Bias in apparent dispersion measure due to de-magnification of plasma lensing on background radio sources

The effect of ionized gas on the propagation of radio signals is known as plasma lensing. Unlike gravitational lensing, plasma lensing causes both magnification and strong de-magnification effects to background sources. We study the cross section of plasma lensing for two density profiles, the Gaussian and power-law models. In general, the cross section increases with the density gradient. Radio sources can be used to measure the free electron density along the line of sight. However, plasma lensing de-magnification causes an underestimate of the electron density. Such a bias increases with the electron density, and can be up to $\sim 15\%$ in the high density region. There is a large probability that high density clumps will be missed due to this bias. The magnification of plasma lensing can also change the luminosity function of the background sources. The number density of sources on both the high and low luminosity ends can be overestimated due to this biasing effect.