Discovery and modelling of broad-scale plasma lensing in black-widow pulsar J2051 ? 0827

We report on an unusually bright observation of PSR J2051$-$0827 recorded during a regular monitoring campaign black-widow pulsar systems with the Effelsberg 100-m telescope. Through fortunate coincidence, particularly scintillation maximum is simultaneous eclipse by companion, enabling precise measurements variations in flux density, dispersion measure (DM), and scattering strength throughout eclipse. The density highly variable eclipse, peak 1.7 times average away from yet does not significantly decrease average. recover measured DM using geometric optics, relative velocity as only free parameter. effective (470 $\pm$ 10) km/s, consistent orbital motion suggesting that outflow lensing material low, or directly along line sight. 2 per cent uncertainty formal error; systematics related to our current model are likely dominate, we detail several extensions be considered full treatment lensing. This demonstration causal link between lensing; can predicted through derivatives DM. Going forward, this approach applied investigate dynamics other eclipsing systems, physical nature ionized interstellar medium.