Parsec-scale jet properties of the quasar PG 1302$-$102

The quasar PG 1302$-$102 is believed to harbour a supermassive binary black hole (SMBBH) system. Using the available 15 GHz and $2-8$ GHz, multi-epoch Very Long Baseline Array data, we constrain the pc-scale jet properties based on the inferred mean proper motion, including a bulk Lorentz factor $\geq 5.1 \pm 0.8$, jet inclination angle $\leq (11.4 \pm 1.7)$ degrees, projected position angle $= 31.8$ degrees, intrinsic half opening angle $\leq (0.9 \pm 0.1)$ degrees and a mean $2-8$ GHz spectral index of 0.31. A general relativistic helical jet model is presented and applied to predict quasi-periodic oscillations of $\sim$ 10 days, power law power spectrum shape and a contribution of up to $\sim$ 53 percent to the observed variable core flux density. The model is used to make a case for high resolution, moderately sampled, long duration radio interferometric observations to reveal signatures due to helical knots and distinguish them from those due to SMBBH orbital activity including a phase difference $\sim \pi$ and an amplitude ratio (helical light curve amplitude/SMBBH light curve amplitude) of $0.2-3.3$. The prescription can be used to identify helical kinematic signatures from quasars, providing possible candidates for further studies with polarization measurements. It can also be used to infer promising SMBBH candidates for the study of gravitational waves if there are systematic deviations from helical signatures.