Cyclotron Line Formation in the Radiative Shock of an Accreting Magnetized Neutron Star

Magnetic neutron stars (NSs) often exhibit a cyclotron resonant scattering feature (CRSF) in their X-ray spectra. Accretion onto their magnetic poles is responsible for the emergence of X-rays, but the site of the CRSF formation is still a puzzle. A promising candidate for high-luminosity sources has always been the radiative shock in the accretion column. Nevertheless, no quantitative calculations of spectral formation at the radiative shock have been performed so far. It is well accepted that, in the accretion column of a high-luminosity, accreting magnetic NS, a radiative shock is formed. Here, we aim to explore the scenario where the shock is the site of the cyclotron-line formation. We studied spectral formation at the radiative shock and the emergent spectral shape across a wide range of the parameter space and determined which parameters hold an important role in shaping a prominent CRSF. We developed a Monte Carlo (MC) code based on the forced first collision numerical scheme to conduct radiation transfer simulations at the radiative shock. The seed photons were due to bremsstrahlung and were emitted in the post-shock region. We properly treated bulk-motion Comptonization in the pre-shock region, thermal Comptonization in the post-shock region, and resonant Compton scattering in both regions. We adopted a fully relativistic scheme for the interaction between radiation and electrons, employing an appropriate polarization-averaged differential cross-section. As a result, we calculated the angle- and energy-dependent emergent X-ray spectrum from the radiative shock, focusing on both the CRSF and the X-ray continuum, under diverse conditions. The accretion column was characterized by cylindrical symmetry, and the radiative shock was treated as a mathematical discontinuity. We find that a power law, hard X-ray continuum, and a CRSF are naturally produced by the first-order Fermi energization as the photons criss-cross the shock. The depth and the width of the CRSF depend mainly on the transverse optical depth and the post-shock temperature. We show that the cyclotron-line energy centroid is shifted by $ to lower energies compared to the classical cyclotron energy; this is due to the Doppler boosting between the shock reference frame and the bulk-motion frame. We demonstrate that a "bump" feature arises in the right wing of the CRSF due to the up-scattering of photons by the accreting plasma and extends to higher energies for larger optical depths and post-shock temperatures. We conclude that resonant Compton scattering of photons by electrons in a radiative shock is efficient in producing a power-law X-ray continuum with a high-energy cutoff accompanied by a prominent CRSF. The implications of the Doppler effect on the centroid of the emergent absorption feature must be considered if an accurate determination of the magnetic field strength is desired.