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Table A.2
Effect of planet engulfment on the surface rotation velocities of red giants.
| M pl | vsurf(Be) | Δtt(FR) | vsurf(Af) | Δtt + e(FR) | Δtt + e(FR) /t(RG) | vsurf(Be) | Δtt(FR) | vsurf(Af) | Δtt + e(FR) | Δtt + e(FR) /t(RG) |
| [MJ] | [km s-1] | [Myr] | [km s-1] | [Myr] | [%trgb] | [km s-1] | [Myr] | [km s-1] | [Myr] | [%trgb] |
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| Ωini/ Ωcrit = 0.1, Z = 0.02 | ||||||||||
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| 1.5 M⊙, ℒ0,⋆ = 0.41 [1050 g cm2 s-1], trgb ≃ 0.37 [Gyr] | 1.7 M⊙, ℒ0,⋆ = 0.46 [1050 g cm2 s-1], trgb ≃ 0.18 [Gyr] | |||||||||
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| aini = 0.5 [AU] | ||||||||||
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| 1 | 1.44 | − | 2.06 | 0.0 | 0.00 | 1.35 | − | 1.8 | 0.0 | 0.00 |
| 5 | 7.26 | − | 13.80 | 15.3 | 4.29 | 6.26 | − | 8.64 | 2.8 | 1.55 |
| 10 | 17.00 | 26.24 | 28.90 | 29.6 | 8.30 | 14.60 | 19.65 | 19.60 | 23.9 | 13.13 |
| 15 | 28.20 | 32.36 | 42.30 | 39.7 | 11.15 | 23.30 | 26.28 | 35.70 | 31.2 | 17.20 |
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| aini = 1 [AU] | ||||||||||
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| 1 | 0.83 | − | 1.20 | 0.0 | 0.00 | 0.78 | − | 1.18 | 0.0 | 0.00 |
| 5 | 4.81 | − | 7.37 | 0.0 | 0.00 | 4.19 | − | 6.28 | 0.0 | 0.00 |
| 10 | 11.90 | 4.28 | 17.40 | 7.6 | 2.13 | 10.30 | 3.03 | 14.4 | 5.7 | 3.13 |
| 15 | 12.50 | 5.60 | 28.00 | 11.5 | 3.22 | 16.50 | 7.03 | 24.8 | 9.7 | 5.35 |
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| aini = 1.5 [AU] | ||||||||||
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| 1 | 0.66 | − | 1.04 | 0.0 | 0.00 | 0.60 | − | 0.95 | 0.0 | 0.00 |
| 5 | 4.81 | − | 6.02 | 0.0 | 0.00 | 3.42 | − | 5.87 | 0.0 | 0.00 |
| 10 | 9.22 | 1.14 | 13.40 | 3.2 | 0.91 | 7.99 | − | 12.50 | 2.8 | 1.55 |
| 15 | 15.80 | 4.12 | 23.60 | 5.7 | 1.61 | 12.8 | 3.07 | 18.70 | 4.8 | 2.64 |
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| 2.0 M⊙, ℒ0,⋆ = 0.61 [1050 g cm2 s-1], trgb ≃ 0.08 [Gyr] | 2.5 M⊙, ℒ0,⋆ = 0.92 [1050 g cm2 s-1], trgb ≃ 10 [Myr] | |||||||||
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| aini = 0.5 [AU] | ||||||||||
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| 1 | 0.99 | − | 1.30 | 0.0 | 0.00 | − | − | − | − | − |
| 5 | 4.90 | − | 7.71 | 0.0 | 0.00 | 3.33 | − | 18.4 | 0.7 | 6.82 |
| 10 | 11.80 | 8.69 | 16.70 | 14.7 | 19.29 | 7.00 | − | 37.9 | 0.7 | 6.82 |
| 15 | 16.18 | 13.51 | 22.00 | 19.9 | 26.01 | 7.94 | − | 47.0 | 0.7 | 6.82 |
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| aini = 1.0 [AU] | ||||||||||
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| 1 | 0.70 | − | 0.99 | 0.0 | 0.00 | − | − | − | − | − |
| 5 | 3.60 | − | 5.42 | 0.0 | 0.00 | − | − | − | − | − |
| 10 | 7.87 | − | 12.10 | 3.8 | 4.98 | − | − | − | − | − |
| 15 | 8.42 | 0.49 | 17.90 | 6.8 | 8.95 | − | − | − | − | − |
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| aini = 1.5 [AU] | ||||||||||
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| 1 | 0.53 | − | 0.82 | 0.0 | 0.00 | − | − | − | − | − |
| 5 | 2.82 | − | 4.22 | 0.0 | 0.00 | − | − | − | − | − |
| 10 | 6.33 | − | 9.18 | 0.9 | 1.14 | − | − | − | − | − |
| 15 | 10.30 | 1.61 | 15.50 | 3.7 | 4.83 | − | − | − | − | − |
Notes. The cases for different initial mass stars beginning their evolution with a rotation equal to Ωini/ Ωcrit = 0.1 are considered.
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