Gravitational wave signals from primordial black holes orbiting solar-type stars

TL;DR

The paper investigates gravitational waves from asteroid-mass primordial black holes in bound orbits around Sun-like stars, focusing on signals that could be detected by LISA and on the contribution of such systems to the stochastic GW background. It develops a Newtonian dynamics framework for PBH–star orbits (including interior orbits), derives quadrupole GW emission, conducts simulations of representative orbits, and assesses the detectability with LISA while estimating the SGWB from cosmic populations. The study finds that near-Earth PBH–Sun systems can yield detectable GW signals in the milliHertz band, whereas a population of these systems could produce a SGWB with a spectral index around 2 that may be compatible with PTA hints; the amplitude is sensitive to PBH mass and orbital configuration. Overall, asteroid-mass PBHs bound to stars offer a novel observational channel to probe dark matter and to complement PTA measurements through a new GW population channel.

Abstract

Primordial black holes (PBHs) with masses between $10^{14}$ and $10^{20}$ kg are candidates to contribute a substantial fraction of the total dark matter abundance. When in orbit around the center of a star, which can possibly be a completely interior orbit, such objects would emit gravitational waves, as predicted by general relativity. In this work, we examine the gravitational wave signals emitted by such objects when they orbit typical stars, such as the Sun. We show that the magnitude of the waves that could eventually be detected on Earth from a possible PBH orbiting the Sun or a neighboring Sun-like star within our galaxy can be significantly stronger than those originating from a PBH orbiting a denser but more distant neutron star (NS). Such signals may be detectable by the LISA gravitational-wave detector. In addition, we estimate the contribution that a large collection of such PBH-star systems would make to the stochastic gravitational-wave background (SGWB) within a range of frequencies to which pulsar timing arrays are sensitive.

Figures (8)

• Figure 1: Illustration for the Sun-Earth example of the geometric configuration for the emission of gravitational waves with polarizations $h_+$ and $h_\times$. The trajectory of the mass $m$ orbiting the mass $M_\odot\gg m$ lies entirely in a plane making an angle $\theta$ with the ecliptic plane. In the best-case scenario, one has $\theta=\pi/2$ so the PBH remains in the $y-z$ plane, with GW emission along the $x-$direction.
• Figure 2: The normalized mass of the star, as determined from the idealized model given by $\rho(r)$ in Eq. (\ref{['rho']}).
• Figure 3: Maximum amplitude of the gravitational wave signals emitted by the system, $h_+$ and $h_\times$, as a function of $\bar{\ell}$, for some representative values of $s_0$.
• Figure 4: The effective potential energy of the PBH as a function of $s=r/ R_\star$, where $R_\star$ is the radius of the star. Here we assumed an angular momentum per unit mass such that $\bar{\ell} = 0.1410$. The three horizontal lines indicate orbits with three distinct values of the total energy. The dotted horizontal line (with $\bar{E}_\textsc{t} > -1$ ) corresponds to a hybrid orbit, while the other two horizontal lines are associated with inner orbits.
• Figure 5: The top panels show the orbit of a PBH of total energy given by $\bar{E}_\textsc{t} =-2.3435$ and with an angular momentum such that $\bar{\ell} = 0.141$. The top-left panel illustrates the path of the PBH in a complete revolution $\Delta\varphi=2\pi$, while the top-right panel shows a complete closed orbit. The corresponding GW scaled strains $\bar{h}_+$ and $\bar{h}_\times$ emitted by the system when performing the closed orbit are shown in the bottom panel, as a function of dimensionless time $\tau$.