Exoplanets - Microlensing

The discovery of ~1000 extrasolar planets has taken humankind one step closer to answering the fundamental question "are we alone?" Now that extrasolar planets are known to be abundant, the next step is to determine if planetary systems like our own are common and if they contain Earth-like planets that could support life.

Rapid advancement in exoplanet research is driven by both extensive observational searches around mature stars as well as the construction of planet formation models. Perhaps the most surprising discovery so far is the great diversity in the planets' dynamical properties, but these results are largely confined to planets that are unusually massive or reside in very close orbits. The core accretion theory suggests most planets are much less massive than gas giants and that the critical region for understanding planet formation is just beyond the "snow-line", which is the region (1.5-4 AU) of greatest microlensing sensitivity (Ida & Lin 2005; Kennedy et al. 2006). Early results from ground-based microlensing searches (Beaulieu et al. 2006; Gould et al. 2006; Bennett et al. 2008) appear to confirm these expectations. WFIRST will extend the current sensitivity of the microlensing method down to masses of about a tenth of the Earth's mass at orbital separations ranging from the outer habitable zone to ∞. This includes analogs to all of the Solar System's planets except for Mercury, as well as most types of planets predicted by planet formation theories. WFIRST measures the frequency of planets orbiting all types of stars with spectral type G or later. WFIRST and Kepler complement each other, and together they cover essentially the entire planet discovery space. Kepler is sensitive to close-in planets but is unable to sense the more distant ones; WFIRST is less sensitive to close-in planets, but surveys beyond the habitable zone better than Kepler. WFIRST's sensitivity extends out even to unbound planets, offering the possibility to constrain their numbers and masses. Other methods, including ground-based microlensing, cannot approach the sensitivity and comprehensive statistics on the mass and semi-major-axis distribution of extrasolar planets that a space-based microlensing mission provides. Thus, WFIRST provides the only way to complete the exoplanet census begun by Kepler and gain a comprehensive understanding of the architecture of planetary systems, needed to understand planet formation and habitability.

The colored shaded regions show approximate regions of sensitivity for Kepler (red) and WFIRST (blue). The colored shaded regions show approximate regions of sensitivity for Kepler (red) and WFIRST (blue). The solar system planets are also shown, as well as the Moon, Ganymede, and Titan. Kepler is sensitive to the abundant, hot and warm terrestrial planets with separations less than about 1.5 AU. On the other hand, WFIRST is sensitive to Earth-mass planets with separations greater than 1 AU, as well as planets down to roughly twice the mass of the moon at slightly larger separations. WFIRST is also sensitive to unbound planets with masses as low as Mars. The small red points show candidate planets from Kepler, whereas the small blue points show simulated detections by WFIRST; the number of such discoveries will be large with roughly 3000 bound and hundreds of free-floating planet discoveries.

The physical basis of microlensing is the gravitational bending of light rays by a star or planet. When a "lens star" passes close to the line of sight to a more distant source star, the gravitational field of the lens star deflects the light rays from the source star. The gravitational bending effect of the lens star "splits", distorts, and magnifies the images of the source star, so the observer sees a microlensing event as a transient brightening of the source as the lens star's proper motion moves it across the line of sight. Gravitational microlensing events are characterized by the Einstein ring radius, where ML is the lens star mass, and DL and DS are the distances to the lens and source, respectively. RE is the radius of the ring image that is seen with perfect alignment between the lens and source stars. The lensing magnification is determined by the alignment of the lens and source stars measured in units of RE, so even low-mass lenses can give rise to high magnification microlensing events. A microlensing event's duration is given by the Einstein ring crossing time, typically 1-3 months for stellar lenses and a few days or less for a planet.

Planets are detected via light curve deviations that differ from the normal stellar lens light curves (Mao & Paczynski 1991). Usually, the signal occurs when one of the two images due to lensing by the host star passes close to the location of the planet, as indicated in the figure below (Gould & Loeb 1992), but planets are also detected at very high magnification where the gravitational field of the planet destroys the symmetry of the Einstein ring (Griest & Safizadeh 1998).

Microlensing is sensitive to a wide range of planet-star separations and host star types. The host stars for planets detected by microlensing are a random sample of stars that happen to pass close to the line-of-sight to the source stars in the Galactic bulge, so all common types of stars are surveyed, including G, K, and M-dwarfs, as well as white dwarfs and brown dwarfs. Microlensing is most sensitive to planets at a separation of ~RE (usually 2-3 AU) due to the strong stellar lens magnification at this separation, but the sensitivity extends to arbitrarily large separations. It is only planets well inside RE that are missed because the stellar lens images that would be distorted by these inner planets have very low magnifications and a very small contribution to the total brightness.

The geomtry of a microlensing planet search towards the Galactic bulge. The geometry of a microlensing planet search towards the Galactic bulge. Main sequence stars in the bulge are monitored for magnification due to gravitational lensing by foreground stars and planets in the Galactic disk and bulge.

Microlensing relies upon the high density of source and lens stars towards the Galactic bulge to generate the stellar alignments needed to generate microlensing events, but this high star density also means that the bulge main sequence source stars are not generally resolved in ground-based images. This means that the precise photometry needed to detect planets of less than a tenth of the Earth's mass is not possible from the ground unless the magnification due to the stellar lens is moderately high. This, in turn, implies that ground-based microlensing is only sensitive to terrestrial planets located close to the Einstein ring (at ~2-3 AU). The full sensitivity to terrestrial planets in all orbits from the outer habitable zone to ∞ comes only from a space-based survey.

The microlensing program observes 10 fields in the Galactic bulge on a 15 minute cadence for six 72 day seasons, interrupted only by monthly lunar avoidance cutouts. The microlensing events are continuously monitored in a single wide band to measure the basic light curve parameters. The 10 fields are monitored in the bluest filter for one exposure every 12 hours in order to measure the color of the microlensing source stars. The first and last observing seasons are separated by more than 2 years to measure lens-source relative proper motion.

The microlensing exoplanet survey with WFIRST is substantially superior to other WFIRST designs, resulting in 25% more planet detections and significantly better sensitivity to small planets, but the more important gain is the larger fraction of events that can be fully characterized thanks to the higher angular resolution of WFIRST.

Time Series Photometry Schematic illustration of how WFIRST discovers signals caused by planetary companions in primary microlensing events, and how planet parameters can be extracted from these signals. The left panel shows a simulated primary microlensing event, containing a planetary deviation from an Earth-mass companion to the primary lens. The offset of the deviation from the peak of the primary event, when combined with the primary event parameters, is related to the projected separation of the planet. The right panel shows an enlargement of the planetary perturbation. The width and precise shape of the planetary deviation yield the mass of the companion relative to that of the primary host lens.

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