Core shift effect in blazars

We studied the pc-scale core shift effect using radio light curves for three blazars, S5 0716+714, 3C 279 and BL Lacertae, which were monitored at five frequencies ($ u$) between 4.8 GHz and 36.8 GHz using the University of Michigan Radio Astronomical Observatory (UMRAO), the Crimean Astrophysical Observatory (CrAO), and Metsahovi Radio Observatory for over 40 years. Flares were Gaussian fitted to derive time delays between observed frequencies for each flare ($Delta t$), peak amplitude ($A$), and their half width. Using $A propto u^{alpha}$ we infer $alpha$ in the range $-$16.67 to 2.41 and using $Delta t propto u^{1/k_r}$, we infer $k_r sim 1$, employed in the context of equipartition between magnetic and kinetic energy density for parameter estimation. From the estimated core position offset ($Omega_{r u}$) and the core radius ($r_{rm core}$), we infer that opacity model may not be valid in all cases. The mean magnetic field strength at 1 pc ($B_1$) and at the core ($B_{rm core}$), are in agreement with previous estimates. We apply the magnetically arrested disk model to estimate black hole spins in the range $0.15-0.9$ for these blazars, indicating that the model is consistent with expected accretion mode in such sources. The power law shaped power spectral density has slopes $-$1.3 to $-$2.3 and is interpreted in terms of multiple shocks or magnetic instabilities.