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 .