Self-Interacting Dark-Matter Spikes and the Final-Parsec Problem: Bayesian constraints from the NANOGrav 15-Year Gravitational-Wave Background

TL;DR

This study investigates whether self-interacting dark matter spikes around merging supermassive black holes can solve the final-parsec problem by providing enough dynamical friction, using Bayesian analysis to compare predictions with NANOGrav gravitational-wave data.

Contribution

It introduces a Bayesian framework to constrain SIDM properties based on gravitational-wave background observations, linking dark matter physics with SMBH binary evolution.

Findings

SIDM parameters are consistent with galaxy and cluster limits.

SIDM spikes can produce GW signals matching NANOGrav data.

The model supports SIDM as a solution to the final-parsec problem.

Abstract

A self-interacting dark-matter (SIDM) density spike around merging supermassive black holes (SMBHs) may be able to supply the dynamical friction needed to shrink binaries from $\sim 1\, \mathrm{pc}$ to $\sim 10^{-2} \,\mathrm{pc}$, thereby resolving the long-standing "final-parsec problem". Embedding the binary-halo system in a cosmological population model, we evolve the inspiral under the combined influence of gravitational-wave (GW) emission and SIDM drag, compute the resulting nanohertz GW background, and confront it with the NANOGrav 15-year pulsar-timing data. A six-parameter Bayesian analysis, performed with a Gaussian-process-accelerated Markov chain Monte Carlo, yields posterior constraints on the cross-section per unit mass and maximum circular velocity values that were consistent with independent galaxy-rotation and cluster-lensing limits. Within this parameter space, the SIDM spike remains intact, supplies sufficient friction to overcome the stellar depletion barrier, and produces a characteristic-strain spectrum that matches the NANOGrav signal as well as phenomenological astrophysical models.