BPF-FFA Algorithm for Efficiently Estimating the Period of X-ray Pulsar

The traditional method for X-ray pulsar period estimation, which relies on epoch folding applied to various candidate periods to identify statistically significant pulse profiles, is computationally demanding. This study introduces a butterfly photon folding (BPF) transform that mitigates redundant computations in the photon folding step. The BPF transform achieves this by simultaneously and coherently merging the phase sections of the base period at many candidate periods which are distributed to the right of the given base period. To overcome the high computational complexity encountered during profile recovery from the phase sets of multiple candidate periods, we introduce an algorithm called BPF-FFA. This algorithm performs the profile recovery at an appropriate BPF level and employing the fast-folding algorithm (FFA) to complete the remaining steps. The efficacy of the BPF-FFA algorithm is further investigated by simulation data and the observation data of Crab pulsar and PSR B1821-24, from the Neutron star Interior Composition Explorer (NICER). Experimental results show that the BPF-FFA algorithm achieves a period estimation accuracy similar to epoch folding but has a lower computational burden. Moreover, this efficiency enhancement becomes increasingly substantial as the average photon counts per period (Nacp) rises, delivering about 24 times and 1480 times efficiency gains over epoch folding at 0.1 and 10 counts/period Nacp levels, respectively.