Table 1.
Value of the different terms of the stability criterion u for different hydro simulations with identical initial conditions except for the masses of the co-orbitals, given in the first two columns.
m1 | m2 |
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R1ζ |
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−R2ζ | 2u |
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CΓ | K1 | K2 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
[M⊕] | [M⊕] | [yr−1] | [yr−1] | [yr−1] | [yr−1] | [yr−1] | [yr−1] | [yr−1] | [rad yr−1] | – | – | – |
3.0 | 5.0 | 3.9e−6 | −2.0e−5 | 1.4e−5 | 1.3e−5 | 2.2e−5 | 4.2e−6 | 3.6e−5 | 5.9e−6 | 6.5e−2 | −1 | 2 |
3.0 | 3.0 | 5.1e−6 | −3.1e−5 | 7.7e−6 | 6.4e−6 | −1.8e−5 | 4.1e−6 | −2.6e−5 | −4.1e−6 | 2.2e−2 | −3 | −0.9 |
5.0 | 3.0 | 1.1e−5 | −7.4e−5 | 7.4e−6 | 5.4e−6 | −5.8e−5 | 7.3e−6 | −1.0e−4 | −1.9e−5 | −1.9e−2 | −5 | −3 |
3.0 | 15.0 | 5.4e−7 | −6.2e−5 | 5.7e−5 | 5.1e−5 | 2.0e−4 | 1.7e−6 | 2.5e−4 | 3.2e−5 | 1.7e−1 | −1e1 | 1e1 |
6.0 | 12.0 | 5.8e−6 | −2.3e−5 | 3.4e−5 | 3.6e−5 | 1.9e−4 | 4.0e−6 | 2.5e−4 | 4.1e−5 | 1.1e−1 | −0.5 | 6 |
10.0 | 10.0 | 1.6e−5 | 1.8e−4 | 2.7e−5 | 2.5e−5 | −2.6e−4 | 6.8e−6 | −9.1e−6 | −2.8e−6 | 4.4e−2 | 6 | −5 |
12.0 | 6.0 | 3.1e−5 | 3.1e−5 | 1.4e−5 | 9.3e−6 | −2.2e−4 | 2.4e−5 | −1.1e−4 | −1.8e−5 | −5.5e−2 | 2 | −5 |
15.0 | 3.0 | 4.8e−5 | −2.6e−4 | 7.1e−6 | 1.9e−6 | −8.2e−5 | 1.8e−5 | −2.7e−4 | −4.5e−5 | −1.4e−1 | −1e1 | −4 |
1.0 | 333 | 8.5e−8 | 2.3e−4 | −3.2e−4 | 2.1e−5 | 1.7e−5 | −1.3e−6 | −4.9e−5 | 4.6e−6 | −1.1e−3 | 5 | 1e2 |
333 | 1.0 | 2.1e−5 | 1.7e−5 | −1.6e−6 | −1.2e−7 | 2.9e−4 | −2.8e−4 | 4.3e−5 | 2.1e−6 | −9.9e−3 | 1e2 | −3 |
Notes. The upper block shows the three models with low-mass planets which do not alter the surface density profile. In the second block, the planets are more massive and perturb the disc by creating a shallow gap around their orbits. In the two models of the last block, we used a full gap-opening planet as one of the co-orbitals in order to eliminate the co-rotation torque on the low-mass one.
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