Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

A distance to the Large Magellanic Cloud that is precise to one per cent

Nature volume 567, pages 200–203 (2019)Cite this article

Subjects

Abstract

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.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: New relation between surface brightness SV and (V − K)0 colour.
Fig. 2: Locations and distances of our 20 eclipsing binary systems in the LMC.
Fig. 3: Range and precision of the geometrical methods.

Similar content being viewed by others

Code availability

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.

Data availability

All data are available upon request from G.P.

References

  1. Komatsu, E. et al. Seven-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation. Astrophys. J. Suppl. Ser. 192, 18–65 (2011).

    Article  ADS  Google Scholar 

  2. Riess, A. et al. New parallaxes of galactic Cepheids from spatially scanning the Hubble Space Telescope: implications for the Hubble constant. Astrophys. J. 855, 136–149 (2018).

    Article  ADS  Google Scholar 

  3. Freedman, W. L. & Madore, B. F. The Hubble constant. Annu. Rev. Astron. Astrophys. 48, 673–710 (2010).

    Article  ADS  Google Scholar 

  4. Walker, A. The Large Magellanic Cloud and the distance scale. Astrophys. Space Sci. 341, 43–49 (2012).

    Article  ADS  Google Scholar 

  5. Pietrzyński, G. et al. An eclipsing-binary distance to the Large Magellanic Cloud accurate to two per cent. Nature 495, 76–79 (2013).

    Article  ADS  Google Scholar 

  6. Di Benedetto, G. P. Predicting accurate stellar angular diameters by the near-infrared surface brightness technique. Mon. Not. R. Astron. Soc. 357, 174–190 (2005).

    Article  ADS  Google Scholar 

  7. Laney, C. D., Joner, M. D. & Pietrzyński, G. A new Large Magellanic Cloud K-band distance from precision measurements of nearby red clump stars. Mon. Not. R. Astron. Soc. 419, 1637–1641 (2012).

    Article  ADS  Google Scholar 

  8. Gallenne, A. et al. Fundamental properties of red-clump stars from long-baseline interferometry. Astron. Astrophys. 616, A68 (2018).

    Article  Google Scholar 

  9. Mermilliod, J. C., Mermilliod, M. & Hauck, B. The General Catalogue of Photometric Data (GCPD). II. Astron. Astrophys. Suppl. Ser. 124, 349–352 (1997).

    Article  ADS  Google Scholar 

  10. Graczyk, D. et al. The Optical Gravitational Lensing Experiment. The OGLE-III catalog of variable stars. XII. Eclipsing binary stars in the Large Magellanic Cloud. Acta Astron. 61, 103–122 (2011).

    ADS  Google Scholar 

  11. Soszynski, I. et al. Concluding Henrietta Leavitt’s work on classical Cepheids in the Magellanic system and other updates of the OGLE collection of variable stars. Acta Astron. 67, 103–113 (2017).

    ADS  Google Scholar 

  12. Gieren, W. et al. Measuring improved distances to nearby galaxies: the Araucaria project. Messenger 121, 23–28 (2005).

    ADS  Google Scholar 

  13. Graczyk, D. et al. The late-type eclipsing binaries in the Large Magellanic Cloud: catalog of fundamental physical parameters. Astrophys. J. 860, 1–30 (2018).

    Article  ADS  Google Scholar 

  14. van der Marel, R. P., Alves, D. R., Hardy, E. & Suntzeff, N. B. New understanding of Large Magellanic Cloud structure, dynamics, and orbit from carbon star kinematics. Astron. J. 124, 2639–2663 (2002).

    Article  ADS  Google Scholar 

  15. van der Marel, R. P. & Kallivayalil, N. Third-epoch Magellanic Cloud proper motions. II. The Large Magellanic Cloud rotation field in three dimensions. Astrophys. J. 781, 121–141 (2014).

    Article  ADS  Google Scholar 

  16. Haschke, R., Grebel, E. K. & Duffau, S. Three-dimensional maps of the Magellanic Clouds using RR Lyrae stars and Cepheids. I. The Large Magellanic Cloud. Astron. J. 144, 106–119 (2012).

    Article  ADS  Google Scholar 

  17. Thompson, I. B. et al. Cluster AgeS experiment: the age and distance of the globular cluster ω Centauri determined from observations of the eclipsing binary OGLEGC 17. Astron. J. 121, 3089–3099 (2001).

    Article  ADS  Google Scholar 

  18. Mazzarella, J. M. NED for a new era. Astron. Soc. Pacif. Conf. 376, 153–162 (2007).

    ADS  Google Scholar 

  19. Persson, S. E. et al. New Cepheid period-luminosity relations for the Large Magellanic Cloud: 92 near-infrared light curves. Astron. J. 128, 2239–2264 (2004).

