arXiv subjects

Robin Buehler

Publications and source records attributed to Robin Buehler.

4 recordsLinked to original sources

arXiv2024

Acoustic wake in an isothermal profile: dynamical friction and gravitational wave emission

We consider the motion of a circularly-moving perturber in a self-gravitating, collisional system with 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 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 $F_\varphi\propto v_p$. 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 $10^6 M_\odot$ located at the center of a (truncated) isothermal sphere, this GW signal could be comparable to the vacuum GW emission of the black hole binary at sub-nanohertz 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.

astro-ph.GA↗

arXiv2023

Orbital evolution of eccentric perturbers under dynamical friction: crossing the sound barrier

In a gaseous medium, dynamical friction (DF) reaches a maximum when the orbital speed of a (point-like) perturber moving on a circular orbit is close to the sound speed. Therefore, in a quasi-steady state, eccentric orbits of perturbers approaching the sound barrier (from below) should rapidly circularize as they experience the strongest drag at pericenter passage. To investigate this effect, we extend the solution of Desjacques et al. 2022 for circular DF in a uniform gaseous medium to eccentric Keplerian orbits. We derive an approximation to the steady-state DF force, which is valid for eccentricities as high as $e=0.9$ in a limited range of Mach number around the transition to supersonic regime. We validate our analytical result with 3-dimensional simulations of the gas density response. Although gaseous DF generally dissipates orbital energy, we find that it can be directed along the motion of the perturber near pericenter passage when the eccentricity is $e\gtrsim 0.9$. We apply our results to compute the long-time evolution of the orbital parameters. Most trajectories tend to circularize as the perturber moves into the supersonic regime. However, orbits with eccentricities $e\gtrsim 0.8$ below the sound barrier experience a slight increase in eccentricity as they loose orbital energy. Possible extensions to our analytical approach are also discussed.

astro-ph.GA↗

arXiv2022

Dynamical Friction in fuzzy dark matter: circular orbits

We investigate the dynamical friction (DF) acting on circularly-moving perturbers in fuzzy dark matter (FDM) backgrounds. After condensation, FDM is described by a single wave function satisfying a Schr\"odinger-Poisson equation. An equivalent, hydrodynamic formulation can be obtained through the Madelung transform. Here, we consider both descriptions and restrict our analysis to linear response theory. We take advantage of the hydrodynamic formulation to derive a fully analytic solution to the DF in steady-state and for a finite time perturbation. We compare our prediction to a numerical implementation of the wave approach that includes a non-vanishing FDM velocity dispersion $\sigma$. Our solution is valid for both a single and a binary perturber in circular motion as long as $\sigma$ does not significantly exceed the orbital speed $v_\text{circ}$. While the short-distance Coulomb divergence of the (supersonic) gaseous DF is no longer present, DF in the FDM case exhibits an infrared divergence which stems from the (also) diffusive nature of the Schr\"odinger equation. Our analysis of the finite time perturbation case reveals that the density wake diffuses through the FDM medium until it reaches its outer boundary. Once this transient regime is over, both the radial and tangential DF oscillate about the steady-state solution with an exponentially decaying envelope. Steady-state is thus never achieved. We use our results to revisit the DF decay timescales of the 5 Fornax globular clusters. We also point out that the inspiral of compact binary may stall because the DF torque about the binary center-of-mass sometimes flips sign to become a thrust rather than a drag (abridged).

astro-ph.CO↗

arXiv2021

Analytic solution to the dynamical friction acting on circularly moving perturbers

We present an analytic approach to the dynamical friction (DF) acting on a circularly moving point mass perturber in a gaseous medium. We demonstrate that, when the perturber is turned on at $t=0$, steady-state (infinite time perturbation) is achieved after exactly one sound-crossing time. At low Mach number $\mathcal{M}~\ll~1$, the circular-motion steady-state DF converges to the linear-motion, finite time perturbation expression. The analytic results describe both the radial and tangential forces on the perturbers caused by the backreaction of the wake propagating in the medium. The radial force is directed inward, toward the motion centre, and is dominant at large Mach numbers. For subsonic motion, this component is negligible. For moderate and low Mach numbers, the tangential force is stronger and opposes the motion of the perturber. The analytic solution to the circular-orbit DF suffers from a logarithmic divergence in the supersonic regime. This divergence appears at short distances from the perturber solely (unlike the linear motion result which is also divergent at large distances) and can be encoded in a maximum multipole. This is helpful to assess the resolution dependence of numerical simulations implementing DF at the level of Li\'enard-Wiechert potentials. We also show how our approach can be generalised to calculate the DF acting on a compact circular binary.

astro-ph.GA↗