Tidal Disruptions of Main-sequence Stars. IV. Relativistic Effects and Dependence on Black Hole Mass

Using a suite of fully relativistic hydrodynamic simulations applied to main-sequence stars with realistic internal density profiles, we examine full and partial tidal disruptions across a wide range of black hole mass ( ${10}^{5}\leqslant {M}_{\mathrm{BH}}/{M}_{\odot }\leqslant 5\times {10}^{7}$ ) and stellar mass ( $0.3\leqslant {M}_{\star }/{M}_{\odot }\leqslant 3$ ) as larger M_BH leads to stronger relativistic effects. For fixed M_⋆, as M_BH increases, the ratio of the maximum pericenter distance yielding full disruptions ( ${{ \mathcal R }}_{{\rm{t}}}$ ) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for ${M}_{\mathrm{BH}}=5\times {10}^{7}\,{M}_{\odot }$ , while the ratio of the energy width of the stellar debris for full disruptions to the Newtonian prediction decreases steeply, resulting in a factor of 2 correction at ${M}_{\mathrm{BH}}=5\times {10}^{7}\,{M}_{\odot }$ . We provide approximate formulae that express the relativistic corrections of both ${{ \mathcal R }}_{{\rm{t}}}$ and the energy width relative to their Newtonian approximate estimates. For partial disruptions, we find that the fractional remnant mass for a given ratio of the pericenter to ${{ \mathcal R }}_{{\rm{t}}}$ is higher for larger M_BH. These results have several implications. As M_BH increases above $\sim {10}^{7}\,{M}_{\odot }$ , the cross section for complete disruptions is suppressed by competition with direct capture. However, the cross-section ratio for partial to complete disruptions depends only weakly on M_BH. The relativistic correction to the debris energy width delays the time of peak mass-return rate and diminishes the magnitude of the peak return rate. For ${M}_{\mathrm{BH}}\gtrsim {10}^{7}\,{M}_{\odot }$ , the M_BH-dependence of the full disruption cross section and the peak mass-return rate and time is influenced more by relativistic effects than by Newtonian dynamics.