Detection of Extrasolar Planets by Gravitational Microlensing

Gravitational microlensing provides a unique window on the properties and prevalence of extrasolar planetary systems because of its ability to find low-mass planets at separations of a few AU. The early evidence from microlensing indicates that the most common types of exoplanet yet detected are the so-called super-Earth planets of 10 Earth-masses at a separation of a few AU from their host stars. The detection of two such planets indicates that roughly one third of stars have such planets in the separation range 1.5–4 AU, which is about an order of magnitude larger than the prevalence of gas-giant planets at these separations. We review the basic physics of the microlensing method, and show why this method allows the detection of Earth-mass planets at separations of 2–3 AU with ground-based observations. We explore the conditions that allow the detection of the planetary host stars and allow measurement of planetary orbital parameters. Finally, we show that a low-cost, space-based microlensing survey can provide a comprehensive statistical census of extrasolar planetary systems with sensitivity down to 0.1 Earth-masses at separations ranging from 0.5 AU to infinity.

[1]  G. Lewis Gravitational microlensing of stars with transiting planets , 2001, astro-ph/0110410.

[2]  The Optical Gravitational Lensing Experiment. the Early Warning System , 1994, astro-ph/9408026.

[3]  D. Queloz,et al.  The HARPS search for southern extra-solar planets. XI. Super-Earths (5 and 8 M{⊕}) in a 3-planet system , 2007, 0704.3841.

[4]  A. Gould,et al.  The Mass Spectrum Of Machos From Parallax Measurements , 1994, astro-ph/9409036.

[5]  Identification of the OGLE-2003-BLG-235/MOA-2003-BLG-53 Planetary Host Star* , 2006, astro-ph/0606038.

[6]  D. Soderblom Planets Beyond the Solar System and the Next Generation of Space Missions , 1997 .

[7]  K. Ulaczyk,et al.  First Space-Based Microlens Parallax Measurement: Spitzer Observations of OGLE-2005-SMC-001 , 2007, astro-ph/0702240.

[8]  M. Bessell,et al.  JHKLM PHOTOMETRY: STANDARD SYSTEMS, PASSBANDS, AND INTRINSIC COLORS , 1988 .

[9]  S. Rhie Can A Gravitational Quadruple Lens Produce 17 images , 2001, astro-ph/0103463.

[10]  O. Szewczyk,et al.  Discovery of a cool planet of 5.5 Earth masses through gravitational microlensing , 2006, Nature.

[11]  E. E. Falco,et al.  The Detectability of Planetary Companions of Compact Galactic Objects from Their Effects on Microlensed Light Curves of Distant Stars , 1994 .

[12]  B. Gaudi,et al.  Planetary Detection Efficiency of the Magnification 3000 Microlensing Event OGLE-2004-BLG-343 , 2005, astro-ph/0507079.

[13]  P. M. Vreeswijk,et al.  Microlensing Constraints on the Frequency of Jupiter-Mass Companions: Analysis of 5 Years of PLANET Photometry , 2001, astro-ph/0104100.

[14]  Y. Saito,et al.  Improving the prospects for detecting extrasolar planets in gravitational microlensing events in 2002 , 2001, astro-ph/0111041.

[15]  M. Dominik,et al.  FIRST MICROLENS MASS MEASUREMENT: PLANET PHOTOMETRY OF EROS BLG-2000-5 , 2002 .

[16]  A. J. Drake,et al.  The MACHO Project: Microlensing Results from 5.7 Years of Large Magellanic Cloud Observations , 2000, astro-ph/0001272.

[17]  C. Alcock Gravitational lenses , 1982, Nature.

[18]  Y. Watase,et al.  Real-time difference imaging analysis of moa galactic bulge observations during 2000 , 2001 .

[19]  Bohdan Paczynski,et al.  Gravitational microlensing by the galactic halo , 1986 .

[20]  J. B. Marquette,et al.  Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds , 2006, astro-ph/0607207.

[21]  Andrew Gould,et al.  SYSTEMATIC ANALYSIS OF 22 MICROLENSING PARALLAX CANDIDATES , 2005, astro-ph/0506183.

[22]  Marcin Kubiak,et al.  The Optical Gravitational Lensing Experiment , 1992 .

[23]  S. Rhie Infimum microlensing amplification of the maximum number of images of n-point lens systems , 1995, astro-ph/9508123.

[24]  P. Wozniak,et al.  Microlensing Optical Depth toward the Galactic Bulge Using Bright Sources from OGLE-II , 2005, astro-ph/0502363.

[25]  A. Drake,et al.  Microlensing Optical Depth toward the Galactic Bulge Using Clump Giants from the MACHO Survey , 2004, astro-ph/0410319.

[26]  H. Bondi,et al.  The Gravitational Lens Effect , 1964 .

[27]  Bohdan Paczynski,et al.  Gravitational microlensing by double stars and planetary systems , 1991 .

[28]  S. Kenyon,et al.  Planet Formation around Low-Mass Stars: The Moving Snow Line and Super-Earths , 2006, astro-ph/0609140.

