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( MM105 105BH7)and stellar mass (MM0.33) as larger MBH leads to stronger relativistic effects. For fixed Må, as MBH increases, the ratio of the maximum pericenter distance yielding full disruptions (t) to its Newtonian prediction rises rapidly, becoming triple the Newtonian value for= ́MM510BH7, 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= ́MM510BH7. We provide approximate formulae that express the relativistic corrections of both 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 t is higher for larger MBH. These results have several implications. As MBH increases above~M107, 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 MBH. 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. ForMM10BH7, the MBH-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.