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 <= M-star M-circle dot <= 10) and six black hole masses 10(5) <= M-BH/M-circle dot <= 5 X 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-star for M-star/M-circle dot less than or similar to 3. Independent of M-star, relativistic effects increase the critical pericenter distance for full disruption events by up to a factor of similar to 3 relative to the Newtonian prediction. The probability of a direct capture is also independent of M-star; at M-BH/M-circle dot x 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 of 0.35 - 2, depending on M-star; and M-BH, implying a corresponding change (proportional to(Delta E)(-3/2)) in the characteristic mass-return timescale. 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.