How an improved implementation of H2 self-shielding influences the formation of massive stars and black holes

High-redshift quasars at z > 6 have masses up to similar to 10(9) M-circle dot. One of the pathways to their formation includes direct collapse of gas, forming a supermassive star, precursor of the black hole seed. The conditions for direct collapse are more easily achievable in metal-free haloes, where atomic hydrogen cooling operates and molecular hydrogen (H-2) formation is inhibited by a strong external (ultraviolet) UV flux. Above a certain value of UV flux (J(crit)), the gas in a halo collapses isothermally at similar to 10(4) K and provides the conditions for supermassive star formation. However, H-2 can self-shield, reducing the effect of photodissociation. So far, most numerical studies used the local Jeans length to calculate the column densities for selfshielding. We implement an improved method for the determination of column densities in 3D simulations and analyse its effect on the value of J(crit). This new method captures the gas geometry and velocity field and enables us to properly determine the direction-dependent self-shielding factor of H-2 against photodissociating radiation. We find a value of J(crit) that is a factor of 2 smaller than with the Jeans approach (similar to 2000 J(21) versus similar to 4000 J(21)). The main reason for this difference is the strong directional dependence of the H-2 column density. With this lower value of J(crit), the number of haloes exposed to a flux > J(crit) is larger by more than an order of magnitude compared to previous studies. This may translate into a similar enhancement in the predicted number density of black hole seeds.