NANOGrav 15-year gravitational-wave signals from binary supermassive black-holes seeded by primordial black holes

TL;DR

The authors address the origin of the NANOGrav 15-year nanohertz gravitational-wave background by proposing that mergers of binary SMBHs seeded by primordial black holes can supplement the astrophysical SMBH population. They compute the GW energy density using an EPS-based BH merger rate augmented by a PBH-seed contribution, adopting a log-normal PBH mass function and a one-to-one halo–BH mass mapping, and they employ an inspiral-dominated waveform appropriate for nHz frequencies. Their analysis finds that PBH seeds with abundances $f_{\rm PBH}$ in the range $10^{-14}$ to $10^{-12}$ and masses $1 M_\odot \lesssim m_{\rm PBH} \lesssim 10^3 M_\odot$ can reproduce the NG15 GW background while remaining consistent with the non-detection of high-redshift 21cm heating; higher abundances are disfavored by 21cm constraints. The work highlights future tests with cosmological 21cm observations, such as SKA Phase 2, to probe the PBH-seeded SMBH growth scenario and potentially connect the GW signal to early-universe physics beyond the Standard Model.

Abstract

In this paper, we explain the recently reported a nHz-band gravitational-wave background from NANOGrav 15-year through the merger of binary super-massive black holes with masses of $10^9 M_{\odot}$ formed by the growth of primordial black holes. When a primordial black hole accretes at a high accretion rate, it emits a large number of high-energy photons. These heat the plasma, causing high-redshift cosmological 21cm line emission. Since this has not been detected, there is a strict upper bound on the accretion rate. We have found that with the primordial black hole abundance $10^{-14} \lesssim f_{\rm PBH} \lesssim 10^{-12}$ and the mass $1 M_{\odot} \lesssim m_{\rm PBH} \lesssim 10^3 M_{\odot}$, we successfully fit the nHz band gravitational wave background from NANOGrav 15-year while avoiding the 21 cm line emission. We propose that future observations of the gravitational wave background and the cosmological 21cm line can test this scenario.

Figures (3)

• Figure 1: Comparison of the best-fit GW spectrum of the NANOGrav 15-year (NG15) under the scenario of the binary SMBH merger (blue solid line: median; shaded region: 90% credible interval) with the prediction by the numerical simulation (red solid line) Enoki:2004ew. The horizontal axis indicates the frequency, and the vertical axis represents the mean GW energy density spectrum defined in Eq. \ref{['eq:Omega_GW2']}. The first five data points of the NG15 are presented as the violin plots.
• Figure 2: BH mass function given by Eq. (\ref{['eq:fullBHMF']}) at different redshifts. The horizontal axis shows the SMBH mass ($M_\odot$), and the vertical axis shows the BH mass function ($\mathrm{Mpc^{-3}dex^{-1}}$). The red solid line denotes the EPS BH mass function, while the blue, green, and yellow lines represent the PBH seed contribution with comoving number densities of $n_{\rm PBH}=10^{-5}, 10^{-4}, 10^{-3} \, \mathrm{Mpc^{-3}}$, respectively. The panels show the cases for (a) $z=0$, (b) $z=1$, (c) $z=2$, (d) $z=3$, (e) $z=4$, (f) $z=5$, (g) $z=6$, and (h) $z=7$.
• Figure 3: Abundance of the PBH seeds required to fit the GW signal of the NANOGrav 15-year. The horizontal axis shows the PBH mass ($m_{\rm PBH}$) in $M_{\odot}$, while the vertical axis shows the fraction of the energy density of the PBHs to the energy density of the CDM ($f_{\rm PBH}$). The oblique magenta band represents the allowed region of $f_{\rm PBH}$ for each PBH mass. The blue shaded area denotes the region excluded by the observations of the cosmological high-redshifted global 21cm line, assuming the growth of the PBHs via accretion to the SMBHs until $z\sim7$.