Spin-up and Phase Fluctuations in the Timing of the Accreting Millisecond Pulsar XTE J1807-294

We have performed a timing analysis of the 2003 outburst of the accreting X-ray millisecond pulsar XTE J1807-294 as observed by the Rossi X-Ray Timing Explorer. Using recently refined orbital parameters, we report for the first time a precise estimate of the spin frequency and of the spin frequency derivative. The phase delays of the pulse profile show a strong erratic behavior superposed on what appears to be a global spin-up trend. The erratic behavior of the pulse phases is strongly related to rapid variations of the light curve, making it very difficult to fit these phase delays with a simple formula. As in previous cases, we therefore separately analyze the phase delays of the first harmonic and of the second harmonic of the spin frequency, finding that the phases of the second harmonic are far less affected by the erratic behavior. Under the hypothesis that the second-harmonic pulse phase delays are a good tracer of the spin frequency evolution, we give for the first time an estimate of the spin frequency derivative for this source. XTE J1807-294 shows a clear spin-up of ν˙=2.5(7)×10-14 Hz s-1 (1 σ confidence level). The majority of the uncertainty in the value of the spin-up rate is due to the uncertainties in the source position on the sky. We discuss the effect of this systematic error on the spin frequency and its derivative.