Abstract
We present observations of the 85.69 GHz continuum emission and H42 alpha line emission from the central 30 arcsec within NGC 4945. Both sources of emission originate from nearly identical structures that can be modelled as exponential discs with scalelengths of similar to 2.1 arcsec (or similar to 40 pc). An analysis of the spectral energy distribution based on combining these data with archival data imply that 84 +/- 10 per cent of the 85.69 GHz continuum emission originates from free-free emission. The electron temperature is 5400 +/- 600 K, which is comparable to what has been measured near the centre of the Milky Way Galaxy. The star formation rate (SFR) based on the H42 alpha and 85.69 GHz free-free emission (and using a distance of 3.8Mpc) is 4.35 +/- 0.25 M-circle dot yr(-1). This is consistent with the SFR from the total infrared flux and with previous measurements based on recombination line emission, and it is within a factor of similar to 2 of SFRs derived from radio data. The Spitzer Space Telescope 24 mu m data and Widefield Infrared Survey Explorer 22 mu m data yield SFRs similar to 10x lower than the Atacama Large Millimeter/submillimeter Array measurements, most likely because the mid-infrared data are strongly affected by dust attenuation equivalent to A(V) = 150. These results indicate that SFRs based on mid-infrared emission may be highly inaccurate for dusty, compact circumnuclear starbursts.