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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.

Detached eclipsing binaries (DEBs) allow for the possibility of precise characterization of its stellar components. They offer a unique opportunity to derive their physical parameters in a near-model-independent way for a number of systems consisting of late-type giant stars. Here we aim to expand the sample of low-metallicity late-type giant stars with precise parameters determined. We aim to determine the fundamental parameters like the mass, radius, or effective temperature for three long-period late-type eclipsing binaries from the Large Magellanic Cloud: OGLE-LMC-ECL-25304, OGLE-LMC-ECL-28283, and OGLE-IV LMC554.19.81. Subsequently we aim to determine the evolutionary stages of the systems. We fit the light curves from the OGLE project and radial velocity curves from high resolution spectrographs using the Wilson-Devinney code. The spectral analysis was performed with the GSSP code and resulted in the determination of atmospheric parameters such as effective temperatures and metallicities. We used isochrones provided by the MIST models based on the MESA code to derive evolutionary status of the stars. We present the first analysis of three DEBs composed of similar He-burning late-type stars passing through the blue loop. Estimated masses for OGLE-LMC-ECL-29293 (G4III + G4III) are \\(M_1=2.898\\pm0.031\\) and \\(M_2=3.153\\pm0.038\\) \\(M_\\odot\\), stellar radii are \\(R_1=19.43\\pm0.31\\) and \\(R_2=19.30\\pm0.31\\) \\(R_\\odot\\). OGLE-LMC-ECL-25304 (G4III + G5III) has stellar masses of \\(M_1=3.267\\pm0.028\\) and \\(M_2=3.229\\pm0.029\\) \\(M_\\odot\\), radii of \\(R_1=23.62\\pm0.42\\) and \\(R_2=25.10\\pm0.43\\) \\(R_\\odot\\). OGLE-IV LMC554.19.81 (G2III + G2III) have masses of \\(M_1=3.165\\pm0.020\\) and \\(M_2=3.184\\pm0.020\\) \\(M_\\odot\\), radii of \\(R_1=18.86\\pm0.26\\) and \\(R_2=19.64\\pm0.26\\) \\(R_\\odot\\). All masses were determined with a precision better than 2\\% and radii better than 1.5\\%. The ages of the stars are in the range of 270-341 Myr.

The Baade-Wesselink (BW) method of distance determination of Cepheids is used to calibrate the distance scale. Various versions of this method are mainly based on interferometry and/or the surface-brightness color relation (SBCR). We quantify the impact of the SBCR, its slope, and its zeropoint on the projection factor. This quantity is used to convert the pulsation velocity into the radial velocity in the BW method. We also study the impact of extinction and of a potential circumstellar environment on the projection factor. We analyzed HARPS-N spectra of eta Aql to derive its radial velocity curve using different methods. We then applied the inverse BW method using various SBCRs in the literature in order to derive the BW projection factor. We find that the choice of the SBCR is critical: a scatter of about 8% is found in the projection factor for different SBCRs in the literature. The uncertainty on the coefficients of the SBCR affects the statistical precision of the projection factor only little (1-2\\%). Confirming previous studies, we find that the method with which the radial velocity curve is derived is also critical, with a potential difference on the projection factor of 9%. An increase of 0.1 in E(B-V) translates into a decrease in the projection factor of 3%. A 0.1 magnitude effect of a circumstellar envelope (CSE) in the visible domain is rather small on the projection factor, about 1.5%. However, we find that a 0.1 mag infrared excess in the K band due to a CSE can increase the projection factor by about 6%. The impact of the surface-brightness color relation on the BW projection factor is found to be critical. Efforts should be devoted in the future to improve the SBCR of Cepheids empirically, but also theoretically, taking their CSE into account as well.

RR Lyrae stars are excellent tracers of the old population II due to their period-luminosity (PL) and period-luminosity-metallicity (PLZ) relations. While these relations have been investigated in detail in many photometric bands, there are few comprehensive studies about them in Sloan-like systems. We present PL and PLZ relations (as well as their counterparts in Wesenheit magnitudes) in the Sloan-Pan-STARSS gP1rP1iP1 bands obtained for Galactic RR Lyrae stars in the vincinity of the Sun. The data used in this paper were collected with the network of 40 cm telescopes of the Las Cumbres Observatory, and geometric parallaxes were adopted from Gaia Data Release 3. We derived PL and PLZ relations separately for RRab and RRc-type stars, as well as for the mixed population of RRab+RRc stars. To our knowledge, these are the first PL and PLZ relations in the Sloan bands determined using RR Lyrae stars in the Galactic field.

