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

TL;DR

The paper addresses how gas in AGN-like discs affects the orbital evolution of intermediate-mass-ratio binaries (IMRIs) and the reliability of hydrodynamics codes for modeling them. It jointly compares eight hydrodynamics codes across thick and thin disc regimes with a fiducial $q=10^{-4}$ system, focusing on gas morphology, torques, and convergence. The study finds broad agreement among grid-based codes in thick discs but substantial code-dependent differences in thinner, nonlinear regimes, and emphasizes the importance of 3D modeling and accurate viscosity implementations. It also discusses implications for LISA gravitational-wave source interpretation and possible electromagnetic counterparts, and offers guidance on code efficiency and environmental impact.

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.

Figures (17)

• Figure 1: Surface density map (top two rows) and radial velocity map (bottom two rows) for the alignment run ($H/r=0.1$) after 100 orbits (33 for GASOLINE. Specifically, the top panels plot $\log_{10}{(\Sigma/\Sigma(t=0)}$ over the range $[-0.2,0.1]$; the bottom panels plot $v_r$ on a scale of $[-0.01,0.01]$, with red indicating negative velocities. Thus, typical deviations in the surface density due to the forcing from the secondary are on the order of $\sim$10%, and deviations in the velocity profile of the disc are of order $\sim$1%. The grid-based codes maintained surface density profiles with the same slope as the initial condition, whereas the particle-based code developed slightly shallower profiles. Both maps illustrate the trailing spiral arm launched by the perturber, which damps away before reaching the outer boundary but interacts with the inner boundary at $r = 0.5a$. A complimentary view in $(r,\phi)$ is provided in Appendix \ref{['app:extra']} in Fig.\ref{['fig:surfacedensitymap_hr01_unrolled']}.
• Figure 2: Torque on the secondary versus time in orbits for the alignment run ($H/r=0.1$), over the first 10 orbits (top panel) and the entire 100 orbit (33 for GASOLINE) series (bottom panel). The black dashed and dotted lines show analytical predictions from Equation \ref{['eq:linear2D']}2010MNRAS.401.1950P for the 2D case and Equation \ref{['eq:linear3D']}TanakaOkada2024 for the 3D case, respectively. The torque is averaged over a 1-orbit window, and the envelope on each lines delineates the the variability seen in the unsmoothed torque data.
• Figure 3: Initial and azimuthally-averaged density profiles after $100$ orbits in the alignment run ($H/r=0.1$) for the codes that reached that point (data for GASOLINE is plotted after 33 orbits). Particle-based code data have been averaged over one orbit.
• Figure 4: Azimuthally-averaged torque profiles after $100$ orbits in the alignment run ($H/r=0.1$), excepting the results of the GASOLINE simulation, which are plotted after 33 orbits. Particle-based code data have been averaged over one orbit.
• Figure 5: Surface density map (top two rows) and radial velocity map (bottom two rows) for the thin-disc run ($H/r=0.03$) after 100 orbits (50 for GASOLINE). Specifically, the top panels plot $\log_{10}{(\Sigma/\Sigma_0)}$ over a range [-0.5,1.5]; the bottom panels plot $v_r$ on a scale of $[-0.05,0.05]$, with red indicating negative velocities. Typical deviations of the surface density due to the forcing from the secondary are much larger than in the thick-disc case, from a depression by about $\sim$50% in the coorbital region to an excess of $\sim$150% within the Hill sphere of the secondary. A slightly deeper gap opens within the coorbital region of the GASOLINE simulation. The DISCO and GASOLINE simulations also find much more dense circumsecondary discs. Both maps illustrate the trailing spiral arm launched by the perturber, which winds more tightly than in the thick-disc case thanks to the lower sound speed. A complimentary view in $(r,\phi)$ is provided in Appendix \ref{['app:extra']} in Fig.\ref{['fig:surfacedensitymap_hr01_unrolled']}.