Super-Eddington accretion of the first Galactic Ultra-luminous X-ray pulsar Swift J0243.6+6124

We present a detailed timing study of the pulse profile of Swift J0243.6+6124 with HXMT and Fermi/GBM data during its 2017 giant outburst. The double-peak profile at luminosity above $5\times10^{38}$erg\,s$^{-1}$ is found to be 0.25 phase offset from that below $1.5\times10^{38}$erg\,s$^{-1}$, which strongly supports for a transition from a pencil beam to a fan beam, and thus for the formation of shock dominated accretion column. During the rising stage of the high double-peak regime, the faint peak got saturated in 10-100 keV band above a luminosity of $L_t\sim1.3\times10^{39}$erg\,s$^{-1}$, which is coincident with sudden spectral changes of both the main and faint peaks. They imply a sudden change of emission pattern around $L_t$. The spin-up rate ($\dot{\nu}$) is linearly correlated with luminosity ($L$) below $L_t$, consistent with the prediction of a radiation pressure dominated (RPD) disk. The $\dot{\nu}-L$ relation flattens above $L_t$, indicating a less efficient transfer of angular momentum and a change of accretion disk geometry above $L_t$. It is likely due to irradiation of the disk by the central accretion column and indicates significant radiation feedback before the inner disk radius reaching the spherization radius.