We report on the discovery and the timing analysis of the first eclipsingaccretion-powered millisecond X-ray pulsar (AMXP): SWIFT J1749.4-2807. Theneutron star rotates at a frequency of ~517.9 Hz and is in a binary system withan orbital period of 8.8 hrs and a projected semi-major axis of ~1.90 lt-s.Assuming a neutron star between 0.8 and 2.2 M_o and using the mass function ofthe system and the eclipse half-angle, we constrain the mass of the companionand the inclination of the system to be in the ~0.46-0.81 M_o and$\sim74.4^o-77.3^o range, respectively. To date, this is the tightestconstraint on the orbital inclination of any AMXP. As in other AMXPs, the pulseprofile shows harmonic content up to the 3rd overtone. However, this is thefirst AMXP to show a 1st overtone with rms amplitudes between ~6% and ~23%,which is the strongest ever seen, and which can be more than two times strongerthan the fundamental. The fact that SWIFT J1749.4-2807 is an eclipsing systemwhich shows uncommonly strong harmonic content suggests that it might be thebest source to date to set constraints on neutron star properties includingcompactness and geometry.
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