[Paper Review] Dark Matter Spike surrounding Supermassive Black Holes Binary and the Nanohertz Stochastic Gravitational Wave Background

Zhao-Qiang Shen, Guan-Wen Yuan+4 more|arXiv (Cornell University)|Jun 29, 2023

Pulsars and Gravitational Waves Research29 citations

TL;DR

The paper investigates how dark matter spikes around supermassive black hole binaries affect the nanohertz stochastic gravitational wave background and constrains spike properties using PTA data.

ABSTRACT

The NANOGrav, PPTA, EPTA, CPTA and MPTA collaborations have reported compelling evidence for the existence of the Stochastic Gravitational-Wave Background (SGWB). This inferred background's amplitude and frequency spectrum align closely with the astrophysical predictions for a signal originating from the population of supermassive black hole (SMBH) binaries. Considering these findings, we explore the possibility of detecting dark matter (DM) spikes surrounding SMBHs, which could alter the gravitational-wave waveform and influence the SGWB. We show that the evolution of SMBH binaries, driven by both gravitational radiation and the dynamic friction of the surrounding DM spike, presents observable effects in the nHz frequency domain of the SGWB. We also employ the Bayesian inference method to fit the SGWB spectra from the NANOGrav, EPTA, and PPTA. The model with DM spike improves the fittings to the former two data sets. The spike slope $γ_{ m sp}$ is slightly smaller than 1, which may suggest that the spike is flattened during the inspiral of the SMBHBs.

Motivation & Objective

• Motivate the search for dark matter spike effects on the nanohertz SGWB in light of NANOGrav/PPTA/EPTA/CPTA evidence.
• Model the DM spike density profile around SMBHs and its impact on SMBHB dynamics.
• Quantify how DM spike-induced dynamical friction modulates the SGWB spectrum.
• Constrain DM spike slope parameters using current pulsar timing array data.

Proposed method

• Adopt a DM density profile including an NFW baseline and a central DM spike with a piecewise form (Eq. 5).
• Relate halo mass to stellar and bulge/black hole masses to set SMBH encircled DM environment (Eqs. 2–4).
• Derive SMBH binary dynamics including GW radiation reaction and dynamical friction from DM spike (Eqs. 6–12).
• Compute GW waveforms in the time and frequency domains using stationary phase approximation (Eqs. 13–15).
• Express SGWB energy density and characteristic strain via standard PopIII-like population modeling (Eqs. 16–19).
• Fit to NANOGrav and PPTA data using a likelihood/chi-square framework (Eq. 21).

Experimental results

Research questions

• RQ1 How does the presence of a DM spike change the SMBHB orbital evolution compared to GW-dominated evolution?
• RQ2 Can DM spike dynamical friction flatten the SGWB spectrum at nanoHertz frequencies?
• RQ3 What constraints on the DM spike slope gamma_sp can be derived from current PTA measurements?
• RQ4 Does including DM spike physics improve the fit to the observed SGWB compared to a null DM model?

Key findings

• Including DM spike dynamical friction slightly improves the fit to PTA data (chi-squared 10.5 for 8 dof vs 12.6 for 9 dof in the null model).
• Best-fit model with DM spike yields gamma_sp = 0.76 with other parameters: (lg n0, lg M*, z0, alpha, beta_z, gamma, gamma_sp) = (-38.2, 7.86, 0.23, -1.35, -1.63, 0.40, 0.76).
• Best-fit with DM spike shows beta_z and other parameters are poorly constrained, but the DM spike tends to flatten the SGWB at lower frequencies.
• When gamma_sp is fixed by using null-model values for some parameters, the fit remains competitive (chi-squared = 10.5 with gamma_sp = 0.77).
• The best-fit gamma_sp value being less than 1 suggests the spike may flatten during SMBHB inspiral.