1 Introduction  

Information obtained with Very Long Baseline Interferometry (VLBI) about radio spectra of parsec-scale jets and their evolution can be crucial for distinguishing between various jet models. However, there are several aspects of VLBI which impede spectral studies of parsec-scale regions. The reliability of spectral information extracted from VLBI data depends on many factors including sampling functions at different frequencies, alignment of the images, calibration and self-calibration errors, a narrow range of observing frequencies, and source variability. The influences of all these factors must be understood and, if possible, corrected for, in order to reconstruct the spectral properties of parsec-scale jets consistently.

Radio emission from the parsec-scale jets is commonly described by the synchrotron radiation from a relativistic plasma (e.g. Pacholczyk 1970). The corresponding spectral shape, $S(\nu) \propto \nu^{\alpha}$, is characterized by the location of spectral maximum ($S_{\rm m}$, $\nu_{\rm m}$) also called the turnover point, and by the two spectral indices, $\alpha_{\rm thick}$ (for frequencies $\nu \ll \nu_{\rm m}$) and $\alpha_{\rm thin}$ (for $\nu \gg \nu_{\rm m}$).

In many kiloparsec-scale objects, spectral index distributions have been mapped, using observations made with scaled arrays. In such observations, the antenna configurations are selected at each frequency in a specific way such that the spatial samplings of the resulting interferometric measurements are identical at all frequencies used for the observations. It is virtually impossible to use the scaled array technique for VLBI observations of parsec-scale jets made at different frequencies. The uneven spatial samplings of VLBI data at different frequencies result in differences of the corresponding synthesized beams, and can ultimately lead to confusion and spurious features appearing in spectral index maps.

In spectral index maps, the only available kind of information is the spectral slope between the two frequencies. While sufficient for many purposes, this information can be misleading in the situation when the frequency of thespectral maximum lies between the frequencies used for spectral index mapping. In the ranges of frequencies between 1.4 and 43GHz, frequently used for VLBI observations, such a situation can be quite common. Using observations at three or more frequencies, it is possible to estimate the shape of the synchrotron spectrum, and derive the turnover frequency (frequency of spectral maximum). Information about the turnover frequency can help to avoid the confusion which is likely to occur in spectral index maps. The turnover frequency is sensitive to changes of physical conditions in the jet such as velocity, particle density, and magnetic field strength. This makes it an excellent tool for probing the physics of the jet in more detail than is allowed by analysis of the flux and spectral index properties of the jet.

In this paper, we present a technique suitable for determining the turnover frequency distribution from multi-frequency VLBI data, and investigate its limitations and ranges of applicability. We discuss the advantages of using the Very Long Baseline Array (VLBA) for spectral imaging. A general approach to imaging of VLBA data from nearly simultaneous, snapshot-type observations at different frequencies is outlined in Sect. 2. The effects of limited sampling and uneven uv-coverages are discussed in Sect. 3. We provide analytical estimates of the sensitivity decrease, and use numerical simulations to evaluate the effect the uneven spatial samplings have on the outcome of a comparison of VLBI images at different frequencies. Alignment of VLBI images is reviewed in Sect. 4. A method used for spectral fitting and determining the turnover frequency is described in Sect. 5. Spectral fitting in the case of limited frequency coverage is discussed in Sect. 5.5. The first results from the turnover frequency mapping are presented in Sect. 6.