Unveiling the spectacular over 24-hour flare of star CD-36 3202

Abstract: We studied the light curve of the star CD-36 3202, observed by TESS for the presence of stellar spots and to analyze the rotationally modulated flare. We mainly wanted to model the light curve of this flare and estimate its location regarding stellar spots. The flare lasted approximately 27$\,$h. Using our tool new \texttt{findinc_mc} we managed to estimate the inclination angle of the star to $70^\circ\pm8^\circ$. With \texttt{BASSMAN} we modeled the light curve of the CD-36 3202 and we estimated that three spots are present on the surface of this star. The mean temperature of the spots was about $4000\pm 765\,$K, and the total spottedness was on average $11.61\%\pm0.13\,$\%. We created a new tool named \texttt{MFUEA} to model rotationally modulated flares. Using this software we estimated the latitude of the flare long-duration event equal to $69^{+2}_{-1}\,$deg in latitude. Our estimation of the flare's location was the first recreation of the exact position of a flare compared with the spots. The flare is placed 12$^\circ$ from the center of the coolest spot. This makes the flare related to the magnetic processes above the active region represented by the spot. Removing the effects of rotational modulation from the flare light curve allowed us to correct the estimation of bolometric energy released during the event from $(1.15\pm 0.35)\times 10^{35}\,$erg to $(3.99\pm 1.22)\times 10^{35}\,$erg.