Effect of cosmic ray/X-ray ionization on supermassive black hole formation

We study the effects of external ionization by cosmic rays (CRs) and X-rays on the thermal evolution of primordial clouds under strong far-ultraviolet (FUV) radiation. A strong FUV radiation field photodissociates H-2 and quenches its cooling. Even in such an environment, a massive cloud with virial temperature greater than or similar to 10(4) K can contract isothermally at 8000 K by hydrogen Lyman alpha cooling. This cloud collapses monolithically without fragmentation, and a supermassive star (greater than or similar to 10(5) M-circle dot) is believed to form at the centre, which eventually evolves into a supermassive black hole (SMBH). However, candidates of FUV sources, including star-forming galaxies, are probably sources of strong CRs and X-rays too. We find that external ionization promotes H-2 production and elevates the threshold FUV intensity J(crit) needed for SMBH formation for CR energy density U-CR greater than or similar to 10(-14) erg cm(-3) or X-ray intensity J(X) greater than or similar to 10(-24) erg s(-1) cm(-2) sr(-1) Hz(-1) at 1 keV. The critical FUV flux increases as J(crit) alpha U-CR(1/2) (alpha J(X)(1/2)) in the high CR (respectively X-ray) limit. With the same value of FUV intensity at the Lyman limit (13.6 eV), the H- photodissociation rate, with a threshold of 0.755 eV, increases and the H-2 abundance decreases with decreasing effective temperature of the FUV sources T-*. A lower value of T-* thus results in a lower critical FUV flux J(crit) at the Lyman limit. Using an empirical relation between the intensities of FUV and CRs/X-rays from nearby star-forming galaxies, we find that the external ionization effect remarkably enhances the critical FUV flux for sources with T-* as high as 10(5) K and composed of stars with mass less than or similar to 100 M-circle dot to a level that is not realized in any halo. This indicates that to induce SMBH formation the FUV sources must be either Population II/I galaxies with low brightness temperature (T-* similar to 10(4) K), Population III galaxies (T-* similar to 10(5) K) with a very top-heavy initial mass function or Population III galaxies too young to harbour sources of CRs/X-rays, for example supernova remnants or high-mass X-ray binaries.