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We report the discovery of a surprising binary configuration of the double-mode Cepheid OGLE-LMC-CEP-1347 pulsating in the first (P_1=0.690d) and second overtone (P_2=0.556d) modes. The orbital period (P_orb=59d) of the system is five times shorter than the shortest known to date (310d) for a binary Cepheid. The Cepheid itself is also the shortest-period one ever found in a binary system and the first double-mode Cepheid in a spectroscopically double-lined binary. OGLE-LMC-CEP-1347 is most probably on its first crossing through the instability strip, as inferred from both its short period and fast period increase, consistent with evolutionary models, and from the short orbital period (not expected for binary Cepheids whose components have passed through the red giant phase). Our evolutionary analysis yielded a first-crossing Cepheid with a mass in a range of 2.9-3.4 Msun (lower than any measured Cepheid mass), consistent with observations. The companion is a stable star, at least two times fainter and less massive than the Cepheid (preliminary mass ratio q=0.55), while also redder and thus at the subgiant or more advanced evolutionary stage. To match these characteristics, the Cepheid has to be a product of binary interaction, most likely a merger of two less massive stars, which makes it the second known classical Cepheid of binary origin. Moreover, further evolution of the components may lead to another binary interaction., 6 pages, 4 figures, 1 table, published in The Astrophysical Journal Letters

Extant research on the gender pay gap suggests that men and women who do the same work for the same employer receive similar pay, so that processes sorting people into jobs are thought to account for the vast majority of the pay gap. Data that can identify women and men who do the same work for the same employer are rare, and research informing this crucial aspect of gender differences in pay is several decades old and from a limited number of countries. Here, using recent linked employer–employee data from 15 countries, we show that the processes sorting people into different jobs account for substantially less of the gender pay differences than was previously believed and that within-job pay differences remain consequential. This research was supported by the National Science Foundation (Award 0525831; D.A., A.M.P. and D.T.), the Humboldt Foundation (grant number AR8227; D.T.), the Research Council of Norway (grant number 287016; A.S.H.), European Research Council ERC Starting Grant (grant number 851149; A.S.H.), the European Research Council ERC Starting Grant (grant number 677739; T.K.), the French Agence Nationale de la Recherche (grant ANR-17-CE41-0009-01; M. Safi and O.G.), the Independent Research Fund Denmark (grant number 5052-00143b; L.H.), the European Social Fund and state budget of the Czechia (grant number CZ.03.1.51/0.0/0.0/15_009/0003702; A.K.), the Czech NPO Systemic Risk Institute (LX22NPO5101; A.K.), and institutional support (RVO: 68378025; A.K.), the Spanish Ministry of Science and Innovation (grant number PID2020-118807RB-I00/AEI /10.13039/501100011033; M.E.), the Fritz Henkel Stiftung (Endowed PhD Scholarship; HS) and Swedish Forte (grant number 2015-00807; M.H.), Z.L. received support from the European Research Council ERC Advanced Grant (grant number 340045), and A.K.M. was supported by the Slovenian Research Agency (ARRS) under grant no. P5-0193.

The majority of classical Cepheids are binary stars, yet the contribution of companions' light to the total brightness of the system has been assumed negligible and lacked a thorough, quantitative evaluation. We present an extensive study of synthetic populations of binary Cepheids, that aims to characterize Cepheids' companions (e.g. masses, evolutionary and spectral types), quantify their contribution to the brightness and color of Cepheid binaries, and assess the relevance of input parameters on the results. We introduce a collection of synthetic populations, which vary in metal content, initial parameter distribution, location of the instability strip edges, and star formation history. Our synthetic populations are free from the selection bias, while the percentage of Cepheid binaries is controlled by the binarity parameter. We successfully reproduce recent theoretical and empirical results: the percentage of binary Cepheids with main sequence (MS) companions, the contrast-mass ratio relation for binary Cepheids with MS companions, the appearance of binary Cepheids with giant evolved companions as outlier data points above the period-luminosity relation. Moreover, we present the first estimation of the percentage of binary Cepheids in the Large Magellanic Cloud and announce the quantification of the effect of binarity on the slope and zero-point of multiband period-luminosity relations, which will be reported in the next paper of this series., Comment: 29 pages, 19 figures (5 in the Appendix), accepted for ApJ, replaced with a version after editor's corrections

For the classical Cepheid V1033 Cyg we have constructed an O—C diagram spanning a time interval of 117 years. The O—C diagram has the shape of a parabola, which has made it possible to determine for the first time the quadratic light elements and to calculate the rate of evolutionary increase in the period dP/dt = 18.19 (±0.08) syr−1, in agreement with the results of theoretical calculations for the first crossing of the instability strip. Thus, V1033 Cyg is the second actually observed Cepheid (after α UMi) that crosses the instability strip for the first time.

