Accurate masses and radii for normal stars derived from observations of detached eclipsing binary stars are of fundamental importance for testing stellar models and may be useful for calibrating free parameters in these model if the masses and radii are sufficiently precise and accurate. We aim to measure precise masses and radii for the stars in the bright eclipsing binary AI Phe, and to quantify the level of systematic error in these estimates. We use several different methods to model the Transiting Exoplanet Survey Satellite (TESS) light curve of AI Phe combined with spectroscopic orbits from multiple sources to estimate precisely the stellar masses and radii together with robust error estimates. We find that the agreement between different methods for the light-curve analysis is very good but some methods underestimate the errors on the model parameters. The semi-amplitudes of the spectroscopic orbits derived from spectra obtained with modern echelle spectrographs are consistent to ´ within 0.1 per cent. The masses of the stars in AI Phe are M1 = 1.1938 ± 0.0008 M and M2 = 1.2438 ± 0.0008 M, and the radii are R1 = 1.8050 ± 0.0022 R and R2 = 2.9332 ± 0.0023 R. We conclude that it is possible to measure accurate masses and radii for stars in bright eclipsing binary stars to a precision of 0.2 per cent or better using photometry from TESS and spectroscopy obtained with modern echelle spectrographs. We provide recommendations for publishing masses and radii of ´ eclipsing binary stars at this level of precision.
Accepted for publication in MNRAS. 12 pages, 4 tables and 8 figures