Multifrequency Observations of Radio Pulse Broadening and Constraints on Interstellar Electron Density Microstructure

We have made observations of 98 low-Galactic-latitude pulsars to measure pulse broadening caused by multipath propagation through the interstellar medium. Data were collected with the 305-m Arecibo telescope at four radio frequencies between 430 and 2380 MHz. We used a CLEAN-based algorithm to deconvolve interstellar pulse broadening from the measured pulse shapes. We employed two distinct pulse broadening functions (PBFs): PBF$_1$ is appropriate for a thin screen of scattering material between the Earth and a pulsar, while PBF$_2$ is appropriate for scattering material uniformly distributed along the line of sight from the Earth to a pulsar. We found that some observations were better fit by PBF$_1$ and some by PBF$_2$. Pulse broadening times ($\tau_d$) are derived from fits of PBFs to the data, and are compared with the predictions of a smoothed model of the Galactic electron distribution. Several lines of sight show excess broadening, which we model as clumps of high density scattering material. A global analysis of all available data finds that the pulse broadening scales with frequency, $\nu$, as $\taud \propto\nu^{-\alpha}$ where $\alpha\sim 3.9\pm 0.2$. This is somewhat shallower than the value $\alpha=4.4$ expected from a Kolmogorov medium, but could arise if the spectrum of turbulence has an inner cutoff at $\sim$300--800 km. A few objects follow particularly shallow scaling laws (the mean scaling index $\meanalpha \sim 3.1 \pm 0.1$ and $\sim 3.8 \pm 0.2$ respectively for the case of PBF$_1$ and PBF$_2$), which may arise from large scale refraction or from the truncation of scattering screens transverse to the Earth--pulsar line of sight.