Signatures of a spinning supermassive black hole binary on the mas-scale jet of the quasar S5 1928+738 based on 25 years of VLBI data

In a previous work, we have identified the spin of the dominant black hole of a binary from its jet properties. Analysing Very Long Baseline Array (VLBA) observations of the quasar S5~1928+738, taken at $15$-GHz during $43$ epochs between $1995.96$ and $2013.06$, we showed that the inclination angle variation of the inner ($<2$~mas) jet symmetry axis naturally decomposes into a periodic and a monotonic contribution. The former emerges due to the Keplerian orbital evolution, while the latter is interpreted as the signature of the spin-orbit precession of the jet emitting black hole. In this paper, we revisit the analysis of the quasar S5~1928+738 by including new $15$-GHz VLBA observations extending over $29$ additional epochs, between $2013.34$ and $2020.89$. The extended data set confirms our previous findings which are further supported by the flux density variation of the jet. By applying an enhanced jet precession model that can handle arbitrary spin orientations $\kappa$ with respect to the orbital angular momentum of a binary supermassive black hole system, we estimate the binary mass ratio as $\nu =0.21\pm 0.04$ for $\kappa =0$ (i.e. when the spin direction is perpendicular to the orbital plane) and as $\nu =0.32\pm 0.07$ for $\kappa =\pi \mathrm{/}2$ (i.e. when the spin lies in the orbital plane). We estimate more precisely the spin precession velocity, halving its uncertainty from $(-0.05\pm 0.02{)}^{\circ }{\mathrm{y}\mathrm{r}}^{-1}$ to $(-0.04\pm 0.01{)}^{\circ }{\mathrm{y}\mathrm{r}}^{-1}$.