Advertisement

Finding Planets via Gravitational Microlensing

  • Virginie BatistaEmail author
Reference work entry

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

  1. Albrow MD, Beaulieu J-P, Caldwell JAR et al (1999) A complete set of solutions for caustic crossing binary microlensing events. ApJ 522:1022ADSGoogle Scholar
  2. Alcock C, Allsman RA, Alves D et al (1995) First observation of parallax in a gravitational microlensing event. ApJ 454:L125+Google Scholar
  3. An JH (1999) The binary gravitational lens and its extreme cases. A&A 349:108Google Scholar
  4. 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 508:467ADSGoogle Scholar
  5. Batista V, Gould A, Dieters S et al (2011) MOA-2009-BLG-387Lb: a massive planet orbiting an M dwarf. A&A 529:102Google Scholar
  6. Batista V, Beaulieu J-P, Gould A et al (2014) MOA-2011-BLG-293Lb: first microlensing planet possibly in the habitable zone. ApJ 780:54ADSGoogle Scholar
  7. 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 808:170ADSGoogle Scholar
  8. Beaulieu J-P, Bennett DP, Fouqué P et al (2006) Discovery of a cool planet of 5.5 Earth masses through gravitational microlensing. Nature 439:437Google Scholar
  9. Beaulieu J-P, Kerins E, Mao S et al (2008) Towards a census of Earth-mass exo-planets with gravitational microlensing. arXiv:0808.0005Google Scholar
  10. 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 824:83ADSGoogle Scholar
  11. Bennett DP (2008) Detection of extrasolar planets by gravitational microlensing. Exoplanets, Springer praxis books. Praxis Publishing Ltd, Chichester, p 47. ISBN:978-3-540-74007-0Google Scholar
  12. Bennett DP (2010) An efficient method for modeling high-magnification planetary microlensing events. ApJ 716:1408ADSGoogle Scholar
  13. Bennett DP, Rhie SH (1996) Detecting Earth-mass planets with gravitational microlensing. ApJ 472:660ADSGoogle Scholar
  14. 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, 7006Google Scholar
  15. 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 38:1105Google Scholar
  16. 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 684:663ADSGoogle Scholar
  17. 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 713:837ADSGoogle Scholar
  18. Bennett DP, Sumi T, Bond I et al (2012) Planetary and other short binary microlensing events from the MOA short-event analysis. ApJ 757:119ADSGoogle Scholar
  19. 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 785:155ADSGoogle Scholar
  20. 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 808:169ADSGoogle Scholar
  21. Bennett DP, Rhie SH, Udalski A et al (2016) The first circumbinary planet found by microlensing: OGLE-2007-BLG-349L(AB)c. AJ 152:125ADSGoogle Scholar
  22. 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, 147Google Scholar
  23. Bond IA, Abe F, Dodd RJ et al (2001) Real-time difference imaging analysis of MOA galactic bulge observations during 2000. MNRAS 327:868ADSGoogle Scholar
  24. Bond IA, Udalski A, Jaroszynski M et al (2004) OGLE 2003-BLG-235/MOA 2003-BLG-53: a planetary microlensing event. ApJ 606:155ADSGoogle Scholar
  25. Bonfils X, Delfosse X, Udry S et al (2013) The HARPS search for southern extra-solar planets. XXXI. The M-dwarf sample. A&A 549:109Google Scholar
  26. Boss A (2006) Rapid formation of gas giant planets around M dwarf stars. ApJ 643:501ADSGoogle Scholar
  27. 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 216:7ADSGoogle Scholar
  28. Bozza V (2010) Microlensing with an advanced contour integration algorithm: green’s theorem to third order, error control, optimal sampling and limb darkening. MNRAS 408:2188ADSGoogle Scholar
  29. Calchi Novati S, Scarpetta G (2016) Microlensing parallax for observers in heliocentric motion. ApJ 824:109ADSGoogle Scholar
  30. 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 804:20ADSGoogle Scholar
  31. Cassan A, Kubas D, Beaulieu J-P et al (2012) One or more bound planets per Milky Way star from microlensing observations. Nature 481:167ADSGoogle Scholar
  32. Chang K, Refsdal S (1979) Flux variations of QSO 0957+561 A, B and image splitting by stars near the light path. Nature 282:561ADSGoogle Scholar
  33. 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 768:129ADSGoogle Scholar
