The K Luminosity-Metallicity Relation for Dwarf Galaxies and the Tidal Dwarf Galaxies in the Tails of HCG 31

We determine a K-band luminosity-metallicity (L-Z) relation for dwarf irregular galaxies over a large range of magnitudes, -20.5 < MK < -13.5, using a combination of K photometry from either the Two Micron All Sky Survey or the recent study of Vaduvescu et al., and metallicities derived mainly with the Te-method, from several different studies. We then use this newly derived relation, together with published Ks photometry and our new spectra of objects in the field of HCG 31, to discuss the nature of the possible tidal dwarf galaxies of this group. We catalog a new member of HCG 31, namely, 'R,' situated ~50 kpc north of the group center and composed of a ring of Ha knots that coincides with a peak in H I. This object is a deviant point in the K-band L-Z relation (it has too high metallicity for its luminosity), and its projected distance to the parent galaxy and large gas reservoir makes it one of the most promising tidal dwarf galaxy candidates of HCG 31, together with object F. The subsystems A1, E, F, H, and R all have metallicities similar to that of the galaxies A+C and B, a result that is expected in a scenario in which those were formed from material expelled from the central galaxies of HCG 31. While objects A1, E, and H will most probably fall back onto their progenitors, F and R may survive as tidal dwarf galaxies. We find that two galaxies of HCG 31, G and Q, have A+em spectral signatures and are probably evolving toward a poststarburst phase. As a useful reference for future investigations, we include a compilation of the most important properties of all members of HCG 31 that were derived either in this work or in previous studies.