Diffuse Intergalactic Dust?

There have been a number of studies claiming that the bulk of metals in the local universe had already formed by (eg. Lilly & Cowie 1987; White & Frenk 1991; Pei & Fall 1995). Similarly, models of dust evolution in the galaxy show that the bulk of its dust content was formed in the first few billion years (Wang 1991). These studies suggest that the global star formation rate peaked at epochs when the bulk of galaxies were believed to have formed. Supernova-driven winds at early epochs may thus have provided an effective mechanism by which chemically enriched material and dust were dispersed into the IGM. As modelled by Babul & Rees (1992), such a mechanism is postulated to be crucial in the evolution of the `faint blue' galaxy population observed to magnitudes . Nath & Trentham (1997) also show that this mechanism could explain the recent detection of metallicities in low density Ly- absorption systems at . Another source of diffuse IGM dust may have been provided by an epoch of population III star formation associated with the formation of galactic haloes (eg. McDowell 1986).

What are the effects expected on background sources if all dust formed to the present day was completely uniform and diffuse throughout the IGM? In this section, we show that such a component will have a low optical depth and have an insignificant effect on the colours of background sources, but will be high enough to significantly bias their number counts in the optical.

Comoving Dust Mass Density

To explore the effects of a diffuse intergalactic dust component, we need to assume a value for the mean mass density in dust in the local universe. This density must not exceed the total mass density in heavy metals at the present epoch. An upper bound for the local mass density in metals (hence dust) can be derived from the assumption that the mean metallicity of the local universe is typically: (ie. the ratio of elements heavier than helium to total gas mass), as found from galactic chemical evolution models (eg. Tinsley 1976) and abundance observations (Grevesse & Anders 1991). Combining this with the upper bound in the baryon density predicted from big-bang nucleosynthesis (Olive et al. 1990) where , it is apparent that
 

Let us now compute the total mass density in dust used in previous studies that modelled the effects of dust in individual galaxies on background quasars. Both Heisler & Ostriker (1988) and Fall & Pei (1993) modelled these effects by assuming that dust in each galaxy was distributed as an exponential disk with scale radius kpc and central face-on optical depth, . The comoving mean mass density in dust (relative to the critical density) in these studies, given a comoving galaxy number density , can be shown to be
 
(see Masci 1997). This is consistent with the constraint in equation (18). Thus, as a working measure, we assume the comoving mass density defined by equation (19) in the calculation that follows.

Obscuration by Diffuse Intergalactic Dust

If the dust mass density given by equation (19) is assumed uniformly distributed and constant on comoving scales to some redshift, the B-band optical depth through a dust sheet of width dl at redshift z in an observer's frame can be written (see equation 3)
 
where for simplicity, we have assumed dust properties characteristic of the galactic ISM. The factor (1+z) is due to our assumption of a dependence for the dust extinction law. This arises from the fact that light received in the B-band corresponds to light of wavelength at redshift z, which consequently suffers greater extinction. Although a law is not fully representative of that observed in the galactic ISM which includes the strong 2200Å  feature, this is a good on average ralation for the dust laws in many external galaxies (eg. Jansen et al. 1994). Such an assumption greatly simplifies the redshift dependence of extinction in an observer's frame. With Mpc (for a and cosmology), the total mean optical depth to some redshift in an observer's B-band will scale as
 
This represents the total optical depth if all dust in the intervening galaxy model of Heisler & Ostriker (1988) were assumed uniformly distributed throughout the universe.

Assuming dust is uniformly distributed to z=2, the observed B-band optical depth from equation (21) will be of order
 
Using a galactic extinction law (Pei 1992), this corresponds to an extinction in B-R colour of mag. Thus, if background faint field galaxies and QSOs are observed through a uniform intergalactic dust distribution, their observed colours are not expected to be significantly affected. We now show however that the numbers of sources missing at such redshifts could be significantly greater than that claimed by previous studies which assume all dust to be associated with massive galaxies alone.

If dust to some distance D covers an area of sky A and hence, has covering factor , the number of background sources lost from a flux-limited sample can be estimated from equation (2). In general, the number of background sources at some redshift lost from an area of sky with dust covering factor will scale as:
 
where is the fraction of sources missing per unit area. For a completely uniform dust distribution, , and to redshift z=2, for .

If dust were confined to individual galaxies along the line-of-sight however, their covering factor, assuming they follow a Poisson distribution is typically , where is the mean number of absorber intersections to redshift z:
 
(see Heisler & Ostriker 1988). We have scaled to the nominal parameters assumed in the intervening galaxy model of Heisler & Ostriker (1988) (hereafter HO). In this model, we find a covering factor of only to z=2. We can estimate the mean effective optical depth observed in the B-band through an individual absorber to in the HO model by using the formalism of Section 2. For a fixed mass of dust, equation (4) implies that the product of the area (or covering factor) and optical depth of a dust distribution: , is a constant, depending on grain properties and dust mass alone. Using this relation, the observed effective absorber optical depth to in the HO model, , can be estimated by scaling from our values of and above for uniformly distributed dust:
 
Using this value, the fraction of background sources missed by obscuration from an individual absorber is `effectively' . Combining these results, we find using equation (23) that the number of sources missing at due to a uniform foreground dust distribution to be greater by a factor of than that predicted by Heisler & Ostriker (1988).

We must note that this estimate makes no allowance for possible evolution in dust content. Effects of foreground diffuse dust on source counts at z>2 may be significantly reduced if appreciable evolution has occured. Effects of models where the dust content evolves have been explored by Masci & Webster (1998)

Summary

We conclude that the existence of a significant amount of diffusely distributed dust (eg. with mass density on comoving scales of order that observed in local galaxies) can enhance the number of background sources missing in optical samples. Due to its relatively large covering factor, diffuse dust predicts a reduction in optical counts at z>2 about three times greater than that claimed by previous studies.

The colours of background sources are not expected to be significantly affected. This implies that the use of background populations to measure a diffuse IGM dust component will be extremely difficult.

© Copyright Astronomical Society of Australia 1997