Lensing of Fast Radio Bursts by Plasma Structures in Host Galaxies

Abstract

Plasma lenses in the host galaxies of fast radio bursts (FRBs) can strongly modulate FRB amplitudes for a wide range of distances, including the ∼ Gpc distance of the repeater FRB121102. To produce caustics, the lens' dispersion-measure depth (DM ), scale size (a), and distance from the source (d sl ) must satisfy DM d sl /a 2 0.65 pc 2 AU −2 cm −3 . Caustics produce strong magnifications ( 10 2 ) on short time scales (∼ hours to days and perhaps shorter) along with narrow, epoch dependent spectral peaks (0.1 to 1 GHz). However, strong suppression also occurs in long-duration (∼ months) troughs. When bursts are multiply imaged, they will arrive differentially by < 1 µs to tens of ms and they will show different apparent dispersion measures, δDM apparent ∼ 1 pc cm −3 . Arrival time perturbations may mask any underlying periodicity with period 1 s. When arrival times differ by less than the burst width, interference effects in dynamic spectra will be seen. Strong lensing requires source sizes smaller than (Fresnel scale) 2 /a, which can be satisfied by compact objects such as neutron star magnetospheres but not by AGNs. Much of the phenomenology of the repeating fast radio burst source FRB121102 can be accounted for with such lenses. The overall picture can be tested by obtaining wideband spectra of bursts (from < 1 to 10 GHz and possibly higher), which can also be used to characterize the plasma environment near FRB sources. A rich variety of phenomena is expected from an ensemble of lenses near the FRB source. We discuss constraints on densities, magnetic fields, and locations of plasma lenses related to requirements for lensing to occur.

A Second Chromatic Timing Event of Interstellar Origin toward PSR J1713+0747

“…Here we will discuss the mechanism and explore the implications of the possible connection with our observations. Plasma lenses have been considered previously in the form of a Gaussian cloud (Clegg et al 1998;Cordes et al 2017) or folded current sheets (Simard & Pen 2018) and are consistent with observed "extreme scattering" events (Fiedler et al 1987;Coles et al 2015;Bannister et al 2016;Kerr et al 2018). These over-or under-densities of interstellar free electrons can alter the TOAs in a frequency-dependent manner and modulate pulse fluxes.…”

“…For a stationary lens situated halfway between the Earth and pulsar, with the pulsar and Earth velocities aligned, v eff ≈18 km s −1 given the proper motion, implying L18 km s −1 ×7.6 years≈30 au. Refraction from such a lens may explain the possible non-ν −2 delays (Equation (5) or see Foster & Cordes 1990) from our multicomponent fitting but again we do not see significant changes in the scattering parameters from the small ΔBIC value though we have only tested a small number of possible models and lensing can produce non-ν −2 delays that have complex dependencies in frequency and time (Cordes et al 2017); assuming that Model B is correct, then the fluctuations in Figure 3 do show significant temporal variations. If refraction does explain the observed delays, then our crude analysis suggests that the change in n e with respect to the surrounding medium is large and/or the lens is highly compact for the geometric delay to become important as per Equation (5); however, the barycentric delay becomes important for compact lenses as suggested above in Equation (6).…”

“…Discrete structures able to cause these delays will likely produce multiple images at some epochs; the mapping from time to transverse physical coordinates in the plane of the lens is nonlinear and involves the lens equation (Cordes et al 2017). Since the two events are asymmetric in time, the lens itself may have an asymmetric structure.…”

“…Again, while our early data are insensitive to multiple chromatic components, we saw variations in the ν −4 component for MJD56,000; the ν −2 power-law process was consistent with a Kolmogorov turbulent fluctuation spectra, i.e., with spectral index ≈−8/3 (e.g., Lam et al 2016b). Note that we parameterized the non-ν −2 delays as a ν −4 component but they need not have this index or even have a power-law dependence (see, e.g., Cordes et al 2017). Replacing the ν −4…”

“…If we assume the events are due to caustic crossings at each end of a lens, then L must be v eff t cross , with crossing time t cross and effective velocity (Cordes & Rickett 1998;Cordes et al 2017…”