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A Multi-Wavelength Survey of Transient Lensing Opportunities for Primordial Black Hole Searches

Stefano Profumo

TL;DR

This work presents the first systematic, multi‑wavelength assessment of transient lensing as a probe of primordial black holes (PBHs) across an expansive mass range. By integrating time‑delay physics, wave‑optics suppression, finite‑source effects, and realistic event rates with optical depths, the authors map diverse transient classes onto a unified PBH mass–abundance diagram. Fast radio bursts emerge as the strongest current/future probes in the 8×10^{-3}–100 M_⊙ window, with projected one‑year constraints f_PBH ≲ 0.3 under SKA‑class surveys, while high‑energy transients extend sensitivity to higher masses and complement microlensing and gravitational‑wave probes. The study provides a practical roadmap for designing time‑domain, multi‑frequency surveys that systematically close remaining PBH dark matter windows and emphasizes synergies with other PBH probes to achieve comprehensive parameter space coverage.

Abstract

Gravitational lensing of short astrophysical transients provides a uniquely direct avenue for searching for primordial black holes (PBHs) across a vast range of masses. While past search efforts have focused on particular source classes-such as fast radio bursts (FRBs) and gamma-ray burst spikes-no systematic, multi-wavelength assessment has compared their relative potential for PBH discovery. We present here a broad assessment of transient lensing search opportunities, spanning more than twenty decades in photon frequency and over twelve orders of magnitude in PBH mass. For each class, we determine the accessible PBH mass window by accounting for wave-optics suppression and time-delay resolution limits, and we estimate potential sensitivities to the PBH abundance using representative event rates, distances, and optical depths. Our survey includes low-frequency radio events (FRBs, pulsar giant pulses, planetary cyclotron bursts), optical/infrared signals, and high-energy phenomena (gamma-ray burst spikes, fast X-ray transients, TeV blazar flares). We synthesize these results in a unified mass-abundance diagram and comprehensive tables summarizing both physical reach and observational requirements. This work serves as a roadmap for optimizing future multi-wavelength lensing searches, guiding the design of instruments and strategies to explore the PBH dark matter hypothesis across its remaining viable parameter space.

A Multi-Wavelength Survey of Transient Lensing Opportunities for Primordial Black Hole Searches

TL;DR

This work presents the first systematic, multi‑wavelength assessment of transient lensing as a probe of primordial black holes (PBHs) across an expansive mass range. By integrating time‑delay physics, wave‑optics suppression, finite‑source effects, and realistic event rates with optical depths, the authors map diverse transient classes onto a unified PBH mass–abundance diagram. Fast radio bursts emerge as the strongest current/future probes in the 8×10^{-3}–100 M_⊙ window, with projected one‑year constraints f_PBH ≲ 0.3 under SKA‑class surveys, while high‑energy transients extend sensitivity to higher masses and complement microlensing and gravitational‑wave probes. The study provides a practical roadmap for designing time‑domain, multi‑frequency surveys that systematically close remaining PBH dark matter windows and emphasizes synergies with other PBH probes to achieve comprehensive parameter space coverage.

Abstract

Gravitational lensing of short astrophysical transients provides a uniquely direct avenue for searching for primordial black holes (PBHs) across a vast range of masses. While past search efforts have focused on particular source classes-such as fast radio bursts (FRBs) and gamma-ray burst spikes-no systematic, multi-wavelength assessment has compared their relative potential for PBH discovery. We present here a broad assessment of transient lensing search opportunities, spanning more than twenty decades in photon frequency and over twelve orders of magnitude in PBH mass. For each class, we determine the accessible PBH mass window by accounting for wave-optics suppression and time-delay resolution limits, and we estimate potential sensitivities to the PBH abundance using representative event rates, distances, and optical depths. Our survey includes low-frequency radio events (FRBs, pulsar giant pulses, planetary cyclotron bursts), optical/infrared signals, and high-energy phenomena (gamma-ray burst spikes, fast X-ray transients, TeV blazar flares). We synthesize these results in a unified mass-abundance diagram and comprehensive tables summarizing both physical reach and observational requirements. This work serves as a roadmap for optimizing future multi-wavelength lensing searches, guiding the design of instruments and strategies to explore the PBH dark matter hypothesis across its remaining viable parameter space.

Paper Structure

This paper contains 41 sections, 26 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Time Delay in Geometric Optics
  4. Wave--Optics and Finite-size-source Suppression
  5. Abundance Sensitivity
  6. Summary of Key Dependencies
  7. Methodology
  8. Observational Parameters
  9. Event Rates, Source Distances, and Clumping Factors
  10. Optical Depth Calculation
  11. Calculation of Mass Ranges and Abundance Limits
  12. Survey of Transient Classes
  13. Low-Frequency Radio Transients
  14. High-Energy and Other Transients
  15. Finite Source Size Effects
  16. ...and 26 more sections

Figures (2)

  • Figure 1: Unified PBH mass–abundance diagram for the transient classes in our survey. Symbols mark the minimum detectable $M_{\mathrm{PBH}}$ and corresponding $f_{\mathrm{PBH}}$ forecast for one year of observations. The horizontal bars indicate the approximate sensitivity range in PBH mass for each class. Orange: FRBs; blue: local low‑frequency transients; red: Galactic transients; green: high‑energy transients.
  • Figure 2: As in Fig. \ref{['fig:mass_abundance']}, but restricted to $f_{\mathrm{PBH}}\lesssim 10^3$ to emphasize differences among the more sensitive classes.