Direct collapse black holes forming in pristine, atomically-cooling haloes at $z approx 10-20$ may act as the seeds of supermassive black holes (BH) at high redshifts. In order to create a massive BH seed, the host halo needs to be prevented from forming stars. H$_2$ therefore needs to be irradiated by a large flux of Lyman-Werner (LW) UV photons in order to suppress H$_2$ cooling. A key uncertainty in this scenario is the escape fraction of LW radiation from first galaxies, the dominant source of UV photons at this epoch. To better constrain this escape fraction, we have performed radiation-hydrodynamical simulations of the growth of HII regions and their associated photodissociation regions in the first galaxies using the ZEUS-MP code. We find that the LW escape fraction crucially depends on the propagation of the ionisation front (I-front). For an R-type I-front overrunning the halo, the LW escape fraction is always larger than 95%. If the halo recombines later from the outside--in, due to a softened and weakened spectrum, the LW escape fraction in the rest-frame of the halo (the near-field) drops to zero. A detailed and careful analysis is required to analyse slowly moving, D-type I-fronts, where the escape fraction depends on the microphysics and can be as small as 3% in the near-field and 61% in the far-field or as large as 100% in both the near-field and the far-field.
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