| Abstract
| - Context. Hydrogen ionized by young, high-mass stars in starburst galaxies radiates radio recombination lines (RRLs), whose strength can be used as a diagnostic of the ionization rate, conditions and gas dynamics in the starburst region, without problems of dust obscuration. However, the lines are weak and only few extragalactic starburst systems have been detected. Aims. We aimed to increase the number of known starburst systems with detectable RRLs for detailed studies, and we used the line properties to study the gas properties and dynamics. Methods. We searched for the RRLs H91 α and H92 α with rest frequencies of 8.6 GHz and 8.3 GHz in the nearby southern Seyfert galaxy NGC 4945 using the Australia Telescope Compact Array with resolution of 3”. This yielded a detection from which we derived conditions in the starburst regions. Results. We detected RRLs from the nucleus of NGC 4945 with a peak line strength integrated over the source of 17.8 mJy, making it the strongest extragalactic RRL emitter known at this frequency. The line and continuum emission from NGC 4945 can be matched by a model consisting of a collection of 10 to 300 H II regions with temperatures of 5000 K, densities of 10 3 cm -3 to 10 4 cm -3 and a total effective diameter of 2 pc to 100 pc. The Lyman continuum production rate required to maintain the ionization is 6 × 10 52 s -1 to 3 × 10 53 s -1, which requires 2000 to 10 000 O5 stars to be produced in the starburst, inferring a star formation rate of 2 $M_odot$ yr -1 to 8 $M_odot$ yr -1. We resolved the rotation curve within the central 70 pc region and this is well described by a set of rotating rings that were coplanar and edge on. We found no reason to depart from a simple flat rotation curve. The rotation speed of 120 km s -1 within the central 1” (19 pc) radius infers an enclosed mass of 3 × 10 7$M_{odot}$, and an average surface density with the central 19 pc of 25 000 pc -2, which exceeds the threshold gas surface density for star formation. Conclusions. We discovered RRLs from NGC 4945. It is the strongest known extragalactic RRL emitter and is suited to high-quality spectroscopic study. We resolved the dynamics of the ionized gas in the central 70 pc and derived conditions and star formation rates in the ionized gas.
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