Coughlin, E.R. orcid.org/0000-0003-3765-6401 and Nixon, C.J. orcid.org/0000-0002-2137-4146 (2022) Stars Crushed by Black Holes. II. A Physical Model of Adiabatic Compression and Shock Formation in Tidal Disruption Events. The Astrophysical Journal, 926 (1). 47. ISSN 0004-637X
Abstract
We develop a Newtonian model of a deep tidal disruption event (TDE), for which the pericenter distance of the star, rp, is well within the tidal radius of the black hole, rt, i.e., when β ≡ rt/rp ≫ 1. We find that shocks form for β ≳ 3, but they are weak (with Mach numbers ∼1) for all β, and that they reach the center of the star prior to the time of maximum adiabatic compression for β ≳ 10. The maximum density and temperature reached during the TDE follow much shallower relations with β than the previously predicted ${\rho }_{\max }\propto {\beta }^{3}$ and ${T}_{\max }\propto {\beta }^{2}$ scalings. Below β ≃ 10, this shallower dependence occurs because the pressure gradient is dynamically significant before the pressure is comparable to the ram pressure of the free-falling gas, while above β ≃ 10, we find that shocks prematurely halt the compression and yield the scalings ${\rho }_{\max }\propto {\beta }^{1.62}$ and ${T}_{\max }\propto {\beta }^{1.12}$. We find excellent agreement between our results and high-resolution simulations. Our results demonstrate that, in the Newtonian limit, the compression experienced by the star is completely independent of the mass of the black hole. We discuss our results in the context of existing (affine) models, polytropic versus non-polytropic stars, and general relativistic effects, which become important when the pericenter of the star nears the direct capture radius, at β ∼ 12.5 (2.7) for a solar-like star disrupted by a 106M⊙ (107M⊙) supermassive black hole.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022. The Author(s). Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Astrophysics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 02 Nov 2023 17:28 |
Last Modified: | 02 Nov 2023 17:28 |
Status: | Published |
Publisher: | American Astronomical Society |
Identification Number: | 10.3847/1538-4357/ac3fb9 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:204833 |