One or more bound planets per Milky Way star from microlensing observations

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Most known extrasolar planets (exoplanets) have been discovered using the radial velocity1, 2 or transit3 methods. Both are biased towards planets that are relatively close to their parent stars, and studies find that around 17–30% (refs 4, 5) of solar-like stars host a planet. Gravitational microlensing6, 7, 8, 9, on the other hand, probes planets that are further away from their stars. Recently, a population of planets that are unbound or very far from their stars was discovered by microlensing10. These planets are at least as numerous as the stars in the Milky Way10. Here we report a statistical analysis of microlensing data (gathered in 2002–07) that reveals the fraction of bound planets 0.5–10au (Sun–Earth distance) from their stars. We find that of stars host Jupiter-mass planets (0.3–10MJ, where MJ = 318Mcircle plus and Mcircle plus is Earth’s mass). Cool Neptunes (10–30Mcircle plus) and super-Earths (5–10Mcircle plus) are even more common: their respective abundances per star are and . We conclude that stars are orbited by planets as a rule, rather than the exception.

At a glance


  1. Survey-sensitivity diagram.
    Figure 1: Survey-sensitivity diagram.

    Blue contours, expected number of detections from our survey if all lens stars have exactly one planet with orbit size a and mass M. Red points, all microlensing planet detections in the time span 2002–07, with error bars (s.d.) reported from the literature. White points, planets consistent with PLANET observing strategy. Red letters, planets of our Solar System, marked for comparison: E, Earth; J, Jupiter; S, Saturn; U,Uranus; N, Neptune. This diagram shows that the sensitivity of our survey extends roughly from 0.5au to 10au for planetary orbits, and from 5Mcircle plus to 10MJ. The majority of all detected planets have masses below that of Saturn, although the sensitivity of the survey is much lower for such planets than for more massive, Jupiter-like planets. Low-mass planets are thus found to be much more common than giant planets.

  2. Cool-planet mass function.
    Figure 2: Cool-planet mass function.

    a, The cool-planet mass function, f, for the orbital range 0.5−10au as derived by microlensing. Red solid line, best fit for this study, based on combining the results from PLANET 2002–07 and previous microlensing estimates18, 25 for slope (blue line; error, light-blue shaded area, s.d.) and normalization (blue point; error bars, s.d.). We find dN/(dlogadlogM) = 10−0.62±0.22(M/MSat)0.73±0.17, where N is the average number of planets per star, a the semi-major axis and M the planet mass. The pivot point of the power-law mass function is at the mass of Saturn (MSat = 95Mcircle plus). The grey shaded area is the 68% confidence interval around the median (dash-dotted black line). For comparison, the constraint from Doppler measurements27 (green line and point; error, green shaded area, s.d.) is also displayed. Differences can arise because the Doppler technique focuses mostly on solar-like stars, whereas microlensing a priori probes all types of host stars. Moreover, microlensing planets are located further away from their stars and are cooler than Doppler planets. These two populations of planets may then follow a rather different mass function. b, PLANET 2002–07 sensitivity, S: the expected number of detections if all stars had exactly one planet, regardless of its orbit. c, PLANET 2002–07 detections, k. Thin black curves, distribution probabilities of the mass for the three detections contained in the PLANET sample; red line, the sum of these distributions.


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Author information


  1. Probing Lensing Anomalies Network (PLANET) Collaboration, Institut d’Astrophysique de Paris, Université Pierre & Marie Curie, UMR7095 UPMC–CNRS 98 bis boulevard Arago, 75014 Paris, France

    • A. Cassan,
    • D. Kubas,
    • J.-P. Beaulieu,
    • M. Dominik,
    • K. Horne,
    • J. Greenhill,
    • J. Wambsganss,
    • J. Menzies,
    • A. Williams,
    • U. G. Jørgensen,
    • D. P. Bennett,
    • M. D. Albrow,
    • V. Batista,
    • S. Brillant,
    • J. A. R. Caldwell,
    • A. Cole,
    • Ch. Coutures,
    • K. H. Cook,
    • S. Dieters,
    • D. Dominis Prester,
    • J. Donatowicz,
    • P. Fouqué,
    • K. Hill,
    • N. Kains,
    • S. Kane,
    • J.-B. Marquette,
    • R. Martin,
    • K. R. Pollard,
    • K. C. Sahu,
    • C. Vinter,
    • D. Warren,
    • B. Watson &
    • M. Zub
  2. Institut d’Astrophysique de Paris, Université Pierre & Marie Curie, UMR7095 UPMC–CNRS 98 bis boulevard Arago, 75014 Paris, France

    • A. Cassan,
    • D. Kubas,
    • J.-P. Beaulieu,
    • V. Batista,
    • Ch. Coutures &
    • J.-B. Marquette
  3. Astronomischen Rechen-Instituts (ARI), Zentrum für Astronomie, Heidelberg University, Mönchhofstrasse 12–14, 69120 Heidelberg, Germany

    • A. Cassan,
    • J. Wambsganss &
    • M. Zub
  4. European Southern Observatory, Alonso de Cordoba 3107, Vitacura, Casilla 19001, Santiago, Chile

