Order in the Chaos: Spin-up and Spin-down during the 2002 Outburst of SAX J1808.4-3658

We present a timing analysis of the 2002 outburst of the accreting millisecond pulsar SAX J1808.4-3658. A study of the phase delays of the entire pulse profile shows a behavior that is surprising and difficult to interpret: superposed to a general trend, a big jump by about 0.2 in phase is visible, starting at day 14 after the beginning of the outburst. An analysis of the pulse profile indicates the presence of a significant first harmonic. Studying the fundamental and the first harmonic separately, we find that the phase delays of the first harmonic are more regular, with no sign of the jump observed in the fundamental. The fitting of the phase delays of the first harmonic with a model that takes into account the observed exponential decay of the X-ray flux (and therefore of the mass accretion rate onto the neutron star) gives important information on the torque acting on the neutron star during the outburst. We find that the source shows spin-up in the first part of the outburst, while a spin-down dominates at the end. From these results we derive an estimate of the neutron star magnetic field strength.