Time variability of the core-shift effect in the blazar 3C 454.3

Using VLBI to measure a so-called core shift effect is a common way of obtaining estimates of the jet magnetic field strength. The VLBI core is typically identified as the bright feature at the jet's base, and the position of the core changes with the observed frequency, $r_\mathrm{core} \propto \nu^{-1/k_r}$. In this work, we investigated the time variability of the core-shift effect in the blazar 3C 454.3. We employed self-referencing analysis of multi-frequency (5, 8, 15, 22-24, and 43 GHz) VLBA data covering 19 epochs from 2005 until 2010. We found significant core shift variability ranging from 0.27 to 0.86 mas between 5 and 43 GHz, confirming the core-shift variability phenomenon observed before. Time variability of the core-shift index ($k_r$) was found typically below one, with an average value of $0.85 \pm 0.08$ and a standard deviation of $0.30$. $k_r<1$ values were found during flaring and quiescent states and our results indicate that commonly assumed conical jet shape and equipartition conditions do not always hold simultaneously. Still, these conditions are often assumed when deriving magnetic field strengths from core shift measurements, leading to unreliable results if $k_r$ significantly deviates from unity. Therefore, it is important to verify that $k_r = 1$ holds before using core shift values and the equipartition assumption to derive physical parameters in the jets. When $k_r = 1$ epochs are selected in the case of 3C 454.3, the magnetic field estimates are indeed quite consistent, even though the core shift varies with time. Additionally, our estimations of the jet's magnetic flux in 3C 454.3 show that the source is indeed in the magnetically arrested disk state. Finally, we found a good correlation of the core position with the core flux density, $r_\mathrm{core}\propto S_\mathrm{core}^{0.7}$, which is consistent with increased particle density during the flares.