X-ray Preionisation Powered by Accretion on the First Black Holes. I: a Model for the WMAP Polarisation Measurement

In this paper we investigate the possibility that there is a first phase of partial ionisation due to X-rays produced by black hole accretion in small-mass galaxies at redshifts 7 < z < 20. This is followed by complete reionisation by stellar sources at z ≃ 7. This scenario is motivated by the large optical depth to Thompson scattering, τe ≃ 0.17 ± 0.04, recently measured by WMAP. But it is also consistent with the observed Gunn-Peterson trough in the spectra of quasars at z ∼ 5 − 6. We use a semianalytic code to explore models with different black hole accretion histories and cosmological parameters. We find that “preionisation” by X-rays can increase the intergalactic medium (IGM) optical depth from τe ≈ 0.06 given by stellar sources only, to 0.1 < ∼ τe < ∼ 0.2, if a fraction of baryons 10 −5 < ∼ ωac < ∼ 10 −4 is accreted onto seed black holes produced in the collapse of low metallicity, high mass stars before z ≃ 15. To be effective, preionisation requires a non-negligible star formation in the first small-mass galaxies in which seed black holes are formed. By z ∼ 20 − 25 the IGM is re-heated to 10, 000 K and the ionisation fraction is about 20%. The increase of the IGM Jeans mass is effective in reducing star formation in the smaller-mass haloes. Large values of τe are obtained in models with top-heavy stellar initial mass function only if pair-instability supernovae are not important. Seed black holes are assumed to accrete at near the Eddington limit with a duty cycle that decreases slowly with increasing time. Alternatively, a moderate fraction of the black holes must be ejected from the host galaxy or exist without merging into the supermassive black holes in galactic centres. The model predicts that dwarf spheroidal galaxies, if they are preserved fossils of the first galaxies, may host a mass in black holes that is 5-40% of their stellar mass. The redshifted X-ray background produced by this early epoch of black hole accretion constitutes about 5 − 10% of the hard X-ray background in the 2-50 keV bands and roughtly half of the currently estimated black hole mass density was formed at early times. Moreover, in most models, the photons from the redshifted background are sufficient to fully reionise He II at redshift z ∼ 3 without any additional contribution from quasars at lower redshifts and the temperature of the mean density intergalactic medium remains close to 10 K down to redshift z ∼ 1.