Near-infrared [Fe ii] emission from supernova remnants and the supernova rate of starburst galaxies

In an effort better to calibrate the supernova rate of starburst galaxies as determined from near-infrared Fe  ii ] features, we report on a Fe  ii ] λ 1.644 μm line-imaging survey of a sample of 42 optically selected supernova remnants (SNRs) in M33. A wide range of Fe  ii ] luminosities are observed within our sample (from less than 6 to 695 L_⊙). Our data suggest that the bright Fe  ii ] SNRs are entering the radiative phase and that the density of the local interstellar medium (ISM) largely controls the amount of Fe  ii ] emission. We derive the following relation between the Fe  ii ] λ 1.644 μm line luminosity of radiative SNRs and the electronic density of the post-shock gas, n _e: L _{Fe  ii ]}     (cm^?3). We also find a correlation in our data between L _{Fe  ii ]} and the metallicity of the shock-heated gas, but the physical interpretation of this result remains inconclusive, as our data also show a correlation between the metallicity and n _e. The dramatically higher level of Fe  ii ] emission from SNRs in the central regions of starburst galaxies is most likely due to their dense environments, although metallicity effects might also be important. The typical Fe  ii ]-emitting lifetime of a SNR in the central regions of starburst galaxies is found to be of the order of 10⁴ yr. On the basis of these results, we provide a new empirical relation allowing the determination of the current supernova rate of starburst galaxies from their integrated near-infrared Fe  ii ] luminosity.