2019MNRAS.484.5723L

In regions with strongly varying electron density, radio emission can be magnified significantly by plasma lensing. With magnetic fields, magnification in time and frequency will be different for two circular polarizations. We show how the effects can be used to measure or constrain the magnetic field parallel to the line of sight, B_||, as well as its spatial structure, σ_B||_, in the lensing region. In addition, we discuss how Faraday conversion can constrain the strength of the perpendicular field, B_⊥. We apply such measurements for the Black Widow pulsar, PSR B1957+20, in which plasma lensing was recently discovered. For this system, pressure equilibrium suggests B≳20 G at the interface between the pulsar and companion winds, where most lensing occurs. We find no evidence for large-scale magnetic fields, with, on average, B_||=0.02±_0.09 G over the egress lensing region. From individual lensing events, we constrain small-scale magnetic structure to σ_B<10 mG, thus excluding scenarios with a strong but rapidly varying field. Finally, from the lack of reduction of average circular polarization in the same region, we rule out a strong quasi-transverse field. We cannot identify any convincing scenario in which a large magnetic field in this system is concealed, leaving the nature of the interface between the pulsar and companion winds an enigma. Our method can be used to study the local magnetic environment of other sources showing plasma lensing, including other eclipsing pulsars and fast radio bursts.