X-ray pre-ionization powered by accretion on the first black holes -: I.: A model for the WMAP polarization measurement

In this paper we investigate the possibility that there is a first phase of partial ionization due to X-rays produced by black hole (BH) accretion in small-mass galaxies at redshifts 7 < z < 20. This is followed by complete reionization by stellar sources at z similar or equal to 7. This scenario is motivated by the large optical depth to Thomson scattering, tau(e) similar or equal to 0.17 +/- 0.04, recently measured by the Wilkinson Microwave Anisotropy Probe (WMAP). However, it is also consistent with the observed Gunn-Peterson trough in the spectra of quasars at z similar to 5-6. We use a semi-analytic code to explore models with different BH accretion histories and cosmological parameters. We find that 'pre-ionization' by X-rays can increase the intergalactic medium (IGM) optical depth from tau(e) approximate to 0.06 given by stellar sources only, to 0.1 less than or similar to tau(e) less than or similar to 0.2, if a fraction of baryons 10(-5) less than or similar to omega(ac) less than or similar to 10(-4) is accreted on to seed BHs produced in the collapse of low-metallicity, high-mass stars before z similar or equal to 5. To be effective, pre-ionization requires a non-negligible star formation in the first small-mass galaxies in which seed BHs are formed. By z similar to 20-25 the IGM is reheated to 10 000 K and the ionization fraction is about 20 per cent. The increase of the IGM Jeans mass is effective in reducing star formation in the smaller mass haloes. Large values of e are obtained in models with top-heavy stellar initial mass function only if pair-instability supernovae (SNe) are not important. Seed BHs 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 BHs in galactic centres. The model predicts that dwarf spheroidal galaxies, if they are preserved fossils of the first galaxies, may host a mass in BHs that is 5-40 per cent of their stellar mass. The redshifted X-ray background produced by this early epoch of BH accretion constitutes about 5-10 per cent of the hard X-ray background in the 2-50 keV bands and roughly half of the currently estimated BH mass density was formed at early times. Moreover, in most models, the photons from the redshifted background are sufficient to fully reionize He II at redshift z similar to 3 without any additional contribution from quasars at lower redshifts and the temperature of the mean density IGM remains close to 10(4) K down to redshift z similar to 1.