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In-Depth Information
Fig. 4.
Case for 1.3 AU
≤ a ≤
1
.
6 AU, a population of the terrestrial planets is about
9:5 MMR at
∼
1
.
40 AU for low eccentricities.
about the 9:5 MMR at
0
.
05.
Most of the unstable orbits are in the region 1
.
43 AU
<a<
1
.
56 AU,
using resonance overlapping criterion,
20
the separation in semi-major axis
∆
a
∼
1
.
40 AU for low eccentricities 0
.
0
<e
≤
1
.
3(
M
1
/M
c
)
2
/
7
a
1
.
=0
.
496 AU (
a
1
, the semi-major axis of Com-
panion B), thus, the inner boundary
R
O
≈
=
a
1
−
∆
a
for 47 UMa b is at
∼
1
.
58 AU, and the orbits in this zone become chaotic during the orbital evo-
lution because the planets are both within 3
R
H
(
R
H
=[
M
1
/
(3
M
c
)]
1
/
3
a
1
is the Hill radius;
M
c
and
M
1
are, respectively, the masses of the host star
and the inner planet) and also close to
R
O
. And the characterized eject-
ing time
τ
∼
1 Myr, which means the apparent gap (e.g., 5:3 MMR at
∼
1
.
48 AU) in the system, except for several stable islands. Another possi-
ble population for terrestrial planets is located at 3:2 resonance
1
.
59 AU
for 0
.
04
<e<
0
.
20, and 18 small bodies can last for 10 Myr and confirm
the results of Paper II. The 3:2 MMR zone in 47 UMa is reminiscent of the
Hilda asteroids in the solar system moving in a stable region.
∼
2.1.5. 1
.
6
AU
<a
≤
2
.
0
AU
About 840 Earth-like planets are placed in this region for integration for
10 Myr, and the simulation revealed that 98% are removed from the system
within a typical ejection time
τ<
3
×
10
4
yr, which is much shorter than
≤
a
≤
1
.
6 AU, implying a thoroughly chaotic situation in this
for 1.3 AU
