Compact Galaxies with Active Star Formation from the SDSS Data Release 16: Star-Formation Rates Based on the Luminosities of Forbidden Emission Lines in the Optical Range

We obtained equations for determining the star-formation rate in local compact star-forming galaxies from the SDSS Data Release 16 using luminosities of the forbidden emission lines [O II] λ 372.7 nm, [Ne III] λ 386.8 nm, [O III] λ 495.9 nm, and [O III] λ 500.7 nm and their combinations. The equations are based on the assumption that the star-formation rates, determined from the luminosity of the forbidden lines and H_β emission lines, are equal. This approach is especially useful because the observation of H_β emission is not always possible. For example, in galaxies with redshift z > 1, this line goes beyond the optical range, and the [O II] λ 372.7 nm line, the [Ne III] λ 386.8 nm line, or their combination can be used instead. On the other hand, in many studies of faint objects using low-resolution spectra, the H_β line merges with the stronger [O III] λ 495.9 nm and [O III] λ 500.7 nm lines. In these cases, [O III] lines and their combination can be used to determine the rate of star formation. The resulting equations can be applied to compact star-forming galaxies in a wide range of redshifts.