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Signature of the presence of a third body orbiting around XB 1916-053

The ultra-compact dipping source \object{XB 1916-053} has an orbital period of close to 50 min and a companion star with a very low mass (less than 0.1 M$_{\odot}$). The orbital period derivative of the source was estimated to be $1.5(3) \times 10^{-11}$ s/s through analysing the delays associated with the dip arrival times obtained from observations spanning 25 years, from 1978 to 2002. The known orbital period derivative is extremely large and can be explained by invoking an extreme, non-conservative mass transfer rate that is not easily justifiable. We extended the analysed data from 1978 to 2014, by spanning 37 years, to verify whether a larger sample of data can be fitted with a quadratic term or a different scenario has to be considered. We obtained 27 delays associated with the dip arrival times from data covering 37 years and used different models to fit the time delays with respect to a constant period model.We find that the quadratic form alone does not fit the data. The data are well fitted using a sinusoidal term plus a quadratic function or, alternatively, with a series of sinusoidal terms that can be associated with a modulation of the dip arrival times due to the presence of a third body that has an elliptical orbit. We infer that for a conservative mass transfer scenario the modulation of the delays can be explained by invoking the presence of a third body with mass between 0.10-0.14 M$_{\odot}$, orbital period around the X-ray binary system of close to 51 yr and an eccentricity of $0.28 \pm 0.15$. In a non-conservative mass transfer scenario we estimate that the fraction of matter yielded by the degenerate companion star and accreted onto the neutron star is $β= 0.08$, the neutron star mass is $\ge 2.2$ M$_{\odot}$, and the companion star mass is 0.028 M$_{\odot}$. (Abridged)