Impact of scale-height derivative on general relativistic slim disks in tidal disruption events

We construct a numerical model of steady-state, general relativistic (GR) super-Eddington accretion flows in an optically thick, advection-dominated regime, motivated by tidal disruption events wherein super-Eddington accretion assumes a pivotal role. Our model takes into account the loss of angular momentum due to radiation and the scale-height derivative in the basic equations of the GR slim disk. For comparison purposes, we also provide a new analytical solution for a radiation-pressure-dominant GR slim disk, which neglects the angular momentum loss due to radiation and the scale-height derivative. We find that the radiation pressure enhances by incorporating the scale-height derivative into the basic equations. As a result, the surface density near the disk's inner edge decreases, whereas the disk temperature and scale-height increase, brightening the disk spectrum in the soft x-ray wave band. Notably, an extremely high-mass accretion rate significantly enhances the effect of the scale-height derivative, affecting the entire disk. In contrast, the inclusion of the radiation-driven angular momentum loss only slightly influences the disk surface density and temperature compared with the case of the scale-height derivative inclusion. The x-ray luminosity increases significantly due to scale-height derivative for (M) over dot/(M) over dot(Edd) greater than or similar to 2, where (M) over dot(Edd) is the Eddington accretion rate with 0.1 energy conversion efficiency. In addition, the increment is higher for the nonspinning black hole than the spinning black hole case, resulting in a one order of magnitude difference for (M) over dot/(M) over dot(Edd) greater than or similar to 100. We conclude that incorporating the scale-height derivative into a GR slim-disk model is crucial as it impacts the disk structure and its resultant spectrum, particularly on a soft x-ray wave band.