5 Conclusions

In this paper we presented the results of VLA multiwavelength observations and the first 8.4 GHz VLBA images of AR Lac we obtained in November 1997. These images show a spatially resolved structure with a diameter of $1.2 \pm 0.2$ mas, as derived from model fits. Since the source was very compact, with dimension close to the beam size, and the flux density level was very low, it was not viable to derive the source diameter for each phase. Still, whenever possible, the source size was derived (within 1-2 $\sigma$). No significant variations of the source size are apparent.

The flux density curves show a slight flux modulation, more evident at lower frequencies, which suggests the presence of inhomogeneous structures. The five-frequency spectra show a slightly negative spectral index, which is characteristic of an optically thin source.

By combining the spectral information, the estimate of the source size and the results obtained from simultaneous X-ray observations (Rodonò et al. 1999), we conclude that:

• the spectral and spatial information of the radio corona of AR Lac indicate a structured morphology, which can be modelled with a core-halo source;
• the physical parameters, as derived from the fit of the observed spectra with the core-halo model, are consistent with the hypothesis of a co-spatial X-ray and radio source;
• the observed radio emission cannot be attributed to the same thermal electron population responsible for the observed X-ray emission.

The application of the core-halo model to the observed spectra allows us to reproduce the flux modulation observed between phases 0.7 and 0.9, by keeping fixed the physical parameters which characterise the two structures but changing the size within the range defined from the VLBA resolution. Further observations will be able to verify the stability of the structure that can cause the modulation. In particular, since the numerous X-ray observations of this binary system seem to indicate structural changes in its corona (see Rodonò et al. 1999 for a summary) it will be extremely important to find out if this is also true for the radio corona and to check if our hypothesis of a co-spatial emitting region is confirmed.

In addition, multiwavelength VLA observations to be carried out during eclipses would be a crucial test of the hypothesis of an active region located in between the system components.