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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 10 4 K can contract isothermally at 8000 K by hydrogen Lyman cooling. This cloud collapses monolithically without fragmentation, and a supermassive star ( 10 5 M ) 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 10 -14 erg cm -3 or X-ray intensity J X 10 -24 erg s -1 cm -2 sr -1 Hz -1 at 1 keV. The critical FUV flux increases as
Inayoshi et al. (Mon,) studied this question.
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