Secular spin-down of the AMP XTE J1751-305

Context. Of the 13 known accreting millisecond pulsars, only a few have displayed more than one outburst during the RXTEera. After its main outburst in 2002, XTE J1751-305 showed an additional three dim outbursts. We report on the timing analysis of the latest one, which occurred on October 8, 2009 and was serendipitously observed from its very beginning by RXTE. Aims: By detecting the pulsation during more than one outburst, we derive a stronger constraint of the orbital parameters and their evolution, and we can track the secular spin frequency evolution of the source. Methods: Using the RXTEdata of the last outburst of the AMP XTE J1751-305, we performed a timing analysis to more accurately constrain the orbital parameters. Because of the low quality of the data statistics, we applied an epoch-folding search technique to 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 over 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) × 10-14 Hz s-1. We estimate the pulsar's magnetic dipole value by assuming that the secular spin-down is due to a rotating magneto dipole emission, to be consistent with what is assumed for radio pulsars. We derive an estimate of the magnetic field strength at the polar cap of BPC = 4.0(4) × 108 G, for a neutron star mass of 1.4 Msun, assuming the Friedman Pandharipande Skyrme equation of state.