  34. 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 819:125ADSGoogle Scholar
  35. 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 834:46ADSGoogle Scholar
  36. 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 120:531ADSGoogle Scholar
  37. Dominik M (1995) Improved routines for the inversion of the gravitational lens equation for a set of source points. A&A 109:597ADSGoogle Scholar
  38. Dominik M (1998) A robust and efficient method for calculating the magnification of extended sources caused by gravitational lenses. A&A 333:79ADSGoogle Scholar
  39. Dominik M (1999) The binary gravitational lens and its extreme cases. A&A 349:108ADSGoogle Scholar
  40. Dominik M, Sahu KC(2000) Astrometric microlensing of stars. ApJ 534:213ADSGoogle Scholar
  41. Dong S, Udalski A, Gould A et al (2007) First space-based microlens parallax measurement: Spitzer observations of OGLE-2005-SMC-001. ApJ 664:862ADSGoogle Scholar
  42. Dong S, Gould A, Udalski A et al (2009) OGLE-2005-BLG-071Lb, the most massive M dwarf planetary companion? ApJ 695:970ADSGoogle Scholar
  43. Duchene G, Kraus A (2013) Stellar multiplicity. A&A 51:269ADSGoogle Scholar
  44. 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 248:485Google Scholar
  45. Einstein A (1936) Lens-like action of a star by the deviation of light in the gravitational field. Science 84:506ADSzbMATHGoogle Scholar
  46. 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 809:74ADSGoogle Scholar
  47. Furusawa K, Udalski A, Sumi T et al (2013) MOA-2010-BLG-328Lb: a sub-Neptune orbiting very late M dwarf? ApJ 779:91ADSGoogle Scholar
  48. Gaudi BS (2012) Microlensing surveys for exoplanets. ARA&A 50:411ADSGoogle Scholar
  49. 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 566:463ADSGoogle Scholar
  50. Gaudi BS, Bennett DP, Udalski A et al (2008) Discovery of a Jupiter/Saturn analog with gravitational microlensing. Science 319:927ADSGoogle Scholar
  51. Gorbikov E, Brosch N, Afonso C (2010) A two-color CCD survey of the North celestial cap: I. The method. Ap&SS 326:203Google Scholar
  52. Gould A (1994) MACHO velocities from satellite-based parallaxes. ApJ 421:75ADSGoogle Scholar
  53. Gould A (1999) Microlens parallaxes with SIRTF. ApJ 514:869ADSGoogle Scholar
  54. Gould A (2008) Hexadecapole approximation in planetary microlensing. ApJ 681:1593ADSGoogle Scholar
  55. Gould A, Gaucherel C (1997) Stokes’s theorem applied to microlensing of finite sources. ApJ 477:580ADSGoogle Scholar
  56. Gould A, Horne K (2013) Kepler-like multi-plexing for mass production of microlens parallaxes. ApJ 779:28ADSGoogle Scholar
  57. Gould A, Loeb A (1992) Discovering planetary systems through gravitational microlenses. ApJ 396:104ADSGoogle Scholar
  58. Gould A, Udalski A, An D et al (2006) Microlens OGLE-2005-BLG-169 implies that cool Neptune-like planets are common. ApJ 644:37ADSGoogle Scholar
  59. 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 720:1073ADSGoogle Scholar
  60. Gould A, Carey S, Yee J (2014a) Galactic distribution of planets from Spitzer microlens parallaxes. sptz.prop11006GGoogle Scholar
  61. 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 345:46ADSGoogle Scholar
  62. Gould A, Yee J, Carey S (2015) Galactic distribution of planets from high-magnification microlensing events. sptz.prop12013GGoogle Scholar
  63. Griest K, Safizadeh N (1998) The use of high-magnification microlensing events in discovering extrasolar planets. ApJ 500:37ADSGoogle Scholar
  64. Han C, Gould A (1995) Statistics of microlensing optical depth. ApJ 449:521ADSGoogle Scholar
  65. Han C, Gould A (2003) Stellar contribution to the galactic bulge microlensing optical depth. ApJ 592:172ADSGoogle Scholar
  66. 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 778:38ADSGoogle Scholar
  67. 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 828:53ADSGoogle Scholar
  68. 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 152:95ADSGoogle Scholar
  69. Henderson CB, Park H, Sumi T et al (2014) Candidate gravitational microlensing events for future direct lens imaging. ApJ 794:71ADSGoogle Scholar
  70. 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 128:14401Google Scholar
  71. Hog E, Novikov ID, Polnarev AG et al (1995) MACHO photometry and astrometry. A&A 294:287ADSGoogle Scholar