    Article  ADS  CAS  Google Scholar 

  20. Perryman, M. A. C. et al. The Hipparcos and Tycho Catalogues (SP-1200, ESA, Noordwijk, 1998).

  21. Bessel, M. S. The Hipparcos and Tycho photometric system passbands. Publ. Astron. Soc. Pacif. 112, 961–965 (2000).

    Article  ADS  Google Scholar 

  22. Laney, C. D. & Stobie, R. S. JHKL observations of galactic Cepheids. Astron. Astrophys. Suppl. Ser. 93, 93–120 (1992).

    ADS  Google Scholar 

  23. Glass, I. S. Some basics of JHKLM photometry. Ir. Astron. J. 17, 1–10 (1985).

    Google Scholar 

  24. Schlegel, D. J., Finkbeiner, D. P. & Davis, M. Maps of dust infrared emission for use in estimation of reddening and cosmic microwave background radiation foregrounds. Astrophys. J. 500, 525–553 (1998).

    Article  ADS  Google Scholar 

  25. Schlafly, E. F. & Finkbeiner, D. P. Measuring reddening with Sloan Digital Sky Survey stellar spectra and recalibrating SFD. Astrophys. J. 737, 103–116 (2011).

    Article  ADS  Google Scholar 

  26. Suchomska, K. et al. The Araucaria Project: accurate stellar parameters and distance to evolved eclipsing binary ASAS J180057-2333.8 in Sagittarius Arm. Mon. Not. R. Astron. Soc. 451, 651–659 (2015).

    Article  ADS  CAS  Google Scholar 

  27. Flower, P. J. Transformations from theoretical Hertzsprung-Russell diagrams to color-magnitude diagrams: effective temperatures, B-V colors, and bolometric corrections. Astrophys. J. 469, 355–365 (1996).

    Article  ADS  Google Scholar 

  28. Worthey, G. & Lee, H. An empirical UBV RI JHK color-temperature calibration for stars. Astrophys. J. Suppl. Ser. 193, 1–11 (2011).

    Article  ADS  Google Scholar 

  29. Alonso, A., Arribas, S. & Martinez-Roger, C. The effective temperature scale of giant stars (F0-K5). II. Empirical calibration of T eff versus colours and [Fe/H]. Astron. Astrophys. Suppl. Ser. 140, 261–277 (1999).

    Article  ADS  CAS  Google Scholar 

  30. Castelli, F. & Kurucz, R. L. New grids of ATLAS9 model atmospheres. In Modelling of Stellar Atmospheres 17–21 (IAU Symp. 210, Astron. Soc. Pacif., Uppsala, 2003).

  31. Gaia Collaboration. Gaia Data Release 1. Testing parallaxes with local Cepheids and RR Lyrae stars. Astron. Astrophys. 605, A79 (2017).

    Article  Google Scholar 

  32. Wright, E. L. et al. The Wide-field Infrared Survey Explorer (WISE): mission description and initial on-orbit performance. Astron. J. 140, 1868–1881 (2010).

    Article  ADS  Google Scholar 

  33. Gallenne, A. et al. Observational calibration of the projection factor of Cepheids. IV. Period-projection factor relation of Galactic and Magellanic Cloud Cepheids. Astron. Astrophys. 608, A18 (2017).

    Article  Google Scholar 

  34. Graczyk, D. et al. The Araucaria Project. The distance to the Small Magellanic Cloud from late-type eclipsing binaries. Astrophys. J. 780, 59 (2014).

    Article  ADS  Google Scholar 

  35. Torres, G., Claret, A. & Young, P. A. Binary orbit, physical properties, and evolutionary state of Capella (α Aurigae). Astrophys. J. 700, 1349–1381 (2009).

    Article  ADS  CAS  Google Scholar 

  36. Gallenne, A. et al. The Araucaria Project: high-precision orbital parallax and masses of the eclipsing binary TZ Fornacis. Astron. Astrophys. 586, A35 (2016).

    Article  Google Scholar 

  37. Andersen, J. Absolute dimensions of eclipsing binaries. XVII — TZ Fornacis: stellar and tidal evolution in a binary with a fully-fledged red giant. Astron. Astrophys. 246, 99–117 (1991).

    ADS  CAS  Google Scholar 

  38. Gallenne, A. et al. A geometrical 1% distance to the short-period binary Cepheid V1334 Cygni. Astrophys. J. 867, 121–130 (2018).

    Article  ADS  Google Scholar 

  39. Lindegren, L. et al. Gaia Data Release 2. The astrometric solution. Astron. Astrophys. 616, A2 (2018).

    Article  Google Scholar 

  40. Arenou, F. et al. Gaia Data Release 2. Catalogue validation. Astron. Astrophys. 616, A17 (2018).

    Article  Google Scholar 

  41. Graczyk, D. et al. Testing systematics of Gaia DR2 parallaxes with empirical surface brightness relations applied to eclipsing binaries. Preprint at https://arxiv.org/abs/1902.00589 (2019).

