Intensity interferometry of P Cygni in the Hα emission line: towards distance calibration of LBV supergiant stars

We present intensity interferometry of the luminous blue variable P Cyg in the light of its H$\alpha$ emission performed with 1\,m-class telescopes. We compare the measured visibility points to synthesized interferometric data based on the CMFGEN physical modeling of a high-resolution spectrum of P Cyg recorded almost simultaneously with our interferometry data. Tuning the stellar parameters of P Cyg and its H$\alpha$ linear diameter we estimate the distance of P Cyg as $1.56\pm0.25$~kpc, which is compatible within $1\sigma$ with $1.36\pm0.24$~kpc reported by the Gaia DR2 catalogue of parallaxes recently published. Both values are significantly smaller than the canonic value of $1.80\pm0.10$~kpc usually adopted in literature. Our method used to calibrate the distance of P Cyg can apply to very massive and luminous stars both in our galaxy and neighbour galaxies and can improve the so-called Wind-Momentum Luminosity relation that potentially applies to calibrate cosmological candles in the local Universe.