We study 147 star clusters in the Large Magellanic Cloud (LMC) in order to determine their mean metallicities and ages, as well as the mean metallicities of 80 surrounding fields. We construct an age-metallicity relation (AMR) for the clusters in the LMC. For this purpose, we used Str\"omgren photometry obtained with the SOI camera on the 4.1 m SOAR telescope. We found the mean metallicity and age for 110 star clusters. For the remaining 37, we provide an age estimation only. To the best of our knowledge, for 29 clusters from our sample, we provide both the metallicity and age for the first time, whereas for 66 clusters, we provide a first determination of the metallicity, and for 43 clusters, the first estimation of the age. We also calculated the mean metallicities for stars from 80 fields around the clusters. The old, metal-poor star clusters occur both in and out of the LMC bar region, while intermediate-age clusters are located mostly outside of the bar. The majority of star clusters younger than 1 Gyr are located in the bar region. We find a good agreement between our AMR and theoretical models of the LMC chemical enrichment, as well as with AMRs for clusters from the literature. Next, we took advantage of 26 stellar clusters from our sample which host Cepheid variables and used them as an independent check of the correctness of our age determination procedure. We used period-age relations for Cepheids to calculate the mean age of a given cluster and compared it with the age obtained from isochrone fitting. We find good agreement between these ages, especially for models taking into account additional physical processes (e.g., rotation). We also compared the AMR of the LMC and Small Magellanic Cloud (SMC) derived in a uniform way and we note that they indicate possible former interaction between these two galaxies.

Our goal is to determine, with high accuracy, the physical and orbital parameters of two double-lined eclipsing binary systems, where the components are two giant stars. We also aim to study the evolutionary status of the binaries, to derive the distances towards them by using a surface brightness-colour relation, and to compare these measurements with the measurements presented by the Gaia mission. In order to measure the physical and orbital parameters of the systems, we analysed the light curves and radial-velocity curves with the Wilson-Devinney code. We used V band and I-band photometry from the OGLE catalogue and near-infrared photometry obtained with the New Technology Telescope (NTT) equipped with the SOFI instrument. The spectroscopic data were collected with the HARPS spectrograph mounted at the ESO 3.6m telescope and the MIKE spectrograph mounted at the 6.5m Clay telescope. We present the first analysis of this kind for two evolved eclipsing binary systems from the OGLE catalogue: OGLE-BLG-ECL-305487 and OGLE-BLG-ECL-116218. The masses of the components of OGLE-BLG-ECL-305487 are \\(M_1\\) = 1.059 \\(\\pm\\) 0.019 and \\(M_2\\) = 0.991 \\(\\pm\\) 0.018 \\(M_\\odot\\), and the radii are \\(R_1\\) = 19.27 \\(\\pm\\) 0.28 and \\(R_2\\) = 29.99 \\(\\pm\\) 0.24 R\\(_\\odot\\). For OGLE-BLG-ECL-116218, the masses are \\(M_1\\)= 0.969 \\(\\pm\\) 0.012 and \\(M_2\\)= 0.983 \\(\\pm\\) 0.012 \\(M_\\odot\\), while the radii are \\(R_1\\)= 16.73 \\(\\pm\\) 0.28 and \\(R_2\\)= 22.06 \\(\\pm\\) 0.26 \\(R_\\odot\\). The evolutionary status of the systems is discussed based on the PARSEC and MIST isochrones. The ages of the systems were established to be between 7.3-10.9 Gyr for OGLE-BLG-ECL-305487 and around 10 Gyr for OGLE-BLG-ECL-116218. We also measured the distances to the binaries. For OGLE-BLG-ECL-305487, \\(d\\)= 7.80 \\(\\pm\\) 0.18 (stat.) \\(\\pm\\) 0.19 (syst.) kpc and for OGLE-BLG-ECL-116218, \\(d\\)= 7.57 \\(\\pm\\) 0.28 (stat.) \\(\\pm\\) 0.19 (syst.) kpc.

