The efficiency of early mixing is important for the interpretation of stars in our own galaxy that have ultra-low metallicity (33)— lower than the mean metallicity that would have been generated in association with the UV background at z>5. If the heavy elements were efficiently mixed, then these stars would themselves need to have formed before galaxies were assembled. To a first approximation they would cluster nondissipatively, they would therefore be distributed in halos (including the halo of our own galaxy) like the dark matter itself. More careful estimates slightly weaken this inference. This is because the subgalaxies would tend, during the subsequent mergers, to sink via dynamical friction toward the centers of the merged systems. There would nevertheless be a tendency for the most extreme metal-poor stars to have a more extended distribution in our galactic halo and to have a bigger spread of motions.
The number of such stars depends on the IMF. If this were flatter, there would be fewer low-mass stars formed concurrently with those that produced the UV background. If, on the other hand, the IMF were initially steeper, there could, in principle, be a lot of very low mass (macho) objects produced at high redshift. These could provide a few percent of the halo if omega were 1 (and a higher proportion of the =30-kpc inner halo probed by lensing searches); a larger proportion could be provided in a low-density universe.
Most of the small, first-generation galaxies by now should have merged into more massive systems (forming part of the halo population of stars in normal galaxies like the Milky Way), but some could survive until today in galactic halos or even as isolated objects. This may be the explanation of present-day dwarf spheroidal galaxies (34).
Our general conclusions are relevant to any model in which the initial fluctuations have amplitudes decreasing with scale, so that cosmic structures form “bottom-up.” Such models differ, of course, in the epoch at which “first light” would have occurred. In models with primordial baryon fluctuations (PIB), this may be at z>100; for CDM (primarily discussed here), it is in the range 10–20; and for “mixed dark matter” models, the first structures may form still more recently. Molecular cooling tends to be more efficient at high densities and, therefore, at large redshifts: but in all cases it determines the scale of the first objects that condense out and contribute the first injection of heat into the universe.
The amount of background UV generated per solar-mass of material in these first objects is very uncertain—it depends on the efficiency of star formation, on whether the IMF favors massive stars (or even supermassive objects or black holes), and on how much of the UV is “soaked up” by dense gas within the bound objects themselves. But irrespective of all these uncertainties, the UV background exerts an important feedback on the cosmogonic process, by quenching H2 cooling, long before reaching the level needed to photoionize the entire IGM.
The IGM remained predominantly neutral until a sufficient number of objects above 109((1+z)/10)-3/2M had gone nonlinear. Such systems are massive enough to have virial temperatures above 10,000 K—hot enough for HI line emission to permit very efficient cooling. Most of the O-B stars (or accreting black holes) that photoionized the IGM had to form in systems at least as large as this.
Formation of such systems would have continued unimpeded until ionization was complete; the UV background rises sharply, to a value of order 10-21 ergs per cm-2·Hz-1·ster-1, when the universe becomes, in effect, an HII region. This must have happened before z=5. The only net cooling of a fully photoionized gas comes from bremsstrahlung, which is less effective than the collisionally excited line emission from gas that is only partly ionized. The completion of photoionization may therefore signal another pause in the cosmogonic process, associated with a further increase in the minimum scale that can collapse, and in the efficiency of cooling.
By the epoch z=5, some structures (albeit perhaps only exceptional ones) must have attained galactic scales. But huge numbers of lower-mass systems should already exist at higher redshifts, and we can make quite firm estimates of their integrated UV output. This paper has addressed how we can probe their indirect effects and perhaps even detect them directly.
I am especially grateful to Jordi-Miralda Escude and would also like to thank Zoltan Haiman, Avi Loeb, and Max Tegmark for discussion and collaboration on some of the topics described here.
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