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 waveband. 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 $\dot{M}/\dot{M}_{\rm Edd} \gtrsim 2$. In addition, the increment is higher for the non-spinning black hole than the spinning black hole case, resulting in a one-order of magnitude difference for $\dot{M}/\dot{M}_{\rm Edd}\gtrsim100$. 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 waveband.