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
($10^{5}\leq M_{\rm BH}/\mathrm{M}_{\odot}\leq 5\times 10^{7}$) and stellar
mass ($0.3 \leq M_{\star} /\mathrm{M}_{\odot}\leq 3$) as larger $M_{\rm BH}$
leads to stronger relativistic effects. For fixed $M_{\star}$, as $M_{\rm BH}$
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 $M_{\rm BH} = 5\times10^{7}~{\rm
M}_\odot$, 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 two correction at $M_{\rm BH} = 5 \times 10^7~{\rm M}_\odot$. We find
that for partial disruptions, the fractional remnant mass for a given ratio of
the pericenter to $\mathcal{R}_{\rm t}$ is higher for larger $M_{\rm BH}$.
These results have several implications. As $M_{\rm BH}$ increases above $\sim
10^7~{\rm M}_\odot$, 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 $M_{\rm BH}$. 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
$M_{\rm BH} \gtrsim 10^7~{\rm M}_\odot$, the $M_{\rm BH}$-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.
