Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Shreyas Tiruvaskar, Chris Gordon

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.

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

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 to , 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.

Paper Structure

This paper contains 20 sections, 70 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Density profile of a self-interacting dark matter halo
  3. NFW parameters
  4. Halo mass and stellar mass from the black hole mass
  5. SIDM core
  6. SIDM spike
  7. Self-interactions
  8. Dynamics of a binary merger
  9. Gravitational wave energy loss
  10. Dynamical friction energy loss
  11. Total energy loss
  12. Gravitational strain spectrum
  13. Binary hardening timescale
  14. Binary population
  15. Statistical analysis
  16. ...and 5 more sections

Figures (4)

  • Figure 1: Density profile in three regions. We set the transition velocity $v_\mathrm{t}=1000$ km/s, $(\sigma_0/m)\times(t_\mathrm{age}/1\,\mathrm{Gyr}) = 0.3$$\mathrm{cm^2/g}$, and ($M, q, z) = (6\times10^9\mathrm{M}_\odot, 1, 0)$ where $M$ is the sum of the two black hole masses, $q$ is the ratio of the two black hole masses, and $z$ is the redshift. We get the SIDM velocity dispersion in core $v_0=497.2$ km/s, core radius $r_1=2.2\times10^4$ pc, and transition radius $r_\mathrm{t}=7.3$ pc. The cutoff radius, which is twice the Schwarzschild radius, $r_\mathrm{cutoff}=4GM_\mathrm{tot}/c^2= 1.15\times10^{-3}$ pc. The transition from the NFW (red) to the isothermal core-dominated (blue) region happens at $r=r_1$. The next transition to the density spike-dominated (green) region takes place at $r=r_\mathrm{t}$.
  • Figure 2: Posterior distribution of the model parameters with 68% and 95% confidence interval contours. Reported values correspond to the medians and their 68% credible intervals. $\sigma/m$ is calculated for $(M, q, z) = (5.44\times10^{9}\mathrm{M}_\odot, 0.81, 1.66)$.
  • Figure 3: Green: Characteristic strain calculated for the maximum posterior parameters. We considered 2000 realizations. Median values are plotted with the solid line with a 68% confidence interval. Grey: NANOGrav 15-year data with HD (Hellings Downs) correlated free spectrum modelled simultaneously with additional MP (monopole-correlated), DP (dipole-correlated) red noise, and CURN (common uncorrelated red-noise), also denoted as HD-w/MP+DP+CURN in gwb_nanogravAgazie_2023. Blue: Best fit strain spectra for the Phenomenological model from Agazie2023. Purple: Best fit strain spectra for the GW-only model from the Fig. 1 (right panel) of Agazie2023
  • Figure 4: Comparison with $\sigma/m$ from roberts2025: $\sigma/m$ is calculated for $(M,q, z) = (5.44 \times 10^9\mathrm{M}_\odot, 0.81, 1.66)$, $(2.94 \times 10^9\mathrm{M}_\odot, 0.96, 1.05)$, and $(1.59 \times 10^9\mathrm{M}_\odot, 0.88, 0.80)$ for the top, middle and bottom panels respectively. Results from this work are shown in green. The light‑green region is the 95% region obtained by considering the constraints derived from GWB PTA data. The dark green region corresponds to incorporating constraints given by the "final parsec problem solution" as well as the GWB PTA constraints. Pink and purple: Results from roberts2025 Fig. 9 right panel. Pink and purple lines correspond to a dark matter mass of 0.3 GeV and 0.5 GeV, respectively, which are consistent with galaxy rotation curve and cluster strong lensing data. The $V_\mathrm{max}$ quantity on the x-axis is related to the core velocity $v_0$ as $V_\mathrm{max} = v_0 / 0.64$. Red and blue: Points from roberts2025 Fig. 9 right panel. Red point corresponds to the values derived in roberts2025 for the dwarf galaxies ($V_\mathrm{max} = 75\pm25$km/s, $\sigma/m = 30\pm10$$\mathrm{cm^2/g}$), and the blue point corresponds to the values for galaxy groups and cluster scales ($V_\mathrm{max} = 1000\pm55$km/s, $\sigma/m < 0.13$$\mathrm{cm^2/g}$).