Probing the Bardeen-Petterson effect in tidal disruption events with spectral line reverberation mapping

Abstract

For an inclined accretion flow around a rotating black hole, the combined effect of the Lense-Thirring precession and viscous torque tends to align the inner part of the flow with the black hole spin, leading to the formation of a warped disc, known as the Bardeen-Petterson effect (Bardeen & Petterson 1975). In tidal disruption events (TDEs) in which a super-massive black hole starts to accrete the bound debris, if the black hole is spinning, in general the stellar orbit is inclined with the black hole spin. So is the accretion disc formed following circularization and radiative cooling of the debris. Xiang-Gruess et al. (2016) studied in detail the stellar debris evolution and disc formation in TDEs when the stellar orbit is inclined, and found that a warped disc would form under certain conditions. In this work we investigate properties of time-resolved fluorescent iron line originating from a warped disc that is irradiated by the initial X-ray flare. We find that the time-resolved spectrum shows distinct features before and after a critical time. This critical time depends on the Bardeen-Petterson radius $r_{\rm BP}$, i.e., the outer boundary of the inner aligned disc; while the line width during the later stage of the X-ray flare is sensitive to the inclination of the outer disc flow. This demonstrates that time-resolved X-ray spectroscopy can be a powerful tool to probe the Bardeen-Petterson effect in TDE flares and can be used to measure the Bardeen-Petterson radius as well as put constraint on the black hole mass and spin.