Asteroseismology of Long-Period Variables with OGLE-IV data: Using Global Seismic Parameters as Luminosity Indicators

Long-period variables (LPVs) are high-luminosity red giants or supergiants with pulsation periods ranging from days to years. Many LPVs in the Large Magellanic Cloud (LMC) and Galactic Bulge (BLG) have been continuously observed over a time span of 26 years by the Optical Gravitational Lensing Experiment (OGLE) survey. Using OGLE-IV data, we applied Gaussian Processes with kernels tailored for solar-like oscillations to extract two global asteroseismic parameters: the frequency of maximum power (numax) and the large frequency separation (Dnu), for LPVs with primary mode periods (P1) between 10 and 100 days in the LMC and BLG. We found that the numax-Dnu relation for LPVs in this work aligns with that of lower-luminosity Kepler red giants, confirming that the pulsations of these LPVs are likely solar-like. We found that numax and Dnu can serve as luminosity indicators. Compared to P1, numax and Dnu exhibit significantly tighter correlations with the absolute magnitude in the 2MASS K_s band (M_{K}), with corresponding scatter of 0.27 mag and 0.21 mag, respectively. Using the calibrated numax-mk and Dnu-mk relations for LPVs in the LMC, we determined the M_{K} values for individual stars in the BLG. By accounting for extinction, we further calculated the distances to 4,948 BLG stars. The peak of the resulting distance distribution corresponds to an estimated distance to the Galactic center of approximately 9.1 kpc, which appears to be overestimated, suggesting that the seismic luminosity relation calibrated from the LMC may not be directly applicable to BLG stars.