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

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.