FRBs Lensed by Point Masses I. Lens Mass Estimation for Doubly Imaged FRBs

TL;DR

This paper demonstrates how strong lensing by point masses can produce double-peaked FRBs and provides a method to estimate lens mass from observable features like time delay and flux ratio.

Contribution

It introduces a novel approach to estimate lens mass in lensed FRBs using observable parameters, considering both point-mass and external shear lens models.

Findings

Double peaks in FRBs can result from strong lensing effects.

Lens mass and redshift can be inferred from time delay and flux ratio.

Constraints on lens mass are tighter with larger flux ratios.

Abstract

Fast radio bursts (FRBs) are bright radio transient events with durations on the order of milliseconds. The majority of FRB sources discovered so far have a single peak, with the exception of a few showing multiple-peaked profiles, the origin of which is unknown. In this work, we show that the strong lensing effect of a point mass or a point mass $+$ external shear on a single-peak FRB can produce double peaks (i.e. lensed images). In particular, the leading peak will always be more magnified and hence brighter than the trailing peak for a point-mass lens model, while the point-mass $+$ external shear lens model can produce a less magnified leading peak. We find that, for a point-mass lens model, the combination of lens mass $M$ and redshift $z_l$ in the form of $M(1+z_l)$ can be directly computed from two observables -- the delayed time $\Delta t$ and the flux ratio of the leading peak to the trailing peak $R$. For a point-mass $+$ external shear lens model, upper and lower limits in $M(1+z_l)$ can also be obtained from $\Delta t$ and $R$ for a given external shear strength. In particular, tighter lens mass constraints can be achieved when the observed $R$ is larger. Lastly, we show the process of constraining lens mass using the observed values of $\Delta t$ and $R$ of two double-peaked FRB sources, i.e. FRB 121002 and FRB 130729, as references, although the double-peaked profiles are not necessarily caused by strong lensing.