A revised period-luminosity relation for carbon Miras

The period-luminosity and period-K magnitude relations of carbon Miras in the Galaxy are derived. The procedure is a two-step process. First, the P-L and P-K relations of carbon Miras in the Large Magellanic Cloud (LMC) are derived from 54 spectroscopically confirmed carbon Miras with periods between 150 and 520 d. The slopes of these relations are assumed to hold for Miras in the Galaxy, an assumption which has proved valid for oxygen-rich Miras. Secondly, the zero-points of the Galactic P-L and P-K relations are determined by shifting the relations for the LMC Miras, assuming a distance modulus of 18.5 mag, and no correction for metallicity differences. An (uncertain) estimate for the zero-point of the P-L relation is derived by combining the observed peak of the period distribution of Galactic carbon Miras with the theoretically predicted peak of the carbon star luminosity function. A direct estimate is also made of the luminosity of the only carbon Mira known to have a normal binary companion. The zero-points derived by these two methods are consistent with that of shifting the LMC relation. The finally adopted P-L and P-K relations of Galactic carbon Miras are M(bol) = -2.59 log P + 2.02 and M(K) = -3.56 log P + 1.14.