On the origin of variability in $\alpha$ Cygni variable $\epsilon$ Ori (HD 37128) using TESS observations and modelling

$\epsilon$ Ori (HD 37128) is an $\alpha$ Cygni variable characterized by irregular and small amplitude variations. From TESS observations, we find the presence of stochastic low-frequency variability in this star. We have constructed a sequence of models for this star in the mass range of 30 to 70 M$_{\odot}$, using recently derived values of luminosity (log $(L/L_{\odot})$ = 5.92) and effective temperature. In these considered models, both radial and non-radial linear stability analyses have been performed. Low-order radial modes are excited in models having mass below 62 M$_{\odot}$. These radially excited modes have periods ranging from 6.8 days for the fundamental mode to a few hours for higher-order modes. Similar to the case of radial modes, several non-radial modes are found to be unstable in models having higher luminosity-to-mass ratios. Linear stability analysis for the case of $l$ = 2 and $l$ = 4 reveals the presence of a strongly unstable mode in models having a mass below 40 M$_{\odot}$. This mode is found to be unstable in all the considered models and the strength of the instability varies as a function of harmonic degree. The non-adiabatic reversible approximation reveals that the origin of instabilities associated with the low-order modes is indeed linked with strange modes. To find out the consequence of radial instabilities, non-linear numerical simulations have been performed in selected models of $\epsilon$ Ori. In the non-linear regime, these instabilities lead to the envelope inflation, finite amplitude regular and irregular pulsations consistent with an $\alpha$ Cygni variable.