Fundamental effective temperature measurements for eclipsing binary stars -- VI. Improved methodology and application to the circumbinary planet host star BEBOP-3

BEBOP-3 is detached eclipsing binary star that shows total eclipses of a faint M~dwarf every 13.2 days by a 9$^{\rm th}$-magnitude F9V star. High precision radial velocity measurements have recently shown that this binary star is orbited by a planet with an orbital period $\approx 550$ days. The extensive spectroscopy used to detect this circumbinary planet has also been used to directly measure the masses of the stars in the eclipsing binary. We have used light curves from the TESS mission combined with these mass measurements to directly measure the following radii and surface gravities for the stars in this system: $R_1 = 1.386 \pm 0.010\,R_{\odot}$, $\log g_1 = 4.190 \pm 0.004$, $R_2 = 0.274 \pm 0.002\,R_{\odot}$, $\log g_2 = 4.979 \pm 0.002$. We describe an improved version of our method to measure the effective temperatures (T$_{\rm eff}$) of stars in binary systems directly from their angular diameters and bolometric fluxes. We measure T$_{\rm eff,1} = 6065{\rm\,K} \pm 44\,{\rm K}$ and T$_{\rm eff,2} = 3191{\rm\,K} \pm 40\,{\rm K}$ for the stars in BEBOP-3 using this method. BEBOP-3 can be added to our growing sample of stars that can be used test the accuracy of spectroscopic and photometric methods to estimate T$_{\rm eff}$ and $\log g$ for solar-type stars.