Frequency dependent core shifts and parameter estimation for the blazar 3C 454.3

Abstract

We study the core shift effect in the parsec scale jet of the blazar 3C 454.3 using the 4.8 GHz - 36.8 GHz radio light curves obtained from three decades of continuous monitoring. From a piecewise Gaussian fit to each flare, time lags \(\Delta t\) between the observation frequencies \(\nu\) and spectral indices \(\alpha\) based on peak amplitudes \(A\) are determined. From the fit \(\Delta t \propto \nu^{1/k_r}\), \(k_r = 1.10 \pm 0.18\) indicating equipartition between the magnetic field energy density and the particle energy density. From the fit \(A \propto \nu^\alpha\), \(\alpha\) is in the range \(-0.24\) to \(1.52\). A mean magnetic field strength at 1 pc, \(B_1 = 0.5 \pm 0.2\) G, and at the core, \(B_{\rm core} = 46 \pm 16\) mG, are inferred, consistent with previous estimates. The measure of core position offset is \(\Omega_{r\nu} = 6.4 \pm 2.8\) pc GHz\(^{1/k_r}\) when averaged over all frequency pairs. Based on the statistical trend shown by the measured core radius \(r_{\rm core}\) as a function of \(\nu\), we infer that the synchrotron opacity model may not be valid for all cases. A Fourier periodogram analysis yields power law slopes in the range \(-1.6\) to \(-3.5\) describing the power spectral density shape and gives bend timescales in the range \(0.52 - 0.66~\)yr. This result, and both positive and negative \(\alpha\), indicate that the flares originate from multiple shocks in a small region. Important objectives met in our study include: the demonstration of the computational efficiency and statistical basis of the piecewise Gaussian fit; consistency with previously reported results; evidence for the core shift dependence on observation frequency and its utility in jet diagnostics in the region close to the resolving limit of very long baseline interferometry observations.