Our work presents an independent calibration of the J-region Asymptotic Giant Branch (JAGB) method using Infrared Survey Facility (IRSF) photometric data and a custom luminosity function profile to determine JAGB mean magnitudes for nine galaxies. We determine a mean absolute magnitude of carbon stars of $M_{LMC}=-6.212 \pm 0.010$ (stat.) $\pm 0.030$ (syst.) mag. We then use near-infrared photometry of a number of nearby galaxies, originally obtained by our group to determine their distances from Cepheids using the Leavitt law, in order to independently determine their distances with the JAGB method. We compare the JAGB distances obtained in this work with the Cepheid distances resulting from the same photometry and find very good agreement between the results from the two methods. The mean difference is 0.01 mag with an rms scatter of 0.06 mag after taking into account seven out of the eight analyzed galaxies that had their distances determined using Cepheids. The very accurate distance to the Small Magellanic Cloud (SMC) based on detached eclipsing binaries (Graczyk et al. 2020) is also in very good agreement with the distance obtained from carbon stars., accepted for ApJ

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., Comment: 22 pages, 12 figures, 6 tables, Published in A&A

Deep near-infrared $J$- and $K$-band photometry of three Local Group dwarf spheroidal galaxies: Fornax, Carina, and Sculptor, is made available for the community. Until now, these data have only been used by the Araucaria Project to determine distances using the tip of the red giant and RR Lyrae stars. Now, we present the entire data collection in a form of a database, consisting of accurate $J$- and $K$-band magnitudes, sky coordinates, ellipticity measurements, and timestamps of observations, complemented by stars' loci in their reference images. Depth of our photometry reaches about 22 mag at 5$\sigma$ level, and is comparable to NIR surveys, like the UKIRT Infrared Deep Sky Survey (UKIDSS) or the VISTA Hemisphere Survey (VHS). Small overlap with VHS and no overlap with UKIDSS makes our database a unique source of quality photometry., Comment: 15 pages, 7 figures, accepted to The Astrophysical Journal Supplement

We present time-series photometry of 21 nearby Type II Cepheids in the near-infrared J, H and Ks passbands. We use this photometry, together with the Third Gaia Early Data Release parallaxes, to determine for the first time period-luminosity relations (PLRs) for Type II Cepheids from field representatives of these old pulsating stars in the near-infrared regime. We found PLRs to be very narrow for BL Herculis stars, which makes them candidates for precision distance indicators. We then use archival photometry and the most accurate distance obtained from eclipsing binaries to recalibrate PLRs for Type II Cepheids in the Large Magellanic Cloud (LMC). Slopes of our PLRs in the Milky Way and in the LMC differ by slightly more than 2{\sigma} and are in a good agreement with previous studies of the LMC, Galactic Bulge and Galactic Globular Clusters Type II Cepheids samples. We use PLRs of Milky Way Type II Cepheids to measure the distance to the LMC and we obtain a distance modulus of 18.540$\pm$0.026(stat.)$\pm$0.034(syst.)mag in the WJKs Wesenheit index. We also investigate the metallicity effect within our Milky Way sample and we find rather significant value of about -0.2mag/dex in each band meaning that more metal-rich Type II Cepheids are intrinsically brighter than their more metal-poor counterparts, in agreement with the value obtained from Type II Cepheids in Galactic Globular Clusters. The main source of systematic error on our Milky Way PLRs calibration and the LMC distance is the current uncertainty of the Gaia parallax zero point., Comment: Accepted for ApJ

In 1998, Hu and Liu developed a strongly polynomial algorithm for solving the inverse arborescence problem that aims at minimally modifying a given cost-function on the edge-set of a digraph D so that an input spanning arborescence of D becomes a cheapest one. In this note, we develop a conceptually simpler algorithm along with a new min-max formula for the minimum modification of the cost-function. The approach is based on a link to a min-max theorem and a simple (two-phase greedy) algorithm by the first author from 1979 concerning the primal optimization problem of finding a cheapest subgraph of a digraph that covers an intersecting family along with the corresponding dual optimization problem, as well. (C) 2021 The Author(s). Published by Elsevier B.V.

