In the era of precision cosmology, it is essential to determine the Hubble constant empirically with an accuracy of one per cent or better1. At present, the uncertainty on this constant is dominated by the uncertainty in the calibration of the Cepheid period–luminosity relationship2,3 (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 scale4,5. 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 relation5,6. 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.

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We do not provide any code because we used only classical tools such as the IRAF, Daophot and Wilson–Devinney code, and they are publicly available.

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The research leading to these results has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 695099). We acknowledge support from the IdP II 2015 0002 64 and DIR/WK/2018/09 grants of the Polish Ministry of Science and Higher Education. We also gratefully acknowledge financial support for this work from the BASAL Centro de Astrofisica y Tecnologias Afines (CATA, AFB-170002), and from the Millennium Institute for Astrophysics (MAS) of the Iniciativa Milenio del Ministerio de Economía, Fomento y Turismo de Chile, project IC120009. We also acknowledge support from the Polish National Science Center grant MAESTRO DEC-2012/06/A/ST9/00269. We acknowledge the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-15-CE31-0012-01 (project UnlockCepheids). S.V. gratefully acknowledges the support provided by Fondecyt reg. no. 1170518. This work is based on observations made with ESO telescopes under programmes 092.D-0297, 094.D-0074, 098.D-0263(A,B), 097.D-0400(A), 097.D-0150(A), 097.D-0151(A) and CNTAC programmes CN2016B-38, CN2016A-22, CN2015B-2 and CN2015A-18. This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe”.

Author information


  1. Nicolaus Copernicus Astronomical Centre, Warsaw, Poland

    • G. Pietrzyński
    • , D. Graczyk
    • , B. Pilecki
    • , M. Taormina
    • , B. Zgirski
    • , P. Wielgórski
    • , Z. Kołaczkowski
    • , R. Smolec
    •  & W. Narloch
  2. Universidad de Concepción, Departamento de Astronomìa, Concepciòn, Chile

    • G. Pietrzyński
    • , D. Graczyk
    • , W. Gieren
    • , M. Górski
    •  & S. Villanova
  3. Millennium Institute of Astrophysics (MAS), Santiago, Chile

    • D. Graczyk
  4. European Southern Observatory, Santiago, Chile

    • A. Gallenne
  5. Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice, France

    • A. Gallenne
    •  & N. Nardetto
  6. Carnegie Observatories, Pasadena, CA, USA

    • I. B. Thompson
  7. Warsaw University Observatory, Warsaw, Poland

    • P. Karczmarek
    • , K. Suchomska
    •  & P. Konorski
  8. Astronomical Institute, Wrocław University, Wrocław, Poland

    • Z. Kołaczkowski
  9. LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Univ. Paris Diderot, Sorbonne Paris Cité, Meudon, France

    • P. Kervella
  10. Institute for Astronomy, Honolulu, HI, USA

    • F. Bresolin
    •  & R. P. Kudritzki
  11. Munich University Observatory, Munich, Germany

    • R. P. Kudritzki
  12. Leibniz Institute for Astrophysics, Potsdam, Germany

    • J. Storm


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G.P., photometric and spectroscopic observations, data analysis. D.G., spectroscopic observations, modelling, data analysis. A.G., interferometric observations, data reduction and analysis. W.G., observations and data analysis. I.B.T., observations, RV determination, data analysis. B.P., spectroscopic observations and reductions, RV measurements. P. Karczmarek, M.G., M.T., B.Z., P.W., Z.K., P. Konorski, observations and data reductions. S.V., analysis of the spectroscopic data. N.N., P. Kervella, F.B., R.P.K., J.S., R.S., K.S. and W.N., data analysis, discussion of results. G.P. and W.G. worked jointly to draft the manuscript with all authors reviewing and contributing to its final form.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to G. Pietrzyński.

Extended data figures and tables

  1. Extended Data Fig. 1 Comparison of our relation with the relation of Di Benedetto obtained for giant stars6.

    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 SV and (V − K)0 are in magnitudes. SV 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.

  2. Extended Data Fig. 2 Observed minus calculated surface brightness versus metallicity6, [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 R2 = 0.0001.

  3. Extended Data Fig. 3 Example of Monte Carlo simulations for one of our objects, ECL-12669.

    We computed 10,000 models with the JKTEBOP code77 from which we obtained statistical uncertainties on the radii R1 and R2, the orbital inclination i, the phase shift φ, the surface brightness ratio j21, radial velocity semi-amplitudes K1 and K2, and the systemic velocities γ1 and γ2. For every model we computed the distance modulus converting j21 into temperature ratio T2/T1 by using Popper’s calibration78 and our original solution with the Wilson–Devinney code79. 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 calibration28.

  4. Extended Data Fig. 4 Error estimate of distance modulus of the LMC from Monte Carlo simulations.

    For each eclipsing binary we calculated random 20,000 distance moduli with Gaussian distribution assuming μ = m − Mmean and σ = σmean from Table 1. Then we fitted 20,000 planes with the linear least-squares method for every set of distance moduli using as free parameters inclination of the disk plane, i, the position of the nodes, Θ, and the distance to the centre of the LMC, d. Apparent positions were converted into the three-dimensional Cartesian positions80. 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 of the LMC.

  5. Extended Data Table 1 V band magnitudes of our target stars
  6. Extended Data Table 2 Collected data for our sample of helium burning giants
  7. Extended Data Table 3 Reddenings determined with three different methods
  8. Extended Data Table 4 Contributions to the total statistical errors

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