Planet formation theories predict that some planets may be ejected from their parent systems as result of dynamical interactions and other processes1,2,3. Unbound planets can also be formed through gravitational collapse, in a way similar to that in which stars form4. A handful of free-floating planetary-mass objects have been discovered by infrared surveys of young stellar clusters and star-forming regions5,6 as well as wide-field surveys7, but these studies are incomplete8,9,10 for objects below five Jupiter masses. Gravitational microlensing is the only method capable of exploring the entire population of free-floating planets down to Mars-mass objects, because the microlensing signal does not depend on the brightness of the lensing object. A characteristic timescale of microlensing events depends on the mass of the lens: the less massive the lens, the shorter the microlensing event. A previous analysis11 of 474 microlensing events found an excess of ten very short events (1–2 days)—more than known stellar populations would suggest—indicating the existence of a large population of unbound or wide-orbit Jupiter-mass planets (reported to be almost twice as common as main-sequence stars). These results, however, do not match predictions of planet-formation theories3,12 and surveys of young clusters8,9,10. Here we analyse a sample of microlensing events six times larger than that of ref. 11 discovered during the years 2010–15. Although our survey has very high sensitivity (detection efficiency) to short-timescale (1–2 days) microlensing events, we found no excess of events with timescales in this range, with a 95 per cent upper limit on the frequency of Jupiter-mass free-floating or wide-orbit planets of 0.25 planets per main-sequence star. We detected a few possible ultrashort-timescale events (with timescales of less than half a day), which may indicate the existence of Earth-mass and super-Earth-mass free-floating planets, as predicted by planet-formation theories3,12.
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Rasio, F. A. & Ford, E. B. Dynamical instabilities and the formation of extrasolar planetary systems. Science 274, 954–956 (1996)
Weidenschilling, S. J. & Marzari, F. Gravitational scattering as a possible origin for giant planets at small stellar distances. Nature 384, 619–621 (1996)
Veras, D. & Raymond, S. N. Planet–planet scattering alone cannot explain the free-floating planet population. Mon. Not. R. Astron. Soc. 421, L117–L121 (2012)
Luhman, K. L. The formation and early evolution of low-mass stars and brown dwarfs. Annu. Rev. Astron. Astrophys. 50, 65–106 (2012)
Zapatero Osorio, M. R. et al. Discovery of young, isolated planetary mass objects in the σ Orionis star cluster. Science 290, 103–107 (2000)
Liu, M. C. et al. The extremely red, young L dwarf PSO J318.5338–22.8603: a free-floating planetary-mass analog to directly imaged young gas-giant planets. Astrophys. J. 777, L20 (2013)
Dupuy, T. J. & Kraus, A. L. Distances, luminosities, and temperatures of the coldest known substellar objects. Science 341, 1492–1495 (2013)
Scholz, A. et al. Substellar objects in nearby young clusters (SONYC). VI. The planetary-mass domain of NGC 1333. Astrophys. J. 756, 24 (2012)
Peña Ramírez, K., Béjar, V. J. S., Zapatero Osorio, M. R., Petr-Gotzens, M. G. & Martín, E. L. New isolated planetary-mass objects and the stellar and substellar mass function of the σ Orionis cluster. Astrophys. J. 754, 30 (2012)
Mužić, K., Scholz, A., Geers, V. C. & Jayawardhana, R. Substellar objects in nearby young clusters (SONYC). IX: The planetary-mass domain of Chamaeleon-I and updated mass function in Lupus-3. Astrophys. J. 810, 159 (2015)
Sumi, T. et al. Unbound or distant planetary mass population detected by gravitational microlensing. Nature 473, 349–352 (2011)
Ma, S., Mao, S., Ida, S., Zhu, W. & Lin, D. N. C. Free-floating planets from core accretion theory: microlensing predictions. Mon. Not. R. Astron. Soc. 461, L107–L111 (2016)
Udalski, A., Szymański, M. K. & Szymański, G. OGLE-IV: fourth phase of the Optical Gravitational Lensing Experiment. Acta Astron. 65, 1–38 (2015)
Woźniak, P. & Paczyzński, B. Microlensing of blended stellar images. Astrophys. J. 487, 55–60 (1997)
Bennett, D. P. et al. Planetary and other short binary microlensing events from the MOA short-event analysis. Astrophys. J. 757, 119 (2012)
