The long-term evolution of the accreting millisecond X-ray pulsar Swift J1756.9−2508

We present a timing analysis of the 2009 outburst of the accreting millisecond X-ray pulsar Swift J1756.9-2508, and a re-analysis of the 2007 outburst. The source shows a short recurrence time of only similar to 2 yr between outbursts. Thanks to the approximately 2 yr long baseline of data, we can constrain the magnetic field of the neutron star to be 0.4 x 10(8) less than or similar to B less than or similar to 9 x 10(8) G, which is within the range of typical accreting millisecond pulsars. The 2009 timing analysis allows us to put constraints on the accretion torque: the spin frequency derivative within the outburst has an upper limit of |(v) over dot| less than or similar to 3 x 10(-13) Hz s(-1) at the 95 per cent confidence level. A study of pulse profiles and their evolution during the outburst is analysed, suggesting a systematic change of shape that depends on the outburst phase. We report also the first evidence that the pulsed fractions increase with energy even if the source is in the hard state