  42. Johnson, H. L., Mitchell, R. I., Iriarte, B. & Wisniewski, W. Z. Ubvrijkl photometry of the bright stars. Commun. Lunar Planet. Lab. 4, 99–110 (1966).

    ADS  Google Scholar 

  43. Wild, P. A. T. UBV photometry of 137 stars in an area near the south galactic pole. Mon. Not. Astron. Soc. S. Afr. 28, 123–130 (1969).

    ADS  Google Scholar 

  44. Pfleiderer, J., Dachs, J. & Haug, U. Z. Lichtelektrische UBV-Photometrie von Standardsternen und in Vier Sternenfelder am Aequator. Z. Astrophys. 64, 116–138 (1966).

    ADS  Google Scholar 

  45. Appenzeller, I. Polarimetrische, Photometrische und Spectroskopische Beobachtungen von Sternen im Cygnus und Orion. Z. Astrophys. 64, 269–295 (1966).

    ADS  CAS  Google Scholar 

  46. Breger, M. UBV and narrow-band uvby photometry of bright stars. Astron. J. 73, 84–85 (1968).

    Article  ADS  Google Scholar 

  47. Cousins, A. W. J. Revised zero points and UBV photometry in the Harvard E and F regions. Mem. R. Astron. Soc. 77, 223–236 (1973).

    ADS  Google Scholar 

  48. Feinstein, A. Photoelectric observations of southern late-type stars. Inform. Bull. South. Hem. 8, 30–35 (1966).

    Google Scholar 

  49. Cousins, A. W. J. UBV photometry of E region standard stars of intermediate brightness. S. Afr. Astron. Obs. Circ. No. 7, 36–46 (1983).

    ADS  Google Scholar 

  50. IAU Supplementary Standard Stars for V and B-V 251 (IAU Trans. IIa, 1961).

  51. Cousins, A. W. J. Photometric data for stars in the equatorial zone (first list). Mon. Not. Astron. Soc. S. Afr. 21, 20–24 (1962).

    ADS  Google Scholar 

  52. Cousins, A. W. J. & Stoy, R. H. Photoelectric magnitudes and colours of southern stars. R. Obs. Bull. 64, 103 (1962)

    ADS  Google Scholar 

  53. Elvius, T. & Lynga, G. Three-colour photometry of 43 stars in Kapteyn’s selected areas at southern galactic latitudes. Ark. Astron. 3, 467–473 (1965).

    ADS  Google Scholar 

  54. Cousins, A. W. J. Photometric data for stars in the equatorial zone (third list). Mon. Not. Astron. Soc. S. Afr. 22, 12–17 (1963).

    ADS  Google Scholar 

  55. Przybylski, A. & Kennedy, P. M. Radial velocities and three-colour photometry of 166 southern stars. Mon. Not. R. Astron. Soc. 131, 95–104 (1965).

    Article  ADS  Google Scholar 

  56. Argue, A. N. UBV photometry of 550 F, G and K type stars. Mon. Not. R. Astron. Soc. 133, 475–493 (1966).

    Article  ADS  Google Scholar 

  57. Cousins, A. W. J. Photometric data for stars in the equatorial zone (fourth list). Mon. Not. Astron. Soc. S. Afr. 22, 58–62 (1963).

    ADS  Google Scholar 

  58. Corben, P. M. Photoelectric magnitudes and colours for bright southern stars. Mon. Not. Astron. Soc. S. Afr. 25, 44–51 (1966).

    ADS  Google Scholar 

  59. Corben, P. M. Photoelectric magnitudes and colours for bright southern stars. Mon. Not. Astron. Soc. S. Afr. 30, 37–50 (1971).

    ADS  Google Scholar 

  60. Corben, P. M. & Stoy, R. H. Photoelectric magnitudes and colours for bright southern stars. Mon. Not. Astron. Soc. S. Afr. 27, 11–16 (1968).

    ADS  Google Scholar 

  61. Cousins, A. W. J. & Stoy, R. H. Standard magnitudes in the E regions. R. Obs. Bull. 49, 3–9 (1962)

    ADS  Google Scholar 

  62. Cousins, A. W. J. & Stoy, R. H. Photoelectric magnitudes and colours of southern stars. R. Obs. Bull. 64, 103–109 (1962)

    ADS  Google Scholar 

  63. Cousins, A. W. J., Lake, R. & Stoy, R. H. Photoelectric magnitudes and colours of southern stars. R. Obs. Bull. No. 121, 1–7 (1966)

    ADS  Google Scholar 

  64. Evans, D. S. Fundamental data for southern stars. R. Obs. Bull. 110, 185–191 (1966)

    Google Scholar 

  65. Irwin, J. B. Southern Cepheid photometry. Astrophys. J. Suppl. Ser. 6, 253–302 (1961).

    Article  ADS  Google Scholar 

  66. Lake, R. Photoelectric magnitudes and colours for 168 southern stars. Mon. Not. Astron. Soc. S. Afr. 21, 56–60 (1962).