[29]  Neda Safizadeh,et al.  The Use of High-Magnification Microlensing Events in Discovering Extrasolar Planets , 1997 .

[30]  S. Refsdal,et al.  On the Possibility of Determining the Distances and Masses of Stars from the Gravitational Lens Effect , 1966 .

[31]  Optical Gravitational Lensing Experiment OGLE‐1999‐BUL‐32: the longest ever microlensing event – evidence for a stellar mass black hole? , 2001, astro-ph/0108312.

[32]  F. Thevenin,et al.  The angular sizes of dwarf stars and subgiants Surface brightness relations calibrated by interferometry , 2004, astro-ph/0404180.

[33]  C. G. Tinney,et al.  Catalog of nearby exoplanets , 2006 .

[34]  Peter Garnavich,et al.  The Microlensing Planet Finder: completing the census of extrasolar planets in the Milky Way , 2004, SPIE Astronomical Telescopes + Instrumentation.

[35]  P. Kervella,et al.  Surface brightness relations calibrated by interferometry , 2004 .

[36]  B. Gaudi,et al.  Microlensing by Multiple Planets in High-Magnification Events , 1998, astro-ph/9803282.

[37]  Shigeru Ida,et al.  Toward a Deterministic Model of Planetary Formation. II. The Formation and Retention of Gas Giant Planets around Stars with a Range of Metallicities , 2004, astro-ph/0408019.

[38]  B. Paczyński,et al.  Acceleration and parallax effects in gravitational microlensing , 2002, astro-ph/0210370.

[39]  K. Masuda,et al.  Microlensing Optical Depth toward the Galactic Bulge from Microlensing Observations in Astrophysics Group Observations during 2000 with Difference Image Analysis , 2002, astro-ph/0207604.

[40]  Stochastic distributions of lens and source properties for observed galactic microlensing events , 2005, astro-ph/0507540.

[41]  T. Lauer The Photometry of Undersampled Point‐Spread Functions , 1999, astro-ph/9907100.

[42]  Rapid Formation of Super-Earths around M Dwarf Stars , 2006, astro-ph/0605061.

[43]  Andrew Gould,et al.  Discovering Planetary Systems through Gravitational Microlenses , 1992 .

[44]  K. Ulaczyk,et al.  Discovery of a Jupiter/Saturn Analog with Gravitational Microlensing , 2008, Science.

[45]  B. Scott Gaudi,et al.  Characterization of Gravitational Microlensing Planetary Host Stars , 2007 .

[46]  J. Beaulieu,et al.  Galactic Bulge microlensing optical depth from EROS-2 , 2006, astro-ph/0601510.

[47]  K. Ulaczyk,et al.  Microlens OGLE-2005-BLG-169 Implies That Cool Neptune-like Planets Are Common , 2006 .

[48]  P. M. Vreeswijk,et al.  LIMITS ON THE ABUNDANCE OF GALACTIC PLANETS FROM 5 YEARS OF PLANET OBSERVATIONS , 2000 .

[49]  K. Ulaczyk,et al.  A Jovian-Mass Planet in Microlensing Event OGLE-2005-BLG-071 , 2005 .

[50]  P. Vreeswijk,et al.  The 1995 Pilot Campaign of PLANET: Searching for Microlensing Anomalies through Precise, Rapid, Round-the-Clock Monitoring , 1998, astro-ph/9807299.

[51]  E. Ofek,et al.  Search for Low-Mass Exoplanets by Gravitational Microlensing at High Magnification , 2004, Science.

[52]  Andrew Gould,et al.  The Mass of the MACHO-LMC-5 Lens Star , 2004 .

[53]  S. Peale,et al.  Comparison of a Ground-based Microlensing Search for Planets with a Search from Space , 2003 .

[54]  M. Dominik The binary gravitational lens and its extreme cases , 1999, astro-ph/9903014.

[55]  Gravitational Microlensing Events Due to Stellar-Mass Black Holes* , 2001, astro-ph/0109467.

[56]  R. Kantowski,et al.  The spheroidal gravitational lens , 1973 .

[57]  A. J. Drake,et al.  The MACHO Project: Microlensing Optical Depth Toward the Galactic Bulge from Difference Image Analysis , 2000 .

[58]  J. Beaulieu,et al.  Limits on stellar and planetary companions in microlensing event OGLE-1998-BUL-14 , 1999, astro-ph/9909325.

[59]  Gregory Laughlin,et al.  The Core Accretion Model Predicts Few Jovian-Mass Planets Orbiting Red Dwarfs , 2004, astro-ph/0407309.

[60]  D. Bennett Large Magellanic Cloud Microlensing Optical Depth with Imperfect Event Selection , 2005, astro-ph/0502354.

[61]  O. Shemmer,et al.  Discovery of a planet orbiting a binary star system from gravitational microlensing , 1999, Nature.

[62]  A. Gal-Yam,et al.  OGLE-2003-BLG-262: Finite-Source Effects from a Point-Mass Lens , 2003, astro-ph/0309302.

[63]  S. Refsdal,et al.  Flux variations of QSO 0957 + 561 A, B and image splitting by stars near the light path , 1979, Nature.

