To be sure that the asymmetry in the chaotic layer is real, and not an artifact of our choice of initial conditions, we need to exclude that our choice of \Omega for the test particles is not introducing spurious effects. Three resonant configurations might alter the values of the eccentricities of the test particles, and so put them closer or farther away from the region of chaos we are interested in. The three resonance we considered are: "nodal" (\Omega-\Omega_sun=const.), secular (\varpi-varpi_sun=0.), and the evection resonance [2(\varpi-\lambda_sun)=const (=45 degrees, so as to have an intermediate value of the evection angle)]. The values of the angles for the sun in our simulation are the following:
\Omega=23.1615891; \omega=311.992355; M=322.291422
We computed the values of \Omega
of the test particles according to the resonant configuration. In
the following plots we report our results.
|
|
|
|
Since the secular resonance seems
to give the more symmetric configuration, we believe its effect is the
dominant one. To further prove this hyphothesis, we perform another
simulation with the resonant angle equal to 180. degrees, and \lambda-\lambda_sat=180.
This configuration should maximize the effect of the secular resonance.
Moreover, we define an "asymmetry" coefficient, which is given by the average
value of the difference between left and right side of the panel (we exclude
the first and last three columns and the central column of \omega=90 degrees).
The closer the value of the log10 of the asymmetry coefficient is to the
value of the noise in frequencies (-4.5), the more symmetric are
the results. Results of the last simulation are in the following
plot, in the table there are the values of the log10 of the asymmetry coefficient
for the four simulations. Our simulations strongly suggest that the
secular resonance is the dominant effect in causing the asymmetry in the
chaotic layer.
|
|
|
|
|
|
|
|
|
|
Secular resonance, \varpi-\varpi_sun=180., \lambda-lambda_sun=180.
