Theory of Parabolic Arcs in Interstellar Scintillation Spectra

Our theory relates the secondary spectrum, the 2D power spectrum of the radio dynamic spectrum, to the scattered pulsar image in a thin scattering screen geometry. Recently discovered parabolic arcs in secondary spectra are generic features for media that scatter radiation at angles much larger than the rms scattering angle. Each point in the secondary spectrum maps particular values of differential arrival-time delay and fringe rate (or differential Doppler frequency) between pairs of components in the scattered image. Arcs correspond to a parabolic relation between these quantities through their common dependence on the angle of arrival of scattered components. Arcs appear even without consideration of the dispersive nature of the plasma. Arcs are more prominent in media with negligible inner scale and with shallow wavenumber spectra, such as the Kolmogorov spectrum, and when the scattered image is elongated along the velocity direction. The arc phenomenon can be used, therefore, to constrain the inner scale and the anisotropy of scattering irregularities for directions to nearby pulsars. Arcs are truncated by finite source size and thus provide sub micro arc sec resolution for probing emission regions in pulsars and compact active galactic nuclei. Multiple arcs sometimes seen signify two or more discrete scattering screens along the propagation path, and small arclets oriented oppositely to the main arc persisting for long durations indicate the occurrence of long-term multiple images from the scattering screen.