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 (K-Z) relation for dwarf irregular galaxies, over a large range of magnitudes, -20.5 < M_K < -13.5, using a combination of K photometry from either the 2-micron all sky survey (2MASS) or the recent study of Vadivescu er al. (2005), and metallicities derived mainly with the T_e method, from several different studies. We then use this newly-derived relation, together with published K_s 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 catalogue a new member of HCG 31, namely "R", situated ~40 kpc north of the group center, composed by a ring of H alpha knots which coincides with a peak in HI. This object is a deviant point in the K-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, result that is expected in a scenario where 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 post-starburst phase.