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Interstellar scintillation (ISS), observed as time variation in the intensity of a compact radio source, is caused by small-scale structure in the electron density of the interstellar plasma. Dynamic spectra of ISS show modulation in radio frequency and time. Here we relate the (two-dimensional) power spectrum of the dynamic spectrum-the secondary spectrum-to the scattered image of the source. Recent work has identified remarkable parabolic arcs in secondary spectra. Each point in a secondary spectrum corresponds to interference between points in the scattered image with a certain Doppler shift and a certain delay. The parabolic arc corresponds to the quadratic relation between differential Doppler shift and delay through their common dependence on scattering angle. We show that arcs will occur in all media that scatter significant power at angles larger than the rms angle. Thus, effects such as source diameter, steep spectra, and dissipation scales, which truncate high angle scattering, also truncate arcs. Arcs are equally visible in simulations of nondispersive scattering. They are enhanced by anisotropic scattering when the spatial structure is elongated perpendicular to the velocity. In weak scattering the secondary spectrum is directly mapped from the scattered image, and this mapping can be inverted. We discuss additional observed phenomena including multiple arcs and reverse arclets oriented oppositely to the main arc. These phenomena persist for many refractive scattering times, suggesting that they are due to large-scale density structures, rather than low-frequency components of Kolmogorov turbulence.

We derive general relationships between the observed timescale of di †ractive interstellar scintillations and the physical velocities of the observer, the source, and the scattering medium. Our treatment applies exclusively to saturated scintillations of point sources in the strong scattering regime. We show how scintillation observations may be combined with other observables (proper motion and dispersion measure) to yield (1) improvements in galactic models for the free-electron density and (2) estimates of the distance and transverse velocity of individual pulsars. We explicitly consider cases of current astrophysical interest, including hypervelocity pulsars too far above the Galactic plane to allow distance estimates from dispersion measures alone. We also brieÑy consider scintillations of extragalactic sources, including gamma-ray burst sources at great distances from the Galaxy.

We have invented a novel technique to measure the radio image of a pulsar scattered by the interstellar plasma with 0.1 mas resolution. We extend the "secondary spectrum" analysis of parabolic arcs by Stinebring et al. (2001) to very long baseline interferometry and, when the scattering is anisotropic, we are able to map the scattered brightness astrometrically with much higher resolution than the diffractive limit of the interferometer. We employ this technique to measure an extremely anisotropic scattered image of the pulsar B0834+06 at 327 MHz. We find that the scattering occurs in a compact region about 420 pc from the Earth. This image has two components, both essentially linear and nearly parallel. The primary feature, which is about 16 AU long and less than 0.5 AU in width, is highly inhomogeneous on spatial scales as small as 0.05 AU. The second feature is much fainter and is displaced from the axis of the primary feature by about 9 AU. We find that the velocity of the scattering plasma is 16±10 km s −1 approximately parallel to the axis of the linear feature. The origin of the observed anisotropy is unclear and we discuss two very different models. It could be, as has been assumed in earlier work, that the turbulence on spatial scales of (∼ 1000 km) is homogeneous but anisotropic. However it may be that the turbulence on these scales is homogeneous and isotropic but the anisotropy is produced by highly elongated (filamentary) inhomogeneities of scale 0.05-16 AU.

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