Theory of Parabolic Arcs in Interstellar Scintillation Spectra

Abstract

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.

Fitting Formula for Flux Scintillation of Compact Radio Sources

“…Appendix C develops a rudimentary analytical theory of arcs that is valid in the two asymptotic regimes U T1 and U 3 1. The discussion there complements the more detailed physical approach taken by Cordes et al (2006). The behavior of arcs in the transition regime U $ few, and in the presence of anisotropic turbulence, deserves further analytical and numerical study, but it is beyond the scope of this work.…”

“…Secondary spectra often show a concentration of power along parabolic ridges f ¼ AEaf 2 t (Stinebring et al 2001). Cordes et al (2006) have given a theoretical explanation of this phenomenon, according to which the coefficient a ¼ zk 2 /(cv 2 ? ), where z is the effective distance of the screen of equation (1).…”

“…Presumably, also, arcs should be more prominent when scattering is dominated by a thin ''screen'' rather than distributed along the line of sight, since integration over z would further soften the final square root in equation (C5). These points are made by Cordes et al (2006).…”

Deflection of Pulsar Signal Reveals Compact Structures in the Galaxy

“…We use a model of scintillation arcs developed in Stinebring et al (2001), Hill et al (2003), Cordes et al (2004), and Walker et al (2004) and summarized here. The essential features of the model are that the dominant scattering occurs in a thin screen along the line of sight and there is detectable scattering through angles large compared to the half-width of the pulsar image.…”

Probing the Eclipse of J0737−3039A with Scintillation

“…Parabolic arcs have been observed in this system, and they provide a different view of the ISS. This method is not fully independent of the timescale analysis but it has a different dependence on anisotropy, which is the critical feature of our analysis (Cordes et al 2004). …”