Stochastic and secular anomalies in measurements of pulsar braking indices

Stochastic (i.e. the achromatic component of timing noise unrelated to interstellar propagation) and secular variations in the spin frequency ν of a rotation-powered pulsar complicate the interpretation of the measured second derivative of the spin frequency ν̈, and hence the braking index, n, in terms of a power-law spin-down torque ∝ νnpl . Both categories of variation can lead to measurements of ν̈ which yield anomalous braking indices, i.e. |n| = |νν̈/ν̇2 | ≫ 1, where the overdot symbolizes a derivative with respect to time. In this talk, I will discuss the following three key results. First, the combined effect of stochastic and secular deviations from pure power-law spin down on measurements of ν̈ and its implications in observationally constraining n. Second, how the variance of ν̈ (or equivalently n) satisfies a falsifiable, analytical result derived from first principles. We quantify said variance through analytic calculations, Monte Carlo simulations involving synthetic data from a phenomenological model, and modern Bayesian techniques. Third, how the variance of ν̈ may be applied to real astronomical situations to predict or interpret the measured braking index n.