The PLANET microlensing follow-up network: results and prospects for the detection of extra-solar planets

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Abstract

Among various techniques to search for extra-solar planets, microlensing has some unique characteristics. Contrary to all other methods which favour nearby objects, microlensing is sensitive to planets around stars at distances of several kpc. These stars act as gravitational lenses leading to a brightening of observed luminous source stars. The lens stars that are tested for the presence of planets are not generally seen themselves. The largest sensitivity is obtained for planets at orbital separations of 1–10AU offering the view on an extremely interesting range with regard to our own solar system and in particular to the position of Jupiter. The microlensing signal of a jupiter-mass planet lasts typically a few days. This means that a planet reveals its existence by producing a short signal at its quasi-instantaneous position, so that planets can be detected without the need to observe a significant fraction of the orbital period. Relying on the microlensing alerts issued by several survey groups that observe ∼107 stars in the Galactic bulge. PLANET (Probing Lensing Anomalies NETwork) performs precise and frequent measurements on ongoing microlensing events in order to detect deviations from a light curve produced by a single point-like object. These measurements allow constraints to be put on the abundance of planets. From 42 well-sampled events between 1995 and 1999, we infer that less than 1/3 of M-dwarfs in the Galactic bulge have jupiter-mass companions at separations between 1 and 4AU from their parent star, and that <45% have 3-jupiter-mass companions between 1 and 7AU.

Introduction

All of our knowledge about objects outside our own solar system is based on observations of electromagnetic radiation with different wavelengths: infrared, optical, ultraviolet, radio, X-ray, γ-ray. In any case, planets are not strong emitters and orbit stars that are much stronger emitters. For optical wavelengths, most of the light coming from the planet is reflected light originating between light from a star and reflected light from a planet is about 109–1010. For infrared wavelengths, this ratio becomes much smaller due to the thermal emission of the planet, but it is still 104–106. Therefore, the direct detection of planets from the emitted or reflected radiation is rather difficult.

For this reason, one has to think about how the presence of the planets yields observable signals in other objects that are easier to detect.

Since both planets and their parent stars move around their common center-of-mass, one can try to detect the small motion of the luminous parent star rather than observing the dark planet. Two techniques make use of this effect: the radial velocity technique observing the one-dimensional radial motion of the star by determining its velocity via Doppler-shift measurements, and the astrometric technique observing the two-dimensional transverse motion by position measurements.

The microlensing technique described here is even more indirect. Its basic concept is the observation of a large number of luminous source stars to wait for their brightening caused by the gravitational bending of light by intervening compact massive objects that pass close to the line-of-sight and act as so-called gravitational lenses. If these lens objects are surrounded by planets, there is some chance that their gravitational field causes additional variations in the observed brightness of the source stars. This means that microlensing can detect unseen planets orbiting unseen stars. Planets orbiting the source stars and passing in front of them would not yield to a microlensing signature resulting in a brightening of the observed stars, but to an occultation resulting in a dimming. Such signals can also be used to detect planets.

Among the different techniques, microlensing has some unique characteristics. Since microlensing relies on a chance alignment between source stars and lens objects, there is no opportunity to select the parent stars to be tested for the existence of planets, contrary to the methods relying on observations of luminous parent stars. Contrary to radial-velocity or astrometric searches, there is no need to wait for the orbital period of the planet. The passage of the star close to the line-of-sight yields a signal that lasts a few months, while the signal due to the planet is even shorter, a few days for a jupiter-mass planet. The favourite range for the detection of planets by microlensing is an orbital separation of 1–10AU, i.e. a range comparable to our own solar system, extending roughly from Earth to Saturn with the most massive planet Jupiter being near its center, whereas radial velocity searches favour small separations or short orbital periods (related to the separations by Kepler's 3rd law), and astrometric searches favour large separations or large orbital periods, and therefore solar systems that are unlike our own. Contrary to methods on luminous stars that favour nearby objects, microlensing favours objects halfway between the observer and the source star, i.e. parent stars at several kpc distance, and is therefore a unique method to determine the abundance of planets around such distant stars.

