The LISA Astrophysics "Disc-IMRI" Code Comparison Project: Intermediate-Mass-Ratio Binaries in AGN-Like Discs

TL;DR

This study compares eight hydrodynamical codes to model intermediate-mass-ratio binaries in accretion discs, highlighting the importance of resolution, disc thickness, and computational methods for accurate gravitational wave source predictions.

Contribution

It provides a comprehensive code comparison for simulating IMRI systems in AGN-like discs, emphasizing the impact of numerical methods and resolution on results.

Findings

High-resolution codes agree well with analytical models for thick discs.

Discrepancies increase for thin discs, especially between 2D and 3D simulations.

Moving mesh and GPU-accelerated codes are more efficient and preferable.

Abstract

Upcoming space-based gravitational wave detectors such as LISA, the Laser Interferometer Space Antenna, will be sensitive to extreme- and intermediate-mass-ratio inspirals (EMRIs and IMRIs). These binaries are comprised of a supermassive black hole and a stellar-mass object or intermediate-mass black hole. Their detection will probe the structure of galactic nuclei and enable tests of general relativity. As these events will be observed over thousands of orbital cycles, they will be extremely sensitive to both the underlying spacetime and astrophysical environment, demanding exquisite theoretical models on both fronts to avoid biased or even erroneous results. In particular, many (E/)IMRIs are expected to occur within accretion discs around supermassive black holes, and the nonlinearities present when modeling these systems require numerical simulations. In preparation for future modeling of LISA sources, we have conducted a comparison between eight different hydrodynamical codes and applied them to the problem of a q = 10^{-4} mass ratio binary interacting with an accretion disc. Thicker discs appear more lenient, and all codes at sufficiently high resolutions are in good agreement with each other and analytical predictions. For thinner discs, beyond the reach of analytical models, we find substantial disagreement between 2D and 3D simulations and between different codes, including both the magnitude and sign of the torque. With time and energy efficiency in mind, codes that leverage moving meshes or grid-based Lagrangian remapping seem preferable, as do codes that can leverage graphical processing units and other energy-efficient hardware.