Period$-$Absolute Magnitude Relations for Oxygen- and Carbon-rich Miras in the Large Magellanic Cloud based on the WISE and Spitzer mid-IR data

We present mid-infrared (mid-IR) period$-$luminosity relations (PLRs) for Mira variables in the Large Magellanic Cloud (LMC). We provide, for the first time, the relations for three WISE (W1, W2, W3) and four Spitzer ($[3.6]$, $[4.5]$, $[5.8]$, $[8.0]$) bands, separately for oxygen-rich (O-rich) and carbon-rich (C-rich) Miras. The models for PLRs have been selected between a linear fit, a double linear fit with a kink, and a quadratic fit using the Bayesian Information Criterion (BIC). Our PLRs have been transformed to the absolute scale by applying the OGLE reddening map of the LMC and the accurate LMC distance determined by the Araucaria Project. Our relations allow measuring distances to individual O-rich and C-rich Mira stars with the accuracy of $7\%$ and $11\%$, respectively. They are the most accurate Mira PLRs in the mid-IR to date.