Calchi Novati, S., de Luca, F., Jetzer, P., Mancini, L. & Scarpetta, G. Microlensing constraints on the Galactic bulge initial mass function. Astron. Astrophys. 480, 723–733 (2008)
Han, C. & Gould, A. The mass spectrum of MACHOs from parallax measurements. Astrophys. J. 447, 53 (1995)
Han, C. & Gould, A. Stellar contribution to the galactic bulge microlensing optical depth. Astrophys. J. 592, 172–175 (2003)
Lafrenière, D. et al. The Gemini Deep Planet Survey. Astrophys. J. 670, 1367–1390 (2007)
Bowler, B. P., Liu, M. C., Shkolnik, E. L. & Tamura, M. Planets around low-mass stars (PALMS). IV. The outer architecture of M dwarf planetary systems. Astrophys. J. Suppl. Ser. 216, 7 (2015)
Clanton, C. & Gaudi, B. S. Constraining the frequency of free-floating planets from a synthesis of microlensing, radial velocity, and direct imaging survey results. Astrophys. J. 834, 46 (2017)
Ida, S., Lin, D. N. C. & Nagasawa, M. Toward a deterministic model of planetary formation. VII. Eccentricity distribution of gas giants. Astrophys. J. 775, 42 (2013)
Pfyffer, S., Alibert, Y., Benz, W. & Swoboda, D. Theoretical models of planetary system formation. II. Post-formation evolution. Astron. Astrophys. 579, A37 (2015)
Barclay, T., Quintana, E. V., Raymond, S. N. & Penny, M. T. The demographics of rocky free-floating planets and their detectability by WFIRST. Astrophys. J. 841, 86 (2017)
Spergel, D. et al. Wide-Field InfraRed Survey Telescope-Astrophysics Focused Telescope Assets WFIRST-AFTA 2015 report. Preprint at https://arxiv.org/abs/1503.03757 (2015)
Penny, M. T. et al. ExELS: an exoplanet legacy science proposal for the ESA Euclid mission—I. Cold exoplanets. Mon. Not. R. Astron. Soc. 434, 2–22 (2013)
Mao, S. & Paczynski, B. Mass determination with gravitational microlensing. Astrophys. J. 473, 57 (1996)
Alard, C. & Lupton, R. H. A method for optimal image subtraction. Astrophys. J. 503, 325–331 (1998)
Woźniak, P. R. Difference image analysis of the OGLE-II bulge data. I. The method. Acta Astron. 50, 421–450 (2000)
Udalski, A. The Optical Gravitational Lensing Experiment. Real time data analysis systems in the OGLE-III survey. Acta Astron. 53, 291–305 (2003)
Skowron, J. et al. Analysis of photometric uncertainties in the OGLE-IV Galactic bulge microlensing survey data. Acta Astron. 66, 1–14 (2016)
Wyrzykowski, Ł. et al. OGLE-III microlensing events and the structure of the Galactic bulge. Astrophys. J. Suppl. Ser. 216, 12 (2015)
Wray, J. J., Eyer, L. & Paczyński, B. OGLE small-amplitude variables in the Galactic bar. Mon. Not. R. Astron. Soc. 349, 1059–1068 (2004)
Park, B.-G. et al. MOA-2003-BLG-37: a bulge jerk-parallax microlens degeneracy. Astrophys. J. 609, 166–172 (2004)
Jiang, G. et al. OGLE-2003-BLG-238: microlensing mass estimate for an isolated star. Astrophys. J. 617, 1307–1315 (2004)
Smith, M. C., Woźniak, P., Mao, S. & Sumi, T. Blending in gravitational microlensing experiments: source confusion and related systematics. Mon. Not. R. Astron. Soc. 380, 805–818 (2007)
Hawley, S. L. et al. Kepler flares. I. Active and inactive M dwarfs. Astrophys. J. 797, 121 (2014)
Holtzman, J. A. et al. The luminosity function and initial mass function in the Galactic bulge. Astron. J. 115, 1946–1957 (1998)
Gould, A. Extending the MACHO search to about 106 solar masses. Astrophys. J. 392, 442 (1992)
Bennett, D. P. & Rhie, S. H. Detecting Earth-mass planets with gravitational microlensing. Astrophys. J. 472, 660–664 (1996)
Kiraga, M. & Paczynski, B. Gravitational microlensing of the Galactic bulge stars. Astrophys. J. 430, L101–L104 (1994)
Han, C. & Gould, A. Statistical determination of the MACHO mass spectrum. Astrophys. J. 467, 540 (1996)
Bissantz, N., Debattista, V. P. & Gerhard, O. Large-scale model of the Milky Way: stellar kinematics and the microlensing event timescale distribution in the Galactic bulge. Astrophys. J. 601, L155–L158 (2004)
Wood, A. & Mao, S. Optical depths and time-scale distributions in Galactic microlensing. Mon. Not. R. Astron. Soc. 362, 945–951 (2005)
Dwek, E. et al. Morphology, near-infrared luminosity, and mass of the Galactic bulge from COBE DIRBE observations. Astrophys. J. 445, 716–730 (1995)
Zheng, Z., Flynn, C., Gould, A., Bahcall, J. N. & Salim, S. M dwarfs from Hubble Space Telescope star counts. Astrophys. J. 555, 393–404 (2001)
Gould, A. Measuring the remnant mass function of the Galactic bulge. Astrophys. J. 535, 928–931 (2000)
