In the era of precision cosmology, it is essential to determine the Hubble constant to an accuracy of three per cent or better. At present, its uncertainty is dominated by the uncertainty in the distance to the Large Magellanic Cloud (LMC), which, being our second-closest galaxy, serves as the best anchor point for the cosmic distance scale. Observations of eclipsing binaries offer a unique opportunity to measure stellar parameters and distances precisely and accurately. The eclipsing-binary method was previously applied to the LMC, but the accuracy of the distance results was lessened by the need to model the bright, early-type systems used in those studies. Here we report determinations of the distances to eight long-period, late-type eclipsing systems in the LMC, composed of cool, giant stars. For these systems, we can accurately measure both the linear and the angular sizes of their components and avoid the most important problems related to the hot, early-type systems. The LMC distance that we derive from these systems (49.97 ± 0.19 (statistical) ± 1.11 (systematic) kiloparsecs) is accurate to 2.2 per cent and provides a firm base for a 3-per-cent determination of the Hubble constant, with prospects for improvement to 2 per cent in the future.

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 distance determination to the Small Magellanic Cloud (SMC) based on an analysis of four detached, long period, late type eclipsing binaries discovered by the OGLE Survey. The components of the binaries show negligible intrinsic variability. A consistent set of stellar parameters was derived with low statistical and systematic uncertainty. The absolute dimensions of the stars are calculated with a precision of better than 3%.The surface brightness -infrared color relation was used to derive the distance to each binary. The four systems clump around a distance modulus of (m − M ) = 18.99 with a dispersion of only 0.05 mag. Combining these results with the distance published by Graczyk et al. for the eclipsing binary OGLE SMC113.3 4007 we obtain a mean distance modulus to the SMC of 18.965 ± 0.025 (stat.) ± 0.048 (syst.) mag. This corresponds to a distance of 62.1 ± 1.9 kpc, where the error includes both uncertainties. Taking into account other recent published determinations of the SMC distance we calculated the distance modulus difference between the SMC and the LMC equal to 0.458 ± 0.068 mag. Finally we advocate µ SMC = 18.95 ± 0.07 as a new "canonical" value of the distance modulus to this galaxy.