The local star formation rate and radio luminosity density

We present a new determination of the local volume-averaged star formation rate from the 1.4-GHz luminosity function of star forming galaxies. Our sample, taken from the   B ≤12  Revised Shapley–Ames catalogue (231 normal spiral galaxies over an effective area of 7.1 sr) has ?100 per cent complete radio detections and is insensitive to dust obscuration and cirrus contamination. After removal of known active galaxies, the best-fitting Schechter function has a faint-end slope of  ?1.27±0.07  in agreement with the local H α luminosity function, characteristic luminosity   L ?=(2.6±0.7)×10²² W Hz^?1  and density   φ ?=(4.8±1.1)×10^?4 Mpc^?3.  The inferred local radio luminosity density of  (1.73±0.37±0.03)×10¹⁹ W Hz^?1 Mpc^?3  (Poisson noise, large-scale structure fluctuations) implies a volume-averaged star formation rate ～2 times larger than the Gallego et al. H α estimate, i.e.   ρ _1.4 GHz=(2.10±0.45±0.04)×10^?2 M_⊙ yr^?1 Mpc^?3  for a Salpeter initial mass function from  0.1–125 M_⊙  and Hubble constant of 50 km s^?1 Mpc^?1. We demonstrate that the Balmer decrement is a highly unreliable extinction estimator, and argue that optical–ultraviolet (UV) star formation rates (SFRs) are easily underestimated, particularly at high redshift.