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.Comment: 32 pages, 4 figures - Submitted to AJ - A version of this paper with
full resolution figures can be found at
http://www.astro.iag.usp.br/~eduardo/HCG31-KZrelation.pd