2019/07/18 by Taeho Ryu, Julian H. Krolik, Ryu, Taeho +5
Physics and Astronomy · #Astrophysical Phenomena and Observations #Astrophysics of Galaxies (astro-ph.GA) #FOS: Physical sciences #Gamma-ray bursts and supernovae #High Energy Astrophysical Phenomena (astro-ph.HE) #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.1907.08205
openalex publication_date 2019/07/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A star is tidally disrupted by a supermassive black hole when their separation is shorter than the "tidal radius". This quantity is often estimated on an order-of-magnitude basis without reference to the star's internal structure. Using MESA models for main sequence stars and fully general relativistic dynamics, we find the physical tidal radius for complete disruption \calRt for a 106M_\odot black hole (BH). We find that across a factor ∼20 in stellar mass M_*, i.e., 0.15M\odot≤ M_*≤3M_\odot, \calRt∼27×(BH's gravitational radius). When comparing \calRt with the commonly used order-of-magnitude estimate rt, we find that \calRt∼1.05-1.45rt for 0.15M_\odot≤ M_*≤0.5M_\odot, but between 0.5 M_\odot and 1 M_\odot, \calRt drops to ∼ 0.45rt, and it remains at this value up to 10 M_\odot. The near-constancy of \calRt implies a weaker dependence of the full disruption rate on M_* than when predicted with rt. The characteristic energy width of the debris ΔE ranges from ∼1.2Δ\calE for low-mass stars to ∼ 0.35Δ\calE for higher-mass stars, where Δ\calE=GM\rm BHR_*/\calRt2. We present analytic fits for the M_* dependence of \calRt and ΔE; these fits lead to analytic expressions for the time of peak mass fallback rate and the maximal mass fallback rate. Our results also bear on the fraction of events leading to fast or slow circularization, as well as on the character of the tidal event occurring when the remnant of a partial disruption returns to the black hole. Using a semi-analytic model, we show that \calRt is primarily determined by the star's central density rather than its mean density. For high-mass stars, the full disruption rate is roughly 1/4 the partial disruption rate, while this ratio is close to unity for low-mass stars.