On Benchmarking SRc $\alpha$ Ori using Period-Luminosity Relationship

We conducted a benchmarking analysis of the semi-regular pulsator and red supergiant $\alpha$ Ori. In its dimming episode last 2020, our observational results include the binned measurements from the space-based telescope SMEI collated. We report a long secondary period of $P_{\text{LSP}}$ = 2350 $\pm$ 10 d and a fundamental mode of pulsation of $P_0$ = 415 d $\pm$ 30 d, with a radial velocity amplitude of the FM at $A_{RV}$ = $2.21_{-0.50}^{+0.95}$ km s$^{-1}$. Meanwhile, we also detected the first overtone component of $P_1$ = 185 d. The derived harmonics of $\alpha$ Ori, including this newly acquired variation, support and align with the current literature. At $\sim$2.20 $\pm$ 0.10 $\mu$m, we acquired Near-Infrared $K$-band photometric measurements from several catalogs and surveys, calibrated accordingly. Our assigned inherent color lies midway between the extremes reported in existing literature. Additionally, we determined a weighted excess color index of $E_{(B-V)}$ = 0.340, and using a $K$-extinction factor of $R_K$ = 0.382, we derived an extinction of $A_K$ = 0.130. By subtracting extinction from all $K$-band photometric measurements and applying both the linearity and the newly derived distance from previous studies, our analysis yields a luminosity of log($L$/$L_{\odot}$) = 5.00 $\pm$ $0.15_{(-0.45)}^{(+0.48)}$ for $\alpha$ Ori. In turn, this allowed us to conduct the benchmarking scheme alongside the data from existing reports that are stitched together using Period-Luminosity ($P$-$L$) relationship. This results in a best-fit relation of log($L$/$L_{\odot}$) = (7.26 $\pm$ 0.10) log $P$ + ($-14.10$ $\pm$ 0.25) and reveals that $\alpha$ Ori can be situated at the lower bound of the 18 $M_{\odot}$ regime due to current pulsation trends.