Williams, K. A., Bolte, M. & Koester, D. Probing the lower mass limit for supernova progenitors and the high-mass end of the initial-final mass relation from white dwarfs in the open cluster M35 (NGC 2168). Astrophys. J. 693, 355–369 (2009)
Kiziltan, B., Kottas, A., De Yoreo, M. & Thorsett, S. E. The neutron star mass distribution. Astrophys. J. 778, 66 (2013)
Özel, F., Psaltis, D., Narayan, R. & McClintock, J. E. The black hole mass distribution in the Galaxy. Astrophys. J. 725, 1918–1927 (2010)
Zoccali, M. et al. The initial mass function of the Galactic bulge down to 0.15 Msolar . Astrophys. J. 530, 418–428 (2000)
Belczynski, K. et al. Compact object modeling with the StarTrack population synthesis code. Astrophys. J. Suppl. Ser. 174, 223–260 (2008)
Kroupa, P. On the variation of the initial mass function. Mon. Not. R. Astron. Soc. 322, 231–246 (2001)
Wegg, C., Gerhard, O. & Portail, M. MOA-II Galactic microlensing constraints: the inner Milky Way has a low dark matter fraction and a near maximal disc. Mon. Not. R. Astron. Soc. 463, 557–570 (2016)
Alves de Oliveira, C. The low mass end of the IMF. Mem. Soc. Astron. Ital. 84, 905 (2013)
Allen, P. R., Koerner, D. W., Reid, I. N. & Trilling, D. E. The substellar mass function: a Bayesian approach. Astrophys. J. 625, 385–397 (2005)
Quanz, S. P., Lafrenière, D., Meyer, M. R., Reggiani, M. M. & Buenzli, E. Direct imaging constraints on planet populations detected by microlensing. Astron. Astrophys. 541, A133 (2012)
We thank M. Kubiak and G. Pietrzyński, former members of the OGLE team, for their contribution to the collection of the OGLE photometric data over the past years. The OGLE project has received funding from the National Science Center, Poland through grant MAESTRO 2014/14/A/ST9/00121 to A.U.
Reviewer Information Nature thanks C. Clanton, S. Raymond and T. Sumi for their contribution to the peer review of this work.
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Extended data figures and tables
a, Deep luminosity function (LF) for subfield BLG513.12, which was observed both by the OGLE-IV survey and by the Hubble Space Telescope (HST)38. Both luminosity functions overlap in the range 16 mag < I < 18 mag. This deep luminosity function was used as a template to generate artificial microlensing events in analysed fields, after shifting to match the centroid of the red clump giant stars in a given field. b, Comparison between the observed luminosity function for subfield BLG512.32 and the simulated luminosity function.
Detection efficiencies as a function of the Einstein timescale tE for all analysed fields (averages for all subfields in the given field). Fields BLG501, BLG505 and BLG512 were observed with a 20-min cadence, and the remaining fields with a 60-min cadence. Error bars are the 1σ Poisson uncertainties on the counts of the number of simulated events in a given tE bin.
Extended Data Figure 3 Comparison between measured Einstein timescales tE,out and ‘real’ (simulated) timescales tE,in for simulated events.
Only events passing selection criteria from Extended Data Table 3 (including the cut on the blending parameter fs > 0.1) are shown. Note that the colour scale is logarithmic. There is no systematic offset between measured and real timescales.
a, Ratio between the measured Einstein timescale tE,out and ‘real’ (simulated) timescale tE,in for simulated events versus the blending parameter fs = Fs/(Fs + Fb). Timescales of faint and highly blended (fs < 0.1) events are not well measured and are biased by a strong degeneration between Einstein timescale, blending and impact parameters. Timescales of events showing a high negative blending (fs > 1.5) are systematically underestimated, but the bias is relatively small and such events comprise a negligible fraction of all events. b, Distributions of tE,out/tE,in for simulated events passing selection criteria from Extended Data Table 3 (including the cut on the blending parameter fs > 0.1). Regardless of the timescale, there is no systematic bias between measured and real timescales within 1%. For 90% of simulated events 0.63 < tE,out/tE,in < 1.65. The MAD is the median absolute deviation from the data’s median.
a, Assuming that all lenses are single; b, assuming binary fraction fbin = 0.4.
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Mróz, P., Udalski, A., Skowron, J. et al. No large population of unbound or wide-orbit Jupiter-mass planets. Nature 548, 183–186 (2017). https://doi.org/10.1038/nature23276
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