Correction for "Rising between-workplace inequalities in highincome countries," by Donald Tomaskovic-Devey, Anthony Rainey, Dustin Avent-Holt, Nina Bandelj, István Boza, David Cort, Olivier Godechot, Gergely Hajdu, Martin Hällsten, Lasse Folke Henriksen, Are Skeie Hermansen, Feng Hou, Jiwook Jung, Aleksandra Kanjuo- Mrčela, Joe King, Naomi Kodama, Tali Kristal, Alena Křížková, Zoltán Lippényi, Silvia Maja Melzer, Eunmi Mun, Andrew Penner, Trond Petersen, Andreja Poje, Mirna Safi, Max Thaning, and Zaibu Tufail, which was first published April 13, 2020; 10.1073/ pnas.1918249117 (Proc. Natl. Acad. Sci. U.S.A. 117, 9277-9283). The authors note that the affiliation for Silvia Maja Melzer should instead appear as Department of Political and Social Sciences, University Pompeu Fabra, Barcelona 08005, Spain. The corrected author and affiliation lines appear below. The online version has been corrected.

Significance Understanding the causes of rising inequality is of concern in many countries. Using administrative data, we find that the share of inequality that is between workplaces is growing in 12 of 14 countries examined, and in no country has it fallen. Countries with declining employment protections see growth in both between- and within-workplace inequalities, but this impact is stronger for between-workplace inequalities. These results suggest that to reduce market income inequality requires policies that raise the bargaining power of lower-skilled workers. The widespread rise in between-workplace inequality additionally suggests policy responses that target the increasing market power of firms in concentrated markets as well as curb the ability of powerful firms to outsource low skill employment., It is well documented that earnings inequalities have risen in many high-income countries. Less clear are the linkages between rising income inequality and workplace dynamics, how within- and between-workplace inequality varies across countries, and to what extent these inequalities are moderated by national labor market institutions. In order to describe changes in the initial between- and within-firm market income distribution we analyze administrative records for 2,000,000,000+ job years nested within 50,000,000+ workplace years for 14 high-income countries in North America, Scandinavia, Continental and Eastern Europe, the Middle East, and East Asia. We find that countries vary a great deal in their levels and trends in earnings inequality but that the between-workplace share of wage inequality is growing in almost all countries examined and is in no country declining. We also find that earnings inequalities and the share of between-workplace inequalities are lower and grew less strongly in countries with stronger institutional employment protections and rose faster when these labor market protections weakened. Our findings suggest that firm-level restructuring and increasing wage inequalities between workplaces are more central contributors to rising income inequality than previously recognized.

We report the discovery of two new lithium-rich Cepheids in the Milky Way (A(Li) ≈ 2.9 dex) among the targets of the MAGIC spectroscopic survey with the Southern African Large Telescope spectrographs. The 6707 Å Li feature is usually not detectable in the atmosphere of Cepheids. Only three Cepheids (two in the Milky Way and one in the Large Magellanic Cloud) had been reported so far with high lithium abundances. We examine the possibility that the Li-rich Cepheids are evolving towards the red giant branch, crossing the instability strip for the first time, as well as other possible scenarios. The two stars are mixed-mode Cepheids pulsating simultaneously in the first and in the second overtone modes. We briefly discuss the possible connection between their unusual chemical composition and their pulsational properties.

