Angle-dependent hardening of the reprocessed spectra in ULXs powered by accretion onto neutron stars

It is anticipated that mass accretion rates exceeding approximately 10^19\, g\, s^{-1} in X-ray pulsars lead to radiation-driven outflows from super-critical accretion discs. The outflows launched from the disc influence the angular distribution of X-ray radiation, resulting in geometrical beaming. The beaming, in turn, impacts the apparent luminosity of the X-ray pulsar, detectability of pulsations, and the spectral composition of the X-ray flux. We employ a straightforward geometrical model of the outflows, perform Monte Carlo simulations, and model the spectra of radiation, reprocessed by the walls of the accretion cavity formed by the outflows. We consider the reprocessed emission only; direct pulsar emission is not included in our modelling. Our results demonstrate that the spectra of reprocessed radiation depend on the actual luminosity of the central engine, the geometry of the outflows, and the viewing angle - most notably on the latter, through changing visibility of the hotter wall regions near the disc plane. The high-energy part of the reprocessed spectrum depends strongly on viewing angle (harder at lower inclinations), while the soft flux varies comparatively little with inclination. In our model, this contrast is a prediction: variable ultra-luminous X-ray sources are expected to exhibit strong high-energy angle sensitivity together with comparatively modest soft-band variation, naturally arising if precession modulates the effective inclination.