{Interstellar Plasma Weather Effects in Long-term Multi-frequency Timing of Pulsar B1937+21

Abstract

We report here on variable propagation effects in over twenty years of multi-frequency timing analysis of pulsar PSR B1937+21 that determine small-scale properties of the intervening plasma as it drifts through the sight line. The phase structure function derived from the dispersion measure variations is in remarkable agreement with that expected from the Kolmogorov spectrum, with a power law index of $3.66\pm 0.04$, valid over an inferred scale range of 0.2--50 A.U. The observed flux variation time scale and the modulation index, along with their frequency dependence, are discrepant with the values expected from a Kolmogorov spectrum with infinitismally small inner scale cutoff, suggesting a caustic-dominated regime of interstellar optics. This implies an inner scale cutoff to the spectrum of $\sim 1.3\times 10^9$ meters. Our timing solutions indicate a transverse velocity of 9 km sec$^{-1}$ with respect to the solar system barycenter, and 80 km sec$^{-1}$ with respect to the pulsar's LSR. We interpret the frequency dependent variations of DM as a result of the apparent angular broadening of the source, which is a sensitive function of frequency ($\proptoν^{-2.2}$). The error introduced by this in timing this pulsar is $\sim$2.2 $μ$s at 1 GHz. The timing error introduced by ``image wandering'' from the slow, nominally refractive scintillation effects is about 125 nanosec at 1 GHz. The error accumulated due to positional error (due to image wandering) in solar system barycentric corrections is about 85 nanosec at 1 GHz.