Geometric Search for Hawking Radiation from Nearby Primordial Black Holes

Abstract

A nearby primordial-black-hole (PBH) evaporation burst would produce a curved gamma-ray wavefront, leading to detectable departures from plane-wave inter-satellite delays. We introduce a purely geometric method that combines imaging localizations with multi-spacecraft timing to determine the distance of a gamma-ray transient. Applied to \textit{Swift}-localized short GRBs, the current sample shows no significant deviation from the plane-wave expectation, with the most constraining event reaching $1.2$ AU and already probing a meaningful Solar-System-scale regime. Our analysis shows that direct distance measurements are achievable to $10^3$ AU scales with the current and near-future technical capabilities. Once a finite source distance is measured, the corresponding PBH mass and lifetime can be directly inferred. Future wide-field localization and long-baseline deep-space gamma-ray detectors could extend such searches to $10^5$ AU and beyond.

Figures (4)

• Figure 1: Geometric test for finite-distance gamma-ray transients. Imaging localization fixes $\hat{\mathbf{n}}$. For a finite distance $D$, the delay follows Eq. (\ref{['eq:finite']}); in the plane-wave limit it reduces to Eq. (\ref{['eq:plane']}). Curvature induces a small deviation scaling as $|\delta t|\propto B_\perp^2/D$, enabling direct geometric distance measurements once the curvature signal is resolved.
• Figure 2: Distance constraints from the non-detection of wavefront curvature for short GRBs jointly observed by Konus-Wind and BAT. Each point shows the conservative $3\sigma$ lower limit $D_{\min}$ inferred for an individual event. The most constraining case reaches $D_{\min}\approx1.2$ AU, showing that current observations have already entered the Solar-System-scale regime relevant to nearby PBH searches. Although the present sample mainly yields lower limits, it already reaches the distance scale at which direct geometric searches for nearby PBH bursts become meaningful.
• Figure 3: Distance constraint versus timing uncertainty $\sigma_t$ for GRB 160726A. Blue points show the central solution and $1\sigma$ interval for $\sigma_{\rm loc}=1$ arcsec, while orange and green points show the corresponding $1\sigma$ lower limits for $\sigma_{\rm loc}=1$ arcsec and $3$ arcmin once the upper bound becomes unbounded. The horizontal dash-dotted line marks $D_{\rm center}=3.307$ AU. The vertical dotted and dashed lines mark $\sigma_t^{\rm crit}=|\Delta t_{\rm obs}-\Delta t_\infty|$ and the current timing uncertainty, respectively. The top axis shows the equivalent effective area relative to GBM. This figure illustrates the threshold at which the method changes from yielding only consistency with the infinite-distance limit to directly measuring a finite source distance.
• Figure 4: Required effective area versus assumed source distance for different localization uncertainties. The curves show the equivalent area, in units of the current GBM effective area, required to retain a finite upper bound on the source distance for the GBM--KW baseline. We adopt $\sigma_{t,\rm stat}=0.5$ ms, consistent with short-GRB timing at $\sim$0.1 ms time resolution xiao2021xiao2022ground. The horizontal dashed line marks the current GBM-equivalent area, and the vertical dotted lines mark the critical distances $D_{\rm crit}$ at which the constraint becomes localization limited. The right axis gives the equivalent statistical delay uncertainty. This figure quantifies how improved timing sensitivity and especially better localization expand the distance range over which the method can directly measure, rather than merely constrain, the source distance.