Hawking Radiation Signatures from Primordial Black Holes Transiting the Inner Solar System: Prospects for Detection

TL;DR

This work proposes a time-dependent, local Hawking-radiation signature from primordial black holes transiting the inner Solar System as a direct probe of the asteroid-mass dark matter window, addressing the limitations of traditional, model-dependent evaporation constraints. It builds a comprehensive framework combining Hawking emission (primary and secondary), extended PBH mass functions, and a realistic local dark matter environment to predict detectable time-resolved positron signals in AMS-like detectors, using a matched-filter analysis. The results show that current AMS data are mainly sensitive to very light PBHs with $M(t_0) \lesssim 2\times10^{14}$ g due to a $Q_{\min}=500$ MeV threshold; however, a detector outside the geomagnetic field with lower energy thresholds (e.g., $Q_{\min}=5$ MeV) could observe several PBH transits per year and substantially constrain PBH mass functions in the asteroid-mass range. The approach provides a model-independent complement to Galactic propagation-based constraints and can be extended to $\gamma$-ray and X-ray Hawking emission to probe heavier PBHs, potentially closing the asteroid-mass window with future instrumentation.

Abstract

Primordial black holes (PBHs) arise from the collapse of density perturbations in the early universe and serve as a dark matter (DM) candidate and a probe of fundamental physics. There remains an unconstrained ``asteroid-mass'' window where PBHs of masses $10^{17} {\rm g} \lesssim M \lesssim 10^{23} {\rm g}$ could comprise up to $100\%$ of the dark matter. Current $e^{\pm}$ Hawking radiation constraints on the DM fraction of PBHs are set by comparing observed spatial- and time-integrated cosmic ray flux measurements with predicted Hawking emission fluxes from the galactic DM halo. These constraints depend on cosmic ray production and propagation models, the galactic DM density distribution, and the PBH mass function. We propose to mitigate these model dependencies by developing a new local, time-dependent Hawking radiation signature to detect low-mass PBHs transiting through the inner Solar System. We calculate transit rates for PBHs that form with initial masses $M \lesssim 5\times10^{17}\text{g}$. We then simulate time-dependent positron signals from individual PBH flybys as measured by the Alpha Magnetic Spectrometer (AMS) experiment in low-Earth orbit. We find that AMS is sensitive to PBHs with masses $M\lesssim 2\times10^{14} \, {\rm g}$ due to its lower energy threshold of $500 \, {\rm MeV}$. We demonstrate that a dataset of daily positron fluxes over the energy range $5-500 \, {\rm MeV}$, with similar levels of precision to the existing AMS data, would enable detection of PBHs drawn from present-day distributions that peak within the asteroid-mass window. Our simulations yield ${\cal O} (1)$ detectable PBH transits per year across wide regions of parameter space, which may be used to constrain PBH mass functions. This technique could be extended to detect $γ$-ray and X-ray Hawking emission to probe further into the asteroid-mass window.

Figures (17)

• Figure 1: Primary (top) and secondary (bottom) Hawking emission spectra for a primordial black hole with mass $M=10^{15}$g. Spectra are calculated numerically with BlackHawk v2.2arbey_blackhawk_2019arbey_blackhawk_nodate and hazmacoogan_hazma_2020 following the discussions in Sections \ref{['sec:PrimarySpectra']} and \ref{['sec:SecondarySpectra']}. Note that no secondary $p$ or $\bar{p}$ appear because these rates are negligible given $T = 10.6 \text{ MeV} \ll m_p$. Fermion spectra shown are the sum of particle and antiparticle emission rates. The primary neutrino spectra are summed over all flavors. No secondary neutrino spectra are shown because such processes are not incorporated within the hazma code.
• Figure 2: Secondary positron emission spectra for PBHs in the positron-producing mass range. Note that the x-axis plots total positron energy $Q$ and thus cuts off at the rest mass $Q = 0.511$ MeV. PBHs with masses $M\gtrsim10^{14} \ {\rm g}$ have secondary spectra well-approximated by their primary spectra because they emit few short-lived heavier particles.
• Figure 3: Comparison of GCC (blue) and LN (red) formation-time mass functions with peaks located at $\bar{M} (t_i) =10^{15} \, {\rm g}$. The vertical black line indicates the universe-lifetime cutoff mass $M_*$ given in Eq. (\ref{['Mstar']}). The main difference between the two parameterizations is the presence or absence of the small-mass tail.
• Figure 4: The Page factor $f (M)$ as a function of PBH mass as defined in Eq. (\ref{['eqn:PageFactor']}). We have normalized the Page factor such that $f(M)=1$ for PBHs emitting only photons and neutrinos, which are assumed massless. PBH mass $M$ here indicates mass at time of particle emission.
• Figure 5: Time-evolution of the mass function $\psi_{\rm GCC} (M, t)$ with $\alpha = 5$ and $\beta = 2$ (top) and $\psi_{\rm LN} (M, t)$ with $\sigma=0.5$ (bottom). Both functions are peaked at $\bar{M}_i=10^{15} \, {\rm g}$. The curves are plotted for different times $\tilde{t}$ in units of the current age of the universe, so that $\tilde{t}=1$ corresponds to the present day.