Abstract
Gravitational microlensing is a technique to probe compact objects toward the center of the galaxy, such as distant stars, planets, white and brown dwarfs, black holes, and neutron stars. Since the first microlensing planet discovered in 2003, more than 40 planets have been detected with this technique, as well as several black hole candidates, and a population of potential free-floating planets. This chapter first provides a presentation of the microlensing theory, including numerical aspects to solve binary and triple lens problems, and a discussion of the microlensing planetary detection efficiency, with a high potential regarding cold planets beyond the snow line. It also explains how the planetary characterization can be facilitated when the microlensing light curves exhibit distortions due to second-order effects, such as parallax, planetary orbital motion, and extended source, and how they can also introduce degeneracies in the models. The chapter then reviews the main discoveries to date and the recent statistical results from high-cadence ground-based surveys and space-based observations, especially on the planet mass function and the distance distribution of the microlensing planetary systems. Finally, future prospects are discussed, with the expected advances from dedicated space missions, extending the planet sensitivity range down to Mercury masses.
References
Albrow MD, Beaulieu J-P, Caldwell JAR et al (1999) A complete set of solutions for caustic crossing binary microlensing events. ApJ 522:1022
Alcock C, Allsman RA, Alves D et al (1995) First observation of parallax in a gravitational microlensing event. ApJ 454:L125+
An JH (1999) The binary gravitational lens and its extreme cases. A&A 349:108
Batista V, Dong S, Gould A et al (2009) Mass measurement of a single unseen star and planetary detection efficiency for OGLE 2007-BLG-050. A&A 508:467
Batista V, Gould A, Dieters S et al (2011) MOA-2009-BLG-387Lb: a massive planet orbiting an M dwarf. A&A 529:102
Batista V, Beaulieu J-P, Gould A et al (2014) MOA-2011-BLG-293Lb: first microlensing planet possibly in the habitable zone. ApJ 780:54
Batista V, Beaulieu J-P, Bennett DP et al (2015) Confirmation of the OGLE-2005-BLG-169 planet signature and its characteristics with lens-source proper motion detection. ApJ 808:170
Beaulieu J-P, Bennett DP, Fouqué P et al (2006) Discovery of a cool planet of 5.5 Earth masses through gravitational microlensing. Nature 439:437
Beaulieu J-P, Kerins E, Mao S et al (2008) Towards a census of Earth-mass exo-planets with gravitational microlensing. arXiv:0808.0005
Beaulieu J-P, Bennett DP, Batista V et al (2016) Revisiting the microlensing event OGLE 2012-BLG-0026: a solar mass star with two cold giant planets. ApJ 824:83
Bennett DP (2008) Detection of extrasolar planets by gravitational microlensing. Exoplanets, Springer praxis books. Praxis Publishing Ltd, Chichester, p 47. ISBN:978-3-540-74007-0
Bennett DP (2010) An efficient method for modeling high-magnification planetary microlensing events. ApJ 716:1408
Bennett DP, Rhie SH (1996) Detecting Earth-mass planets with gravitational microlensing. ApJ 472:660
Bennett DP, Becker AC, Calitz JJ et al (2002) The microlensing event MACHO-99-BLG-22/OGLE-1999-BUL-32: an intermediate mass black hole, or a lens in the bulge. astro.ph, 7006
Bennett DP, Anderson J, Gaudi BS et al (2006) Characterization of gravitational microlensing planetary host stars. In: DPS meeting 38, id.45.14; Bull Am Astron Soc 38:1105
Bennett DP, Bond IA, Udalski A et al (2008) A low-mass planet with a possible sub-stellar-mass host in microlensing event MOA-2007-BLG-192. ApJ 684:663
Bennett DP, Rhie SH, Nikolaev S et al (2010) Masses and orbital constraints for the OGLE-2006-BLG-109Lb,c Jupiter/Saturn analog planetary system. ApJ 713:837
Bennett DP, Sumi T, Bond I et al (2012) Planetary and other short binary microlensing events from the MOA short-event analysis. ApJ 757:119
Bennett DP, Batista V, Bond I et al (2014) MOA-2011-BLG-262Lb: a sub-Earth-mass moon orbiting a gas giant primary or a high velocity planetary system in the galactic bulge. ApJ 785:155