[64]  S. Refsdal,et al.  Star disturbances in gravitational lens galaxies , 1984 .

[65]  Andrew Gould,et al.  Extending the MACHO Search to approximately 10 6 M sub sun , 1992 .

[66]  A. Gould,et al.  Stokes's Theorem Applied to Microlensing of Finite Sources , 1997 .

[67]  Germany,et al.  Resolving gravitational microlensing events with long-baseline optical interferometry Prospects for the ESO Very Large Telescope Interferometer , 2001 .

[68]  David P. Bennett,et al.  Detecting Earth-Mass Planets with Gravitational Microlensing , 1996, astro-ph/9603158.

[69]  P. Schneider,et al.  A gravitational lens origin for AGN-variability? Consequences of micro-lensing , 1987 .

[70]  Bohdan Paczynski,et al.  The Optical Gravitational Lensing Experiment. The Early Warning System: Real Time Microlensing , 1994 .

[71]  Bohdan Paczynski,et al.  The optical gravitational lensing experiment. Discovery of the first candidate microlensing event in the direction of the Galactic Bulge , 1993 .

[72]  R. Rosenfeld Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[73]  D. Frail,et al.  A planetary system around the millisecond pulsar PSR1257 + 12 , 1992, Nature.

[74]  B. Peterson,et al.  Real-Time Detection and Multisite Observations of Gravitational Microlensing , 1996 .

[75]  R. A. Street,et al.  Surveys, Temporal Variability, and the Las Cumbres Observatory Global Telescope , 2007 .

[76]  B. Scott Gaudi,et al.  Distinguishing Between Binary-Source and Planetary Microlensing Perturbations , 1998 .

[77]  Parallax microlensing events in the OGLE II data base toward the Galactic bulge , 2001, astro-ph/0108214.

[78]  P. J. Quinn,et al.  Possible gravitational microlensing of a star in the Large Magellanic Cloud , 1993, Nature.

[79]  Andrew Gould,et al.  Extreme Microlensing toward the Galactic Bulge , 1997 .

[80]  K. Sahu Stars within the Large Magellanic Cloud as potential lenses for observed microlensing events , 1994, Nature.

[81]  B. Gaudi,et al.  Ground-based Microlensing Surveys , 2007, 0704.0767.

[82]  David P. Bennett,et al.  Simulation of a Space-based Microlensing Survey for Terrestrial Extrasolar Planets , 2002 .

[83]  P. Schneider,et al.  The two-point-mass lens: detailed investigation of a special asymmetric gravitational lens , 1986 .

[84]  P. Yock,et al.  Wide-Field Camera for Gravitational Microlensing Survey: MOA-cam2 , 2000 .

[85]  F. Bouchy,et al.  The HARPS search for southern extra-solar planets - XVII. Super-Earth and Neptune-mass planets in multiple planet systems HD 47 186 and HD 181 433 , 2008, 0812.1608.

[86]  B.A.Peterson,et al.  Observations of the Binary Microlens Event MACHO 98-SMC-1 by the Microlensing Planet Search Collaboration , 1998, astro-ph/9812252.

[87]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[88]  T. Nakamura,et al.  Study by MOA of extrasolar planets in gravitational microlensing events of high magnification , 2001, astro-ph/0102184.

[89]  A. Drake,et al.  Erratum: "The MACHO Project: Microlensing Optical Depth toward the Galactic Bulge from Difference Image Analysis" (ApJ, 541, 734 [2000]) , 2001 .

[90]  H.Sato,et al.  On Planetary Companions to the MACHO-98-BLG-35 Microlens Star , 1999 .

[91]  M. Dominik,et al.  Detection of Rotation in a Binary Microlens: PLANET Photometry of MACHO 97-BLG-41* , 2000 .

[92]  K. Zebrun,et al.  OGLE 2003-BLG-235/MOA 2003-BLG-53: A Planetary Microlensing Event , 2004 .

[93]  Real-Time Detection of Gravitational Microlensing , 1995, astro-ph/9508039.

[94]  S. Refsdal On the possibility of determining Hubble's parameter and the masses of galaxies from the gravitational lens effect , 1964 .

[95]  William J. Borucki,et al.  The Kepler Mission: A wide-field transit search for terrestrial planets , 2005 .

[96]  B. Gaudi,et al.  Direct Detection of Large Close-in Planets around the Source Stars of Caustic-crossing Microlensing Events , 2000, astro-ph/0004089.

[97]  David P. Bennett The Detection of Terrestrial Planets via Gravitational Microlensing: Space vs. Ground-based Surveys , 2004 .

[98]  M. J. Lehner,et al.  First Observation of Parallax in a Gravitational Microlensing Event , 1995, astro-ph/9506114.

[99]  Predicting Stellar Angular Sizes , 1999, astro-ph/9904295.

[100]  Andrew Gould,et al.  Planet Parameters in Microlensing Events , 1996, astro-ph/9610123.

[101]  The Many Possible Interpretations of Microlensing Event OGLE 2002-BLG-055 , 2004, astro-ph/0402417.