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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2024-01-01
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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 |
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| 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. |
| format | Article |
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| institution | Kabale University |
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| language | English |
| publishDate | 2024-01-01 |
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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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