Wide-field VLBI observations of the nearby starburst galaxy NGC 4945, obtained with the Australian LBA, have produced 2.3 GHz images over two epochs with a maximum spatial resolution of 0.3 pc. 15 sources were detected, 13 of which correspond to sources identified in higher frequency (3 cm and 12 mm) ATCA images. Four of the sources are resolved into shell-like structures ranging between 1.1 to 2.1 pc in diameter. From these data the spectra of 13 compact radio sources in NGC 4945 were modelled; nine were found to be consistent with free-free absorbed power laws and four with a simple power law spectrum. The free-free opacity is highest toward the nucleus but varies significantly throughout the nuclear region, implying that the overall structure of the ionised medium is clumpy. Of the 13 sources, 10 have steep intrinsic spectra associated with synchrotron emission from supernova remnants, the remaining sources have flat intrinsic spectra which may be associated with thermal radio emission. A non-thermal source with a jet-like morphology is detected ~1 from the assumed location of the AGN. A type II supernova (SN) rate upper limit of 15.3/yr is determined for the inner 250 pc region of the galaxy at the 95% confidence level, based on the lack of detection of new sources in observations spanning 1.9 years and a simple model for the evolution of supernova remnants. A type II SN rate of >0.1(v/1e4)/yr is implied from estimates of supernova remnant source counts, sizes and expansion rates, where v is the radial expansion velocity of the supernova remnant in km/s. A SFR of 2.4(v/1e4)<SFR(M>=5Msun)<370 Msun/yr has been estimated directly from the SN rate limits and is of the same order of magnitude as rates determined from integrated FIR and radio luminosities.
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