Scatter broadening of pulsars and implications on the interstellar medium turbulence

Observations reveal a uniform Kolmogorov turbulence throughout the diffuse ionized interstellar medium (ISM) and supersonic turbulence preferentially located in the Galactic plane. Correspondingly, we consider the Galactic distribution of electron density fluctuations consisting of not only a Kolmogorov density spectrum but also a short-wave-dominated density spectrum with the density structure formed at small scales due to shocks. The resulting dependence of the scatter broadening time on the dispersion measure (DM) naturally interprets the existing observational data for both low and high-DM pulsars. According to the criteria that we derive for a quantitative determination of scattering regimes over wide ranges of DMs and frequencies $\nu$, we find that the pulsars with low DMs are primarily scattered by the Kolmogorov turbulence, while those at low Galactic latitudes with high DMs undergo more enhanced scattering dominated by the supersonic turbulence, where the corresponding density spectrum has a spectral index $\approx 2.6$. Besides, by considering a volume filling factor of the density structures with the dependence on $\nu$ as $\propto \nu^{1.4}$ in the supersonic turbulence, our model can also explain the observed shallower $\nu$ scaling of the scattering time than the Kolmogorov scaling for the pulsars with relatively large DMs. The comparison between our analytical results and the scattering measurements of pulsars in turn makes a useful probe of the properties of the large-scale ISM turbulence, e.g., an injection scale of $\sim 100$ pc, and also characteristics of small-scale density structures.