Planet Parameters in Microlensing Events

A planetary microlensing event occurs when a planet perturbs one of the two images created in a point-mass microlensing event, causing a deviation from the standard Paczynski curve. Determination of the two physical parameters that can be extracted from a planetary microlensing event, the planet/star mass ratio q, and the planet/star separation in units of the stellar Einstein ring, yp, is hampered by several types of degeneracies. There are two distinct and qualitatively different classes of planetary events: major and minor image perturbations. For major image perturbations, there is a potentially crippling continuous degeneracy in q which is of order δ -->−1d, where δd is the maximum fractional deviation of the planetary perturbation. Since the threshold of detection is expected to be δd ~ 5%, this degeneracy in q can be a factor of ~20. For minor image perturbations, the continuous degeneracy in q is considerably less severe, and is typically less than a factor of 4. We show that these degeneracies can be resolved by observations from dedicated telescopes on several continents together with optical/infrared photometry from one of these sites. There also exists a class of discrete degeneracies. These are typically easy to resolve given good temporal coverage of the planetary event. Unambiguous interpretation of planetary microlensing events requires the resolution of both types of degeneracy. We describe the degeneracies in detail and specify the situations in which they are problematic. We also describe how individual planet masses and physical projected separations can be measured.

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

[2]  C. Alard.  First results of the DUO program , 1996 .

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

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

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

[6]  H. Witt.  The Effect of the Stellar Size on Microlensing at the Baade Window , 1995 .

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

[8]  Cheongho Han,et al.  The Effects of Amplification Bias in Gravitational Microlensing Experiments , 1996, astro-ph/9608008.

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

[10]  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 .

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

[12]  C. Kochanek,et al.  Astrophysical Applications of Gravitational Lensing , 1996 .

[13]  M. J. Lehner,et al.  The Macho Project: 45 Candidate Microlensing Events from the First Year Galactic Bulge Data , 1997 .

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

[15]  Andrew Gould,et al.  Satellite Parallaxes of Lensing Events toward the Galactic Bulge , 1996 .

[16]  A. Gould.  MICROLENSING AND THE STELLAR MASS FUNCTION , 1996, astro-ph/9604014.

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

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

[19]  Andrew Gould.  MACHO Parallaxes from a Single Satellite , 1995 .

[20]  B. Paczynski,et al.  The Optical Gravitational Lensing Experiment. The Optical Depth to Gravitational Microlensing in the Direction of the Galactic Bulge , 1994 .

[21]  D. Sasselov,et al.  Removing Degeneracy of Microlensing Light Curves through Narrowband Photometry of Giants , 1995, astro-ph/9504001.