2025ApJ...988..275C

Magnetized high-mass X-ray binary pulsars accreting from a surrounding disk have been recently studied by a time-dependent Kalman filter (KF) model of accretion capable of studying correlations between dynamical variables and producing time series of their behaviors. We return to the intrinsic KF equations that describe the accretion process, and we rewrite them in simpler forms that allow for straightforward interpretations and a deeper understanding of the KF output data. We describe the influence of the KF defined frequencies β₁, β₂, and γ_Ω, and we investigate the surface dipolar magnetic fields of 24 Magellanic pulsars produced by the KF analysis in comparison to the values obtained from standard accretion theory using the long-term trending changes of the pulsar spin periods (known as the long-term P-dot values). Good agreement is obtained over a wide range of pulsar spin periods when the KF magnetic field values are scaled down to the propeller regime by a factor of $\sqrt{1-{\omega }_{s}\,}$, where ω_s = β₂/β₁ is the fastness parameter that also distinguishes the regime of “stable polar” accretion (ω_s > 0.6) from Rayleigh-Taylor-driven “two-tongue equatorial” (ω_s < 0.45) matter inflow.