Revised orbital parameters of the accreting millisecond pulsar SAX J1808.4-3658

We present a temporal analysis of the three outbursts of the X-ray millisecond pulsar SAX J1808.4 - 3658 that occurred in 1998, 2000, and 2002. With a technique that uses the chi(2) obtained with an epoch-folding search to x discriminate between different possible orbital solutions, we find an unique solution valid over the whole 5 yr period for which high temporal resolution data are available. We revise the estimate of the orbital period, P-orb = 7249.1569(1) s, and reduce the corresponding error by 1 order of magnitude with respect to that previously reported. Moreover, we report the first constraint on the orbital period derivative, -6.6 x 10(-12) <(P) over dot P-orb < +0.8 x 10(-12)s s(-1). These values allow us to produce, via a folding technique, pulse profiles at any given time. Analysis of these profiles shows that the pulse shape is clearly asymmetric in 2002, occasionally showing a secondary peak at about 145 degrees from the main pulse, which is quite different from the almost sinusoidal shape reported at the beginning of the 1998 outburst.