Description
Pulsar timing arrays (PTAs) have now revealed a nano-hertz stochastic gravitational-wave background whose amplitude and spectral shape are consistent with a cosmic population of merging super-massive black-hole (SMBH) binaries. Explaining how such binaries bridge the ``final parsec’’ separation before gravitational radiation dominates remains a key challenge. Following the mechanism proposed by Alonso-Álvarez et al. (2024), we investigate whether dynamical friction from a dense spike of self-interacting dark matter (SIDM) surrounding each SMBH can simultaneously solve the final-parsec problem and imprint the mild low-frequency turnover hinted at in current PTA data.
We perform the first full-likelihood Bayesian analysis of this scenario using the NANOGrav 15-year data set. Employing a custom-corrected version of the holodeck pipeline, we sample
the joint posterior of SMBH-population, host-galaxy and SIDM parameters with an MCMC and marginalise over astrophysical uncertainties. The velocity-weighted cross section per unit mass is
constrained to
$$ \bigl\langle \sigma v / m \bigr\rangle \;=\; 10^{\,2.9 \pm 0.5}\, \mathrm{cm^{2}}\!/\!(\mathrm{g\,km\,s^{-1}}), $$ This range is fully compatible with independent inferences from dwarf-galaxy cores and galaxy-cluster offsets, favouring a Yukawa-like velocity dependence mediated by an $O(10\text{–}100)$ MeV dark photon. In our model, the SIDM spike supplies enough dynamical friction to merge typical $10^{8\text{–}9}\,M_\odot$ binaries within a Hubble time, whereas collisionless cold-DM spikes are disrupted too early.
