Annu. Rev. Astron. Astrophys. 1994. 32: 531-590
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5.4. Black Hole Accretion Constraints

Any black hole remnants of Population III stars would tend to generate radiation through accretion; this could be important at both the present and pregalactic epochs. In particular, if we assume that halo or disk black holes accrete ambient gas at the Bondi rate and that the accreted material is converted into radiation with efficiency eta, then one may impose interesting constraints on the density of the black holes OmegaB(M) merely by requiring that the radiation density generated since the epoch of galaxy formation does not exceed the observed density in the appropriate waveband. For example, if we assume that the radiation emerges at 10 keV and that eta = 0.1, we infer OmegaB(M) < (M/105 Msun)-1 for halo holes and OmegaB(M) < (M) / 10Msun)-1 for disk holes (Carr 1979). These limits have also been studied by Hegyi et al (1986). Stronger limits may come from constraints on the number of individual sources in our own Galaxy. Thus Ipser & Price (1977), using a particular accretion model, preclude 105 Msun holes from comprising the halo because of the non-observation of suitable infrared and optical sources.

One might expect the background light constraints to be even stronger for pregalactic black holes since the background gas density would have been higher at early times. If we assume Bondi accretion, then the luminosity will exceed the Eddington value for some period after decoupling if M > 103eta-1 Msun. However, the pregalactic limit is actually weaker: It takes the form OmegaB(M) < (M / 106 Msun)-1 for eta = 0.1 with only a weak dependence on the photon energy (Carr 1979). This is a consequence of two factors: 1. a large fraction of the emitted radiation goes into heating the matter content of the Universe rather than into background light; and 2. the heating of the Universe will boost the matter temperature well above the usual Friedmann value and this will reduce the accretion rate (Meszaros 1975, Carr 1981a, Gnedin & Ostriker 1992). Nevertheless, the effect on the thermal history of the Universe could be of great interest in its own right. For example, accreting black holes could easily keep the Universe ionized throughout the period after decoupling. The sort of background generated by the pregalactic accretion phase of a population of 106 Msun black holes is indicated in Figure 6.

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