Tidal Disruptions of Main Sequence Stars -- I. Observable Quantities and
  their Dependence on Stellar and Black Hole Mass
  This paper introduces a series of papers presenting a quantitative theory for
the tidal disruption of main sequence stars by supermassive black holes. Using
fully general relativistic hydrodynamics simulations and MESA-model initial
conditions, we explore the pericenter-dependence of tidal disruption properties
for eight stellar masses ($0.15 \leq M_*/M_\odot \leq 10$) and six black hole
masses ($10^5 \leq M_{BH}/M_\odot \leq 5 \times 10^7$). We present here the
results most relevant to observations. The effects of internal stellar
structure and relativity decouple for both the disruption cross section and the
characteristic energy width of the debris. Moreover, the full disruption cross
section is almost independent of $M_*$ for $M_*/M_\odot \lesssim 3$.
Independent of $M_*$, relativistic effects increase the critical pericenter
distance for full disruptions by up to a factor $\sim 3$ relative to the
Newtonian prediction. The probability of a direct capture is also independent
of $M_*$; at $M_{BH}/M_\odot \simeq 5 \times 10^6$ this probability is equal to
that of a complete disruption. The width of the debris energy distribution
$\Delta E$ can differ from the standard estimate by factors from 0.35 to 2,
depending on $M_*$ and $M_{BH}$, implying a corresponding change in the
characteristic mass-return timescale. The "frozen-in approximation" is
inconsistent with $\Delta E$, and mass-loss continues over a long span of time.
We provide analytic forms, suitable for use in both event rate estimates and
parameter inference, to describe all these trends. For partial disruptions, we
find a nearly-universal relation between the star's angular momentum and the
fraction of $M_*$ remaining. Within the "empty loss-cone" regime, partial
disruptions must precede full disruptions. These partial disruptions can
drastically affect the rate and appearance of subsequent total disruptions.
