Geoscience Reference
In-Depth Information
2. Simulations Results
In the study, we use N-body codes 12 of direct numerical simulations with
the RKF7(8) and symplectic integrators. 13 We always take the stellar mass
and the minimum planetary masses from Table 1. The adopted time stepsize
is usually
1%-2.5% of the orbital period of the innermost planet, which is
suciently small for the integration. Additionally, the numerical errors were
effectively controlled over the integration timescale, and the total energy
is conserved to 10 6 -10 8 for the integrations (see also Ref. 6). In the
dynamical study, there are other numerical tools used to explore stability
zones for Earth-like planets in planetary systems, e.g., the Fast Lyapunov
Indicator (FLI) (e.g., Ref. 14) and the Mean Exponential Growth Factor of
Nearby Orbits (MEGNO) (e.g., Ref. 15). Our main results now follow.
2.1. Terrestrial planets in Habitable zones
The Habitable Zones are generally conceived as places where the biological
evolution of life is able to develop on planetary surfaces of the environment
of liquid-water, subtle temperature and atmosphere components of CO 2 ,
H 2 O, and N 2 . 16
1AU
(M c / M ) 2 (see Ref. 16). For 47 UMa, the inner and outer boundaries of
HZ range from 0.7 to 1.3 AU, 17 however, in our practical simulations, we
extended the HZ to other areas for the purpose of a more comprehensive
study.
In this series of runs, we extensively investigated the case of two giant
companions with one terrestrial planet in the HZ. The mass of the assumed
terrestrial planet ranges from 0.1 to 10 M . And the adopted initial orbital
parameters are as follows: numerical scanning was performed for the [ a, e ]
space by direct integrations, where the low-mass bodies were placed at
equal intervals of 0.01 AU from 0.05 to 2.0 AU in a , the eccentricities e were
taken every 0.01 from 0.0 to 0.2 (and up to 0.1 for 0.05 AU
The HZ could be considered to be centered at
a< 0 . 4AU),
the inclinations are 0 <I< 5 , and the other angles were randomly dis-
tributed between 0 and 360 . Thus, over 3,000 simulations were exhaus-
tively performed for typical integrations from 1 to 10 Myr.
2.1.1. 0 . 05 AU
a< 0 . 4 AU
In these runs, we explored the secular evolution of 385 “hot Earths” or
“hot Neptunes” for a time span of 1 Myr. All the simulations are dynami-
cally stable for 10 6 years, and 96% of the orbits bear e final < 0 . 20. However,
Search WWH ::




Custom Search