  72. Howard AW, Marcy GW, Johnson JA et al (2010) The occurrence and mass distribution of close-in super-Earths, Neptunes, and Jupiters. Science 330:653ADSGoogle Scholar
  73. Howell SB, Sobeck C, Haas M et al (2014) The K2 mission: characterization and early results. PASP 126:398ADSGoogle Scholar
  74. 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 604:388ADSGoogle Scholar
  75. Janczak J, Fukui A, Dong S et al (2010) Sub-Saturn planet MOA-2008-BLG-310Lb: likely to be in the galactic bulge. ApJ 711:731ADSGoogle Scholar
  76. Johnson JA, Aller KM, Howard AW et al (2010) Giant planet occurrence in the stellar mass-metallicity plane. PASP 122:905ADSGoogle Scholar
  77. 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 798:123ADSGoogle Scholar
  78. Kaib NA, Raymond SN, Duncan M (2013) Planetary system disruption by galactic perturbations to wide binary stars. Nature 493:381ADSGoogle Scholar
  79. 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 552:70Google Scholar
  80. Kains N, Bramich DM, Sahu KC et al (2016) Searching for intermediate-mass black holes in globular clusters with gravitational microlensing. MNRAS 460:2025ADSGoogle Scholar
  81. Kervella P, Thévenin F, Di Folco E (2004) The angular sizes of dwarf stars and subgiants. Surface brightness relations calibrated by interferometry. A&A 426:297ADSGoogle Scholar
  82. 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 49:37ADSGoogle Scholar
  83. 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 153:1ADSGoogle Scholar
  84. 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 540:78Google Scholar
  85. Lafrenière D, Doyon R, Marois C et al (2007) The gemini deep planet survey. ApJ 670:1367ADSGoogle Scholar
  86. Laughlin G, Bodenheimer P, Adams FC (2004) The core accretion model predicts few Jovian-mass planets orbiting red dwarfs. ApJ 612:73ADSGoogle Scholar
  87. Lodato G, Delgado-Donate E, Clarke CJ (2005) Constraints on the formation mechanism of the planetary mass companion of 2MASS 1207334-393254. MNRAS 364:91ADSGoogle Scholar
  88. Mao S (1999) An ongoing parallax microlensing event OGLE-1999-CAR-1 toward Carina. A&A 350:L19ADSGoogle Scholar
  89. Mao S, Paczynski B (1991) Gravitational microlensing by double stars and planetary systems. ApJ 374:37ADSGoogle Scholar
  90. 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 329:349ADSGoogle Scholar
  91. 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 507:487ADSGoogle Scholar
  92. Montet BT, Crepp JR, Johnson JA (2014) The TRENDS High-contrast imaging survey. IV. The occurrence rate of giant planets around M dwarfs. ApJ 781:28ADSGoogle Scholar
  93. 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 741:22ADSGoogle Scholar
  94. 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 769:88ADSGoogle Scholar
  95. Nemiroff RJ, Wickramasinghe (1994) Finite source sizes and the information content of macho-type lens search light curves. ApJ 424:21ADSGoogle Scholar
  96. Paczynski B (1986) Gravitational microlensing by the galactic halo. ApJ 304:1ADSGoogle Scholar
  97. Pejcha O, Heyrovsky D (2009) Extended-source effect and chromaticity in two-point-mass microlensing. ApJ 690:1772ADSGoogle Scholar
  98. Penny MT, Kerins E, Rattenbury N et al (2013) ExELS: an exoplanet legacy science proposal for the ESA Euclid mission – I. Cold exoplanets. MNRAS 434:2Google Scholar
  99. 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:1605.01059Google Scholar
  100. Poindexter S, Afonso C, Bennett DP et al (2005) Systematic analysis of 22 microlensing parallax candidates. ApJ 633:914ADSGoogle Scholar
  101. 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 795:42ADSGoogle Scholar
  102. Raghavan D, McAlister HA, Henry TJ et al (2002) A survey of stellar families: multiplicity of solar-type stars. ApJ 190:1Google Scholar
  103. Rattenbury NJ, Bond IA, Skuljan J et al (2002) Planetary microlensing at high magnification. MNRAS 335:159ADSGoogle Scholar
  104. Refsdal S(1964) The gravitational lens effect. MNRAS 128:295ADSMathSciNetzbMATHGoogle Scholar
  105. Refsdal S(1966) On the possibility of determining the distances and masses of stars from the gravitational lens effect. MNRAS 134:315ADSGoogle Scholar