Bennett DP, Bhattacharya A, Anderson J et al (2015) Confirmation of the planetary microlensing signal and star and planet mass determinations for event OGLE-2005-BLG-169. ApJ 808:169
Bennett DP, Rhie SH, Udalski A et al (2016) The first circumbinary planet found by microlensing: OGLE-2007-BLG-349L(AB)c. AJ 152:125
Bensby T, Yee YC, Feltzing S et al (2013) Chemical evolution of the galactic bulge as traced by microlensed dwarf and subgiant stars. V. Evidence for a wide age distribution and a complex MDF. A&A 549, 147
Bond IA, Abe F, Dodd RJ et al (2001) Real-time difference imaging analysis of MOA galactic bulge observations during 2000. MNRAS 327:868
Bond IA, Udalski A, Jaroszynski M et al (2004) OGLE 2003-BLG-235/MOA 2003-BLG-53: a planetary microlensing event. ApJ 606:155
Bonfils X, Delfosse X, Udry S et al (2013) The HARPS search for southern extra-solar planets. XXXI. The M-dwarf sample. A&A 549:109
Boss A (2006) Rapid formation of gas giant planets around M dwarf stars. ApJ 643:501
Bowler BP, Liu MC, Shkolnik E et al (2015) Planets around low-mass stars (PALMS). IV. The outer architecture of M dwarf planetary systems. ApJS 216:7
Bozza V (2010) Microlensing with an advanced contour integration algorithm: green’s theorem to third order, error control, optimal sampling and limb darkening. MNRAS 408:2188
Calchi Novati S, Scarpetta G (2016) Microlensing parallax for observers in heliocentric motion. ApJ 824:109
Calchi Novati S, Gould A, Udalski A et al (2015) Pathway to the galactic distribution of planets: combined Spitzer and ground-based microlens parallax measurements of 21 single-lens events. ApJ 804:20
Cassan A, Kubas D, Beaulieu J-P et al (2012) One or more bound planets per Milky Way star from microlensing observations. Nature 481:167
Chang K, Refsdal S (1979) Flux variations of QSO 0957+561 A, B and image splitting by stars near the light path. Nature 282:561
Choi J-Y, Han C, Udalski A et al (2013) Microlensing discovery of a population of very tight, very low mass binary brown dwarfs. ApJ 768:129
Clanton C, Gaudi BS (2016) Synthesizing exoplanet demographics: a single population of long-period planetary companions to M dwarfs consistent with microlensing, radial velocity, and direct imaging surveys. ApJ 819:125
Clanton C, Gaudi BS (2017) Constraining the frequency of free-floating planets from a synthesis of microlensing, radial velocity, and direct imaging survey results. ApJ 834:46
Cumming A, Butler RP, Marcy GW et al (2008) The Keck planet search: detectability and the minimum mass and orbital period distribution of extrasolar planets. PASP 120:531
Dominik M (1995) Improved routines for the inversion of the gravitational lens equation for a set of source points. A&A 109:597
Dominik M (1998) A robust and efficient method for calculating the magnification of extended sources caused by gravitational lenses. A&A 333:79
Dominik M (1999) The binary gravitational lens and its extreme cases. A&A 349:108
Dominik M, Sahu KC(2000) Astrometric microlensing of stars. ApJ 534:213
Dong S, Udalski A, Gould A et al (2007) First space-based microlens parallax measurement: Spitzer observations of OGLE-2005-SMC-001. ApJ 664:862
Dong S, Gould A, Udalski A et al (2009) OGLE-2005-BLG-071Lb, the most massive M dwarf planetary companion? ApJ 695:970
Duchene G, Kraus A (2013) Stellar multiplicity. A&A 51:269
Duquennoy A, Mayor M (1991) Multiplicity among solar-type stars in the solar neighbourhood. II – distribution of the orbital elements in an unbiased sample. A&A 248:485
Einstein A (1936) Lens-like action of a star by the deviation of light in the gravitational field. Science 84:506
Fukui A, Gould A, Sumi T et al (2015) OGLE-2012-BLG-0563Lb: a saturn-mass planet around an M dwarf with the mass constrained by Subaru AO imaging. ApJ 809:74
Furusawa K, Udalski A, Sumi T et al (2013) MOA-2010-BLG-328Lb: a sub-Neptune orbiting very late M dwarf? ApJ 779:91
Gaudi BS (2012) Microlensing surveys for exoplanets. ARA&A 50:411
Gaudi BS, Albrow MD, An J et al (2002) Microlensing constraints on the frequency of Jupiter-mass companions: analysis of 5 years of PLANET photometry. ApJ 566:463