The far side of the Milky Way's disk is one of the most concealed parts of the known Universe due to extremely high interstellar extinction and point source density toward low Galactic latitudes. Large time-domain photometric surveys operating in the near-infrared hold great potential for the exploration of these vast uncharted areas of our Galaxy. We conducted a census of distant classical and type II Cepheids along the southern Galactic mid-plane using near-infrared photometry from the VISTA Variables in the V\'ia L\'actea survey. We performed a machine-learned classification of the Cepheids based on their infrared light curves using a convolutional neural network. We have discovered 640 distant classical Cepheids with up to ~40 magnitudes of visual extinction, and over 500 type II Cepheids, most of them located in the inner bulge. Intrinsic color indices of individual Cepheids were predicted from sparse photometric data using a neural network, allowing their use as accurate reddening tracers. They revealed a steep, spatially varying near-infrared extinction curve toward the inner bulge. Type II Cepheids in the Galactic bulge were also employed to measure robust mean selective-to-absolute extinction ratios. They trace a centrally concentrated spatial distribution of the old bulge population with a slight elongation, consistent with earlier results from RR Lyrae stars. Likewise, the classical Cepheids were utilized to trace the Galactic warp and various substructures of the Galactic disk, and to uncover significant vertical and radial age gradients of the thin disk population at the far side of the Milky Way., Comment: Accepted for publication by The Astrophysical Journal

Prompted by some inconsistencies in the photometry of the VISTA Variables in the V\'ia L\'actea (VVV) survey, we conduct a revision of the standard calibration procedure of VISTA data in the $J$, $H$, and $K_S$ passbands. Two independent sources of bias in the photometric zero-points are identified: First, high sky backgrounds severely affect the $H$-band measurements, but this can mostly be minimized by strict data vetting. Secondly, during the zero-point calibration, stars serving as standards are taken from the 2MASS catalog, which can suffer from high degrees of blending in regions of high stellar density, affecting both the absolute photometric calibration, as well as the scatter of repeated observations. The former affects studies that rely on an absolute magnitude scale, while the latter can also affect the shapes and amount of scatter in the VVV light curves, thus potentially hampering their proper classification. We show that these errors can be effectively eliminated by relatively simple modifications of the standard calibration procedure, and demonstrate the effect of the recalibration on the VVV survey's data quality. We give recommendations for future improvements of the pipeline calibration of VISTA photometry, while also providing preliminary corrections to the VVV $JHK_\mathrm{S}$ observations as a temporary measure., Comment: Accepted for publication in Experimental Astronomy; Table 1 is available from the first author upon request

We use deep multi-epoch near-IR images of the VISTA Variables in the Via Lactea (VVV) Survey to measure proper motions (PMs) of stars in the Milky Way globular cluster FSR1716 = VVV-GC05. The color-magnitude diagram of this object, made using PM selected members, shows an extended horizontal branch, nine confirmed RR Lyrae members in the instability strip, and possibly several hotter stars extending to the blue. Based on the fundamental-mode (ab-type) RR Lyrae stars that move coherently with the cluster, we confirmed that FSR1716 is an Oosterhoff I globular cluster with a mean period Pab = 0.574 days. Intriguingly, we detect tidal extensions to both sides of this cluster in the spatial distribution of PM selected member stars. Also, one of the confirmed RRabs is located 11 arcmin in projection from the cluster center, suggesting that FSR1716 may be losing stars due to the gravitational interaction with the Galaxy. We also measure radial velocities (RVs) for five cluster red giants selected using the PMs. The combination of RVs and PMs allow us to compute for the first time the orbit of this globular cluster, using an updated Galactic potential. The orbit results to be confined within |Zmax | < 2.0 kpc, and has eccentricity 0.4 < e < 0.6, with perigalactic distance 1.5 < Rperi (kpc) < 2.3, and apogalactic distance 5.3 < Rapo (kpc) < 6.4. We conclude that, in agreement with its relatively low metallicity ([Fe/H]= -1.4 dex), this is an inner halo globular cluster plunging into the disk of the Galaxy. As such, this is a unique object to test the dynamical processes that contribute to the disruption of Galactic globular clusters., 6 figures, 4 tables, accepted in APJ

This study's objective was to exploit infrared VVV (VISTA Variables in the Via Lactea) photometry for high latitude RRab stars to establish an accurate Galactic Centre distance. RRab candidates were discovered and reaffirmed ($n=4194$) by matching $K_s$ photometry with templates via $\chi^2$ minimization, and contaminants were reduced by ensuring targets adhered to a strict period-amplitude ($\Delta K_s$) trend and passed the Elorietta et al. classifier. The distance to the Galactic Centre was determined from a high latitude Bulge subsample ($|b|>4^{o}$, $R_{GC}=8.30 \pm 0.36$ kpc, random uncertainty is relatively negligible), and importantly, the comparatively low color-excess and uncrowded location mitigated uncertainties tied to the extinction law, the magnitude-limited nature of the analysis, and photometric contamination. Circumventing those problems resulted in a key uncertainty being the $M_{K_s}$ relation, which was derived using LMC RRab stars ($M_{K_s}=-(2.66\pm0.06) \log{P}-(1.03\pm0.06)$, $(J-K_s)_0=(0.31\pm0.04) \log{P} + (0.35\pm0.02)$, assuming $\mu_{0,LMC}=18.43$). The Galactic Centre distance was not corrected for the cone-effect. Lastly, a new distance indicator emerged as brighter overdensities in the period-magnitude-amplitude diagrams analyzed, which arise from blended RRab and red clump stars. Blending may thrust faint extragalactic variables into the range of detectability., Comment: To appear in Ap&SS

