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Evidence of Multiple Slow Acoustic Oscillations in the Stellar Flaring Loops of Proxima Centauri

We present the first observational evidence of multiple slow acoustic oscillations in the post flaring loops of the corona of Proxima Centauri using XMM-Newton observations. We find the signature of periodic oscillations localized in the decay phase of the flare in its soft (0.3-10.0 keV) X-ray emissions. Using the standard wavelet tool, we find the multiple periodicities of 1261 s and 687 s. These bursty oscillations persist for durations of 90 minutes and 50 minutes, respectively, for more than 4 cycles. The intensity oscillations with the period of 1261 s may be the signature of the fundamental mode of slow magnetoacoustic waves with the phase-speed of 119 km s$^{-1}$ in the loop of the length 7.5$\times 10^{9}$ cm heated initially to obtain the flare peak temperature of 33 MK and later cooled down in the decay phase maintained at the average temperature of 7.2 MK. The other period of 687 s may be associated with the first overtone of slow magnetoacoustic oscillations in the flaring loop. The fundamental mode oscillations show a dissipation with damping time of 47 min. The period ratio P$_{1}$/P$_{2}$ is found to be 1.83 indicating that such oscillations are most likely excited in longitudinal density stratified stellar loops. We estimate the density scale height of stellar loop system as 22.6 Mm, which is smaller than the hydrostatic scale height of the hot loop system, and implies the existence of non-equilibrium conditions.