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Inference on inner galaxy structure via gravitational waves from supermassive binaries

Yifan Chen, Matthias Daniel, Daniel J. D'Orazio, Xuanye Fan, Andrea Mitridate, Laura Sagunski, Xiao Xue, Gabriella Agazie, Akash Anumarlapudi, Anne M. Archibald, Zaven Arzoumanian, Jeremy G. Baier, Paul T. Baker, Bence Bécsy, Laura Blecha, Adam Brazier, Paul R. Brook, Sarah Burke-Spolaor, Rand Burnette, J. Andrew Casey-Clyde, Maria Charisi, Shami Chatterjee, Tyler Cohen, James M. Cordes, Neil J. Cornish, Fronefield Crawford, H. Thankful Cromartie, Kathryn Crowter, Megan E. DeCesar, Paul B. Demorest, Heling Deng, Lankeswar Dey, Timothy Dolch, Elizabeth C. Ferrara, William Fiore, Emmanuel Fonseca, Gabriel E. Freedman, Emiko C. Gardiner, Nate Garver-Daniels, Peter A. Gentile, Kyle A. Gersbach, Joseph Glaser, Deborah C. Good, Kayhan Gültekin, Jeffrey S. Hazboun, Ross J. Jennings, Aaron D. Johnson, Megan L. Jones, David L. Kaplan, Luke Zoltan Kelley, Matthew Kerr, Joey S. Key, Nima Laal, Michael T. Lam, William G. Lamb, Bjorn Larsen, T. Joseph W. Lazio, Natalia Lewandowska, Tingting Liu, Duncan R. Lorimer, Jing Luo, Ryan S. Lynch, Chung-Pei Ma, Dustin R. Madison, Alexander McEwen, James W. McKee, Maura A. McLaughlin, Natasha McMann, Bradley W. Meyers, Patrick M. Meyers, Chiara M. F. Mingarelli, Cherry Ng, David J. Nice, Stella Koch Ocker, Ken D. Olum, Timothy T. Pennucci, Benetge B. P. Perera, Polina Petrov, Nihan S. Pol, Henri A. Radovan, Scott M. Ransom, Paul S. Ray, Joseph D. Romano, Jessie C. Runnoe, Alexander Saffer, Shashwat C. Sardesai, Ann Schmiedekamp, Carl Schmiedekamp, Kai Schmitz, Brent J. Shapiro-Albert, Xavier Siemens, Joseph Simon, Magdalena S. Siwek, Sophia V. Sosa Fiscella, Ingrid H. Stairs, Daniel R. Stinebring, Kevin Stovall, Abhimanyu Susobhanan, Joseph K. Swiggum, Jacob Taylor, Stephen R. Taylor, Jacob E. Turner, Caner Unal, Michele Vallisneri, Rutger van Haasteren, Sarah J. Vigeland, Haley M. Wahl, Caitlin A. Witt, David Wright, Olivia Young

Abstract

The detection of a stochastic gravitational wave background by pulsar-timing arrays indicates the presence of a population of supermassive black hole binaries. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to substantial hardening during a transition from early environmental influences to later stages dominated by emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. Here we model how the gravitational-wave spectrum depends on the initial inner galactic profile before scouring by binary ejections while accounting for a range of initial binary eccentricities. By analysing the NANOGrav 15-year data, we find that a parsec-scale galactic-centre density of around $10^6 M_{\odot} \mathrm{pc}^{-3}$ is favoured across most of the parameter space, thus shedding light on the environmental effects that shape black hole evolution and the combined matter density near galaxy centres.

Inference on inner galaxy structure via gravitational waves from supermassive binaries

Abstract

The detection of a stochastic gravitational wave background by pulsar-timing arrays indicates the presence of a population of supermassive black hole binaries. Although the observed spectrum generally matches predictions for orbital evolution driven by gravitational-wave emission in circular orbits, there is a preference for a spectral turnover at the lowest observed frequencies, which may point to substantial hardening during a transition from early environmental influences to later stages dominated by emission. In the vicinity of these binaries, the ejection of stars or dark matter particles through gravitational three-body slingshots efficiently extracts orbital energy, leading to a low-frequency turnover in the spectrum. Here we model how the gravitational-wave spectrum depends on the initial inner galactic profile before scouring by binary ejections while accounting for a range of initial binary eccentricities. By analysing the NANOGrav 15-year data, we find that a parsec-scale galactic-centre density of around is favoured across most of the parameter space, thus shedding light on the environmental effects that shape black hole evolution and the combined matter density near galaxy centres.