Gaudi BS, Bennett DP, Udalski A et al (2008) Discovery of a Jupiter/Saturn analog with gravitational microlensing. Science 319:927
Gorbikov E, Brosch N, Afonso C (2010) A two-color CCD survey of the North celestial cap: I. The method. Ap&SS 326:203
Gould A (1994) MACHO velocities from satellite-based parallaxes. ApJ 421:75
Gould A (1999) Microlens parallaxes with SIRTF. ApJ 514:869
Gould A (2008) Hexadecapole approximation in planetary microlensing. ApJ 681:1593
Gould A, Gaucherel C (1997) Stokes’s theorem applied to microlensing of finite sources. ApJ 477:580
Gould A, Horne K (2013) Kepler-like multi-plexing for mass production of microlens parallaxes. ApJ 779:28
Gould A, Loeb A (1992) Discovering planetary systems through gravitational microlenses. ApJ 396:104
Gould A, Udalski A, An D et al (2006) Microlens OGLE-2005-BLG-169 implies that cool Neptune-like planets are common. ApJ 644:37
Gould A, Dong S, Gaudi BS (2010) Frequency of solar-like systems and of ice and gas giants beyond the snow line from high-magnification microlensing events in 2005–2008. ApJ 720:1073
Gould A, Carey S, Yee J (2014a) Galactic distribution of planets from Spitzer microlens parallaxes. sptz.prop11006G
Gould A, Udalski A, Shin I-G et al (2014b) A terrestrial planet in a ∼1-AU orbit around one member of a ∼15-AU binary. Science 345:46
Gould A, Yee J, Carey S (2015) Galactic distribution of planets from high-magnification microlensing events. sptz.prop12013G
Griest K, Safizadeh N (1998) The use of high-magnification microlensing events in discovering extrasolar planets. ApJ 500:37
Han C, Gould A (1995) Statistics of microlensing optical depth. ApJ 449:521
Han C, Gould A (2003) Stellar contribution to the galactic bulge microlensing optical depth. ApJ 592:172
Han C, Jung YK, Udalski A et al (2016) Microlensing discovery of a tight, low-mass-ratio planetary-mass object around an old field brown dwarf. ApJ 778:38
Han C, Udalski A, Gould A et al (2016a) OGLE-2015-BLG-0479LA,B: binary gravitational microlens characterized by simultaneous ground-based and space-based observations. ApJ 828:53
Han C, Udalski A, Gould A et al (2016b) OGLE-2015-BLG-0051/KMT-2015-BLG-0048Lb: a giant planet orbiting a low-mass bulge star discovered by high-cadence microlensing surveys. AJ 152:95
Henderson CB, Park H, Sumi T et al (2014) Candidate gravitational microlensing events for future direct lens imaging. ApJ 794:71
Henderson CB, Poleski R, Penny M et al (2016) Campaign 9 of the K2 mission: observational parameters, scientific drivers, and community involvement for a simultaneous space- and ground-based microlensing survey. PASP 128:14401
Hog E, Novikov ID, Polnarev AG et al (1995) MACHO photometry and astrometry. A&A 294:287
Howard AW, Marcy GW, Johnson JA et al (2010) The occurrence and mass distribution of close-in super-Earths, Neptunes, and Jupiters. Science 330:653
Howell SB, Sobeck C, Haas M et al (2014) The K2 mission: characterization and early results. PASP 126:398
Ida S, Lin DNC (2004) Toward a deterministic model of planetary formation. I. A desert in the mass and semimajor axis distributions of extrasolar planets. ApJ 604:388
Janczak J, Fukui A, Dong S et al (2010) Sub-Saturn planet MOA-2008-BLG-310Lb: likely to be in the galactic bulge. ApJ 711:731
Johnson JA, Aller KM, Howard AW et al (2010) Giant planet occurrence in the stellar mass-metallicity plane. PASP 122:905
Jung YK, Udalski A, Sumi T et al (2015) OGLE-2013-BLG-0102LA,B: microlensing binary with components at star/brown dwarf and brown dwarf/planet boundaries. ApJ 798:123
Kaib NA, Raymond SN, Duncan M (2013) Planetary system disruption by galactic perturbations to wide binary stars. Nature 493:381
Kains N,Street RA, Choi J-Y et al (2013) A giant planet beyond the snow line in microlensing event OGLE-2011-BLG-0251. A&A 552:70
Kains N, Bramich DM, Sahu KC et al (2016) Searching for intermediate-mass black holes in globular clusters with gravitational microlensing. MNRAS 460:2025
Kervella P, Thévenin F, Di Folco E (2004) The angular sizes of dwarf stars and subgiants. Surface brightness relations calibrated by interferometry. A&A 426:297
Kim S-L, Lee C-U, Park B-G et al (2016) KMTNET: a network of 1.6 m wide-field optical telescopes installed at three Southern observatories. JKAS 49:37
