Fundamental effective temperature measurements for eclipsing binary stars - V. The circumbinary planet system EBLM J0608-59

EBLM J0608$-$59/TOI-1338/BEBOP-1 is a 12$^{\rm th}$-magnitude, F9 V star in an eclipsing binary with a much fainter M dwarf companion on a wide, eccentric orbit (P = 14.6 d). The binary is orbited by two circumbinary planets: one transiting on a 95-d orbit and one non-transiting on a 215-d orbit. We have used high-precision photometry from the TESS mission combined with direct mass measurements for the two stars published recently to measure the following model-independent radii: $R_1 = 1.32 \pm 0.02 {\rm R}_{\odot }$, $R_2 = 0.309 \pm 0.004 {\rm R}_{\odot }$. Using $R_1$ and the parallax from Gaia EDR3, we find that this star's angular diameter is $\theta = 0.0309 \pm 0.0005$ mas. The apparent bolometric flux of the primary star corrected for both extinction and the contribution from the M dwarf ($\lt 0.4$ per cent) is ${\mathcal {F}}_{{\oplus },0} = (0.417\pm 0.005)\times 10^{-9}$ erg cm$^{-2}$ s$^{-1}$. Hence, this F9 V star has an effective temperature $T_{\rm eff,1} = 6031{\rm \, K} \pm 46{\rm \, K\, (rnd.)} \pm 10 {\rm \, K\, (sys.)}$. EBLM J0608$-$59 is an ideal benchmark star that can be added to the sample of such systems we are establishing for 'end-to-end' tests of the stellar parameters measured by large-scale spectroscopic surveys.