Paper Structure

This paper contains 7 sections, 18 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Binary Hardening by Three-body Scattering
  3. Inference of galactic-centre matter distributions
  4. Discussions
  5. Methods
  6. Supermassive Black Hole Binary Population
  7. Other Possible Environmental Effects

Figures (6)

  • Figure 1: Illustrative SGWB spectra from a simplified SMBHB population. Examples of the SGWB spectra derived from an SMBHB population modelled as delta functions in the space of $(M,q,z)$, specifically $\mathrm{d}^3\eta/(\mathrm{d}z\,\mathrm{d}M\,\mathrm{d}q) = \delta(M-M_0)\delta(z-z_0)\delta(q-q_0)\,\mathrm{Mpc^{-3}}$. The values of the constants $(M_0, z_0, q_0)$ are indicated at the top. In all scenarios, the evolution of the semimajor axis begins at $1$ pc, with the eccentricity $e_{\rm pc}$ defined at that separation. Colours indicate different $e_{\rm pc}$ values, and line styles denote variations in $\rho_i/\sigma_i$ for three-body scattering, using $\bar{\rho}_{\rm ref}\equiv 10^5\,M_\odot/\mathrm{pc}^3$ and $\bar{\sigma}_{\rm ref}\equiv 10^{-3}\,c$.
  • Figure 1: Distribution of SMBHBs in mass, mass ratio, and redshift. Comoving volumetric number density of SMBHBs for the fiducial model, shown as a function of total SMBH mass $M$ (left), mass ratio $q$ (middle), and redshift $z$ (right).
  • Figure 2: Posterior constraints on eccentricity and environmental parameters. Posterior distribution of the parameters $(e_0, \log_{10}(\rho_{\rm pc}[M_\odot/\mathrm{pc}^3]/10^5), \gamma)$, representing the initial eccentricity and the pre-scouring density profile, inferred from the lowest five frequency bins of the NANOGrav 15-year dataset. The $1\sigma$ and $2\sigma$ confidence regions are shown in dark blue and light blue, respectively.
  • Figure 2: Normalization distribution for SMBHB population models. Distribution of the normalization factor $N$, defined as the ratio between the $h_c^2$ amplitude predicted by SMBHB population models (using astrophysical priors) and the fiducial value in Supplementary Table \ref{['tab:SAMP']}, evaluated without environmental hardening or eccentricity effects. The distribution is fitted as $\log_{10} N = \mathcal{N}(-1.56, 1.12)$ and adopted as the prior on the normalization in the data analysis. The fiducial value, fixed at $N=1$, is indicated by the red line.
  • Figure 3: Constraints and corresponding SGWB spectra for fixed initial eccentricities.Left: Posterior distribution of the density-profile parameters $(\log_{10}(\rho_{\rm pc}[M_\odot/\mathrm{pc}^3]/10^5), \gamma)$ for three representative initial eccentricities, $e_0 = 0$ (blue), $0.5$ (yellow), and $0.9$ (purple). The $1\sigma$ and $2\sigma$ confidence regions are shown in darker shades and with dashed contours, respectively. Benchmark matter-density profiles, including the stellar distribution in M87 (black star), the stellar core of the Milky Way (brown star), a dark-matter spike in M87 (gray dot), and a flattened dark-matter core in the Milky Way (green dot), are included for comparison, with parameters detailed in the text. Right: Best-fit SGWB spectra corresponding to parameter choices $(\log_{10}(\rho_{\rm pc}[M_\odot/\mathrm{pc}^3]/10^5), \gamma) = (1.3,0.08)$, $(-0.09,0.06)$, and $(-1.9,0.27)$ for $e_0 = 0$, $0.5$, and $0.9$, respectively, as indicated by the crosses $(\times)$ in the left panel. The spectra are compared against the lowest five frequency bins of the NANOGrav 15-year dataset NANOGrav:2023gor.
  • ...and 1 more figures