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 RX J0720.4-3125, spanning a total period of similar to7 yr. We develop a maximum likelihood periodogram for our analysis based on the DeltaC 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 data set 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 are of extreme importance in discriminating between the possible mechanisms suggested for the nature of the X-ray emission. The value of P., here measured for the first time, is approximate to10 (-14) s s(-1). This value cannot be explained in terms of torque from a fossil disc. When interpreted in terms of dipolar losses, it gives a magnetic field of B approximate to10(13) G, making it also implausible that the source is accreting from the underdense surroundings. On the other hand, we also find it unlikely that the field decayed from a much larger value (B approximate to10(15) G, as expected for a magnetar powered by dissipation of a superstrong field) since this scenario predicts a source age of approximate to10(4) yr, too young to match the observed X-ray luminosity. The observed properties are more compatible with a scenario in which the source is approximate to10(6) yr old, and its magnetic field has not changed substantially over the lifetime.