The bright black hole X-ray binary 4U 1543--47 during 2021 outburst: a thick accretion disk inflated by high luminosity

The black hole X-ray binary source 4U 1543--47 experienced a super-Eddington outburst in 2021, reaching a peak flux of up to $\sim1.96\times10^{-7}\rm erg\ \rm cm^{-2}\ \rm s^{-1}$ ($\sim 8.2$ Crab) in the 2--10\,keV band. Soon after the outburst began, it rapidly transitioned into the soft state. Our goal is to understand how the accretion disk structure deviates from a standard thin disk when the accretion rate is near Eddington. To do so, we analyzed spectra obtained from quasi-simultaneous observations conducted by the Hard X-ray Modulation Telescope (Insight-HXMT), the Nuclear Spectroscopic Telescope Array (NuSTAR), and the Neil Gehrels Swift Observatory (Swift). These spectra are well-fitted by a model comprising a disk, a weak corona, and a reflection component. We suggest that the reflection component is caused by disk self-irradiation, that is by photons emitted from the inner disk which return to the accretion disk surface, as their trajectories are bent by the strong gravity field. In this scenario, the best-fitting parameters imply that the reflected flux represents more than half of the total flux. Using general relativistic ray-tracing simulations, we show that this scenario is viable when the disk becomes geometrically thick, with a funnel-like shape, as the accretion rate is near or above the Eddington limit. In the specific case of 4U 1543--47, an angle $\gtrsim$ 45 deg between the disk surface and the equatorial plane can explain the required amount of self-irradiation.