Koshimoto N, Udalski A, Beaulieu J-P et al (2016) OGLE-2012-BLG-0950Lb: the first planet mass measurement from only microlens parallax and lens flux. AJ 153:1
Kubas D, Beaulieu J-P, Bennett DP et al (2012) A frozen super-Earth orbiting a star at the bottom of the main sequence. A&A 540:78
Lafrenière D, Doyon R, Marois C et al (2007) The gemini deep planet survey. ApJ 670:1367
Laughlin G, Bodenheimer P, Adams FC (2004) The core accretion model predicts few Jovian-mass planets orbiting red dwarfs. ApJ 612:73
Lodato G, Delgado-Donate E, Clarke CJ (2005) Constraints on the formation mechanism of the planetary mass companion of 2MASS 1207334-393254. MNRAS 364:91
Mao S (1999) An ongoing parallax microlensing event OGLE-1999-CAR-1 toward Carina. A&A 350:L19
Mao S, Paczynski B (1991) Gravitational microlensing by double stars and planetary systems. ApJ 374:37
Mao S, Smith MC, Wazniak P et al (2002) Optical gravitational lensing experiment OGLE-1999-BUL-32: the longest ever microlensing event – evidence for a stellar mass black hole? MNRAS 329:349
Mayor M, Bonfils X, Forveille T et al (2009) The HARPS search for southern extra-solar planets. XVIII. An Earth-mass planet in the GJ 581 planetary system. A&A 507:487
Montet BT, Crepp JR, Johnson JA (2014) The TRENDS High-contrast imaging survey. IV. The occurrence rate of giant planets around M dwarfs. ApJ 781:28
Muraki Y, Han C, Bennett DP et al (2011) Discovery and mass measurements of a cold, 10 Earth mass planet and its host star. ApJ 741:22
Nataf DM, Gould A, Fouqué P et al (2013) Reddening and extinction toward the galactic bulge from OGLE-III: the inner milky way’s Rv 2.5 extinction curve. ApJ 769:88
Nemiroff RJ, Wickramasinghe (1994) Finite source sizes and the information content of macho-type lens search light curves. ApJ 424:21
Paczynski B (1986) Gravitational microlensing by the galactic halo. ApJ 304:1
Pejcha O, Heyrovsky D (2009) Extended-source effect and chromaticity in two-point-mass microlensing. ApJ 690:1772
Penny MT, Kerins E, Rattenbury N et al (2013) ExELS: an exoplanet legacy science proposal for the ESA Euclid mission – I. Cold exoplanets. MNRAS 434:2
Penny MT, Rattenbury NJ, Gaudi BS et al (2016) Predictions for the detection and characterization of a population of free-floating planets with K2 campaign 9. arXiv:1605.01059
Poindexter S, Afonso C, Bennett DP et al (2005) Systematic analysis of 22 microlensing parallax candidates. ApJ 633:914
Poleski R, Skowron J, Udalski A et al (2014) Triple microlens OGLE-2008-BLG-092L: binary stellar system with a circumprimary Uranus-type planet. ApJ 795:42
Raghavan D, McAlister HA, Henry TJ et al (2002) A survey of stellar families: multiplicity of solar-type stars. ApJ 190:1
Rattenbury NJ, Bond IA, Skuljan J et al (2002) Planetary microlensing at high magnification. MNRAS 335:159
Refsdal S(1964) The gravitational lens effect. MNRAS 128:295
Refsdal S(1966) On the possibility of determining the distances and masses of stars from the gravitational lens effect. MNRAS 134:315
Rhie SH (1997) Infimum Microlensing Amplification of the maximum number of images of n-Point lens systems. ApJ 484:63
Rhie SH (2002) How cumbersome is a tenth order polynomial? The case of gravitational triple lens equation. Astroph 2294R. arXiv:astro-ph/0202294
Rhie SH, Bennett DP, Becker AC et al (2000) On planetary companions to the MACHO 98-BLG-35 microlens star. ApJ 533:378
Sako T, Sekiguchi T, Sasaki M et al (2008) MOA-cam3: a wide-field mosaic CCD camera for a gravitational microlensing survey in New Zealand. ExA 22:51
Schneider DP, Weiss A (1986) The two-point-mass lens – detailed investigation of a special asymmetric gravitational lens. A&A 164:237
Shvartzvald Y, Udalski A, Gould A et al (2015) Spitzer microlens measurement of a massive remnant in a well-separated binary. ApJ 814:111
Shvartzvald Y, Maoz D, Udalski A et al (2016) The frequency of snowline-region planets from four years of OGLE-MOA-Wise second-generation microlensing. MNRAS 457:4089
Skowron, J, Udalski A, Gould A et al (2011) Binary microlensing event OGLE-2009-BLG-020 gives verifiable mass, distance, and orbit predictions. ApJ 738:87
