Secular spin-down of the AMP XTE J1751-305
  Context. Of the 13 known accreting millisecond pulsars, only a few showed more than one outburst during the RXTE era. XTE J1751-305 showed, after the main outburst in 2002, other three dim outbursts. We report on the timing analysis of the latest one, occurred on October 8, 2009 and serendipitously observed from its very beginning by RXTE. Aims. The detection of the pulsation during more than one outburst permits to obtain a better constraint of the orbital parameters and their evolution as well as to track the secular spin frequency evolution of the source. Methods. Using the RXTE data of the last outburst of the AMP XTE J1751-305, we performed a timing analysis to improve the orbital parameters. Because of the low statistics, we used an epoch folding search technique on the whole data set to improve the local estimate of the time of ascending node passage. Results. Using this new orbital solution we epoch folded data obtaining three pulse phase delays on a time span of 1.2 days, that we fitted using a constant spin frequency model. Comparing this barycentric spin frequency with that of the 2002 outburst, we obtained a secular spin frequency derivative of -0.55(12) x 10^{-14} Hz s^{-1}. In the hypothesis that the secular spin-down is due to a rotating magneto-dipole emission, consistently with what is assumed for radio pulsars, we estimate the pulsar's magnetic dipole value. We derive an estimate of the magnetic field strength at the polar cap of B_{PC} = 4.0(4) x 10^8 Gauss, for a neutron star mass of 1.4M\odot, assuming the Friedman Pandharipande Skyrme equation of state. 
A. Riggio, L. Burderi, T. Di Salvo, A. Papitto, A. D'A\`i, R. Iaria,   M. T. Menna
astro-ph.HE