Period-luminosity and period-luminosity-colour relations for Mira variables at maximum light

In this paper we discuss the evidence for a period-luminosity (PL) relation and periodluminosity-colour (PLC) at maximum light for Mira variables. We confirm the existence of such relations in the J, H and K bands, and also based on bolometric magnitudes, for oxygen-rich (O) and carbon-rich (C) Miras in the LMC. We demonstrate that in the J and H bands the maximum light PL relations have a significantly smaller dispersion than their counterparts at mean light, while the K band and bolometric PL relations have a dispersion comparable to that at mean light. In the J, H and K bands the fitted PL relations for the O Miras are found to have smaller dispersion than those for the C Miras, at both mean and maximum light, while the converse is true for the relations based on bolometric magnitudes. The reduction in dispersion between mean and maximum light is generally found to be more significant in the J, H and bolometric bands than in the K band – in which the mean PL relations display the smallest dispersion. The inclusion of a non-zero log period term in the regression fits is found to be highly significant in all cases except that of the C Miras in the J band, for which the data are found to be consistent with having constant absolute magnitude. Moreover, if we consider only C Miras with periods in excess of 250 days, then the data are also substantially more consistent with constant absolute magnitude at mean and maximum light in the H, K and bolometric wavebands. This suggests the possibility of employing C Miras as standard candles. We suggest both a theoretical justification for the existence of Mira PL relations at maximum light and a possible explanation of why these relations should have a smaller dispersion than at mean light. The existence of such maximum light relations offers the possibility of extending the range and improving the accuracy of the Mira distance scale to Galactic globular clusters and to other galaxies.