Tidal effects on primordial black hole capture in neutron stars

TL;DR

This paper demonstrates that tidal perturbations from nearby stars and planetary bodies can disrupt weakly bound PBH–NS orbits, hindering the transmutation of neutron stars by asteroid-mass PBHs and weakening previously proposed DM bounds in that mass range. It develops a perturbative three-body framework with a stationary perturber approximation to quantify changes in orbital angular momentum and post-capture energy losses, and it derives environment-dependent capture and merger rates, including analytic approximations across four regimes. A key result is the identification of a critical perturber mass m_pert and a corresponding suppressed merger rate Γ_pert, illustrating that tidal effects can substantially reduce NS transmutation signals for m below ~10^18–10^22 g depending on environment. The study also extends the analysis to planetary perturbations and stellar companions, highlighting how realistic astrophysical environments influence PBH dark matter constraints and emphasizing the need to incorporate environmental context in PBH capture predictions.

Abstract

We revisit the problem of the capture of a primordial black hole (PBH) by a neutron star, accounting for the tidal perturbation from a nearby star or planet. For asteroid-mass PBHs, which could constitute all of the dark matter in the universe, a weakly bound post-capture orbit could be tidally disturbed to the point of preventing the PBH from settling in the neutron star and consuming it within a cosmologically short timescale. We show how this effect depends on environmental parameters and can weaken the proposed constraints based on observations of old neutron stars in high-density dark matter environments for PBH masses $\lesssim 10^{22}\,$g. We also provide approximate analytical formulae for the capture rates.

Figures (7)

• Figure 1: Diagram of the PBH--NS--perturber system illustrating the geometry and relevant free parameters.
• Figure 2: Rates for PBHs crossing through a NS (dashed light blue $\blacksquare$), becoming captured (dotted red $\blacksquare$), merging by present day (yellow $\blacksquare$), and merging by present day with the addition of a tidal perturber (blue $\blacksquare$). The two blue lines are calculated with different values of perturber number density $n_p$, indicated in units of pc$^{-3}$. The left panel is calculated using a velocity dispersion $\sigma$ appropriate for the Milky Way, and the right for a dispersion typical of dwarf galaxies.
• Figure 3: Impact of tidal perturbations on the proposed, hypothetical NS transmutation bounds on the PBH dark matter fraction. In keeping with previous work CapelaConstraintsPBHDMNeutronStar2013, we show the case for a DM density of $\rho=2\times 10^3\, \mathrm{GeV}/\mathrm{cm}^3$ in blue $\blacksquare$, alongside present constraints on PBH dark matter Iguaz:2021irxBerteaud:2022twsSmyth:2019whb in red $\blacksquare$. A monochromatic PBH mass function is assumed. Note that the blue region should not be interpreted as actual constraints, because the DM density inside globular clusters is not currently known with small enough uncertainties.
• Figure 4: Impact on the transmutation rates of tidal perturbations due to NS companions of planetary masses: Earth-like ($M_p = M_\oplus$ and $R_p = 1\,\mathrm{au}$), Jupiter-like ($M_p = M_J$ and $R_p = 5.2\,\mathrm{au}$), and a brown dwarf/super-Jupiter in a very close orbit ($M_p = 0.01\,M_\odot$ and $R_p = 0.01\,\mathrm{au}$). The curves can be interpreted as the expected suppression if every NS had a planet with those properties. If only a fraction $\mathcal{F}$ does, the suppression plateaus at $(1-\mathcal{F})$ times the maximum rate shown.
• Figure 5: Trajectory of the first pass of the PBH through the NS for several values of $b_0$. The white dotted lines show the initial hyperbolic trajectories, the solid colored lines show the non-Keplerian interior trajectories, and the dashed colored lines show the resulting precessed orbits. The lines have $b_0$ values ranging from $0$ to $b_c$ in steps of $0.25 b_c$.