Extrasolar Planets 891
to the crossing of the caustics. The mass ratioqof the two
lenses can be derived from modeling the lightcurve. If the
resulting mass ratio is very small (typicallyq> 0 .001), the
second object in this binary might be a planet.
Like transit surveys, microlensing planet searches have
to observe a large number of targets because the probability
of observing a single event for a given target is negligible.
For microlensing, the situation is even more complex be-
cause of the need of a sufficiently large reservoir of lenses
moving in front of a high density sample of background
sources. Moreover, microlensing events for a particular lens
do not repeat. Each microlensing event is a single isolated
transient in the lightcurve. There is only one chance to ob-
serve it. Hence microlensing surveys monitor regions like
the bulge of our galaxy (the central cluster of stars that sur-
round the galactic center) where microlensing events can
be observed more frequently.
2.5 Timing Method
The timing method is exceptional with respect to the other
techniques because it actually is the method that led to the
very first detection of planets outside the solar system. As in
the astrometric and radial velocity techniques, the fact that
a host star has to orbit the common center of mass with an
orbiting planet is utilized to detect the unseen companion.
But this time the reflex orbit is observed by the change of
the arrival time of signals coming from the star. The change
is caused by the difference in the distance the signal has
to travel from the source to the observer. If the star is at
the location in its orbit where it is the farthest away from
Earth then the signal needs the longest time to arrive here,
and vice versa for the smallest separation. Because reflex
motions due to planets are small compared to the speed of
light the changes in arrival time are very small.
The timing method can only be applied to cases where
(a) a very short duration signal is emitted by a source with a
constant periodicity and (b) the observers are able to mea-
sure the arrival time of the signal with very high precision.
One astrophysical case where these conditions are met are
the so-called pulsars. Pulsars are neutron stars, the end stage
in the life of massive stars with 15 and 30 times the mass
of the Sun. They are the collapsed core of the star (with
about 1.4 times the mass of the Sun) left behind after a
supernova explosion. A neutron star is very small with a di-
ameter of only 10–20 km, and hence a very dense object that
also rotates very fast. Rotation periods of neutron stars can
be as short as milliseconds. Strong magnetic fields produce
bipolar jets of radio waves and high-energy radiation like
X-rays and gamma rays. Because the magnetic field axis is
misaligned with the rotational axis, these stars act like cos-
mic lighthouses from which we see a pulse every time the
jet sweeps over the Earth. Pulsars were first discovered by
radio telescopes in 1967, and to the fastest rotators (the
millisecond pulsars) the timing method can be applied to
detect orbiting companions.
A second case where the timing method is applicable
is stably pulsating white dwarf stars. White dwarfs are the
end stage of the life of stars that are not massive enough
to form a neutron star (like our Sun). They are also small
(about the size of the Earth) and very dense objects. These
stars undergo nonradial pulsations for certain temperature
ranges that can be detected by precise photometric obser-
vations. The periods of these pulsations are of the order of
a few minutes. Some of the white dwarfs exhibit the same
pulsation modes over decades and are thus suitable targets
for the timing method.2.6 Direct Imaging
Obtaining a direct image of an extrasolar planet is the type
of observation the public expects. Besides the obvious ad-
vantage of discovering planets with only a few observations,
the images might also allow us to characterize the planets in
new depth. From the colors and albedos, we might obtain
thermal and chemical information. After the direct detec-
tion, follow-up observations can be carried out to collect
first spectra of the planet.
In many ways, direct imaging of a planet around a nearby
star represents the largest challenge in the development
of telescope/instrument systems. Surprisingly, it is not the
faintness of an irradiated extrasolar planet that is the hurdle
to overcome (theHubble Space Telescopewould be sensi-
tive enough to detect these faint objects) but rather their
proximity to a much brighter source of photons: the planet’s
own host star.
The distances to even the nearest stars are so large that,
due to the perspective, any image of a companion orbiting
at separations comparable to our solar system would be
located in the side wings of the image of the central object.
In the optical, the flux difference between a solar-type star
and a giant planetary companion is of the order of a billion.
In the infrared, the difference is more of the order of a
million (see Fig. 3). But the light coming from the planet is
completely overwhelmed by the large amount of scattered
light from the star.
There are several techniques to minimize the scattered
light from the host star. From the ground, the observa-
tions are also affected by atmospheric turbulences, the
so-called seeing. Seeing usually prevents telescopes from
obtaining images at their theoretical resolving power even
at the best observing sites in the world. In the near infrared,
atmospheric turbulence can be compensated by an adaptive
optics (AO) system. AO systems use wavefront sensors to
measure the wavefront errors caused by turbulence in the
atmosphere above the telescope and then to adjust the op-
tical path to compensate for these errors using deformable
mirrors. This helps to attain images at a spatial resolving
power close to the limit set by the diffraction of light. AO