Timing properties of the X-ray accreting pulsar RX J0440.9+4431 studied with Insight-HXMT and NICER

RX J0440.9+4431, a Be/X-ray binary, had its brightest outburst in 2022 since its discovery, with a peak X-ray flux of 2.25 Crab (as recorded by Swift/BAT, 15–50 keV). We analyze the timing properties of this giant outburst using data from Insight-HXMT and NICER, focusing on the evolution of the pulse profile and pulse fraction. We observe that when the luminosity reached around ~$3\times 10^{37}\ {\rm erg\ \rm s^{-1}}$, a transition from double-peaked to single-peaked pulse profiles occurred across the energy range, with the peak of the low-energy profile aligning gradually with the peak of the high-energy profile. This change indicates a transition from subcritical to supercritical accretion. Additionally, we found a concave in the pulse fraction as a function of energy around 20–30 keV throughout the entire outburst period. Compared to the low luminosity, the concave becomes weaker in high luminosities, and overall, the pulse fraction is higher. We propose that this concave could be caused by the scattering of high-energy photons by the atmosphere of a neutron star, leading to a dilution of the pulse fraction. As the accretion reaches the supercritical state, the accretion column height increases, resulting in a larger direct component of strongly beamed X-ray flux, and an elevated pulse fraction.