Gravitational Microlensing Time Delays at High Optical Depth: Image Parities and the Temporal Properties of Fast Radio Bursts

Due to differing gravitational potentials and path lengths, gravitational lensing induces time delays between multiple images of a source which, for solar mass objects, is of order $\sim10^{-5}$ seconds. If an astrophysically compact source, such as a Fast Radio Burst (FRB), is observed through a region with a high optical depth of such microlensing masses, this gravitational lensing time delay can be imprinted on short timescale transient signals. In this paper, we consider the impact of the parity of the macroimage on the resultant microlensing time delays. It is found that this parity is directly imprinted on the microlensing signal, with macroimages formed at minima of the time arrival surface beginning with the most highly magnified microimages and then progressing to the fainter microimages. At macroimages at the maxima of the time arrival surface, this situation is reversed, with fainter images observed first and finishing with the brightest microimages. For macroimages at saddle-points, the signal again begins with fainter images, followed by brighter images before again fading through the fainter microimages. The growing populations of cosmologically distant bursty transient sources will undoubtedly result in the discovery of strong lensed, multiply imaged FRBs, which will be susceptible to microlensing by compact masses. With the temporal resolution being offered my modern and future facilities, the detection of microlensing induced time delays will reveal the parities of the gravitational lens macroimages, providing additional constraints on macrolensing mass models and improving the efficacy of these transient sources as a cosmological probes.