A New Discrete Dynamical Friction Estimator Based on $N$-body Simulations

Abstract

A longstanding problem in galactic simulations is to resolve the dynamical friction (DF) force acting on massive black hole particles when their masses are comparable to or less than the background simulation particles. Many sub-grid models based on the traditional Chandrasekhar DF formula have been proposed, yet they suffer from fundamental ambiguities in the definition of some terms in Chandrasekhar's formula when applied to real galaxies, as well as difficulty in evaluating continuous quantities from (spatially) discrete simulation data. In this work we present a new sub-grid dynamical friction estimator based on the discrete nature of $N$-body simulations, which also avoids the ambiguously-defined quantities in Chandrasekhar's formula. We test our estimator in the GIZMO code and find that it agrees well with high-resolution simulations where DF is fully captured, with negligible additional computational cost. We also compare it with a Chandrasekhar estimator and discuss its applications in real galactic simulations.

Accepted to MNRAS

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• Sharpening the dark matter signature in gravitational waveforms II: Numerical simulations with the NbodyIMRI code
• Modelling the accretion and feedback of supermassive black hole binaries in gas-rich galaxy mergers
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• Cosmic evolution of black hole-spin and galaxy orientations: clues from the NewHorizon and Galactica simulations
• Examining the effects of dark matter spikes on eccentric intermediate mass ratio inspirals using N-body simulations
• Novel Conservative Methods for Adaptive Force Softening in Collisionless and Multi-Species N-Body Simulations
• Diverse dark matter profiles in FIRE dwarfs: black holes, cosmic rays and the cusp-core enigma
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• Dynamical friction and massive black hole orbits: analytical predictions and numerical solutions
• The In Situ Growth of Stellar-mass "Light" Seed Black Holes in Nuclear Star Clusters
• Rapid sinking and efficient mergers of supermassive black holes in compact high-redshift galaxies