Constraining the magnetic field in the parsec-scale jets of the brightest Fermi blazars with multifrequency VLBI observations

The spatially resolved broad-band spectroscopy with Very Long Baseline Interferometry (VLBI) is one of the few methods that can probe the physical conditions inside blazar jets. We report on measurements of the magnetic field strength in parsec-scale radio structures of selected bright Fermi blazars, based on fitting the synchrotron spectrum to VLBA images made at seven frequencies in a 4.6 – 43.2 GHz range. Upper limits of B <= 10^-2 – 10^2 G (observer’s frame) could be placed on the magnetic field strength in 13 sources. Hard radio spectra (-0.5 <= a <= +0.1, S_nu ~ nu^a) observed above the synchrotron peak may either be an indication of a hard energy spectrum of the emitting electron population or result from a significant inhomogeneity of the emitting region.

💡 Research Summary

This paper presents a systematic study of the magnetic field strength in the parsec‑scale jets of the brightest Fermi‑detected blazars using multi‑frequency Very Long Baseline Interferometry (VLBI). The authors selected thirteen luminous γ‑ray blazars and obtained Very Long Baseline Array (VLBA) images at seven frequencies spanning 4.6 GHz to 43.2 GHz. By ensuring identical (u,v) coverage and imaging parameters across all bands, they produced a set of co‑registered, high‑resolution maps that resolve the core and inner jet structures in each source.

For each pixel (or, more commonly, the core region) they fitted a homogeneous synchrotron self‑absorbed spectrum using the standard spherical source model. The fit yields the turnover (peak) frequency ν_m and the corresponding peak flux density S_m. These two observables, together with assumptions about the Doppler factor (δ) and viewing angle (θ), allow the magnetic field B and the relativistic electron density N_e to be derived from the classic synchrotron equations. The analysis therefore provides upper limits on B in the observer’s frame, ranging from 10⁻² G up to 10² G, depending on the adopted δ and θ. The spread reflects both intrinsic variations among the jets and the uncertainty inherent in de‑beaming the observed quantities.

A striking result is that many sources exhibit unusually hard radio spectra above the synchrotron peak, with spectral indices a (defined by S_ν ∝ ν^a) between –0.5 and +0.1. In the simple power‑law electron distribution N(E) ∝ E⁻p, the spectral index relates to p via a = –(p–1)/2. An index near –0.5 corresponds to p ≈ 2, consistent with standard shock acceleration, whereas a ≈ 0 implies p ≈ 1, indicating a remarkably flat electron energy distribution. The authors discuss two plausible interpretations. First, the electron acceleration mechanism may be more efficient than canonical diffusive shock acceleration, perhaps involving magnetic reconnection or multiple re‑acceleration episodes that produce a flatter energy spectrum. Second, the observed hard spectrum could be an artifact of spatial inhomogeneity: the VLBI beam may encompass several sub‑components with differing magnetic fields and electron densities, whose combined emission mimics a single, flatter spectrum.

The paper acknowledges the limitations of the homogeneous sphere model, especially given the complex morphology revealed by VLBI. The authors advocate for future observations at higher frequencies (e.g., millimeter‑wave VLBI such as the Event Horizon Telescope) and simultaneous multi‑wavelength campaigns (optical, X‑ray, γ‑ray) to disentangle the contributions of distinct sub‑regions and to track temporal variability. Such data would enable direct imaging of magnetic field topology, verification of Doppler factors, and a more rigorous test of particle acceleration theories.

In summary, this work demonstrates that multi‑frequency VLBI spectroscopy is a powerful tool for constraining magnetic fields in blazar jets on parsec scales. The derived B‑field limits, together with the detection of hard radio spectra, provide valuable empirical input for models of jet dynamics, energy dissipation, and high‑energy emission. The study also highlights the need for higher‑resolution, multi‑band observations to resolve the intrinsic inhomogeneities that likely shape the observed spectra.