On the feasibility of primordial black hole abundance constraints using lensing parallax of GRBs

TL;DR

This paper investigates the potential of using lensing parallax of Gamma ray bursts observed by a proposed satellite mission to constrain the abundance of primordial black holes in a specific low-mass range, highlighting the method's feasibility and limitations.

Contribution

It introduces a novel approach using GRB lensing parallax to probe primordial black hole abundance within an unexplored mass window, including detailed sensitivity analysis for the Daksha mission.

Findings

Daksha can detect lensing events if PBHs constitute dark matter in the specified mass range.

Non-detections can still provide meaningful constraints if satellites are separated by at least Earth-Moon distance.

The method's effectiveness depends on the number of observed GRBs and satellite separation.

Abstract

Primordial black holes, which could have formed during the early Universe through overdensities in primordial density fluctuations during inflation, are potential candidates for dark matter. We explore the use of lensing parallax of Gamma ray bursts (GRBs), which results in different fluxes being observed from two different vantage points, in order to probe the abundance of primordial black holes in the unexplored window within the mass range $[10^{-15}-10^{-11}]M_\odot$. We derive the optical depth for the lensing of GRBs with a distribution of source properties and realistic detector sensitivities. We comment on the ability of the proposed Indian twin satellite mission Daksha in its low earth orbit to conduct this experiment. If the two Daksha satellites observe 10000 GRBs simultaneously and the entirety of dark matter is made up of $[10^{-15}-10^{-12}]M_\odot$ black holes, Daksha will detect non-zero lensing events with a probability ranging from 80 to 50 per cent at the bin edges, respectively. Non-detections will not conclusively rule out primordial black holes as dark matter in this mass range. However, we show that meaningful constraints can be obtained in such a case if the two satellites are separated by at least the Earth-Moon distance.