A possible solution of the puzzling variation of the orbital period of MXB 1659-298

MXB 1659-298 is a transient neutron-star low-mass X-ray binary system that shows eclipses with a periodicity of 7.1 h. MXB 1659-298 went to outburst in 2015 August, after 14 years of quiescence. We investigate the orbital properties of this source with a baseline of 40 years, obtained by combining the eight eclipse arrival times present in the literature with 51 eclipse arrival times collected during the last two outbursts. A quadratic ephemeris does not fit the delays associated with the eclipse arrival times and the addition of a sinusoidal term with a period of 2.31 ± 0.02 yr is required. We infer a binary orbital period of P = 7.1161099(3) h and an orbital period derivative of \dot{P}=-8.5(1.2) × 10^{-12} s s^-1. We show that the large orbital period derivative can be explained with a highly non-conservative mass-transfer scenario, in which more than 98 per cent of the mass provided by the companion star leaves the binary system. We predict an orbital period derivative value of \dot{P}=-6(3) × 10^{-12} s s^-1 and constrain the companion-star mass between 0.3 and 1.2 M_⊙. Assuming that the companion star is in thermal equilibrium, the periodic modulation can be due to either a gravitational quadrupole coupling arising from variations of the oblateness of the companion star or the presence of a third body of mass M₃ > 21 Jovian masses.