Timing analysis of the isolated neutron star RX J0720.4-3125

We present a combined analysis of XMM-Newton, Chandra and Rosat observations of the isolated neutron star RXJ0720.4-3125, spanning a total period of \sim 7 years. We develop a maximum likelihood periodogramme for our analysis based on the \Delta C-statistic and the maximum likelihood method, which are appropriate for the treatment of sparse event lists. Our results have been checked "a posteriori" by folding a further BeppoSAX dataset with the period predicted at the time of that observation: the phase is found to be consistent. The study of the spin history and the measure of the spin-down rate is of extreme importance in discriminating between the possible mechanisms suggested for the nature of the X-ray emission. The value of \dot P, here measured for the first time, is \approx 10^{-14} s/s. This value can not be explained in terms of torque from a fossil disk. When interpreted in terms of dipolar losses, it gives a magnetic field of B \approx 10^{13} G, making also implausible that the source is accreting from the underdense surroundings. On the other hand, we also find unlikely that the field decayed from a much larger value (B\approx 10^{15} G, as expected for a magnetar powered by dissipation of a superstrong field) since this scenario predicts a source age of \approx 10^4 yrs, too young to match the observed X-ray luminosity. The observed properties are more compatible with a scenario in which the source is \approx 10^6 yrs old, and its magnetic field has not changed substantially over the lifetime.