In the dense gas clouds that harbour starbursts, the ultraviolet (UV) light of young stars is absorbed by dust grains which, in turn, release their thermal energy at infrared (IR) and submillimetre (submm) wavelengths. Thus, understanding the star formation history of galaxies clearly requires a correct assessment of the UV to submm luminosity budget. The most straightforward and simple observational probe of such a luminosity budget is the analysis of the faint galaxy counts obtained at various wavelengths. In this purview, this paper proposes self-consistent theoretical predictions of faint galaxy counts at optical, IR and submm wavelengths that can be directly compared with the current host of data, and used to prepare observational strategies with forthcoming instruments.
In the local universe, only 30 % of the bolometric luminosity is released in the IR/submm wavelength range (Soifer & Neugebauer 1991), and the effect of extinction can thus be considered as a mere correction that does not change the main evolutionary trends elaborated from optical studies. However, there is now a growing amount of evidence that this fraction was much higher in the past. Indeed, the discovery of the Cosmic Infrared Background (CIRB) at a level ten times higher than the no-evolution predictions based on the IRAS local IR luminosity function, and twice as high as the Cosmic Optical Background obtained from optical counts, showed that dust extinction and emission play a major role in defining the luminosity budget of high-redshift galaxies (Puget et al. 1996; Guiderdoni et al. 1997; Schlegel et al. 1998; Fixsen et al. 1998; Hauser et al. 1998). Since this major breakthrough, deep surveys with the ISO satellite at 15 µm (Oliver et al. 1997; Aussel et al. 1999; Elbaz et al. 1999) and 175 µm (Kawara et al. 1998; Puget et al. 1999), and with the SCUBA instrument at 850 µm (Smail et al. 1997; Barger et al. 1998; Hughes et al. 1998; Eales et al. 1999; Barger et al. 1999a) have begun to break the CIRB into its brightest contributors. Although identification and spectroscopic follow-up of the submm sources are not easy, the preliminary results of such studies seem to show that part of these sources are the high-redshift counterparts of the local luminous and ultraluminous IR galaxies (LIRGs and ULIRGs) discovered by IRAS (Smail et al. 1998; Lilly et al. 1999; Barger et al. 1999b). In parallel to this pioneering exploration of the "optically-dark" and "infrared-bright" side of the universe, a more careful examination of the Canada-France Redshift Survey (CFRS) galaxies at , and Lyman Break Galaxies at and 4 do show a significant amount of extinction (Flores et al. 1999; Steidel et al. 1999; Meurer et al. 1999). The previous estimates of the UV fluxes, and consequently of the star formation rates, in these objects have to be respectively multiplied by factors 3 and 5 to take into account the effect of extinction. Dust seems to be present at still higher redshifts. For instance, it is seen in a lensed galaxy at (Soifer et al. 1998) and even in a Lyman galaxy at (Chen et al. 1999).
The synthetic spectra of stellar populations in galaxies are easily computed from spectrophotometric models of galaxy evolution. Unfortunately, most of these models neglect the influence of dust on the spectral appearance of galaxies. Guiderdoni & Rocca-Volmerange (1987) proposed a first modelling of the effect of dust extinction. Later, Mazzei et al. (1992) basically used the same recipe for extinction, but they also computed dust emission to get spectral energy distributions (SEDs) from the UV to the far-IR. Complete sets of synthetic spectra are now available from the GRASIL (Silva et al. 1998) and STARDUST models (Devriendt et al. 1999, hereafter Paper I) of spectrophotometric evolution. These models share the same spirit, but they differ by a number of details. The GRASIL SEDs in the IR are computed from a more sophisticated model of transfer, that is more explicit physically, but involves several free parameters, whereas STARDUST SEDs in the IR are computed with a minimal number of free parameters, by weighing various dust components to reproduce the observed IRAS colour-luminosity relations.
These spectra can be used in phenomenological models of faint galaxy counts, that extrapolate the evolution of the local galaxies backwards under the assumption of pure luminosity evolution. For instance, the predictions of faint galaxy counts at optical wavelengths by Guiderdoni & Rocca-Volmerange (1990) used their optical spectra with extinction, whereas Franceschini et al. (?) used the Mazzei et al. spectra with dust extinction and emission to produce the first set of counts at optical and FIR wavelengths. However, semi-analytic models of galaxy formation (hereafter SAMs) are a much more powerful approach to describe the physical processes that rule galaxy formation and evolution within an explicit cosmological context (White & Frenk 1991; Lacey & Silk 1991; Kauffmann et al. 1993; Cole et al. 1994; Somerville & Primack 1999). White & Frenk (1991), Lacey et al. (1993), Kauffmann et al. (1994), and Cole et al. (1994) proposed predictions of faint galaxy counts at optical wavelengths (basically the B and K bands) from their models. However, predictions at IR/submm wavelengths from a SAM were produced much later by Guiderdoni et al. (1997; 1998, hereafter GHBM). But this first study did not give the corresponding predictions at optical wavelengths, and was restricted to the standard Cold Dark Matter (CDM) model.
In this paper, we implement the STARDUST spectra into a SAM to make predictions of faint galaxy counts and redshift distributions from the UV to the submm wavelength range, very much in the spirit of GHBM. We also extend the SAM to other cosmologies, and study the sensitivity of the results to the cosmological parameters and star formation history. Although our approach has a number of shortcomings which are due to the simplicity of our model, this paper primarily intends to show that (i) the implementation of STARDUST SEDs into SAMs is straightforward because of its small number of free parameters; (ii) the model gives fits that are already very satisfactory in spite of the simplicity of the approach; and (iii) the outputs are a physically motivated tool to interpolate or extrapolate the current observations of faint counts to other wavelengths and/or flux levels. This is needed to prepare the observational strategies with the forthcoming IR/submm satellites SIRTF , FIRST and PLANCK , as well as with the Atacama Large Millimetre Array.
In Sect. 2, we briefly describe how we connect the STARDUST spectra with the various physical processes that are relevant to galaxy formation, within our SAM. We point out the differences with GHBM. Sect. 3 discusses the values of the free parameters that define the so-called "quiescent" mode of star formation. Sect. 4 focuses on the sensitivity of the faint galaxy counts to a change in the cosmological parameters. Sect. 5 studies the sensitivity of the faint galaxy counts to galaxy evolution, and more specifically to the presence of a heavily-extinguished "starburst" mode of star formation similar to the one in ULIRGs. Finally, a fiducial model is proposed. We discuss our results in Sect. 6.
© European Southern Observatory (ESO) 2000
Online publication: December 5, 2000