Here, we discuss the prospects of planet detection by microlensing and in particular, the prospects and recent results of our ongoing PLANET (Probing Lensing Anomalies NETwork) experiment.

Section snippets

Microlensing surveys

As pointed out by Paczyński 1986, Paczyński 1991 and Kiraga and Paczyński (1994), the probability for an alignment of massive compact foreground objects with luminous source stars in our Galaxy that yields a significant brightening (30%) at a given time is of the order of 10−6. One must therefore observe a large number of stars in order to see a significant number of ongoing ‘microlensing events’. Therefore, fields on the sky with a large number of stars, such as the Galactic bulge, are of

The PLANET experiment

The aim of PLANET is to perform precise and frequent multi-band observations of ongoing microlensing events in order to study departures from a light curve that is due to lensing of a point source by a single point-like lens. The origin of these departures can be due to blending of the light of the source star by other stars (in particular the lens) or due to effects by binary lenses (including planets), binary and extended sources, or the parallax effect due to the motion of the Earth around

The theory behind microlensing

Microlensing uses the effect of the deflection of light due to the gravitational field of a massive compact object. If M denotes the mass of this object, and r denotes the separation of the light ray from it, the light ray is deflected by the angle (Einstein, 1915)α̂=4GMc21r,where G is the constant of gravitation, and c is the speed of light. This deflection yields two possible light trajectories from the source to the observer resulting in two images of the same source object on the sky, where

Microlensing and planets

The fact that planets around lens stars cause observable effects in microlensing light curves was first pointed out by Mao and Paczyński (1991). The shape of the light curve is dominated by the effect from the star, and the effect of the planet can be treated as a perturbation.

However, the planet cannot be modelled as an isolated single lens: the tidal field of the star at the position of the planet strongly enhances the planetary perturbation by introducing an effective shear (Chang and

Determining planet parameters

From a microlensing light curve involving the signal of a planet, only 3 parameters related to the nature of the planet, its parent star, and the orbit can be extracted: the event time scale tE, the mass ratio between planet and star q, and the instantaneous projected separation d=θp/θE between planet and star in units of Einstein radii (Gaudi and Gould, 1997). The measured time scale tE is a convolution of the mass of the star M, its distance DL, and the relative lens-source proper motion μ,

PLANET's search for planets

To be able to characterize the properties of planets, we need to take data points with a photometric precision of 1–2% (in order to see 5% deviations) at a sampling rate of one point every 1.5–2.5h. Though deviations caused by jupiters last about 1 day, about 10–15 points over such a deviation are required to be able to extract its true nature. The photometric precision determines the exposure time needed for the images and the exposure time dictates the number of events that can be followed

Results

Though we would currently expect to detect ∼3 jupiter-mass planets per year if every lens star had such a planet within its lensing zone, we have not detected any clear planetary signal in our data yet. Because of the dense sampling of many microlensing events, constraints on the presence of planets with certain mass and orbital separation can be derived from the fact that no signals have been observed.

For each event, there is a fractional probability that a planet would have yielded a

The future

While the termination of the MACHO project at the end of 1999 led to a decrease in the number of useful alerts, the 3rd phase of the OGLE project starting in 2002 will yield 150–250 useful alerts per year, among these 25–40 high-magnification alerts and about the same number of alerts on bright source stars. This will bring the effective number of lens stars being probed by PLANET for jupiter-mass planets in the lensing zone to ∼15–25 per year.

An inexpensive pixel-lensing survey towards the

Acknowledgements

We thank the survey teams OGLE, MACHO, EROS, and MOA for providing alerts on ongoing microlensing events. We also thank the computer staff at Kapteyn Astronomical Institute for their assistance in developing tools that have improved the communication between the different PLANET sites. The work of PLANET has been financially supported by grants AST 97-27520 and AST 95-30619 from the NSF, by grant NAG5-7589 from NASA, by grant ASTRON 781.76.018 from the Dutch Foundation for Scientific Research

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