7.5 ] 108 Mpc~3, which is in agree-M

_ment with the local density. Madau & Pozzetti (2000)argued for a similar IMF based on their analysis of the totalEBL. Interestingly, our model predicts that the local baryondensity in stars and remnants, derived by integrating thestar formation in ULIGs with a redshift distribution asshown in Figure 16, is similar to that seen in local spheroids,suggesting that high-redshift infrared luminous galaxiesmay be the progenitors of present-day spheroids.

5. CONCLUSIONS

A variety of observational data at mid-infrared throughsubmillimeter wavelengths trace the fraction of emissionfrom stars that is thermally reprocessed by dust. By usingthe counts of galaxies at these wavelengths, it is possible toestimate the amount of star formation that is enshroudedby optically thick H II regions and thereby invisible toobservations at ultraviolet and visible wavelengths. In addi-tion, the spectrum of the CIRB at mid- and far-infraredwavelengths places an upper limit on the fraction of star-light that has undergone thermal reprocessing by dust.

We have developed a set of template SEDs for galaxies asa function of infrared luminosity, which reproduce existingdata at 0.44, 7, 12, 15, 25, 60, 100, and 850 km from ISO,IRAS, and SCUBA on nearby galaxies. The 15 km LLFwas then evolved with redshift, taking both luminosity anddensity evolution models into account, and using the tem-plate SEDs to Ðt the observed counts at 15, 90, 170, and 850km. A number of evolutionary models provide reasonableÐts to the data and the spectrum of the CIRB. The principalreason for this is that all the long-wavelength surveys aretypically sensitive to only the most luminous galaxies

at z[ 0.5. So, evolutionary models that(L IR[ 1011 L_)

result in similar luminosity functions at areL IR [ 1011 L_degenerate. However, our models accurately constrain the

comoving number density of these luminous galaxies as afunction of redshift. In the local universe, it is these galaxies,many of which show morphological signatures of inter-action, that show an infrared-determined SFR that is aboutan order of magnitude higher than the corresponding UV-determined SFR. By integrating the infrared luminosity ofthese luminous galaxies, we then obtain an estimate of thedust-enshrouded SFR. The dust-enshrouded SFR density

No. 2, 2001 CONSTRAINTS ON DUST-ENSHROUDED SFR 581

appears to peak at a much lower redshift than previouslythought, at z\ 0.8^ 0.1 with a value of yr~10.25~0.1`0.12 M

_Mpc~3, and remains approximately constant at least untilzD 2. Any drop-o† at a lower redshift would result in anunderestimate of the 850 km galaxy counts. Although ourmodels do not constrain the evolution of the faint end

of the luminosity function, their net contri-(L IR\ 1010 L_)

bution to the high-redshift dust-enshrouded star formationis negligible, as can be seen in the range of evolutionarymodels considered. The evolution at z[ 2 is constrainedmuch more weakly. Having a constant SFR between red-shifts of 0.8 and 4 is consistent with the CIRB spectrum andthe submillimeter counts, as is a decay by a factor of 7between redshift 2 and D5. However, we Ðnd that there isexcellent agreement between our luminosity function andthe IRLF derived from extinction correction to optical/UVobservations of LBGs at zD 3. This suggests that dustobscuration is signiÐcant even at z[ 3 and that the dust-enshrouded SFR is constant to within a factor of 2 betweenredshifts 2 and 4.

The models also provide a census of the luminosity ofgalaxies that contribute to the counts at di†erent wave-lengths, their redshift distribution, and the relative contri-bution to the CIRB at j [ 5 km as a function of redshift.Furthermore, we Ðnd that ultradeep observations withSIRT F at 24 km down to a sensitivity of 25 kJy can poten-tially break the degeneracy in the evolutionary models bydetecting galaxies with out to zD 2.5,L IR D 1011.5 L

_which is well beyond the turnover redshift of 0.8 that isderived from our models.

R. C. wishes to thank Harland Epps and Rodger Thomp-son for kindly funding this research through NASA grantNAG 5-3042. D. E. wishes to thank the American Astrono-mical Society for its support through the Chretien Interna-tional Research Grant and Joel Primack, David Koo, andJoe Miller for supporting his research through NASAgrants NAG 5-8218 and NAG 5-3507. We wish to acknow-ledge Pierre Chanial for collating published data from alarge number of surveys and making them available to us.

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