Transient Solar Oscillations Driven by Primordial Black Holes

Stars are transparent to the passage of primordial black holes (PBHs) and serve as seismic detectors for such objects. The gravitational field of a PBH squeezes a star and causes it to ring acoustically. We calculate the seismic signature of a PBH passing through the Sun. The background for this signal is the observed spectrum of solar oscillations excited by supersonic turbulence. We predict that PBHs more massive than ${10}^{21}\mathrm{g}$ (comparable in mass to an asteroid) are detectable by existing solar observatories. The oscillations excited by PBHs peak at large scales and high frequencies, making them potentially detectable in other stars. The discovery of PBHs would have profound implications for cosmology and high-energy physics.

Figure 1

Radial velocities $V^{\mathrm{BH}}$ induced by a ${10}^{-10}{M}_{\odot }$ PBH passing through the Sun along the $z$ axis. The gray sphere at $R<0.24R_{\odot }$ is excluded from our simulations. The colors indicate the radial velocity of the fluid weighted by the square root of the density. Wave amplitudes are linearly proportional to the black-hole mass, so we may rescale our simulations to any desired value of $m_{\mathrm{BH}}$.

Figure 2

Power spectra $P_l(\nu )$ of our simulated PBH signal $V^{\mathrm{BH}}$ (left panel) and the turbulently driven noise $V^n$ observed by HMI (right panel) as functions of frequency $\nu$ and harmonic degree $l$. Each discrete ridge in both power spectra corresponds to a set of $p$ modes with the same number of radial nodes. The signal peaks near $l\simeq 40$, $\nu \simeq 5.5\mathrm{mHz}$, at larger scales and higher frequencies than the noise background, helping us to distinguish them.

Figure 3

Orbits of the PBHs in our simulations. The green vertical line along the $z$ axis shows the two radial orbits (RFF and RGC). The other two orbits are parabolic ($E=0$). The inner black curve shows the orbit which spends the maximum amount of time within the Sun (MT), while the outer tan curve shows the orbit which skims the surface (SS).

Figure 4

Signal-to-noise ratio $S/N$ as a function of maximum harmonic degree $l$ for ${10}^{-10}{M}_{\odot }$ PBHs on the orbits shown in Fig. 3. The total $S/N$ for each orbit is listed on each curve.