The field of the globular cluster M10 (NGC 6254) was monitored between 1998 and 2015 in a search for variable stars. V -light curves were derived for 40 variables or likely variables, most of which are new detections. Proper motions obtained within the CASE project indicate that 18 newly detected variables and 14 previously known ones are members or likely members of the cluster, including one RRc-type, three type II Cepheids, and 14 SX Phe-type pulsators, one contact binary, and six semi-regular red giants. As a byproduct of the search we discovered a candidate binary comprised of main sequence stars with the record-short orbital period of 0.042 d. We also confirmed the photometric variability of the red straggler M10-VLA1 hinted at by Shishkovsky et al. (2018), who discovered this object spectroscopically. In Appendix 1 we show that CASE proper motion measurements are in a good agreement with those retrieved from the Gaia archive, while Appendix 2 presents evidence for low frequency {\\gamma} Doradus-type oscillations in SX Phe stars belonging to M10.

Surface brightness -- colour relations (SBCRs) are very useful tools for predicting the angular diameters of stars. They offer the possibility to calculate very precise spectrophotometric distances by the eclipsing binary method or the Baade-Wesselink method. Double-lined Detached Eclipsing Binary stars (SB2 DEBs) with precisely known trigonometric parallaxes allow for a calibration of SBCRs with unprecedented precision. In order to improve such calibrations, it is important to enlarge the calibration sample of suitable eclipsing binaries with very precisely determined physical parameters. We carefully chose a sample of ten SB2 DEBs in the solar neighbourhood which contain inactive main-sequence components. The components have spectral types from early A to early K. All systems have high-precision parallaxes from the Gaia mission. We analysed high precision ground- and space-based photometry simultaneously with the radial velocity curves derived from HARPS spectra. We used spectral disentangling to obtain the individual spectra of the components and used these to derive precise atmospheric parameters and chemical abundances. For almost all components, we derived precise surface temperatures and metallicities. We derived absolute dimensions for 20 stars with an average precision of 0.2% and 0.5% for masses and radii, respectively. Three systems show slow apsidal motion. One system, HD 32129, is most likely a triple system with a much fainter K6V companion. Also three systems contain metallic-line components and show strong enhancements of barium and ittrium. The components of all systems compare well to the SBCR derived before from the detached eclipsing binary stars. With a possible exception of HD 32129, they can be used to calibrate SBCRs with a precision better than 1% with available Gaia DR3 parallaxes.

We present results obtained from Stromgren photometry of 13 young (~30-220 Myr) Magellanic Cloud (MC) clusters, most of them lacking in the literature from direct metallicity measurements. We derived for them [Fe/H] values from a high-dispersion spectroscopy-based empirical calibration of the Stromgren metallicity sensitive index m1 for yellow and red supergiants (SGs). Particular care was given while estimating their respective uncertainties. In order to obtain the mean cluster metallicities, we used [Fe/H] values of selected SGs for which we required to be located within the cluster radii, placed in the expected SG region in the cluster colour-magnitude diagrams, and with [Fe/H] values within the FWHM of the observed cluster metallicity distributions. The resulting metallicities for nearly 75 per cent of the cluster sample agree well with the most frequently used values of the mean MCs' present-day metallicities. The remaining clusters have mean [Fe/H] values that fall near the edge of the MC present-day metallicity distributions. When comparing the cluster metallicities with their present positions, we found evidence that supports the claimed recent interaction of the MCs with the Milky Way, that could have caused that some clusters were scattered from their birthplaces. Indeed, we show examples of clusters with metal contents typical of the galaxy inner regions placed outward them. Likewise, we found young clusters, at present located in the inner regions of both MCs, formed out of gas that has remained unmixed since several Gyr ago.

In this work we study 35 stellar clusters in the Small Magellanic Cloud (SMC) in order to provide their mean metallicities and ages. We also provide mean metallicities of the fields surrounding the clusters. We used Str\"omgren photometry obtained with the 4.1 m SOAR telescope and take advantage of \\((b - y)\\) and \\(m1\\) colors for which there is a metallicity calibration presented in the literature. The spatial metallicity and age distributions of clusters across the SMC are investigated using the results obtained by Str\"omgren photometry. We confirm earlier observations that younger, more metal-rich star clusters are concentrated in the central regions of the galaxy, while older, more metal-poor clusters are located farther from the SMC center. We construct the age-metallicity relation for the studied clusters and find good agreement with theoretical models of chemical enrichment, and with other literature age and metallicity values for those clusters. We also provide the mean metallicities for old and young populations of the field stars surrounding the clusters, and find the latter to be in good agreement with recent studies of the SMC Cepheid population. Finally, the Str\"omgren photometry obtained for this study is made publicly available.