2023 DA1 | Distance to the LMC from eclipsing binaries

In 2019 an international collaboration led by Polish astronomers measured the distance to the Large Magellanic Cloud (LMC) with very high precision and accuracy, setting the zero point of the extragalactic distance scale. They measured distances to 20 eclipsing binaries in the LMC using the surface brightness of a star,

where $m_V$ is the V magnitude and $\theta$ the angular diameter in milliarcseconds (mas). $S_V$ is the magnitude a star would have if its angular diameter were 1 mas.

There is an empirical relation between $S_V$ and the colour $m_V - m_K$ for G and K giants. In the paper it is shown as a scatter plot of about 30 stars lying tightly along a straight line, from $(m_V - m_K, S_V)\approx(2.05, 5.38)$ to $(2.73, 6.29)$. Two well-separated points read off that figure are $(2.07, 5.41)$ and $(2.71, 6.28)$.

The distance to an eclipsing binary follows from comparing the physical radii of its components (from photometry and spectroscopy) with the angular diameters predicted by the $S_V$–$(m_V - m_K)$ relation. The table gives three detached eclipsing binaries: $R_1$, $R_2$ are the component radii, $V_{1+2}$ and $K_{1+2}$ the combined magnitudes, and $L_2/L_1$ the luminosity ratio in each band.

Apply this method to all three systems and calculate the distance to the LMC in kiloparsecs. Estimate the total error of the result. Assume the fit of the $S_V$ relation contributes a bias of up to 0.8% to all measurements simultaneously. Keep at least three significant figures. Interstellar extinction is negligible and the angular size of the LMC is small. (50)