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In the era of precision cosmology, it is essential to determine the Hubble constant empirically 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 the 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 a calibration of the surface brightness–colour relation with a precision of 0.8 per cent. We use this calibration to determine a geometrical distance to the Large Magellanic Cloud that is precise to 1 per cent based on 20 eclipsing binary systems. The final distance is 49.59 ± 0.09 (statistical) ± 0.54 (systematic) kiloparsecs. A new calibration of the surface brightness–colour relation of eclipsing binary stars gives a distance to the Large Magellanic Cloud that is precise to one per cent.

Observations of eight long-period, late-type eclipsing-binary systems composed of cool, giant stars are used to determine a distance to the Large Magellanic Cloud accurate to 2.2 per cent, providing a base for a determination of the Hubble constant to an accuracy of 3 per cent. Accurate distance to our nearest-neighbour galaxy The physical properties of stars in eclipsing binary systems can be accurately determined thanks to the intimate interactions between the two bodies, and by monitoring the fluctuating light from such systems it is possible to obtain accurate extragalactic distance measurement. This technique has now been used to determine the most accurate distance estimate yet for the Large Magellanic Cloud (LMC), our nearest-neighbour galaxy. The data from eight long-period, late-type eclipsing systems particularly suitable for this calibration technique suggest that the LMC is around 49.97 kiloparsecs from us, to an accuracy of 2.2%. The distance to the LMC is a key element in determining the Hubble constant, an important measure of the rate of expansion of the Universe. In the era of precision cosmology, it is essential to determine the Hubble constant to an accuracy of three per cent or better 1 , 2 . 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 2 , 3 . Observations of eclipsing binaries offer a unique opportunity to measure stellar parameters and distances precisely and accurately 4 , 5 . The eclipsing-binary method was previously applied to the LMC 6 , 7 , 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.

We discuss the high dispersion echelle observations of the hot binary companions of six Cepheids with known radial-velocity orbits that we have obtained with the STIS FUV E140H mode on board the Hubble Space Telescope, with the goal of determining the masses of these Cepheids. We discuss the stability and repeatability of the STIS echelle wavelength scale and other issues that may limit the final accuracy of our mass determinations.

We give an update on our long-term program of Galactic Cepheids started in 2012, whose goal is to measure the visual orbits of Cepheid companions. Using the VLTI/PIONIER and CHARA/MIRC instruments, we have now detected several companions, and we already have a good orbital coverage for several of them. By combining interferometry and radial velocities, we can now derive all the orbital elements of the systems, and we will be soon able to estimate the Cepheid masses.

The mass of a Cepheid is a fundamental parameter for studying the pulsation and evolution of intermediate-mass stars. But determining this variable has been a long-standing problem for decades. Detecting the companions (by spectroscopy or imaging) is a difficult task because of the brightness of the Cepheids and the close orbit of the components. So most of the Cepheid masses are derived using stellar evolution or pulsation modeling, but they differ by 10-20 %. Measurements of dynamical masses offer the unique opportunity to make progress in resolving this mass discrepancy. The first problem in studying binary Cepheids is the high contrast between the components for wavelengths longer than 0.5 μm, which make them single-line spectroscopic binaries. In addition, the close orbit of the companions (<40 mas) prevents us from spatially resolving the systems with a single-dish 8m-class telescope. A technique able to reach high spatial resolution and high-dynamic range is long-baseline interferometry. We have started a long-term program that aims at detecting, monitoring and characterizing physical parameters of the Cepheid companions. The GAIA parallaxes will enable us to combine interferometry with single-line velocities to provide unique dynamical mass measurements of Cepheids.

Cepheids are one of the most famous standard candles used to calibrate the Galactic distance scale. However, it is fundamental to develop and test independent tools to measure their distances, in order to reach a better calibration of their period-luminosity (P-L) relationship. We present here the first results obtained with the Integrated Parallax of Pulsation (IPoP) method, an extension of the classical Baade-Wesselink method that derives the distance by making a global modelisation of all the available data. With this method we aim to reach a 2% accuracy on distance measurements. Cepheid masses are also an essential key for our comprehension of those objects. We briefly present an original approach to derive observational constraint on Cepheid masses. Unfortunately, it does not lead to promising results.

Optical interferometry is the only technique giving access to milli-arcsecond (mas) resolution at infrared wavelengths. For Cepheids, this is a powerful and unique tool to detect the orbiting companions and the circumstellar envelopes (CSE). CSEs are interesting because they might be used to trace the Cepheid evolution history, and more particularly they could impact the distance scale. Cepheids belonging to binary systems offer an unique opportunity to make progress in resolving the Cepheid mass discrepancy. The combination of spectroscopic and interferometric measurements will allow us to derive the orbital elements, distances, and dynamical masses. Here we focus on recent results using 2- to 6-telescopes beam combiners for the Cepheids X Sgr, T Mon and V1334 Cyg.

