Measuring the Magnetic Dipole Moment and Magnetospheric Fluctuations of Accretion-powered Pulsars in the Small Magellanic Cloud with an Unscented Kalman Filter

Abstract

Many accretion-powered pulsars rotate in magnetocentrifugal disequilibrium, spinning up or down secularly over multiyear intervals. The magnetic dipole moment μ of such systems cannot be inferred uniquely from the time-averaged aperiodic X-ray flux 〈L(t)〉 and pulse period 〈P(t)〉, because the radiative efficiency of the accretion is unknown and degenerate with the mass accretion rate. Here, we circumvent the degeneracy by tracking the fluctuations in the unaveraged time series L(t) and P(t) using an unscented Kalman filter, whereupon μ can be estimated uniquely, up to the uncertainties in the mass, radius, and distance of the star. The analysis is performed on Rossi X-ray Timing Explorer observations for 24 X-ray transients in the Small Magellanic Cloud, which have been monitored regularly for ∼16 yr. As well as independent estimates of μ, the analysis yields time-resolved histories of the mass accretion rate and the Maxwell stress at the disk–magnetosphere boundary for each star, and hence auto- and cross-correlations involving the latter two state variables. The inferred fluctuation statistics convey important information about the complex accretion physics at the disk–magnetosphere boundary.