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X-ray and Gamma-ray Emissions from Different Evolutionary Stage of Rotation Powered Millisecond Pulsars

The $Fermi$-LAT has revealed that rotation powered millisecond pulsars (MSPs) are a major contributor to the Galactic $γ$-ray source population. Such pulsars may also be important in modeling the quiescent state of several low mass X-ray binaries (LMXBs), where optical observations of the companion star suggest the possible existence of rotation powered MSPs. To understand the observational properties of the different evolutionary stages of MSPs, the X-ray and $γ$-ray emission associated with the outer gap model is investigated. For rotation powered MSPs, the size of the outer gap and the properties of the high-energy emission are controlled by either the photon-photon pair-creation process or magnetic pair-creation process near the surface. For these pulsars, we find that the outer gap model controlled by the magnetic pair-creation process is preferable in explaining the possible correlations between the $γ$-ray luminosity or non-thermal X-ray luminosity versus the spin down power. For the accreting MSPs in quiescent LMXBs, the thermal X-ray emission at the neutron star surface resulting from deep crustal heating can control the conditions in the outer gap. We argue that the optical modulation observed in the quiescent state of several LMXBs originates from the irradiation of the donor star by $γ$-rays from the outer gap. In these systems, the irradiation luminosity required for the optical modulation of the source such as SAX J1808.4-3658 can be achieved for a neutron star of high mass. Finally, we discuss the high-energy emission associated with an intra-binary shock in black widow systems, e.g. PSR B1957+20.