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...

Context. The universality of the Cepheid period-luminosity (PL) relations has been under discussion since metallicity effects were assumed to play a role in the value of the intercept and, more recently, of the slope of these relations. Aims. The goal of the present study is to calibrate the Galactic PL relations in various photometric bands (from B to K) and to compare the results to the well-established PL relations in the LMC. Methods. We use a set of 59 calibrating stars, the distances of which are measured using five different distance indicators: Hubble Space Telescope and revised Hipparcos parallaxes, infrared surface brightness and interferometric Baade-Wesselink parallaxes, and classical Zero-Age-Main-Sequence-fitting parallaxes for Cepheids belonging to open clusters or OB stars associations. A detailed discussion of absorption corrections and projection factor to be used is given. Results. We find no significant difference in the slopes of the PL relations between LMC and our Galaxy. Conclusions. We conclude that the Cepheid PL relations have universal slopes in all photometric bands, not depending on the galaxy under study (at least for LMC and Milky Way). The possible zero-point variation with metal content is not discussed in the present work, but an upper limit of 18.50 for the LMC distance modulus can be deduced from our data.

In this paper, we present an improved theoretical scenario concerning near‐infrared and visual magnitudes of RR Lyr variables, as based on up‐to‐date pulsating models. New relations connecting V and K absolute magnitudes with periods, mass, luminosity and metal content are discussed separately for fundamental and first‐overtone pulsators. We also show that the V−K colours are predicted to supply tight constraints on the pulsator intrinsic luminosity. On this basis, we revisit the case of the prototype variable RR Lyr, showing that the parallax inferred by this new pulsational approach appears in close agreement with Hubble Space Telescope absolute parallax. Moreover, available K and V measurements for field and cluster RR Lyr variables with known reddening and metal content are used to derive a relation connecting the K absolute magnitude to period and metallicity (MK–[Fe/H]–log P) as well as a new calibration of the MV–[Fe/H] relation. The comparison between theoretical prescriptions and observations suggests that RR Lyr stars in the field and in galactic globular clusters (GGCs) should have quite similar evolutionary histories. The comparison between theory and observations also discloses a general agreement that supports the reliability of the current pulsational scenario. On the contrary, current empirical absolute magnitudes based on the Baade–Wesselink (BW) method suggest relations with a zero‐point which is fainter than is predicted by pulsation models, together with a milder metallicity dependence. However, preliminary results based on a new calibration of the BW method provided by Cacciari et al. (2000) for RR Cet and SW And appear in a much better agreement with the pulsational predictions.

Aims. We determine period-luminosity relations for Milky Way Cepheids in the optical and near-IR bands. These relations can be used directly as reference for extra-galactic distance determination to Cepheid populations with solar metallicity, and they form the basis for a direct comparison with relations obtained in exactly the same manner for stars in the Magellanic Clouds, presented in an accompanying paper. In that paper we show that the metallicity effect is very small and consistent with a null effect, particularly in the near-IR bands, and we combine here all 111 Cepheids from the Milky Way, the LMC and SMC to form a best relation. Methods. We employ the near-IR surface brightness (IRSB) method to determine direct distances to the individual Cepheids after we have recalibrated the projection factor using the recent parallax measurements to ten Galactic Cepheids and the constraint that Cepheid distances to the LMC should be independent of pulsation period. Results. We confirm our earlier finding that the projection factor for converting radial velocity to pulsational velocity depends quite steeply on pulsation period, p = 1.550− 0.186 log(P) in disagrement with recent theoretical predictions. We find PL relations based on 70 Milky Way fundamental mode Cepheids of M K = −3.33(±0.09)(log(P) − 1.0) − 5.66(±0.03), W VI = −3.26(±0.11)(log(P) − 1.0) − 5.96(±0.04). Combining the 70 Cepheids presented here with the results for 41 Magellanic Cloud Cepheids which are presented in an accompanying paper, we find M K = −3.30(±0.06)(log(P) − 1.0) − 5.65(±0.02), W VI = −3.32(±0.08)(log(P) − 1.0) − 5.92(±0.03). Conclusions. We delineate the Cepheid PL relation using 111 Cepheids with direct distances from the IRSB analysis. The relations are by construction in agreement with the recent HST parallax distances to Cepheids and slopes are in excellent agreement with the slopes of apparent magnitudes versus period observed in the LMC.