We aim to measure very precise and accurate model-independent masses and distances of detached binary stars. Precise masses at the \\(< 1\\)% level are necessary to test and calibrate stellar interior and evolution models, while precise and independent orbital parallaxes are essential to check for the next Gaia data releases. We combined RV measurements with interferometric observations to determine orbital and physical parameters of ten double-lined spectroscopic systems. We report new relative astrometry from VLTI/GRAVITY and, for some systems, new VLT/UVES spectra to determine the radial velocities of each component. We measured the distance of ten binary systems and the mass of their components with a precision as high as 0.03% (average level 0.2%). They are combined with other stellar parameters (effective temperatures, radii, flux ratios, etc.) to fit stellar isochrones and determine their evolution stage and age. We also compared our orbital parallaxes with Gaia and showed that half of the stars are beyond \\(1\\sigma\\) with our orbital parallaxes; although, their RUWE is below the frequently used cutoff of 1.4 for reliable Gaia astrometry. By fitting the telluric features in the GRAVITY spectra, we also estimated the accuracy of the wavelength calibration to be \\(\\sim 0.02\\)% in high and medium spectral resolution modes. We demonstrate that combining spectroscopic and interferometric observations of binary stars provides extremely precise and accurate dynamical masses and orbital parallaxes. As they are detached binaries, they can be used as benchmark stars to calibrate stellar evolution models and test the Gaia parallaxes.

Aims: We derive SBCRs for classical Cepheids in the Milky Way and in the Magellanic Clouds using the photometric data available in the Gaia database, and we quantify the metallicity effect. Methods: We first selected the data on the basis of a number of quality criteria and chose the best photometric data and the best parallaxes available in Gaia for Milky Way classical Cepheids. Secondly, we compiled an extensive list of period-radius (PR) relations available in the literature, and we also provide a new PR relation based on interferometric data in our previous work. Thirdly, combining the radius of classical Cepheids with distance estimates (based on Gaia parallaxes for the Milky Way and on eclipsing binaries for the Magellanic Clouds), we derived the surface brightness and colour of about 1700 classical Cepheids. Results: We first derived a new PR relation based on interferometric data and distances from the literature of seven classical Cepheids: \\(\\mathrm{\\log(R/R_{\\odot}) = 1.133_{\\pm 0.019} + 0.688_{\\pm 0.016} log(P)}\\). The metallicity does not affect the PR relations. Secondly, we calculated three different SBCRs for the Milky Way and Large and Small Magellanic Cloud classical Cepheids based on this new PR relation that clearly show the dependence of the metallicity on the SBCR based on Gaia magnitudes alone. Finally, we derived relations between the slopes, the zero points (ZP), and the metallicity ([Fe/H]) of these three SBCRs: \\(\\mathrm{Slope_{SBCR}=-0.0663_{\\pm 0.0121} [Fe/H] - 0.3010_{\\pm 0.0030}}\\) and \\(\\mathrm{ZP_{SBCR}=-0.1016_{\\pm 0.0091} [Fe/H] + 3.9988_{\\pm 0.0029}}\\). Conclusions: These new SBCRs, dedicated to classical Cepheids in the Milky Way and Magellanic Clouds, are of particular importance to apply the inverse Baade-Wesselink method to classical Cepheids observed by Gaia in a forthcoming study.

We aim to investigate the IR excess of 45 MW Cepheids combining different observables to constrain the presence of CSE. We used the SPIPS algorithm, a robust implementation of the parallax-of-pulsation method that combines photometry, angular diameter, stellar effective temperature, and RV measurements in a global modelling of the pulsation. We obtained new photometric measurements at mid-IR with the VLT/VISIR complemented with literature data. We then compared the mean magnitude from 0.5\\(\\mu\\)m to 70\\(\\mu\\)m with stellar atmosphere models to infer the IR excess, which we attribute to the presence of a CSE. We report that at least 29% of our sample have a detected IR excess. We estimated a mean excess of 0.08mag in K and 0.13mag in N. Other Cepheids possibly have IR excess, but they were rejected due to their low detection level compared to a single-star model. We do not see any correlation between the IR excess and the pulsation period as previously suspected for MW Cepheids, but a rather constant trend. We also do not find any correlation between the CO absorption and the presence of a CSE, but rather with the stellar effective temperature, which confirms that the CO features previously reported are mostly photospheric. No bias caused by the presence of the CSE is detected on the average distance estimates from a SPIPS analysis with a fitted colour excess. We also do not find correlation between the presence of IR excess and the evolution stage. We report a fraction of 29% of Cepheids with an IR excess likely produced by the CSE. Longer period Cepheids do not exhibit greater excess than short periods as previously suspected from observations and theoretical dusty-wind models. Other mechanisms such as free-free emission, among others, may be at the origin of their formation. We also show that not fitting the colour excess leads to a bias on the distance estimates in our Galaxy.