Obscuration by Diffuse Cosmic Dust
Frank J. Masci, PASA, 15 (3), 299
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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.
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.
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)
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