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 _ { \star } / 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 .
We find that 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 _ { \star } for M _ { \star } / M _ { \odot } \lesssim 3 .
Independent of M _ { \star } , relativistic effects increase the critical pericenter distance for full disruption events by up to a factor \sim 3 relative to the Newtonian prediction .
The probability of a direct capture is also independent of M _ { \star } ; at M _ { BH } / M _ { \odot } \simeq 5 \times 10 ^ { 6 } this probability is equal to the probability of a complete disruption .
The breadth of the debris energy distribution \Delta E can differ from the standard estimate by factors ranging from 0.35 to 2 , depending on M _ { \star } and M _ { BH } , implying a corresponding change ( \propto ( \Delta E ) ^ { -3 / 2 } ) 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 _ { \star } 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 .