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

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.