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 Δt 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 Δt 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 Δt 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.
We present an improved inverse-ray-shooting code based on graphics processing units (GPUs) to generate microlensing magnification maps. In addition to introducing GPUs to accelerate the calculations, we also invest effort into two aspects: (i) A standard circular lens plane is replaced by a rectangular one to reduce the number of unnecessary lenses as a result of an extremely prolate rectangular image plane. (ii) An interpolation method is applied in our implementation, achieving significant acceleration when dealing with the large number of lenses and light rays required by high-resolution maps. With these applications, we have greatly reduced the running time while maintaining high accuracy: The speed was increased by about 100 times compared with an ordinary GPU-based inverse-ray-shooting code and a GPU-D code when handling a large number of lenses. If a high-resolution situation with up to 10,0002 pixels, resulting in almost 1011 light rays, is encountered, the running time can also be reduced by two orders of magnitude.
The microlensing effect has developed into a powerful technique for a diverse range of applications including exoplanet discoveries, structure of the Milky Way, constraints on MAssive Compact Halo Objects, and measurements of the size and profile of quasar accretion disks. In this paper, we consider a special type of microlensing events where the sources are fast radio bursts (FRBs) with ∼milliseconds (ms) durations for which the relative motion between the lens and source is negligible. In this scenario, it is possible to temporally resolve the individual microimages. As a result, a method beyond the inverse ray shooting method, which only evaluates the total magnification of all microimages, is needed. We therefore implement an algorithm for identifying individual microimages and computing their magnifications and relative time delays. We validate our algorithm by comparing to analytical predictions for a single microlens case and find excellent agreement. We show that the superposition of pulses from individual microimages produces a light curve that appears as multipeaked FRBs. The relative time delays between pulses can reach 0.1–1 ms for stellar-mass lenses and hence can already be resolved temporally by current facilities. Although not yet discovered, microlensing of FRBs will become regular events and surpass the number of quasar microlensing events in the near future when 104−5 FRBs are expected to be discovered on a daily basis. Our algorithm provides a way of generating the microlensing light curve that can be used for constraining stellar-mass distribution in distant galaxies.
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