RR~Lyrae variables are widely used tracers of Galactic halo structure and kinematics, but they can also serve to constrain the distribution of the old stellar population in the Galactic bulge. With the aim of improving their near-infrared photometric characterization, we investigate their near-infrared light curves, as well as the empirical relationships between their light curve and metallicities using machine learning methods. We introduce a new, robust method for the estimation of the light-curve shapes, and hence the average magnitudes of RR~Lyrae variables in the $K_\mathrm{S}$ band, by utilizing the first few principal components (PCs) as basis vectors, obtained from the PC analysis of a training set of light curves. Furthermore, we use the amplitudes of these PCs to predict the light-curve shape of each star in the $J$-band, allowing us to precisely determine their average magnitudes (hence colors), even in cases where only one $J$ measurement is available. Finally, we demonstrate that the $K_\mathrm{S}$-band light-curve parameters of RR~Lyrae variables, together with the period, allow the estimation of the metallicity of individual stars with an accuracy of $\sim 0.2 - 0.25$ dex, providing valuable chemical information about old stellar populations bearing RR~Lyrae variables. The methods presented here can be straightforwardly adopted for other classes of variable stars, bands, or for the estimation of other physical quantities., Accepted for publication in the Astrophysical Journal; 21 pages, 14 figures

RR Lyrae stars (RRLs) are tracers of the Milky Way's fossil record, holding valuable information on its formation and early evolution. Owing to the high interstellar extinction endemic to the Galactic plane, distant RRLs lying at low Galactic latitudes have been elusive. We attained a census of 1892 high-confidence RRLs by exploiting the near-infrared photometric database of the VVV survey's disk footprint spanning $\sim$70$^\circ$ of Galactic longitude, using a machine-learned classifier. Novel data-driven methods were employed to accurately characterize their spatial distribution using sparsely sampled multi-band photometry. The RRL metallicity distribution function (MDF) was derived from their $K_s$-band light curve parameters using machine-learning methods. The MDF shows remarkable structural similarities to both the spectroscopic MDF of red clump giants and the MDF of bulge RRLs. We model the MDF with a multi-component density distribution and find that the number density of stars associated with the different model components systematically changes with both the Galactocentric radius and vertical distance from the Galactic plane, equivalent to weak metallicity gradients. Based on the consistency with results from the ARGOS survey, three MDF modes are attributed to the old disk populations, while the most metal-poor RRLs are probably halo interlopers. We propose that the dominant [Fe/H] component with a mean of $-1$ dex might correspond to the outskirts of an ancient Galactic spheroid or classical bulge component residing in the central Milky Way. The physical origins of the RRLs in this study need to be verified by kinematical information., Comment: ApJ, in press

V582 Aur is an FU Ori-type young eruptive star in outburst since $\sim$1985. The eruption is currently in a relatively constant plateau phase, with photometric and spectroscopic variability superimposed. Here we will characterize the progenitor of the outbursting object, explore its environment, and analyse the temporal evolution of the eruption. We are particularly interested in the physical origin of the two deep photometric dips, one occurred in 2012, and one is ongoing since 2016. We collected archival photographic plates, and carried out new optical, infrared, and millimeter wave photometric and spectroscopic observations between 2010 and 2017, with high sampling rate during the current minimum. Beside analysing the color changes during fading, we compiled multiepoch spectral energy distributions, and fitted them with a simple accretion disk model. Based on pre-outburst data and a millimeter continuum measurement, we suggest that the progenitor of the V582 Aur outburst is a low-mass T Tauri star with average properties. The mass of an unresolved circumstellar structure, probably a disk, is 0.04 M$_{\odot}$. The optical and near-infrared spectra demonstrate the presence of hydrogen and metallic lines, show the CO bandhead in absorption, and exhibit a variable H$\alpha$ profile. The color variations strongly indicate that both the $\sim$1 year long brightness dip in 2012, and the current minimum since 2016 are caused by increased extinction along the line of sight. According to our accretion disk models, the reddening changed from $A_V$=4.5 mag to 12.5 mag, while the accretion rate remained practically constant. Similarly to the models of the UXor phenomenon of intermediate and low-mass young stars, orbiting disk structures could be responsible for the eclipses., Comment: 20 pages, 11 figures, accepted for publication in ApJ

