Spin up and phase fluctuations in the timing of the accreting millisecond pulsar XTE J1807-294

We performed a timing analysis of the 2003 outburst of the accreting X-ray millisecond pulsar XTE J1807-294 observed by RXTE. 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 to what appears as 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 law. As in previous cases, we have therefore analyzed separately 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. In the hypothesis that the second harmonic pulse phase delays are a good tracer of the spin frequency evolution we give for the first time a estimation of the spin frequency derivative in this source. The source shows a clear spin-up of $\dot \nu = 2.5(7) \times 10^{-14}$ Hz sec$^{-1}$ (1 $\sigma$ confidence level). The largest source of uncertainty in the value of the spin-up rate is given by the uncertainties on the source position in the sky. We discuss this systematics on the spin frequency and its derivative.