  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.
