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

## TL;DR

This study analyzes 40 years of eclipse data from MXB 1659-298, revealing a sinusoidal orbital period variation likely caused by either stellar quadrupole effects or a third body, and models a highly non-conservative mass transfer scenario.

## Contribution

It provides the first detailed long-term orbital analysis of MXB 1659-298, identifying a sinusoidal period variation and proposing explanations involving stellar or third-body influences.

## Key findings

- Orbital period of 7.1161099 hours with a derivative of -8.5e-12 s/s.
- Sinusoidal modulation with a 2.31-year period.
- Mass transfer is highly non-conservative, with over 98% of mass leaving the system.

## Abstract

MXB 1659-298 is a transient neutron star Low-Mass X-ray binary system that shows eclipses with a periodicity of 7.1 hr. The source went to outburst in August 2015 after 14 years of quiescence. We investigate the orbital properties of this source with a baseline of 40 years obtained combining the eight eclipse arrival times present in 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 $2.31 \pm 0.02$ yr is required. 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$^{-1}$. We show that the large orbital period derivative can be explained with a highly non conservative mass transfer scenario in which more than 98\% of the mass provided by the companion star leaves the binary system. We predict an orbital period derivative value of $\dot{P}=-6(3) \times 10^{-12}$ s s$^{-1}$ and constrain the companion star mass between $\sim$0.3 and $ 0.9 \pm 0.3$ M$_{\odot}$. Assuming that the companion star is in thermal equilibrium the periodic modulation can be due to either a gravitational quadrupole coupling due to variations of the oblateness of the companion star or with the presence of a third body of mass M$_3 >21 $ Jovian masses.