888 Encyclopedia of the Solar System
The amplitudeSof an astrometric signal is given byS=m
Mr
dwheremis the mass of the unseen companion,Mthe mass
of the central star,ris the semimajor axis of the companion’s
orbit, anddis the distance to the star. Forrin AU anddin
parsecs,Sis given in seconds of arc (1 arcsec is 1/60 of an
arcmin, which itself is 1/60 of a degree). For the Sun/Jupiter
system withm/M= 0 .001 andr= 5 .2 AU the amplitude
of the signal would be 0.001 arcsec (1 mas) seen from a
distance of 5 pc and 0.5 mas from 10 pc.
The motion of our Sun around the barycenter of our
solar system is complicated because of the presence of the
other outer planets. Figure 1 shows the astrometric signal
due to the Sun’sreflex motionas seen directly face-on to
the ecliptic from a distance of 10 pc.
From the preceding equation, it is obvious that astrom-
etry is more sensitive to companions with large mass ratios
(massive planets around less massive stars), at large orbital
separationsrand around nearby stars (dis small). Because
of therdependence, this technique is a complementary
method to the radial velocity technique (which will be dis-
cussed next).
As is the case for most of the detection methods, the
largest hurdle to overcome in detecting extrasolar planets by
FIGURE 1 The astrometric motion of the center of the Sun
(black line) around the barycenter of the solar system due to the
gravitational perturbations of the planets, viewed from a point
exactly above the ecliptic and from a distance of 10 pc
(∼32.6 light years). One dash mark on the axes is 0.0002 arcsec.
The red circle represents the size of the sun.
astrometry is the need for very precise measurements and
the extreme care required to avoid systematic errors (like
instrumental effects) in order to prevent the introduction
of spurious signals, which may be misinterpreted as real
planets, over a long time baseline.
The astrometric signals for most extrasolar planets are
typically less than 1 mas and are beyond the scope of most
current state-of-the-art instruments. The European Space
Agency’s satelliteHipparcoswas a space mission entirely
dedicated to stellar astrometry. Despite the fact that al-
though its precision was not sufficient to detect planetary
companions, theHipparcosdata placed very useful upper
limits on the masses of some companions detected by other
methods.
The highest astrometric precision can be achieved by us-
ing interferometry. By letting the light, which arrives from
the same source at two different locations (two or more tele-
scopes positioned on a well-defined baseline), interfere, one
can measure the small difference in the arrival time at these
points and thus determine the angle between the source and
the baseline very precisely. The Fine Guidance Sensors on-
board theHubble Space Telescope(HST) can actually be
used as an interferometer and they yield currently the best
astrometric precision.2.2 The Radial Velocity Method
Astronomers using the radial velocity technique measure
the line of sight component of the space velocity vector of
a star (hence the term “radial,” i.e., the velocity component
along the radius between observer and target). The radial
velocity of a star can be determined in absolute values or
differentially, if only changes of the velocity are of interest.
In order to measure stellar radial velocities, we rely on
the well-known Doppler effect. Depending on whether the
star moves toward us or away from us, its light will be blue
or red shifted, as compared to a nonmoving source. Such
a shift reveals itself as a change in the wavelength position
of the absorption lines in the spectrum of the star. There-
fore, astronomers use high-resolution spectrometers to per-
form radial velocity studies. The incoming light of the star
is split up into its individual wavelengths, and the spectrum
is recorded on a charge-coupled device (CCD) detector. As
in astrometry, this method tries to detect the reflex motion
of the primary object around the common center of mass
with an unseen companion. Only this time this motion re-
veals itself as a change in the velocity rather than a change
in position of the star.
The radial velocity method is traditionally used in stellar
astronomy for the discovery and characterization of binary
stars. In a binary system, the barycenter of the system is
located somewhere between the two stars (the exact loca-
tion is defined by the mass ratio), and the observed velocity
amplitudes are of the order of several kilometer per second.
In principle, the same method can be applied to the search