Smith C, Rest A, Hiriart R et al (2002) Real-time time-variability analysis of GB to TB datasets: experience from SuperMACHO and supernova projects at NOAO/CTIO. In: Tyson JA, Woll S (eds) Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) conference, vol 4836, pp 395–405
Snodgrass C, Horne K, Tsapras Y (2004) The abundance of galactic planets from OGLE-III 2002 microlensing data. MNRAS 351:967
Spergel D, Gehrels N, Baltay C et al (2015) Wide-field infrarRed survey telescope-astrophysics focused telescope assets WFIRST-AFTA 2015 report. eprint arXiv:1503.03757
Street RA, Udalski A, Calchi Novati S et al (2015) Spitzer parallax of OGLE-2015-BLG-0966: a cold Neptune in the galactic disk. ApJ 819:93
Sumi T, Bennett DP, Bond IA et al (2010) A cold Neptune-mass planet OGLE-2007-BLG-368Lb: cold Neptunes are common. ApJ 710:1641
Sumi T, Kamiya K, Bennett DP et al (2011) Unbound or distant planetary mass population detected by gravitational microlensing. Nature 473:349
Sumi T, Bennett DP, Bond IA et al (2013) The microlensing event rate and optical depth toward the galactic bulge from MOA-II. ApJ 778:150
Sumi T, Udalski A, Bennett DP et al (2016) The first Neptune analog or super-Earth with a Neptune-like orbit: MOA-2013-BLG-605Lb. ApJ 825:112
Suzuki D, Bennett DP, Sumi T et al (2016) The exoplanet mass-ratio function from the MOA-II survey: discovery of a break and likely peak at a Neptune mass. ApJ 833:145
Thompson TA (2013) Gas giants in hot water: inhibiting giant planet formation and planet habitability in dense star clusters through cosmic time. MNRAS 431:63
Udalski A (2003) The optical gravitational lensing experiment. Real time data analysis systems in the OGLE-III survey. Acta Astron 53:291
Udalski A, Yee JC, Gould A et al (2015) Spitzer as a microlens parallax satellite: mass measurement for the OGLE-2014-BLG-0124L planet and its host star. ApJ 799:237
Wambsganss J (1997) Discovering galactic planets by gravitational microlensing: magnification patterns and light curves. MNRAS 284:172
Wang J, Fischer DA (2015) Revealing a universal planet-metallicity correlation for planets of different sizes around solar-type stars. AJ 149:14
Werner MW, Roellig TL, Low FJ et al (2004) The Spitzer space telescope mission. ApJ 154:1
Winn JN, Fabrycky DC (2015) The occurrence and architecture of exoplanetary systems. ARA&A 53:409
Witt HJ (1990) Statistical investigations of the amplification near gravitational lens caustics. In: Mellier Y, Fort B, Saucail G (eds) Gravitational lensing. Lecture notes in physics, vol 360. Springer, Berlin, pp 192–+
Witt HJ, Mao S (1995) On the minimum magnification between caustic crossings for microlensing by binary and multiple stars. ApJ 447:L105+
Wyrzykowski L, Kostrzewa-Rutkowska Z, Skowron J et al (2016) Black hole, neutron star and white dwarf candidates from microlensing with OGLE-III. MNRAS 458:3012
Yee JC, Udalski A, Calchi Novati S et al (2015) First space-based microlens parallax measurement of an isolated star: Spitzer observations of OGLE-2014-BLG-0939. ApJ 802:76
Yee JC, Johnson JA, Skowron J et al (2016) Two stars two ways: confirming a microlensing binary lens solution with a spectroscopic measurement of the orbit. ApJ 821:121
Zhu W, Wang J, Huang C et al (2016) Dependence of small planet frequency on stellar metallicity hidden by their prevalence. ApJ 832:196
Zhu W, Udalski A, Calchi Novati S et al (2017) Toward a galactic distribution of planets. I. Methodology & planet sensitivities of the 2015 high-cadence Spitzer microlens sample. arXiv:1701.05191
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Batista, V. (2018). Finding Planets via Gravitational Microlensing. In: Deeg, H., Belmonte, J. (eds) Handbook of Exoplanets . Springer, Cham. https://doi.org/10.1007/978-3-319-30648-3_120-2
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Finding Planets via Gravitational Microlensing- Published:
- 15 December 2017
DOI: https://doi.org/10.1007/978-3-319-30648-3_120-2
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Finding Planets via Gravitational Microlensing- Published:
- 13 October 2017
DOI: https://doi.org/10.1007/978-3-319-30648-3_120-1