Discovery of a bimodal luminosity distribution in persistent Be/X-ray pulsar 2RXP J130159.6-635806

We present a comprehensive analysis of 2RXP J130159.6-635806, a persistent low-luminosity Be/X-ray pulsar, focusing on its transition to a spin equilibrium state and the discovery of a bimodal luminosity distribution revealing possibly a new accretion regime. Using data from NuSTAR, Swift, XMM-Newton, and Chandra observatories, we investigate changes in the pulsar's timing and spectral properties. After more than 20 years of continuous spin-up, the pulsar's spin period stabilized, marking the onset of spin equilibrium. This transition was accompanied by the emergence of a previously unobserved accretion regime at $L_{\rm bol} = (2.0_{-1.0}^{+2.3})\times 10^{34}$ erg s$^{-1}$, an order of magnitude lower than its earlier quiescent state. After that, the source occasionally switched between these regimes, remaining in each state for extended periods, with the transition time from a luminosity of $10^{35}$ erg s$^{-1}$ to $10^{34}$ erg s$^{-1}$ taking less than 2.3 day. The analysis of the spectral data collected during this new low-luminosity state revealed a two-hump shape which is different from the cutoff power-law spectra observed at higher luminosities. The discovery of pulsations in this state, together with the hard spectral shape, demonstrates ongoing accretion. We estimate the magnetic field strength to be $\sim 10^{13}$ G based on indirect methods. Additionally, we report a hint of a previously undetected $\sim$90-day orbital period in the system.