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