Max Planck Institute for Astronomy - Annual Report 2007

Stars with 50% Completeness
40
30
20
10
0
0
2 4 6
Mass [M Jup ]
Semi-Major Axis
5 AU
10 AU
20 AU
30 AU
40 AU
8 10 12
Fig. II.2.6: Planets with varying masses which should have been
discoverable with a likelihood of 50 percent at varying minimal
distances from a star.
Fig. II.2.6 shows those areas in which the survey
should have found, with a likelihood of at least 50 percent
and a significance of 5 s, a planet with an appropriate
mass and major orbital axis. One sees that the survey is
particularly sensitive for planets of 4 to 8 Jupiter masses
and orbits of 20 to 40 AU. Young planets of more than 8
Jupiter masses are theoretically so hot, that they do not
show any strong methane bands in their spectra.
Companion Mass [M Jup ]
14
12
10
8
6
4
2
20
5 sensitivity
threshold
40
Separation [AU]
CH 4 – limit: T eff = 1400 K
Primary
M4V
m H = 4.8 mag
70 Myr
14.9 pc
Detection limit: m H = 21.0 mag
60
II.2 A Search for Extrasolar Planets Around 54 Nearby Stars 27
Fig. II.2.7 shows, as an example, the minimal verifiable
planet mass for two stars in dependence on the
distance to the stars. To produce these diagrams, one million
model planets with varying masses, major semiaxes
(of 0.02 to 45 AU) and eccentricities were simulated for
each star. In the distribution of the major semiaxis a, it
was assumed that its number N remains constant with increasing
distance. Arbitrary phases of the planets in their
orbit and varying orbital tendencies were also taken into
consideration. Planets that should have been discovered
during the Na c O-SDI survey are shown in blue. The others
are red. Assuming that these stars each had planets,
the likelihood of discovery noted above the diagrams is
obtained. Thus, for example, one should have been able
to find a planet of at least two Jupiter masses at a distance
of between 10 and 20 AU with a likelihood of 20 percent
around the 12 million year old, 33.5 light years distant,
GJ 799B.
If one takes these probabilities for all observed stars
together, then one obtains the likelihood of discovery
for this survey. As Fig. II.2.8 shows, the astronomers
should have been able to find two to three planets. Thus
they can exclude with a very high probability (93 %)
that large planets are distributed evenly over the large
semiaxis (N(a) const) up to a distance of 45 AU from
their central stars.
The SDI survey’s null result thus sets for the first time
limits to the distance distribution of younger, extrasolar
giant planets. Apparently there are not many giant
Fig. II.2.7: Two examples for detectable planet masses (the values
corresponding to the blue dots) in relation to the distance to the
central star: left a 50 light year distant, 70 million year old K1V
star; right a 33.5 light year, 12 million year old M4V star.
Companion Mass [M Jup ]
14
12
10
8
6
4
2
20
5 sensitivity
threshold
40
Separation [AU]
Primary
M4V
m H = 5.2 mag
12 Myr
10.2 pc
CH 4 limit: T eff = 1400 K
60