2009 Fermi Symposium, Washington, D.C., Nov. 2-5 2 4.2. Electron energy spectrum 3. Results 5. Summary and prospects 4. Discussion 4.1. Model reliability eConf C091122 side a radius R = Θ(lowest frequency) / 3, where Θ(lowest frequency) is the half-power beam width at the lowest observing frequency (4.6 GHz). This ap- proach has a major advantage over the direct use of flux densities from reconstructed images because it avoids artifacts introduced by convolution with a Gaussian beam while preserving the angular resolu- tion achieved. The radio spectra in the parsec-scale core regions (marked as shaded areas on Fig. 1) of the observed blazars have diverse properties. Most of them are nearly flat, with signs of curvature at lower fre- quencies, which we interpret as synchrotron self- absorption. In one source (NRAO 530, Fig. 1r), the spectral turnover is particularly prominent and well sampled by our observations. Cores in three sources, 0716+714 (Fig. 2a), OJ 287 (Fig. 2b), and 3C 454.3 (Fig. 2d), show inverted spectra which are slightly curved. The core spectrum of only one source $^{(1510}$−089, Fig. 2c) can be adequately described by a simple power law in the whole 4.6–43.2 GHz frequency range. In the following, we focus on sources that show a well defined spectral turnover, and thus can be used to determine the physical conditions in the emitting plasma. We fit a homogeneous synchrotron source model [10] (see the Appendix for more details) to the ob- served spectra in order to obtain the magnetic field strength and particle energy distribution. The sources for which the data reduction is complete are presented in Table I. For 13 sources, the model provided an ad- equate fit to the observed spectra (Fig. 1) while four sources exhibit flat or inverted spectra (Fig. 2) that cannot be described by the homogeneous synchrotron model. for the 8 GHz core region which is comparable in size to the region probed in our research. This value is in a good agreement with our upper limit at B$_{⊥}$ ≤ 0 . 016 G given in Table I. The spectra above the synchrotron turnover are nearly flat or slightly inverted in core regions of all sources investigated in this work. This may result from blending of a few emitting regions with different peak frequencies (an example of such blending may be found in the core region of BL Lacertae, see the top right panel in Fig. 3, see also [3] for 3C 273). Alter- natively, a nearly flat spectrum may imply a hard en- ergy spectrum of the emitting electrons (as may be the case for the component B1 in the jet of BL Lacertae whose spectrum is presented in the lower right panel of Fig. 3; see also Table II). The hard electron spec- trum is difficult to explain by the conventional first- order Fermi acceleration mechanism. However, the hard spectrum can be produced by the second-order Fermi mechanism (“stochastic acceleration”) [11]. We have placed upper limits of B$_{⊥}$ ≤ 10 − $^{2}$–102 G (observer’s frame) on the magnetic field strength in 13 out of 17 Fermi blazars (Table I). Spectra of four blazars could not be described by the simple homoge- neous synchrotron source model, and no constraints on the magnetic field and particle energy spectrum could be obtained for these sources. Hard spectra $^{(}$−0 . 5 ≤ α ≤ +0 . 1, S$_{ν}$ ∼ ν $^{α}$) observed in the blazar cores above the synchrotron peak may either indicate a hard energy spectrum of the relativistic electron population in the jet or result from significant inhomo- geneity (of the magnetic field and plasma parameters or just optical depth) across the emitting region. Since γ -ray emission in blazars is suggested to orig- inate from regions spatially close to the VLBI core [12], the estimates of the magnetic field strength and electron energy distribution presented in Ta- ble I could be used to constrain broad-band Spectral Energy Distribution (SED) models. Simultaneously with the VLBA observations described here, Swift X- ray/ultraviolet/optical target of opportunity observa- tions were performed. When combined with the Fermi γ -ray data this will provide a unique data set for the SED modeling. Analysis of this data set is presently underway. The physical parameters presented in Table I cor- respond to typical values for emitting electrons inside a large area of a few milliarcseconds in size (shaded areas on Fig. 1). In most cases, only an upper limit on the magnetic field strength could be placed, because most regions where the spectral turnover is detected remain unresolved. The results are consistent with es- timates obtained by a method based on model-fitting bright VLBI components with 2D Gaussian compo- nents (see Fig. 3 for results on BL Lacertae). The model-fitting based method is described in detail in [3] where it was applied to 3C 273 and the average magnetic field strength B$_{⊥}$ ∼ 10 − 2 G was obtained