χ² confidence regions in the neutron star mass and radius plane for the CCO in HESS J1731−347 obtained with the carbon atmosphere models. The plotted contours correspond to the 50, 68, and 90% confidence level. The black contours (bottom left) correspond to the fixed distance of 3.2 kpc, the green contours (top right) to 4.5 kpc. The crosses indicate the corresponding χ²-minima. The shaded areas in the top left and bottom right of the plot indicate the regions excluded by the requirements of causality and from the fastest rotation-powered pulsar known so far, PSR J1748−2446ad (716 Hz).