Timing of the accreting millisecond pulsar SAX J1748.9-2021 during its 2015 outburst

We report on the timing analysis of the 2015 outburst of the intermittent accreting millisecond X-ray pulsar SAX J1748.9-2021 observed on March 4 by the X-ray satellite XMM-Newton. By phase-connecting the time of arrivals of the observed pulses, we derived the best-fit orbital solution for the 2015 outburst. We investigated the energy pulse profile dependence finding that the pulse fractional amplitude increases with energy while no significant time lags are detected. Moreover, we investigated the previous outbursts from this source, finding previously undetected pulsations in some intervals during the 2010 outburst of the source. Comparing the updated set of orbital parameters, in particular the value of the time of passage from the ascending node, with the orbital solutions reported from the previous outbursts, we estimated for the first time the orbital period derivative corresponding with $\dot{P}_{orb}=(1.1\pm0.3)\times 10^{-10}$ s/s. We note that this value is significant at 3.5 sigma confidence level, because of significant fluctuations with respect to the parabolic trend and more observations are needed in order to confirm the finding. Assuming the reliability of the result, we suggest that the large value of the orbital-period derivative can be explained as a result of an highly non-conservative mass transfer driven by emission of gravitational waves, which implies the ejection of matter from a region close to the inner Lagrangian point. We also discuss possible alternative explanations.