We analyze archival Chandra HRC observations of the ultra luminous accreting pulsar M82-X2 (NuSTAR J095551+6940.8), and determine an upper limit of $< 1.7\times 10^{38}$~erg/s to its luminosity at an epoch at which it was undetected. Combined with other recent measurements, this confirms that the source X-ray emission has been highly variable during the last 15 years, ranging from a maximum of $10^{40}$ erg/s through intermediate values $\sim$ a few $\times 10^{39}$ erg/s, and down to a minimum that must be below the current detection threshold $\sim (2-3) \times 10^{38}$ erg/s . We interpret these results by means of a magnetically-threaded disk model: when at peak luminosity, the neutron star (NS) is close to spin equilibrium, its inner disk edge r_m ~ 10^8 cm is approximately half the corotation radius r_{co}, and radiation pressure dominates the disk out to r_{tr} ~ 10^9 cm. In the radiation pressure-dominated regime, r_m grows very slowly as the mass inflow rate drops: as a result, r_m < r_{co} remains valid until the mass accretion rate becomes ~ the Eddington accretion rate, allowing a wide range of accretion luminosities to the NS. Once the mass accretion rate is below Eddington, accretion onto the NS is inhibited because r_m > r_{co}, and the source luminosity is expected to drop by a large factor. We conclude that a magnetically threaded, radiation pressure-dominated disk, around a highly magnetized NS (B~10^{13} G) offers the best intepretation for all the currently observed properties of NuSTAR J095551+6940.8. This source offers an unprecedented opportunity to study the disk-magnetosphere interaction in a new regime of supercritical accretion, and across the transition between-radiation pressure and gas-pressure dominance inside the disk.
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