Orbital Evolution of an Accreting Millisecond Pulsar: Witnessing the Banquet of a Hidden Black Widow

We have performed a timing analysis of all the four X-ray outbursts from the accreting millisecond pulsar SAX J1808.4−3658 observed so far by RXTE. For each of the outbursts we have found the local best orbital solution, keeping fixed to their best fit values the orbital period and the a sin i amplitude, and fitting for the time of ascending node passage. Plotting the best-fit values obtained in this way versus time, we find a highly statistically significant parabolic trend, which gives an orbital period of 7249.156499(9) s and an orbital period derivative of (3.40± 0.09)× 10 s/s. This derivative is positive, suggesting a degenerate or fully convective companion star, and is more than one order of magnitude higher than what is expected from angular momentum losses caused by gravitational radiation under the hypothesis of conservative mass transfer. We find that the only way to explain this puzzling result is that during X-ray quiescence the source is ejecting matter (and angular momentum) from the inner Lagrangian point. We propose a possible orbital evolution of the system and demonstrate that this kind of sources are capable to efficiently ablate the companion star, and therefore are hidden black widows visible in X-rays during transient mass transfer episodes.