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Fig. 15

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Summary of the analytical laws we established. The dashed red lines correspond to the analysis when using only the 1.0 M simulations, the blue lines the analysis when using only the 1.5 M simulations. For the correlation between the pulsation period and the effective temperature, all available simulations were used. In the left part, we have the laws between the photocentre displacement and the pulsation period from the simulations. We assume that the parallax uncertainty, σϖ, is equivalent to σP as σP is the main contributor of the σϖ budget. In the right part, we have the laws between the pulsation period and the stellar parameters (log(g), Teff, R). Combining these laws provides the parameters of the Mira stars based on the parallax uncertainty. The relative difference between the calculated and the observational pulsation periods can be used to estimate the uncertainties of the stellar parameters.

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