Updated orbital ephemeris of the ADC source X 1822-371: a stable orbital expansion over 40 years

The source X 1822-371 is an eclipsing compact binary system with a period close to 5.57 hr and an orbital period derivative $\dot{P}_{\rm orb}$ of 1.51(7)$\times 10^{-10}$ s s$^{-1}$. The very large value of $\dot{P}_{\rm orb}$ is compatible with a super-Eddington mass transfer rate from the companion star, as suggested by X-ray and optical data. The XMM-Newton observation taken in 2017 allows us to update the orbital ephemeris and verify whether the orbital period derivative has been stable over the last 40 yr. We added to the X-ray eclipse arrival times from 1977 to 2008 two new values obtained from the RXTE and XMM-Newton observations performed in 2011 and 2017, respectively. We estimated the number of orbital cycles and the delays of our eclipse arrival times spanning 40 yr using as reference time the eclipse arrival time obtained from the Rossi-XTE observation taken in 1996. Fitting the delays with a quadratic model, we found an orbital period $P_{\rm orb}=5.57062957(20)$ hr and a $\dot{P}_{\rm orb}$ value of $1.475(54) \times 10^{-10}$ s s$^{-1}$. The addition of a cubic term to the model does not significantly improve the quality of the fit. We also determined a spin-period value of $P_{\rm spin}=0.5915669(4)$ s and its first derivative $\dot{P}_{\rm spin}= -2.595(11) \times 10^{-12}$ s s$^{-1}$. The obtained results confirm the scenario of a super-Eddington mass transfer rate; we also exclude a gravitational coupling between the orbit and the change in the oblateness of the companion star triggered by the nuclear luminosity of the companion star.