Refractive effects in pulsar scintillation

Recent studies have focused attention on the refractive effects of long-wavelength (≲ 1014 cm) electron density fluctuations in the interstellar medium upon radio observations of pulsars and compact extragalactic radio sources. In earlier work, a simple scattering model was introduced which allowed us to compute fluctuations in mean intensity, image size, pulse width and pulse arrival time, along with their cross-correlations and fluctuation time-scales, when there is a power-law spectrum of density perturbations in a thin ‘equivalent screen’ of scattering material. In this work, we extend the analysis to include refraction-induced fluctuations in intrinsically diffractive quantities such as the scintillation time-scale, ts, and the decorrelation bandwidth, νdc. We then use the theory to study the drifting bands in dynamic scintillation spectra caused by the dispersive steering of the diffraction pattern. We also estimate the fluctuations in the position of the image on the sky, rates of variation of intensity and position, and the root mean square elongation of the scatter-broadened image. We make two further extensions of the theory. First we show that, despite certain formal divergences, the theory can be extended to accommodate steeper density fluctuation spectra (power-law indices β>4) than the conventionally assumed Kolmogorov spectrum (β=11/3). Secondly, we test the validity of the thin-screen approximation, developing a formalism to treat scattering in an extended medium. We find that the thin-screen theory sometimes underestimates the refractive fluctuations by a factor ∼2. The auto- and cross-correlations of the various observables are calculated and comparison is made with the known scintillation properties of pulsars to select those effects most suited to observational verification. The predicted cross-correlation between decorrelation bandwidth and flux fluctuations seems particularly suitable for this purpose. These measurements should, in turn, provide insights into the density fluctuation spectrum and the distribution of the scattering along the line-of-sight.