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.

Stellar pulsation theory provides a means of determining the masses of pulsating classical Cepheid supergiants-it is the pulsation that causes their luminosity to vary. Such pulsational masses are found to be smaller than the masses derived from stellar evolution theory: this is the Cepheid mass discrepancy problem, for which a solution is missing. An independent, accurate dynamical mass determination for a classical Cepheid variable star (as opposed to type-II Cepheids, low-mass stars with a very different evolutionary history) in a binary system is needed in order to determine which is correct. The accuracy of previous efforts to establish a dynamical Cepheid mass from Galactic single-lined non-eclipsing binaries was typically about 15-30% (refs 6, 7), which is not good enough to resolve the mass discrepancy problem. In spite of many observational efforts, no firm detection of a classical Cepheid in an eclipsing double-lined binary has hitherto been reported. Here we report the discovery of a classical Cepheid in a well detached, double-lined eclipsing binary in the Large Magellanic Cloud. We determine the mass to a precision of 1% and show that it agrees with its pulsation mass, providing strong evidence that pulsation theory correctly and precisely predicts the masses of classical Cepheids.

RR Lyrae pulsating stars have been extensively used as tracers of old stellar populations for the purpose of determining the ages of galaxies, and as tools to measure distances to nearby galaxies 1,2,3 . There was accordingly considerable

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%.

A novel method of analysis of double-lined eclipsing binaries containing a radially pulsating star is presented. The combined pulsating-eclipsing light curve is built up from a purely eclipsing light curve grid created using an existing modeling tool. For every pulsation phase the instantaneous radius and surface brightness are taken into account, being calculated from the disentangled radial velocity curve of the pulsating star and from its out-of-eclipse pulsational light curve and the light ratio of the components, respectively. The best model is found using the Markov Chain Monte Carlo method.The method is applied to the eclipsing binary Cepheid OGLE-LMC-CEP-0227 (P puls = 3.80 d, P orb = 309 d). We analyze a set of new spectroscopic and photometric observations for this binary, simultaneously fitting OGLE V-band, I-band and Spitzer 3.6 µm photometry. We derive a set of fundamental parameters of the system significantly improving the precision comparing to the previous results obtained by our group. The Cepheid mass and radius are M 1 = 4.165 ± 0.032 M ⊙ and R 1 = 34.92 ± 0.34 R ⊙ , respectively.For the first time a direct, geometrical and distance-independent determination of the Cepheid projection factor is presented. The value p =1.21 ± 0.03(stat.) ± 0.04(syst.) is consistent with theoretical expectations for a short period Cepheid and interferometric measurements for δ Cep. We also find a very high value of the optical limb darkening coefficients for the Cepheid component, in strong disagreement with theoretical predictions for static atmospheres at a given surface temperature and gravity.

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,