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area. Such situation can be well understood by adopting the 3
R
H
stability
criterion.
3. Summary and Discussions
In this work, we have systematically studied the existence of Earth-like
planets in the region for 0.05 AU
2
.
0 AU for 47 UMa by numerical
simulations. We now summarize the main results as follows:
≤
a
≤
(1) The Earth-like planets can eventually remain in the system for 10 Myr
in the areas associated with mean motion resonance (e.g., 3:2 MMR)
with the inner detected giant companion. We also showed that the
2:1 and 3:1 resonances could be on the fringe of stability, but the 5:2
MMR is unstable and the bodies can be ejected as “extrasolar comets”.
And this may sketch out an asteroidal belt structure similar to the
solar system. Moreover, the 2:1 MMR (near the outer boundary of
HZ at 1.30 AU) marks out a significant barrier between chaotic and
regular motions, implying that a large fraction of the orbits inside this
resonance can be survive, while most of them are lost in the simulations
outside the 2:1 resonance. Again, considering the inner boundary of HZ
and dynamical stability, we point out that the most likely candidate for
habitable environment is terrestrial planets with orbits in the ranges
0.8 AU
a<
1
.
0AU and 1.0AU
<a<
1
.
30 AU (except 5:2 MMR, and
several unstable cases) with low eccentricities.
(2) However, in our own solar system there are no terrestrial planets from
the 1:4 MMR out to Jupiter, although there are stable orbits there.
This may suggest that although some orbits are stable, conditions are
such that terrestrial planets cannot form so close to giant planets. Per-
haps this is because runaway growth is suppressed due to the increased
eccentricities from the perturbations of the giant planet. In 47 UMa,
the corresponding region runs from 0.82 AU on out, almost completely
covering the HZ. Hence, it would be reasonable to conclude that the
only proper place to find habitable planets in this system would be at
about 0.8 AU. But this should be carefully examined by forthcoming
space measurements (e.g., SIM) capable of detecting low-mass planets.
≤
Finally, we can say that the 47 UMa planetary system may bear a sim-
ilar dynamical structure to our solar system. As a comparison, we also
conducted similar studies in other multi-planet systems (e.g., HD 12661,
HD 169830, and GJ 876) and found the potential existence of the Earth-like
