Unveiling the nature of cyclic behavior in the period evolution of the Anomalous X ray Pulsar XTE j1810-197

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The goal of our analysis is to probe a possible long term (5 yr) free-body precession of this neutron star for which we found several indications based on a non-phase-connected timing analysis. Although only 3 NS up to now have shown indication of precession, such evidence strongly challenges our current understanding of the NS interior. The standard picture of the outer core, in which superfluid neutrons coexist with type II superconducting protons, requires revision. One possibility is that protons are type I which would imply a significant revision of our picture of the physical conditions in the NS core. Another possibility is that the neutrons are normal in the outer core which again affects our understanding of the physical state of NSs core. The presence of long period modulation can shed light on the physical properties of NS and thus help constraining its equation of state

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