    ADS  Google Scholar 

  67. Lake, R. Photoelectric magnitudes and colours for 100 southern stars. Mon. Not. Astron. Soc. S. Afr. 21, 191 (1962).

    ADS  Google Scholar 

  68. Lake, R. Photoelectric magnitudes and colours for 100 southern stars. Mon. Not. Astron. Soc. S. Afr. 23, 136–139 (1964).

    ADS  Google Scholar 

  69. Lake, R. Photoelectric magnitudes and colours for bright southern stars. Mon. Not. Astron. Soc. S. Afr. 24, 41–50 (1965).

    ADS  Google Scholar 

  70. Stoy, R. H. Photoelectric three colour magnitudes for 354 southern stars. Mon. Not. Astron. Soc. S. Afr. 22, 157 (1963).

    ADS  Google Scholar 

  71. Stoy, R. H. Photoelectric magnitudes and colours for bright southern stars. Mon. Not. Astron. Soc. S. Afr. 27, 119–128 (1968).

    ADS  Google Scholar 

  72. Cousins, A. W. J. Cape ubv magnitudes and colours of south circumpolar stars. S. Afr. Astron. Obs. Circ. No. 1, 51–58 (1977).

    ADS  Google Scholar 

  73. Johnson, H. L., Mitchell, R. I., Iriarte, B. & Wisniewski, W. Z. UBVRIJKL photometry of the bright stars. Lunar Planet. Lab. 63, 99–110 (1966).

    ADS  Google Scholar 

  74. Mendoza, E. E. Bvri photometry of 46 southern bright stars. Bol. Obs. Tonantzintla Tacubaya 5, 57–58 (1969).

    ADS  Google Scholar 

  75. Mermilliod, J. C. & Mermilliod, M. Catalogue Of Eggen’s UBV Data (1986).

  76. Jennens, P. A. & Helfer, H. A new photometric metal abundance and luminosity calibration for field G and K giants. Mon. Not. R. Astron. Soc. 172, 667–679 (1975).

    Article  ADS  CAS  Google Scholar 

  77. Southworth, J. Homogeneous studies of transiting extrasolar planets – I. Light-curve analyses. Mon. Not. R. Astron. Soc. 386, 1644–1666 (2008).

    Article  ADS  CAS  Google Scholar 

  78. Popper, D. M. Stellar masses. Annu. Rev. Astron. Astrophys. 18, 115–164 (1980).

    Article  ADS  CAS  Google Scholar 

  79. Wilson, R. E. & Devinney, E. J. Realization of accurate close-binary light curves: application to MR Cygni. Astrophys. J. 166, 605–620 (1971).

    Article  ADS  Google Scholar 

  80. Jacyszyn-Dobrzeniecka, A. M. et al. OGLE-ing the Magellanic System: three-dimensional structure of the clouds and the bridge using classical Cepheids. Acta Astron. 66, 149–196 (2016).

    ADS  Google Scholar 

Download references

Acknowledgements

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

Authors and Affiliations

  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

Authors
  1. G. Pietrzyński
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Graczyk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Gallenne
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. W. Gieren
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. I. B. Thompson
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. B. Pilecki
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. P. Karczmarek
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. M. Górski
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. K. Suchomska
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. M. Taormina
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. B. Zgirski
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. P. Wielgórski
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Z. Kołaczkowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. P. Konorski
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. S. Villanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. N. Nardetto
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. P. Kervella
    View author publications

    You can also search for this author in PubMed Google Scholar

  18. F. Bresolin
    View author publications

    You can also search for this author in PubMed Google Scholar

  19. R. P. Kudritzki
    View author publications

    You can also search for this author in PubMed Google Scholar

  20. J. Storm
    View author publications

    You can also search for this author in PubMed Google Scholar

  21. R. Smolec
    View author publications

    You can also search for this author in PubMed Google Scholar

  22. W. Narloch
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding author

Correspondence to G. Pietrzyński.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

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.

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.

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.

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.

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pietrzyński, G., Graczyk, D., Gallenne, A. et al. A distance to the Large Magellanic Cloud that is precise to one per cent. Nature 567, 200–203 (2019). https://doi.org/10.1038/s41586-019-0999-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-019-0999-4

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing