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 ( \nu ) 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 \nu ^ { \alpha } we infer \alpha in the range - 16.67 to 2.41 and using \Delta t \propto \nu ^ { 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 \nu } ) and the core radius ( r _ { 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 _ { 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 .