Variable stars of RR Lyrae type are a prime tool to obtain distances to old stellar populations in the Milky Way, and one of the main aims of the Vista Variables in the Via Lactea (VVV) near-infrared survey is to use them to map the structure of the Galactic Bulge. Due to the large number of expected sources, this requires an automated mechanism for selecting RR Lyrae,and particularly those of the more easily recognized type ab (i.e., fundamental-mode pulsators), from the 10^6-10^7 variables expected in the VVV survey area. In this work we describe a supervised machine-learned classifier constructed for assigning a score to a K_s-band VVV light curve that indicates its likelihood of being ab-type RR Lyrae. We describe the key steps in the construction of the classifier, which were the choice of features, training set, selection of aperture and family of classifiers. We find that the AdaBoost family of classifiers give consistently the best performance for our problem, and obtain a classifier based on the AdaBoost algorithm that achieves a harmonic mean between false positives and false negatives of ~7% for typical VVV light curve sets. This performance is estimated using cross-validation and through the comparison to two independent datasets that were classified by human experts., 11 pages, 7 figures. Astronomy & Astrophysics, in press

A new, extended time-series photometry of M3 RR Lyrae stars has revealed that four of the ten double-mode stars show large-amplitude Blazhko modulation of both radial modes. The first, detailed analysis of the peculiar behavior of the unique, Blazhko RRd stars is given. While the P1/P0 period ratio is normal, and the overtone mode is dominant in the other RRd stars of the cluster, the period ratio is anomalous and the fundamental mode has a larger (or similar) mean amplitude than the overtone has in Blazhko RRd stars. The modulations of the fundamental and overtone modes are synchronized only in one of the Blazhko RRd stars. No evidence of any connection between the modulations of the modes in the other three stars is found. The Blazhko modulation accounts, at least partly, for the previously reported amplitude and period changes of these stars. Contrary to the $\sim50$$%$ Blazhko statistics of RRab and RRd stars, Blazhko modulation occurs only in 10$%$ of the overtone variables in M3. Four of the five Blazhko RRc stars are bright, evolved objects, and one has a similar period and brightness as Blazhko RRd stars have. The regions of the instability strip with high and low occurrence rate of the Blazhko modulation overlap with the regions populated by first- and second-generation stars according to theoretical and observational studies, raising up the possibility that the Blazhko modulation occurs preferentially in first-generation RR Lyrae stars., Comment: 6 pages, 4 figures, accepted for publication in ApJL

The surface brightness -- colour relation (SBCR) is a basic tool in establishing precise and accurate distances within the Local Group. Detached eclipsing binary stars with accurately determined radii and trigonometric parallaxes allow for a calibration of the SBCRs with unprecedented accuracy. We analysed four nearby eclipsing binary stars containing late F-type main sequence components: AL Ari, AL Dor, FM Leo and BN Scl. We determined very precise spectroscopic orbits and combined them with high precision ground- and space-based photometry. We derived the astrophysical parameters of their components with mean errors of 0.1% for mass and 0.4% for radius. We combined those four systems with another 24 nearby eclipsing binaries with accurately known radii from the literature for which $Gaia$ EDR3 parallaxes are available, in order to derive the SBCRs. The resulting SBCRs cover stellar spectral types from B9 V to G7 V. For calibrations we used Johnson optical $B$ and $V$, $Gaia$ $G_{\rm BP}$ and $G$ and 2MASS $JHK$ bands. The most precise relations are calibrated using the infrared $K$ band and allow to predict angular diameters of A-, F-, and G-type dwarf and subgiant stars with a precision of 1%., Accepted for publication in Astronomy & Astrophysics, 17 pages