    • D. Kubas &
    • S. Brillant
  5. Scottish Universities Physics Alliance (SUPA), University of St Andrews, School of Physics & Astronomy, North Haugh, St Andrews, KY16 9SS, UK

    • M. Dominik &
    • K. Horne
  6. University of Tasmania, School of Maths and Physics, Private bag 37, GPO Hobart, Tasmania 7001, Australia

    • J. Greenhill,
    • A. Cole,
    • S. Dieters,
    • K. Hill,
    • D. Warren &
    • B. Watson
  7. South African Astronomical Observatory, PO Box 9 Observatory 7935, South Africa

    • J. Menzies
  8. Perth Observatory, Walnut Road, Bickley, Perth 6076, Australia

    • A. Williams &
    • R. Martin
  9. Niels Bohr Institute and Centre for Star and Planet Formation, Juliane Mariesvej 30, 2100 Copenhagen, Denmark

    • U. G. Jørgensen &
    • C. Vinter
  10. Optical Gravitational Lensing Experiment (OGLE) Collaboration, Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

    • A. Udalski,
    • M. K. Szymański,
    • M. Kubiak,
    • R. Poleski,
    • I. Soszynski,
    • K. Ulaczyk,
    • G. Pietrzyński &
    • Ł. Wyrzykowski
  11. Warsaw University Observatory, Al. Ujazdowskie 4, 00-478 Warszawa, Poland

    • A. Udalski,
    • M. K. Szymański,
    • M. Kubiak,
    • R. Poleski,
    • I. Soszynski,
    • K. Ulaczyk,
    • G. Pietrzyński &
    • Ł. Wyrzykowski
  12. University of Notre Dame, Physics Department, 225 Nieuwland Science Hall, Notre Dame, Indiana 46530, USA

    • D. P. Bennett
  13. University of Canterbury, Department of Physics & Astronomy, Private Bag 4800, Christchurch 8140, New Zealand

    • M. D. Albrow &
    • K. R. Pollard
  14. Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, Maryland 21218, USA

    • J. A. R. Caldwell &
    • K. C. Sahu
  15. Institute of Geophysics and Planetary Physics, Lawrence Livermore National Laboratory, PO Box 808, California 94550, USA

    • K. H. Cook
  16. Department of Physics, University of Rijeka, Omladinska 14, 51000 Rijeka, Croatia

    • D. Dominis Prester
  17. Technical University of Vienna, Department of Computing, Wiedner Hauptstrasse 10, 1040 Vienna, Austria

    • J. Donatowicz
  18. Laboratoire Astrophysique de Toulouse (LATT), Université de Toulouse, CNRS, 31400 Toulouse, France

    • P. Fouqué
  19. European Southern Observatory Headquarters, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany

    • N. Kains
  20. NASA Exoplanet Science Institute, Caltech, MS 100-22, 770 South Wilson Avenue, Pasadena, California 91125, USA

    • S. Kane
  21. Microlensing Observations in Astrophysics (MOA) Collaboration, Department of Earth and Space Science, Osaka University, Osaka 560-0043, Japan

    • T. Sumi
  22. Department of Earth and Space Science, Osaka University, Osaka 560-0043, Japan

    • T. Sumi
  23. Universidad de Concepción, Departamento de Fisica, Casilla 160-C, Concepción, Chile

    • G. Pietrzyński
  24. Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

    • Ł. Wyrzykowski
  25. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK

    • J.-P. Beaulieu


A.Ca. led the analysis and conducted the modelling and statistical analyses. A.Ca. and D.K. selected light curves from 2002–07 PLANET/OGLE microlensing seasons, analysed the data and wrote the Letter and Supplement. D.K. computed the magnification maps used for the detection-efficiency calculations. J.-P.B. and Ch.C. wrote the software for online data reduction at the telescopes. J.-P.B. led the PLANET collaboration, with M.D., J.G., J.M. and A.W.; P.F. and M.D.A. contributed to online and offline data reduction. M.D. contributed to the conversion of the detection efficiencies to physical parameter space and developed the PLANET real-time display system with A.W., M.D.A. and Ch.C.; K.Ho. and A.Ca. developed and tested the Bayesian formulation for fitting the two-parameter power-law mass function. J.G. edited the manuscript, conducted the main data cleaning and managed telescope operations at Mount Canopus (1m) in Hobart. J.W. wrote the original magnification maps software, discussed the main implications and edited the manuscript. J.M., A.W. and U.G.J. respectively managed telescope operations in South Africa (South African Astronomical Observatory 1m), Australia (Perth 0.61m) and La Silla (Danish 1.54m). A.U. led the OGLE campaign and provided the final OGLE photometry. D.P.B, V.B., S.B., J.A.R.C., A.Co., K.H.C., S.D., D.D.P., J.D., P.F., K.Hi., N.K., S.K., J.-B.M., R.M., K.R.P., K.C.S., C.V., D.W., B.W. and M.Z. were involved in the PLANET observing strategy and/or PLANET data acquisition, reduction, real-time analysis and/or commented on the manuscript. T.S. commented on the manuscript. M.K.S., M.K., R.P., I.S., K.U., G.P. and Ł.W. contributed to OGLE data.

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