One of the most interesting constraints posed by the observed brightness of the
night sky concerns the possibility that a large fraction of the dark mass in
present-day galaxy halos may be associated with faint white-dwarf (WD)
remnants
of a population of intermediate-mass stars that formed at high redshifts. The
results of the microlensing MACHO experiment
towards the LMC indicates that 60 ± 20% of the sought dark
matter in the halo of the Milky Way may be in the form of
0.5+0.3-0.2 M objects
(Alcock et al. 1997).
The mass scale is a
natural one for white dwarfs, a scenario also supported by the lack of a
numerous spheroidal population of low-mass main sequence stars in the HDF
(Gould et al. 1998).
The total mass of MACHOs inferred within 50 kpc is
2+1.2-0.7 x 1011 M
, implying a ``MACHO-to-blue light''
ratio for the Milky Way in the range 5 to 25 solar (cf
Fields et al. 1998).
If these values were typical of the luminous universe as a whole, i.e. if
MACHOs could be viewed as a new stellar population having similar
properties in all disk galaxies, then the cosmological mass density
of MACHOS today would be
MACHO = (5-25)
fB
B /
crit =
(0.0036-0.017) fB
h-1, a significant entry in the cosmic baryon budget
(Fields et al. 1998).
Here fB
0.5 is
the fraction of the blue luminosity density radiated by stellar disks
(FHP).
Note that if MACHOs are halo WDs, the contribution of their progenitors
to the mass density parameter is several times higher.
Halo IMFs which are very different from that of the solar
neighborhood, i.e. which are heavily-biased towards WD progenitors and
have very few stars forming with masses below 2 M (as these would
produce bright WDs in the halo today that are not seen), and above
8 M
(to avoid
the overproduction of heavy elements), have been
suggested as a suitable mechanism for explaining the microlensing data
(Adams & Laughlin 1996;
Chabrier et al. 1996).
While the halo WD scenario
may be tightly constrained by the observed rate of Type Ia SN in galaxies
(Smecker & Wyse 1991),
the expected C and N overenrichment of halo stars
(Gibson & Mould 1997),
and the number counts of faint galaxies in deep optical surveys
(Charlot & Silk 1995),
here we explore a potentially more
direct method (as it is does not depend on, e.g. extrapolating stellar yields
to primordial metallicities, on galactic winds removing the excess heavy
elements
into the intergalactic medium, or on the reddening of distant halos by dust),
namely we will compute the contribution of WD progenitors in dark galaxy halos
to the extragalactic background light.
Following Chabrier (1999), we adopt a truncated power-law IMF,
This form mimics a mass function strongly peaked
at 0.84
Consider the
Note that these limits are not necessarily in contrast with the microlensing
results, as they may imply either that WDs are not ubiquitous in
galaxy halos (i.e. the Milky Way is atypical), or that the bulk of the baryons
are actually not galactic. One possible way to relax the above constraints
on WD baryonic halos is to push their formation epoch to extreme redshifts
(zF > 10), and hide the ensuing background light in
the poorly constrained
spectral region between 5 and 100 µm.
In Figure 2 we show the EBL
produced by a WD-progenitor dominated IMF with
We have benefited from useful discussions with R. Bernstein, G. Bruzual,
C. Hogan, A.
Loeb, and G. Zamorani. We are indebted to R. Bernstein, W. Freedman, & B.
Madore for communicating their unpublished
results on the EBL. Partial support for this work was provided by NASA through
grant AR-06337.10-94A from the
Space Telescope Science
Institute.
. To examine the
dependence of the IMF on the results we consider two functions (shown in
Fig. 3),
= 2.4 and
= 4: both yield a present-day
Galactic halo mass-to-light ratio
> 100 after a Hubble time, as required in the absence of a large non-baryonic
component. We further assume that a population of halo WD progenitors
having mass density X
b h2 = 0.0193 X formed
instantaneously at redshift zF with this IMF and
nearly primordial
(Z = 0.02 Z
) metallicity. The resulting EBL from such an event is
huge, as shown in Figure 5 for X = 0.1,
0.3, and 0.6 and a
-dominated
universe with
M = 0.3,
=
0.7, and h = 0.65 (tH = 14.5 Gyr).
=
2.4 case first. With zF = 3 and X = 0.6, this
scenario would generate
an EBL at a level of 300 n W m-2 sr-1.
Even if only 30% of the nucleosynthetic baryons formed at
zF = 5 with
a WD-progenitor dominated IMF, the resulting background light at
Earth would exceed the value of 100 n W m-2 sr-1,
the ``best-guess'' upper limit
to the observed EBL from the data plotted in
Figure 2.
The return fraction is R
0.8,
so only 20% of this stellar mass would be leftover as WDs, the rest
being returned to the ISM. Therefore, if galaxy halos comprise 100%
of the nucleosynthetic baryons, only a small fraction of their mass,
XWD
0.2 x
0.30 = 0.06 could be in the form of white dwarfs.
Pushing the peak of the IMF to more massive stars,
=
4, helps only marginally. With
=
2.4, the energy radiated
per stellar baryon over a timescale of 13 Gyr is equal to 2 MeV,
corresponding to 10 MeV per baryon in WD remnants. A similar value is
obtained in the
= 4 case:
because of the shorter lifetimes of
more massive stars the expected EBL is reduced, but only by 20% or so
(see Fig. 5). Moreover, the decreasing fraction of
leftover WDs raises even more severe problems of metal galactic enrichment.
= 4 and
(zF, X, XWD) = (36, 0.5, 0.1), assuming
negligible dust reddening. While this
model may be consistent with the observations if the large corrections factors
inferred by
Bernstein et al. (1999)
extend into the near-IR, we draw attention
to the fact that even a tiny fraction of dust reprocessing in the
(redshifted) far-IR would inevitably lead to a violaton of the FIRAS
background.
Acknowledgments