In the era of precision cosmology, it is essential to empirically determine the Hubble constant with an accuracy of one per cent or better 1 . At present, the uncertainty on this constant is dominated by the uncertainty in the calibration of the Cepheid period -luminosity relationship 2, 3 (also known as Leavitt Law). The Large Magellanic Cloud has traditionally served as the best galaxy with which to calibrate Cepheid period-luminosity relations, and as a result has become the best anchor point for the cosmic distance scale 4,5 . Eclipsing binary systems composed of late-type stars offer the most precise and accurate way to measure the distance to the Large Magellanic Cloud. Currently the limit of the precision attainable with this technique is about two per cent, and is set by the precision of the existing calibrations of the surface brightness -colour relation 5,6 . Here we report the calibration of the surface brightness-colour relation with a precision of 0.8 per cent. We use this calibration to determine the geometrical distance to the Large Magellanic Cloud that is precise to 1 per cent based on 20 eclipsing binary systems. The final distane is 49.59 ± 0.09 (statistical) ± 0.54 (systematic) kiloparsecs.All data are available upon request from G.P. Extended DataFig.1. Comparison of our relation with the relation of Di Benedetto obtained for giant stars 6 . Top panel, comparison of relations: data points show our results, with the fitted line shown in blue. The blue shaded area represents our obtained r.m.s. scatter of 0.018 mag. The green line is from ref. 6 . Very good agreement is demonstrated. Both S V and (V − K) 0 are in magnitudes. S V physically corresponds to the V band magnitude of a red giant star whose angular diameter is 1 mas. The error bars correspond to 1σ errors. Bottom panel, observed minus calculated values. Extended Data Fig.2. Observed minus calculated surface brightness versus metallicity 6 , [Fe/H]. In a relatively large range of metallicities (about 1 dex) no correlation is found. A formal linear fit gives O − C = 0.0009[Fe/H] -0.002 dex with coefficient of determination R 2 = 0.0001. Fig.3. Example of Monte Carlo simulations for one of our objects, ECL-12669. We computed 10,000 models with the JKTEBOP code 77 from which we obtained statistical uncertainties on the radii R 1 and R 2 , the orbital inclination i, the phase shift φ, the surface brightness ratio j 21 , radial velocity semi-amplitudes K 1 and K 2 , and the systemic velocities γ 1 and γ 2 . For every model we computed the distance modulus converting j 21 into temperature ratio T 2 /T 1 by using Popper's calibration 78 and our original solution with the Wilson-Devinney code 79 . We plot the number of calculated models versus distance modulus (m − M). The dashed line is the best fitted Gaussian and the blue line is the distance determined for this object. The intrinsic (V − K) 0 colours used to estimate the angular diameters of the components were computed using a temperature-colour calibration 28 . Extended DataExtended Data...

We present a new study of late-type eclipsing binary stars in the Small Magellanic Cloud (SMC) undertaken with the aim of improving the distance determination to this important galaxy. A sample of 10 new detached, double-lined eclipsing binaries identified from the OGLE variable star catalogs and consisting of F- and G-type giant components has been analyzed. The absolute physical parameters of the individual components have been measured with a typical accuracy of better than 3%. All but one of the systems consist of young and intermediate population stars with masses in the range of 1.4 to 3.8 M ☉. This new sample has been combined with five SMC eclipsing binaries previously published by our team. Distances to the binary systems were calculated using a surface brightness—color calibration. The targets form an elongated structure, highly inclined to the plane of the sky. The distance difference between the nearest and most-distant system amounts to 10 kpc with the line-of-sight depth reaching 7 kpc. We find tentative evidence of the existence of a spherical stellar substructure (core) in the SMC coinciding with its stellar center, containing about 40% of the young and intermediate age stars in the galaxy. The radial extension of this substructure is ∼1.5 kpc. We derive a distance to the SMC center of D SMC = 62.44 ± 0.47 (stat.) ±  0.81 (syst.) kpc corresponding to a distance modulus (m − M)SMC = 18.977 ± 0.016 ± 0.028 mag, representing an accuracy of better than 2%.

We present reddening maps of the Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC), based on color measurements of the red clump. Reddening values of our maps were obtained by calculating the difference of the observed and intrinsic color of the red clump in both galaxies. To obtain the intrinsic color of the red clump, we used reddenings obtained from late-type eclipsing binary systems, measurements for blue supergiants and reddenings derived from Strömgren photometry of B-type stars. We obtained intrinsic color of the red clump (V − I) 0 = 0.838 ± 0.034 mag in the LMC, and (V − I) 0 = 0.814 ± 0.034 mag in the SMC. We prepared our map with 3 arcmin resolution,