The Frequency Dependence of Scintillation Arc Thickness in Pulsar B1133+16

Scintillation arcs have become a powerful tool for exploring scattering in the ionized interstellar medium. There is accumulating evidence that the scattering from many pulsars is extremely anisotropic resulting in highly elongated, linear brightness functions. We present a three-frequency (327~MHz, 432~MHz, 1450~MHz) Arecibo study of scintillation arcs from one nearby, bright, high-velocity pulsar, PSR~B1133+16. We show that a one-dimensional (1D), linear brightness function is in good agreement with the data at all three observing frequencies. We use two methods to explore the broadening of the 1D brightness function $B(\theta)$ as a function of frequency: 1) crosscuts of the forward arc at constant delay and 2) a 1D modeling of $B(\theta)$ using a comparison between model and observed secondary spectrum as a goodness-of-fit metric. Both methods show that the half-power width of $B(\theta)$ deviates from the expected dependence $\propto \nu^{-a}$, where $\nu$ is the observing frequency . Our estimates of $a$ have moderately large uncertainties but imply $a \lesssim1.8$, and so are inconsistent with the expected $a = 2.0$ for plasma refraction or $a = 2.2$ for Kolmogorov turbulence. In addition the shape of $B(\theta)$ cuts off more steeply than predicted for Kolmogorov turbulence. Ultimately, we conclude that the underlying physics of the broadening mechanism remains unexplained. Our results place the scattering screen at a distance that is broadly consistent with an origin at the boundary of the Local Bubble.