Imaging and variability studies of CTA~102 during the 2016 January $\gamma$-ray flare

The $\gamma$-ray bright blazar CTA 102 is studied using imaging (new 15 GHz and archival 43 GHz Very Long Baseline Array, VLBA data) and time variable optical flux density, polarization degree and electric vector position angle (EVPA) spanning between 2015 June 1 and 2016 October 1, covering a prominent $\gamma$-ray flare during 2016 January. The pc-scale jet indicates expansion with oscillatory features upto 17 mas. Component proper motions are in the range 0.04 - 0.33 mas/yr with acceleration upto 1.2 mas followed by a slowing down beyond 1.5 mas. A jet bulk Lorentz factor $\geq$ 17.5, position angle of 128.3 degrees, inclination angle $\leq$ 6.6 degrees and intrinsic half opening angle $\leq$ 1.8 degrees are derived from the VLBA data. These inferences are employed in a helical jet model to infer long term variability in flux density, polarization degree, EVPA and a rotation of the Stokes Q and U parameters. A core distance of $r_{\rm core,43 \ GHz}$ = 22.9 pc, and a magnetic field strength at 1 pc and the core location of 1.57 G and 0.07 G respectively are inferred using the core shift method. The study is useful in the context of estimating jet parameters and in offering clues to distinguish mechanisms responsible for variability over different timescales.