This thesis covers two very different topics: a complete study of the radio emission of supernova SN1993J and the first wide-field astrometric analysis ever performed on a complete sample of radio sources (the S5 polar cap sample) by means of high-precision (differenced-phase-delay) VLBI astrometry, In the first part of the thesis, we report on the analysis of all the available VLBI data of supernova SN1993J. With new methods developed by us for accurate estimation of the size and width of the supernova radio-emitting shell-like region, we study the resulting supernova expansion at different frequencies. We find discrepancies between the sizes measured at 1.6GHz and those measured at higher frequencies. These discrepancies increase with supernova age (we rule out that this is due to resolution effects). We are able to explain all the peculiarities of the supernova expansion with some corrections to the standard model of radio emission in supernovae. These corrections are a time-evolving opacity of the supernova ejecta and a radial dependence of the amplified magnetic fields in the radio shell. All these corrections (along with effects arising from the finite sensitivity of the VLBI interferometers) have been implemented into a new simulation program (RAMSES), capable of generating synthetic expansion curves and radio light curves, which are directly compared to observational results. We find excellent agreement between the RAMSES simulations and all the observations of SN1993J.
In the second part of this thesis, we report on the first wide-field high precision astrometric analysis of the 13 extragalactic radio sources of the complete S5 polar cap sample. This analysis has been carried out at 15.4GHz for two epochs (1999.57 and 2000.46). Several upgrades of existing software were necessary for the implementation of this kind of astrometric analysis. We have thus created a new software package (UVPAP), capable of performing multi-source differenced-phase-delay astrometry. In this thesis, we describe the main characteristics of UVPAP. We also describe new algorithms developed to enable the use of differenced phase delays in wide-field astrometric observations involving more than 2-3 sources and discuss the impact of using differenced phase delays on the precision of the global astrometry. From these fits, we obtain estimates of the relative source positions with precisions ranging from approx. 15 to approx. 200 microarcseconds (for epoch 1999.57) and from approx. 20 to 700 microarcseconds (for epoch 2000.46), depending on the angular separation of the sources (from approx. 1.6 to 20.8 degrees). These precisions are around 10 times higher than those achievable using the conventional phase-reference technique.
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