  106. Rhie SH (1997) Infimum Microlensing Amplification of the maximum number of images of n-Point lens systems. ApJ 484:63ADSGoogle Scholar
  107. Rhie SH (2002) How cumbersome is a tenth order polynomial? The case of gravitational triple lens equation. Astroph 2294R. arXiv:astro-ph/0202294Google Scholar
  108. Rhie SH, Bennett DP, Becker AC et al (2000) On planetary companions to the MACHO 98-BLG-35 microlens star. ApJ 533:378ADSGoogle Scholar
  109. 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 22:51ADSGoogle Scholar
  110. Schneider DP, Weiss A (1986) The two-point-mass lens – detailed investigation of a special asymmetric gravitational lens. A&A 164:237ADSGoogle Scholar
  111. Shvartzvald Y, Udalski A, Gould A et al (2015) Spitzer microlens measurement of a massive remnant in a well-separated binary. ApJ 814:111ADSGoogle Scholar
  112. 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 457:4089ADSGoogle Scholar
  113. Skowron, J, Udalski A, Gould A et al (2011) Binary microlensing event OGLE-2009-BLG-020 gives verifiable mass, distance, and orbit predictions. ApJ 738:87ADSGoogle Scholar
  114. 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 395–405Google Scholar
  115. Snodgrass C, Horne K, Tsapras Y (2004) The abundance of galactic planets from OGLE-III 2002 microlensing data. MNRAS 351:967ADSGoogle Scholar
  116. Spergel D, Gehrels N, Baltay C et al (2015) Wide-field infrarRed survey telescope-astrophysics focused telescope assets WFIRST-AFTA 2015 report. eprint arXiv:1503.03757Google Scholar
  117. 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 819:93ADSGoogle Scholar
  118. Sumi T, Bennett DP, Bond IA et al (2010) A cold Neptune-mass planet OGLE-2007-BLG-368Lb: cold Neptunes are common. ApJ 710:1641ADSGoogle Scholar
  119. Sumi T, Kamiya K, Bennett DP et al (2011) Unbound or distant planetary mass population detected by gravitational microlensing. Nature 473:349ADSGoogle Scholar
  120. Sumi T, Bennett DP, Bond IA et al (2013) The microlensing event rate and optical depth toward the galactic bulge from MOA-II. ApJ 778:150ADSGoogle Scholar
  121. 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 825:112ADSGoogle Scholar
  122. 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 833:145ADSGoogle Scholar
  123. Thompson TA (2013) Gas giants in hot water: inhibiting giant planet formation and planet habitability in dense star clusters through cosmic time. MNRAS 431:63ADSGoogle Scholar
  124. Udalski A (2003) The optical gravitational lensing experiment. Real time data analysis systems in the OGLE-III survey. Acta Astron 53:291Google Scholar
  125. 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 799:237ADSGoogle Scholar
  126. Wambsganss J (1997) Discovering galactic planets by gravitational microlensing: magnification patterns and light curves. MNRAS 284:172ADSGoogle Scholar
  127. Wang J, Fischer DA (2015) Revealing a universal planet-metallicity correlation for planets of different sizes around solar-type stars. AJ 149:14ADSGoogle Scholar
  128. Werner MW, Roellig TL, Low FJ et al (2004) The Spitzer space telescope mission. ApJ 154:1Google Scholar
  129. Winn JN, Fabrycky DC (2015) The occurrence and architecture of exoplanetary systems. ARA&A 53:409ADSGoogle Scholar
  130. 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–+Google Scholar
  131. Witt HJ, Mao S (1995) On the minimum magnification between caustic crossings for microlensing by binary and multiple stars. ApJ 447:L105+Google Scholar
  132. Wyrzykowski L, Kostrzewa-Rutkowska Z, Skowron J et al (2016) Black hole, neutron star and white dwarf candidates from microlensing with OGLE-III. MNRAS 458:3012ADSGoogle Scholar
  133. 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 802:76ADSGoogle Scholar
  134. 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 821:121ADSGoogle Scholar
  135. Zhu W, Wang J, Huang C et al (2016) Dependence of small planet frequency on stellar metallicity hidden by their prevalence. ApJ 832:196ADSGoogle Scholar
  136. 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:1701.05191Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut d’astrophysique de ParisParisFrance
  2. 2.Centre National d’Etudes SpatialesParis Cedex 1France

Personalised recommendations