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 ( $0.15\leqslant {M}_{\star }/{M}_{\odot }\leqslant 10$ ) and six black hole masses ( ${10}^{5}\leqslant {M}_{\mathrm{BH}}/{M}_{\odot }\leqslant 5\times {10}^{7}$ ). 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_⊙ ≲ 3. Independent of M_⋆, relativistic effects increase the critical pericenter distance for full disruption events by up to a factor of ∼3 relative to the Newtonian prediction. The probability of a direct capture is also independent of M_⋆; at M_BH/M_⊙ ≃ 5 × 10⁶ this probability is equal to the probability of a complete disruption. The breadth of the debris energy distribution ΔE can differ from the standard estimate by factors of 0.35 - 2, depending on M_⋆ and M_BH, implying a corresponding change (∝(ΔE)^-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_⋆ 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.