Probing the Nature of Dark Matter Self-Interactions Through Observations of Massive Black Hole Mergers

TL;DR

The paper investigates whether LISA can indirectly probe dark matter self-interactions by comparing merger histories of massive black holes in CDM and SIDM-1 halos. Using ChaNGa zoom-in simulations of two Milky Way-mass galaxies, it models black hole seeding, accretion, feedback, and a dynamical-friction correction under both CDM and SIDM-1 with a constant cross section of $\sigma/m = 1 \, \mathrm{cm^2\, g^{-1}}$. By constructing and comparing the cosmic-time and mass-ratio distributions of MBH mergers via inverse transform sampling and Kolmogorov-Smirnov tests, the study estimates the number of LISA-detected events required to distinguish the models, finding $\sim$80 mergers suffice for cosmic times and $\sim$180 for mass ratios to achieve a ~2$\sigma$ separation. The results suggest LISA could open a new observational window on dark sector physics, while also highlighting the need for larger simulation suites, varying cross sections (including velocity-dependent cases), and improved modeling of merger delays and baryonic feedback. Overall, this work lays groundwork for using gravitational-wave observations to constrain SIDM and motivates more realistic future studies.

Abstract

Though the nature of dark matter remains elusive, two models have come to prominence with testable predictions: cold dark matter (CDM) and self-interacting dark matter (SIDM). While CDM remains the widely accepted model, SIDM was introduced to potentially help resolve the discrepancies between the predictions of the CDM model and observational data, in particular the predicted central density profiles. Previous work involving simulations of small numbers of Milky Way-mass galaxies shows that SIDM delays massive black hole mergers as compared to CDM when the host halo has a flattened central density profile. It is, however, unclear how well massive black hole observations are able to differentiate between CDM and SIDM. In this work, we use mock gravitational wave observations of massive black hole mergers from LISA, a space-based gravitational wave observatory set to launch in the 2030s, to test LISA's capability to indirectly probe dark matter physics. As a proof of concept, we show that LISA may be able to distinguish between CDM and SIDM with a short-range interaction and a constant cross section of 1 $\rm{cm^2~ g^{-1}}$ at the $\sim2σ$ level or greater, provided at least $\sim80$ massive black hole mergers are observed with signal-to-noise ratios greater than 10. Our exploratory work shows that LISA may provide a pathway to probe dark matter self-interactions, motivating future work with more realistic, currently-favored models and larger simulation suites.

Figures (6)

• Figure 1: One of the simulated galaxies with CDM (left) and SIDM-1 (right), at redshift zero. With CDM, the total mass (gas + stars + dark matter) is $7.24 \times 10^{11}$ M$_{\odot}$, the stellar mass is $1.04 \times 10^{10}$ M$_{\odot}$, and the dark matter mass is $6.50 \times 10^{11}$ M$_{\odot}$. With SIDM-1, the total mass is $8.73 \times 10^{11}$ M$_{\odot}$, the stellar mass is $3.89 \times 10^{10}$ M$_{\odot}$, and the dark matter mass is $7.39 \times 10^{11}$ M$_{\odot}$. These masses are calculated using Pynbody, and include all particles that are gravitationally bound to the halo Pynbody. Here, the clearly visible differences are primarily due to the effects of SIDM-1 on the star-formation history. As SIDM-1 delays the growth of black holes via mergers, star formation is not suppressed to the same degree.
• Figure 2: Cumulative probability distributions of massive binary black hole merger properties for galaxies simulated with CDM (purple) and SIDM-1 (green). Left: Cumulative massive binary merger probability as a function of cosmic time. Note that the CDM model exhibits more rapid assembly of massive black holes by mergers at early times. Right: Cumulative massive binary merger probability as a function of mass ratio. The SIDM-1 model favors moderate mass ratio mergers, while nearly half the mergers in the CDM model are nearly equal mass.
• Figure 3: We plot the distribution of 10000 empirical CDFs for cosmic times of 80 MBH mergers, CDM (purple) and SIDM-1 (green). The darker regions contain the 25th and 75th percentiles, whereas the lighter regions enclose the 5th and 95th percentiles. The dark line traces the 50th percentile.
• Figure 4: We plot the distribution of 10000 empirical CDFs for 180 MBH merger mass ratios, CDM (purple) and SIDM-1 (green). The darker regions contain the 25th and 75th percentiles, whereas the lighter regions enclose the 5th and 95th percentiles. The dark line traces the 50th percentile.
• Figure 5: Average p--values (black-dots) for comparing cosmic times (left) or mass-ratios (right) of mergers with CDM to mergers with SIDM-1. We indicate the average plus $2\sigma$ with an X. The red line indicates the significance threshold of 0.05. We note that the distribution of p--values is not Gaussian, thus $2 \sigma$ should be interpreted as an indicator of empirical scatter instead of a Gaussian confidence interval. For differentiating between CDM and SIDM-1, we wish to have an average p--value that is at least two standard deviations below the significance threshold. We find that $\sim80$ mergers are sufficient to attain this when comparing cosmic times, or $\sim180$ mergers when comparing mass ratios.