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

K.V. Sokolovsky $^{∗}$, Y.Y. Kovalev 

MPIfR, Bonn, Germany and ASC Lebedev, Moscow, Russia 

A.P. Lobanov, T. Savolainen 

MPIfR, Bonn, Germany 

A.B. Pushkarev 

MPIfR, Bonn, Germany; Pulkovo Obs., St Petersburg, Russia; CrAO, Crimea, Ukraine 

M. Kadler 

Dr. Remeis-Sternwarte & ECAP, Bamberg, Germany; CRESST/NASA GSFC and USRA, MD, USA 

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 − $^{2}$–102 G (observer’s frame) could be placed on the magnetic field strength in 13 sources. Hard radio spectra ( − 0 . 5 ≤ α ≤ +0 . 1, S$_{ν}$ ∼ ν α ) 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. 

## 1. Introduction 

Blazars are active galactic nuclei characterized by highly variable non-thermal continuum emission across the electromagnetic spectrum. The Large Area Telescope (LAT, [1]) on board the Fermi γ -ray obser- vatory, launched on 2008 June 11, provides a wealth of new information about high-energy radiation of blazars. It is believed that this high-energy emission is intimately connected with the emission at lower energies (radio – optical) through the process of in- verse Compton scattering. Very Long Baseline Inter- ferometry (VLBI), with its spectacular angular reso- lution, provides the most detailed view of inner re- gions in blazars [2]. In most cases, VLBI observations reveal one-sided relativistically beamed parsec-scale jets originating in a bright, compact region called the “core”. 

The spatially resolved broad-band spectroscopy is one of the few methods that can probe the physical conditions inside blazar jets. Despite the great po- tential of this method, its applications are still rela- tively rare (see [3] and references therein), owing to difficulties in implementing it and interpreting results obtained [4]. In addition, multifrequency VLBI obser- vations require large amounts of observing time and most VLBI arrays lack technical capability to perform simultaneous multifrequency observations. 

We utilize the Very Long Baseline Array (VLBA, [5]) which has a unique capability to conduct ob- servations quasi-simultaneously at many frequencies, 

needed to constrain physical conditions in the regions where blazar radio emission originates. We recon- struct radio spectra of parsec-scale features in jets of selected γ -ray-bright blazars and compare them with the simple homogeneous synchrotron source model, which allows us to derive information about the mag- netic field strength and particle energy distribution. During the first year of the Fermi scientific operations, we used the VLBA to observe 20 blazars, that were identified prior to the launch of Fermi as expected bright γ -ray emitters. In this paper, we present results for 17 of them. The data analysis for three remaining sources is still ongoing. 

## 2. Observations and data reduction 

The observations were conducted simultaneously at seven frequencies in a 4.6–43.2 GHz range. After the initial calibration in the AIPS package [6], the sources were self-calibrated and imaged independently at each frequency using the Difmap software [7]. Whenever feasible, the frequency-dependent core position (the “core shift” effect, see for a detailed discussion [8, 9]) was taken into account. Image alignment is a ma- jor problem for spectral VLBI analysis because the self-calibration technique used to obtain high-quality images causes loss of information about the absolute position of a source. Positions of optically thin jet features or the core itself (if the “core shift” effect is negligible for a given source) are then used to align VLBI images obtained at different frequencies. 

In order to reconstruct the spectrum in a given pixel of an image (“pixel-based approach”), the sum of CLEAN components around this pixel was used. The CLEAN components were summed in- 

