Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission

We consider the motion of a circularly moving perturber in a self-gravitating, collisional system with a spherically symmetric density profile. We concentrate on the singular isothermal sphere, which, despite its pathological features, admits a simple polarization function in linear response theory....

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Main Authors: Gali Eytan, Vincent Desjacques, Robin Buehler
Format: Article
Language:English
Published: IOP Publishing 2024-01-01
Series:The Astrophysical Journal
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Online Access:https://doi.org/10.3847/1538-4357/ad758b
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author Gali Eytan
Vincent Desjacques
Robin Buehler
author_facet Gali Eytan
Vincent Desjacques
Robin Buehler
author_sort Gali Eytan
collection DOAJ
description We consider the motion of a circularly moving perturber in a self-gravitating, collisional system with a spherically symmetric density profile. We concentrate on the singular isothermal sphere, which, despite its pathological features, admits a simple polarization function in linear response theory. This allows us to solve for the acoustic wake trailing the perturber and the resulting dynamical friction, in the limit where the self-gravity of the response can be ignored. In a steady state and for subsonic velocities v _p < c _s , the dynamical friction torque ${F}_{\varphi }\propto {v}_{p}^{3}$ is suppressed for perturbers orbiting in an isothermal sphere relative to the infinite, homogeneous medium expectation F _φ ∝ v _p . For highly supersonic motions, both expectations agree and are consistent with a local approximation to the gravitational torque. At fixed resolution (a given Coulomb logarithm), the response of the system is maximal for Mach numbers near the constant circular velocity of the singular isothermal profile. This resonance maximizes the gravitational-wave (GW) emission produced by the trailing acoustic wake. For an inspiral around a massive black hole of mass 10 ^6 M _⊙ located at the center of a (truncated) isothermal sphere, this GW signal could be comparable to the vacuum GW emission of a black hole binary at subnanohertz frequencies when the small black hole enters the Bondi sphere of the massive one. The exact magnitude of this effect depends on departures from hydrostatic equilibrium and on the viscosity present in any realistic astrophysical fluid, which are not included in our simplified description.
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spelling doaj-art-2f9550df3e4547f39081b2545feedda42024-11-14T12:39:56ZengIOP PublishingThe Astrophysical Journal1538-43572024-01-0197618910.3847/1538-4357/ad758bAcoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave EmissionGali Eytan0https://orcid.org/0009-0009-0366-7103Vincent Desjacques1https://orcid.org/0000-0003-2062-8172Robin Buehler2https://orcid.org/0000-0003-3073-9036Physics Department , Technion—Israel Institute of Technology, Haifa 3200003, Israel ; gali.eytan@campus.technion.ac.il, dvince@physics.technion.ac.il, robinbuehler@campus.technion.ac.ilPhysics Department , Technion—Israel Institute of Technology, Haifa 3200003, Israel ; gali.eytan@campus.technion.ac.il, dvince@physics.technion.ac.il, robinbuehler@campus.technion.ac.ilPhysics Department , Technion—Israel Institute of Technology, Haifa 3200003, Israel ; gali.eytan@campus.technion.ac.il, dvince@physics.technion.ac.il, robinbuehler@campus.technion.ac.ilWe consider the motion of a circularly moving perturber in a self-gravitating, collisional system with a spherically symmetric density profile. We concentrate on the singular isothermal sphere, which, despite its pathological features, admits a simple polarization function in linear response theory. This allows us to solve for the acoustic wake trailing the perturber and the resulting dynamical friction, in the limit where the self-gravity of the response can be ignored. In a steady state and for subsonic velocities v _p < c _s , the dynamical friction torque ${F}_{\varphi }\propto {v}_{p}^{3}$ is suppressed for perturbers orbiting in an isothermal sphere relative to the infinite, homogeneous medium expectation F _φ ∝ v _p . For highly supersonic motions, both expectations agree and are consistent with a local approximation to the gravitational torque. At fixed resolution (a given Coulomb logarithm), the response of the system is maximal for Mach numbers near the constant circular velocity of the singular isothermal profile. This resonance maximizes the gravitational-wave (GW) emission produced by the trailing acoustic wake. For an inspiral around a massive black hole of mass 10 ^6 M _⊙ located at the center of a (truncated) isothermal sphere, this GW signal could be comparable to the vacuum GW emission of a black hole binary at subnanohertz frequencies when the small black hole enters the Bondi sphere of the massive one. The exact magnitude of this effect depends on departures from hydrostatic equilibrium and on the viscosity present in any realistic astrophysical fluid, which are not included in our simplified description.https://doi.org/10.3847/1538-4357/ad758bDynamical frictionGravitational wavesIsothermal sphere profile
spellingShingle Gali Eytan
Vincent Desjacques
Robin Buehler
Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission
The Astrophysical Journal
Dynamical friction
Gravitational waves
Isothermal sphere profile
title Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission
title_full Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission
title_fullStr Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission
title_full_unstemmed Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission
title_short Acoustic Wake in a Singular Isothermal Profile: Dynamical Friction and Gravitational-wave Emission
title_sort acoustic wake in a singular isothermal profile dynamical friction and gravitational wave emission
topic Dynamical friction
Gravitational waves
Isothermal sphere profile
url https://doi.org/10.3847/1538-4357/ad758b
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AT robinbuehler acousticwakeinasingularisothermalprofiledynamicalfrictionandgravitationalwaveemission