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The Direct Collapse of a Massive Black Hole Seed Under the Influence of an Anisotropic Lyman-Werner Source

The direct collapse model of supermassive black hole seed formation provides an attractive solution to the origin of the quasars now routinely observed at $z \gtrsim 6$. We use the adaptive mesh refinement code Enzo to simulate the collapse of gas at high redshift, including a nine species chemical model of H, He, and H$_2$. The direct collapse model requires that the gas cools predominantly via atomic hydrogen. To this end we simulate the effect of an anisotropic radiation source on the collapse of a halo at high redshift. The radiation source is placed at a distance of 3 kpc (physical) from the collapsing object. The source is set to emit monochromatically in the center of the Lyman-Werner (LW) band only at $12.8 \ \rm{eV}$. The LW radiation emitted from the high redshift source is followed self-consistently using ray tracing techniques. We find that, due to self-shielding, a small amount of H$_2$ is able to form at the very center of the collapsing halo even under very strong LW radiation. Furthermore, we find that a radiation source, emitting $> 10^{54}\ (\sim10^3\ \rm{J_{21}})$ photons per second is required to cause the collapse of a clump of $\rm{M \sim 10^5}$ M$_{\odot}$. The resulting accretion rate onto the collapsing object is $\sim 0.25$ M$_{\odot}$ $\rm{yr^{-1}}$. Our results display significant differences, compared to the isotropic radiation field case, in terms of H$_2$ fraction at an equivalent radius. These differences will significantly effect the dynamics of the collapse. With the inclusion of a strong anisotropic radiation source, the final mass of the collapsing object is found to be $\rm{M \sim 10^5}$ M$_{\odot}$. This is consistent with predictions for the formation of a supermassive star or quasi-star leading to a supermassive black hole.