| Abstract
| - Context. Since the discovery of the first accreting millisecond X-ray pulsar (AMXP) SAX J1808.4−3658 in 1998, the family of these sources has kept growing. Currently, it has 22 members. All AMXPs are transients with usually very long quiescence periods, implying that the mass accretion rate in these systems is quite low and not constant. Moreover, for at least three sources, a non-conservative evolution was also proposed. Aims. Our purpose is to study the long term averaged mass-accretion rates in all the AMXPs discovered so far, to investigate a non-conservative mass-transfer scenario. Methods. We calculated the expected mass-transfer rate under the hypothesis of a conservative evolution based on their orbital periods and on the (minimum) mass of the secondary star (as derived from the mass function), driven by gravitational radiation and/or magnetic braking. Using this theoretical mass transfer, we determined the expected accretion luminosity of the systems. Thus, we achieved the lower limit to the distance of the sources by comparing the computed theoretical luminosity and the observed flux averaged over a time period of 20 years. Then, the lower limit to the distance of the sources was compared to the value of the distance reported in the literature to evaluate how reasonable the hypothesis of a conservative mass transfer is. Results. Based on a sample of 18 sources, we found strong evidence of a non-conservative mass transfer for five sources, for which the estimated distance lower limits are higher than their known distances. We also report hints of mass outflows in a further six sources. The discrepancy can be fixed under the hypothesis of a non-conservative mass transfer in which a fraction of the mass transferred onto the compact object is swept away from the system, likely due to the (rotating magnetic dipole) radiation pressure of the pulsar.
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