Damping of Electron Density Structures and Implications for Interstellar Scintillation

Abstract

The forms of electron density structures in kinetic Alfven wave turbulence are studied in connection with scintillation. The focus is on small scales $L \sim 10^8-10^{10}$ cm where the Kinetic Alfvén wave (KAW) regime is active in the interstellar medium. MHD turbulence converts to a KAW cascade, starting at 10 times the ion gyroradius and continuing to smaller scales. These scales are inferred to dominate scintillation in the theory of Boldyrev et al. From numerical solutions of a decaying kinetic Alfvén wave turbulence model, structure morphology reveals two types of localized structures, filaments and sheets, and shows that they arise in different regimes of resistive and diffusive damping. Minimal resistive damping yields localized current filaments that form out of Gaussian-distributed initial conditions. When resistive damping is large relative to diffusive damping, sheet-like structures form. In the filamentary regime, each filament is associated with a non-localized magnetic and density structure, circularly symmetric in cross section. Density and magnetic fields have Gaussian statistics (as inferred from Gaussian-valued kurtosis) while density gradients are strongly non-Gaussian, more so than current. This enhancement of non-Gaussian statistics in a derivative field is expected since gradient operations enhance small-scale fluctuations. The enhancement of density gradient kurtosis over current kurtosis is not obvious, yet it suggests that modest fluctuation levels in electron density may yield large scintillation events during pulsar signal propagation in the interstellar medium. In the sheet regime the same statistical observations hold, despite the absence of localized filamentary structures. Probability density functions are constructed from statistical ensembles in both regimes, showing clear formation of long, highly non-Gaussian tails.