XSS J12270-4859 is the only low mass X-ray binary (LMXB) with a proposed persistent gamma-ray counterpart in the Fermi-LAT domain, 2FGL 1227.7-4853. Here, we present the results of the analysis of recent INTEGRAL observations, aimed at assessing the long-term variability of the hard X-ray emission, and thus the stability of the accretion state. We confirm that the source behaves as a persistent hard X-ray emitter between 2003 and 2012. We propose that XSS J12270-4859 hosts a neutron star in a propeller state, a state we investigate in detail, developing a theoretical model to reproduce the associated X-ray and gamma-ray properties. This model can be understood as being of a more general nature, representing a viable alternative by which LMXBs can appear as gamma-ray sources. In particular, this may apply to the case of millisecond pulsars performing a transition from a state powered by the rotation of their magnetic field, to a state powered by matter in-fall, such as that recently observed from the transitional pulsar PSR J1023+0038. While the surface magnetic field of a typical NS in a LMXB is lower by more than four orders of magnitude than the much more intense fields of neutron stars accompanying high-mass binaries, the radius at which the matter in-flow is truncated in a NS-LMXB system is much lower. The magnetic field at the magnetospheric interface is then orders of magnitude larger at this interface, and as consequence, so is the power to accelerate electrons. We demonstrate that the cooling of the accelerated electron population takes place mainly through synchrotron interaction with the magnetic field permeating the interface, and through inverse Compton losses due to the interaction between the electrons and the synchrotron photons they emit. We found that self-synchrotron Compton processes can explain the high energy phenomenology of XSS J12270-4859.
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