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.
