Gravitational Ionization by Schwarzschild Primordial Black Holes

TL;DR

This work proposes gravitational ionization as a new observable of Schwarzschild primordial black holes in the asteroid-mass window, showing that tidal gravity can ionize neutral atoms and deposit energy into media during PBH transits. While GI-induced photon emission today is overwhelmed by Hawking radiation for single PBHs, a population-level GI energy deposition after recombination can exceed Hawking energy transfer for broad PBH mass distributions centered near $M_{\rm peak}^{\rm H}\approx 1.07\times10^{22}\,\mathrm{g}$. The paper also demonstrates that GI can dissociate deuterons during BBN for sub-asteroid PBHs and can trigger fission in heavy nuclei like $^{235}_{92}$U, outlining specific mass ranges where these effects are most effective. Collectively, these results present GI and related tidal effects as potential new probes and constraints on asteroid-mass PBHs and their role as dark matter.

Abstract

Primordial black holes (PBHs) are theorized to form from the collapse of overdensities in the very early Universe. PBHs in the asteroid-mass range $10^{17} \, {\rm g}\lesssim M \lesssim 10^{23} \, {\rm g}$ could serve as all or most of the dark matter today, but are particularly difficult to detect due to their modest rates of Hawking emission and sub-micron Schwarzschild radii. We consider whether the steep gradients of a PBH's gravitational field could generate tidal forces strong enough to disrupt atoms and nuclei. Such phenomena may yield new observables that could uniquely distinguish a PBH from a macroscopic object of the same mass. We first consider the gravitational ionization of ambient neutral hydrogen and evaluate prospects for detecting photon radiation from the recombination of ionized atoms. During the present epoch, this effect would be swamped by Hawking radiation -- which would itself be difficult to detect for PBHs at the upper end of the asteroid-mass window. We then consider the gravitational ionization and heating of neutral hydrogen immediately following recombination at $z\simeq1090$, and identify a broad class of PBH distributions with typical mass $5\times10^{21}\,{\rm g}\lesssim M \lesssim 10^{23}\, {\rm g}$ within which gravitational interactions would have been the dominant form of energy deposition to the medium. We also identify conditions under which tidal forces from a transiting PBH could overcome the strong nuclear force, either by dissociating deuterons, which would be relevant during big bang nucleosynthesis (BBN), or by inducing fission of heavy nuclei. We find that gravitational dissociation of deuterons dominates photodissociation rates due to Hawking radiation for PBHs with masses $10^{14}\,{\rm g}\lesssim M \lesssim 10^{16}\,{\rm g}$. We additionally identify the phenomenon of gravitationally induced fission of heavy nuclei via tidal deformation.

Figures (10)

• Figure 1: Schematic diagram of the gravitational ionization of a hydrogen atom by a passing PBH of mass $M$ and relative velocity $v_{\rm rel}$ in the hydrogen atom rest frame. The hydrogen atom $1s$ ground state is represented by the orange cloud and the transiting PBH by the black circle. The Bohr radius and PBH radius would be drawn to relative scale ($r_s(M) = r_{\rm Bohr}/2$) if we took $M=1.78\times10^{19} \, {\rm g}$. The distances, however, are not shown to scale for such a system, which would have $b_{\rm th}(M) = 3.3\times10^{-9} \, {\rm m} \simeq 62 \, r_{\rm Bohr}$. The interaction timescale $\Delta T$, given by Eq. (\ref{['dT']}), is set by the system parameters $b$, $M$, and $v_{\rm rel}$.
• Figure 2: A comparison of the maximum impact parameter $b_{\rm max}^{\rm H} (M, v_{\rm rel})$ from Eq. (\ref{['bMax']}), the threshold impact parameter $b_{\rm th}^{\rm H} (M)$ from Eq. (\ref{['bmaxH1']}), and the Schwarzschild radius $r_s (M)$. Note that $M_{\rm trans} = 6.93\times10^{11} \, {\rm g}$ (vertical, gray) marks the mass at which the scaling of $b_{\rm max}^{\rm H}$ with $M$ changes. The regime in which $b_{\rm max}^{\rm H} \simeq b_{\rm th}^{\rm H}$ covers the whole asteroid-mass range (green, shaded). The maximum PBH mass which can gravitationally ionize hydrogen is $M_{\rm max} = 2.43 \times 10^{22} \, {\rm g}$ (vertical, dotted), as in Eq. (\ref{['Mmax']}). The maximum impact parameter $b_{\rm max}^{\rm H}$ is shown for PBH transits through neutral hydrogen atoms at the epoch of recombination (Rec) and through the present-day interplanetary medium (IPM), with appropriate values for $v_{\rm rel}$ taken from Table \ref{['tab:medium']}.
• Figure 3: Comparison of the electron timescale $E_1^{-1}$ to the energy-transfer timescale $\tau$ for gravitational ionization of a hydrogen atom by a PBH of mass $M$. Here $E_1 = 13.6 \, {\rm eV}$ is the hydrogen ground-state energy. We find that $\tau/E_1^{-1}<1$ for all $M \leq M_{\rm max}^{\rm H}$, which implies that energy transfer can always be treated as instantaneous and that the encounter effectively results in a non-adiabatic perturbation to the hydrogen atom potential.
• Figure 4: Gravitational ionization rates $\Gamma(M)$ for a PBH of mass $M$ transiting through the three different neutral hydrogen media listed in Table \ref{['tab:medium']}. Note that $\Gamma$ is maximized at $M_{\rm peak}^{\rm H} =1.07\times10^{22} \, {\rm g}$, as given in Eq. (\ref{['Msigma']}), and cuts off sharply at $M_{\rm max}^{\rm H} =2.43\times10^{22} \, {\rm g}$, as in Eq. (\ref{['Mmax']}).
• Figure 5: Primary Hawking emission of photons from a Schwarzschild black hole of mass $M$ within the range $10^{17} \, {\rm g} \leq M \leq 10^{24} \, {\rm g}$. The spectra are sharply peaked, thus $E \frac{d^2N_{\gamma}^{(1)}}{dtdE}|_{E_{\rm peak}} \approx \frac{dN_\gamma^{(1)}}{dt}$, the total primary-emission rate for photons. Plot prepared using BlackHawk v2.2arbeyBlackHawkV20Public2019arbeyPhysicsStandardModel2021a.