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 in the light curve with a peiodicity of 7.1 hr. MXB 1659-298 on outburst in August 2015 after 14 years of quiescence. We span a baseline of 40 years using the eight eclipse arrival times present in literature and adding 51 eclipse arrival times collected during the last two outbursts. We find that the companion star mass is $0.76 $ M$_{\odot}$, the inclination angle of the system is $72^{\circ}\!.4$ and the corona surrounding the neutron star has a size of $R_c \simeq 3.5 \times 10^8$ cm. A simple quadratic ephemeris do not fit the delays associated with the eclipse arrival times, the addition of a sinusoidal term is needed. We infer a binary orbital period of $P=7.1161099(3)$ hr and an orbital period derivative of $\dot{P}=-8.5(1.2) \times 10^{-12}$ s s$^{-1}$; the sinusoidal modulation has a period of $2.31 \pm 0.02$ yr. These results are consistent with a conservative mass transfer scenario during the outbursts and with a totally non-conservative mass transfer scenario during X-ray quiescence with the same mass transfer rate. The periodic modulation can be explained by either a gravitational quadrupole coupling due to variations of the oblateness of the companion star or with a presence of celestial body by orbiting around the binary system; in the latter case the mass of a third body is M$_3 = 21 \pm 2$ M$_J$.

Comments: 9 pages, 6 figures. Submitted to MNRAS on 2016 November 21, revised version after referee report

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