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Register a new userThe Use of High Magnification Microlensing Events in Discovering Extra-solar Planets
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Hundreds of gravitational microlensing events have now been detected towards the Galactic bulge, with many more to come. The detection of fine structure in these events has been theorized to be an excellent way to discover extra-solar planetary systems along the line-of-sight to the Galactic center. We show that by focusing on high magnification events the probability of detecting planets of Jupiter mass or greater in the lensing zone (.6 -1.6 $R_E$) is nearly 100%, with the probability remaining high down to Saturn masses and substantial even at 10 Earth masses. This high probability allows a nearly definitive statement to made about the existence of lensing zone planets in each such system that undergoes high magnification. One might expect lightcurve deviations caused by the source passing near the small primary lens caustic to be small due to the large distance of the perturbing planet, but this effect is overcome by the high magnification. High magnification events are relatively rare (e.g. $sim 1/20$th of events have peak magnifications greater than 20), but they occur regularly and the peak can be predicted in advance, allowing extra-solar planet detection with a relatively small use of resources over a relatively small amount of time.
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A search for extra-solar planets was carried out in three gravitational microlensing events of high magnification, MACHO 98-BLG-35, MACHO 99-LMC-2, and OGLE 00-BUL-12. Photometry was derived from observational images by the MOA and OGLE groups using an image subtraction technique. For MACHO 98-BLG-35, additional photometry derived from the MPS and PLANET groups was included. Planetary modeling of the three events was carried out in a super-cluster computing environment. The estimated probability for explaining the data on MACHO 98-BLG-35 without a planet is <1%. The best planetary model has a planet of mass ~(0.4-1.5) X 10^-5 M_Earth at a projected radius of either ~1.5 or ~2.3 AU. We show how multi-planet models can be applied to the data. We calculated exclusion regions for the three events and found that Jupiter-mass planets can be excluded with projected radii from as wide as about 30 AU to as close as around 0.5 AU for MACHO 98-BLG-35 and OGLE 00-BUL-12. For MACHO 99-LMC-2, the exclusion region extends out to around 10 AU and constitutes the first limit placed on a planetary companion to an extragalactic star. We derive a particularly high peak magnification of ~160 for OGLE 00-BUL-12. We discuss the detectability of planets with masses as low as Mercury in this and similar events.
Microlensing is increasingly gaining recognition as a powerful method for the detection and characterization of extra-solar planetary systems. Naively, one might expect that the probability of detecting the influence of more than one planet on any single microlensing light curve would be small. Recently, however, Griest & Safizadeh (1998) have shown that, for a subset of events, those with minimum impact parameter $u_{min} lsim 0.1$ (high magnification events), the detection probability is nearly 100% for Jovian mass planets with projected separations in the range 0.6--1.6 of the primary Einstein ring radius $R_E$, and remains substantial outside this zone. In this Letter, we point out that this result implies that, regardless of orientation, all Jovian mass planets with separations near 0.6--1.6$R_E$ dramatically affect the central region of the magnification pattern, and thus have a significant probability of being detected (or ruled out) in high magnification events. The probability, averaged over all orbital phases and inclination angles, of two planets having projected separations within 0.6--$1.6R_E$ is substantial: 1-15% for two planets with the intrinsic orbital separations of Jupiter and Saturn orbiting around 0.3--1.0$M_odot$ parent stars. We illustrate by example the complicated magnification patterns and light curves that can result when two planets are present, and discuss possible implications of our result on detection efficiencies and the ability to discriminate between multiple and single planets in high magnification events.
We introduce a new method of searching for and characterizing extra-solar planets. We show that by monitoring the center-of-light motion of microlensing alerts using the next generation of high precision astrometric instruments the probability of detecting a planet orbiting the lens is high. We show that adding astrometric information to the photometric microlensing lightcurve greatly helps in determining the planetary mass and semi-major axis. We introduce astrometric maps as a new way for calculating astrometric motion and planet detection probabilities. Finite source effects are important for low mass planets, but even Earth mass planets can give detectable signals.
Exoplanet surveys have confirmed one of humanitys (and all teenagers) worst fears: we are weird. If our Solar System were observed with present-day Earth technology -- to put our system and exoplanets on the same footing -- Jupiter is the only planet that would be detectable. The statistics of exo-Jupiters indicate that the Solar System is unusual at the ~1% level among Sun-like stars (or ~0.1% among all stars). But why are we different? Successful formation models for both the Solar System and exoplanet systems rely on two key processes: orbital migration and dynamical instability. Systems of close-in super-Earths or sub-Neptunes require substantial radial inward motion of solids either as drifting mm- to cm-sized pebbles or migrating Earth-mass or larger planetary embryos. We argue that, regardless of their formation mode, the late evolution of super-Earth systems involves migration into chains of mean motion resonances, generally followed by instability when the disk dissipates. This pattern is likely also ubiquitous in giant planet systems. We present three models for inner Solar System formation -- the low-mass asteroid belt, Grand Tack, and Early Instability models -- each invoking a combination of migration and instability. We identify bifurcation points in planetary system formation. We present a series of events to explain why our Solar System is so weird. Jupiters core must have formed fast enough to quench the growth of Earths building blocks by blocking the flux of inward-drifting pebbles. The large Jupiter/Saturn mass ratio is rare among giant exoplanets but may be required to maintain Jupiters wide orbit. The giant planets instability must have been gentle, with no close encounters between Jupiter and Saturn, also unusual in the larger (exoplanet) context. Our Solar System system is thus the outcome of multiple unusual, but not unheard of, events.
All extra-solar planet masses that have been derived spectroscopically are lower limits since the inclination of the orbit to our line-of-sight is unknown except for transiting systems. It is, however, possible to determine the inclination angle, i, between the rotation axis of a star and an observers line-of-sight from measurements of the projected equatorial velocity (v sin i), the stellar rotation period (P_rot) and the stellar radius (R_star). This allows the removal of the sin i dependency of spectroscopically derived extra-solar planet masses under the assumption that the planetary orbits lie perpendicular to the stellar rotation axis. We have carried out an extensive literature search and present a catalogue of v sin i, P_rot, and R_star estimates for exoplanet host stars. In addition, we have used Hipparcos parallaxes and the Barnes-Evans relationship to further supplement the R_star estimates obtained from the literature. Using this catalogue, we have obtained sin i estimates using a Markov-chain Monte Carlo analysis. This allows proper 1-sigma two-tailed confidence limits to be placed on the derived sin is along with the transit probability for each planet to be determined. While a small proportion of systems yield sin is significantly greater than 1, most likely due to poor P_rot estimations, the large majority are acceptable. We are further encouraged by the cases where we have data on transiting systems, as the technique indicates inclinations of ~90 degrees and high transit probabilities. In total, we estimate the true masses of 133 extra-solar planets. Of these, only 6 have revised masses that place them above the 13 Jupiter mass deuterium burning limit. Our work reveals a population of high-mass planets with low eccentricities and we speculate that these may represent the signature of different planetary formation mechanisms at work.
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