Asteroseismology of the fast-rotating high-amplitude $\delta$ Scuti star V2367 Cygni

We present the comprehensive analysis of the high-amplitude $\delta$ Sct star V2367 Cygni. Firstly, we perform the frequency analysis for the whole available set of the {\it Kepler} and {\it TESS} photometry. Most of the frequency peaks are harmonics or combinations of the three known independent frequencies with the highest amplitudes, i.e., $\nu_1=5.66106$\,d$^{-1}$, $\nu_2=7.14898$\,d$^{-1}$ and $\nu_3=7.77557$\,d$^{-1}$. The total number of independent frequencies is 26 and 25 from the {\it Kepler} and {\it TESS} light curve, respectively. Then, using the $UBVRI$ time-series photometry, we unambiguously identify the dominant frequency $\nu_1$ as the radial mode, whereas in the case of frequencies $\nu_2$ and $\nu_3$ the most probable mode degrees are $\ell=0$ or $\ell=2$. However, only the frequency $\nu_2$ can be associated with a radial mode, and only if higher order effects of rotation are taken into account. Including the rotational mode coupling, we constructed complex seismic models of V2367\,Cyg, which fit $\nu_1$ and $\nu_2$ as radial modes, and reproduce the amplitude of bolometric flux variations (the parameter $f$) for the dominant mode. The empirical values of $f$ are derived from the $UBVRI$ amplitudes and phases. We rely on the Bayesian analysis based on Monte Carlo simulations to derive constraints on evolutionary stage, mass, rotation, overshooting from the convective core and efficiency of convective transport in the envelope. Our seismic analysis clearly indicates that V2367\,Cyg is in a post-MS phase of evolution. This is the first extensive seismic modelling that takes into account the effect of rotational coupling between pulsation modes.