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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 Msun 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 Msun, 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 OmegaMACHO = (5-25) fB curlyLB / rhocrit = (0.0036-0.017) fB h-1, a significant entry in the cosmic baryon budget (Fields et al. 1998). Here fB approx 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 Msun (as these would produce bright WDs in the halo today that are not seen), and above 8 Msun (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,

Equation 9 (9)

This form mimics a mass function strongly peaked at 0.84 barm. To examine the dependence of the IMF on the results we consider two functions (shown in Fig. 3), barm = 2.4 and barm = 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 Omegab h2 = 0.0193 X formed instantaneously at redshift zF with this IMF and nearly primordial (Z = 0.02 Zsun) 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 Lambda-dominated universe with OmegaM = 0.3, OmegaLambda = 0.7, and h = 0.65 (tH = 14.5 Gyr).

Figure 5a Figure 5b

Figure 5. Left: Synthetic bolometric luminosity versus age of a simple stellar population having total mass M = 1 Msun, metallicity Z = 0.02 Zsun, and a WD-progenitor dominated IMF (see text for details) with barm = 2.4 (solid line) and barm = 4 (dashed line). Right: EBL observed at Earth from the instantaneous formation at redshift zF of a stellar population having the same IMF and metallicity, and mass density X Omegab h2 = 0.012, 0.006 and 0.002 (corresponding to 60, 30, and 10 per cent of the nucleosynthetic value), as a function of zF. A Lambda-dominated universe with OmegaM = 0.3, OmegaLambda = 0.7, and h = 0.65 has been assumed. Solid line: barm = 2.4. Dashed line: barm = 4.

Consider the barm = 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 approx 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 approx 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, barm = 4, helps only marginally. With barm = 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 barm = 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.

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 barm = 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.


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.

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