4:1 mass ratio tidal models and resulting fractions of realizations fulfilling the criteria.
| Type | Model | N | Time step 5 Gyr | fboth (per cent) | N | Time step 7.5 Gyr | fboth (per cent) | N | Time step 10 Gyr | fboth (per cent) | |||
| fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | ||||||||
| fb | 2deg200vel | 1045 | 99.4 | 99.9 | 99.3 | 1136 | 98.4 | 99.3 | 98.0 | 1084 | 98.3 | 98.1 | 97.0 |
| fb | 4deg175vel | 11 882 | 66.0 | 79.9 | 59.8 | 12 389 | 29.5 | 63.6 | 26.5 | 11 793 | 31.8 | 49.8 | 24.7 |
| fb | 4deg200vel | 14 127 | 34.7 | 77.6 | 33.8 | 13 732 | 36.3 | 70.8 | 33.2 | 12 205 | 39.9 | 69.2 | 36.4 |
| fb | 4deg225vel | 16 477 | 28.8 | 83.9 | 28.6 | 16 812 | 27.4 | 71.0 | 25.7 | 16 276 | 25.6 | 56.9 | 21.0 |
| fb | 4deg250vel | 11 858 | 38.3 | 87.0 | 38.1 | 12 016 | 48.9 | 92.2 | 48.9 | 11 330 | 45.0 | 85.3 | 44.4 |
| fb | 6deg175vel | 6284 | 97.6 | 86.7 | 85.6 | 7730 | 42.3 | 67.5 | 37.1 | 8245 | 27.4 | 41.9 | 18.3 |
| fb | 6deg200vel | 6205 | 97.9 | 95.2 | 93.7 | 7730 | 38.8 | 65.0 | 33.0 | 7337 | 31.5 | 56.4 | 24.9 |
| fb | 6deg225vel | 8659 | 98.7 | 94.7 | 93.8 | 8213 | 85.4 | 82.1 | 73.5 | 8509 | 57.4 | 60.1 | 40.7 |
| fb | 6deg250vel | 4970 | 94.3 | 96.0 | 91.4 | 5067 | 77.4 | 62.0 | 50.3 | No data, galaxies left model volume | |||
| fb | 8deg175vel | 4522 | 96.2 | 93.1 | 91.0 | 5129 | 80.9 | 84.3 | 73.5 | 4815 | 74.2 | 76.5 | 63.4 |
| Average | 75.2 | 89.4 | 71.5 | 56.5 | 75.8 | 50.0 | 47.9 | 66.0 | 41.2 | ||||
| mp | 2.5deg050vel | 66 917 | 32.8 | 12.7 | 6.9 | 62 262 | 23.9 | 27.4 | 10.8 | 63 893 | 14.8 | 28.2 | 6.2 |
| mp | 2.5deg100vel | 81 684 | 44.9 | 23.9 | 16.2 | 82 953 | 31.2 | 17.7 | 7.4 | 81 788 | 25.9 | 27.2 | 7.5 |
| mp | 5deg050vel | 64 938 | 38.4 | 24.9 | 16.6 | 60 115 | 29.0 | 17.8 | 7.9 | 64 109 | 24.3 | 28.9 | 6.9 |
| mp | 5deg100vel | 86 824 | 86.1 | 68.5 | 63.5 | 82 448 | 77.8 | 58.5 | 51.1 | 81 435 | 75.9 | 59.9 | 50.4 |
| mp | 7.5deg100vel | 93 940 | 82.6 | 82.3 | 74.6 | 80 454 | 89.1 | 74.6 | 70.9 | 77 768 | 74.0 | 53.9 | 47.0 |
| mp | 10deg100vel | 83 850 | 89.8 | 90.0 | 85.7 | 72 029 | 77.1 | 74.3 | 64.0 | 68 751 | 65.2 | 53.2 | 43.4 |
| Average | 62.4 | 50.4 | 43.9 | 54.7 | 45.0 | 35.3 | 46.7 | 41.9 | 26.9 | ||||
| mr | 2.5deg050vel | 69 336 | 27.8 | 72.8 | 25.9 | 65 802 | 25.7 | 45.9 | 18.3 | 72 171 | 25.7 | 43.1 | 17.2 |
| mr | 2.5deg100vel | 80 994 | 42.1 | 53.0 | 29.1 | 78 535 | 21.6 | 41.7 | 13.4 | 78 556 | 22.9 | 45.2 | 15.5 |
| mr | 5deg050vel | 64 109 | 30.8 | 62.8 | 25.3 | 61 710 | 25.3 | 46.7 | 16.9 | 64 159 | 20.9 | 45.3 | 14.5 |
| mr | 5deg100vel | 72 679 | 22.9 | 42.8 | 15.7 | 61 278 | 19.7 | 34.2 | 10.6 | 59 795 | 23.1 | 41.1 | 15.3 |
| mr | 7.5deg100vel | 70 490 | 56.5 | 4.3 | 3.3 | 51 645 | 41.1 | 36.3 | 18.4 | 49 391 | 17.4 | 19.4 | 4.4 |
| mr | 10deg100vel | 75 431 | 32.8 | 36.2 | 18.8 | 60 248 | 16.2 | 28.4 | 6.9 | 61 157 | 7.9 | 13.8 | 0.9 |
| Average | 35.5 | 45.3 | 19.7 | 24.9 | 38.9 | 14.1 | 19.6 | 34.6 | 11.3 | ||||
| Type | Model | N | Time step 5 Gyr | fboth (per cent) | N | Time step 7.5 Gyr | fboth (per cent) | N | Time step 10 Gyr | fboth (per cent) | |||
| fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | ||||||||
| fb | 2deg200vel | 1045 | 99.4 | 99.9 | 99.3 | 1136 | 98.4 | 99.3 | 98.0 | 1084 | 98.3 | 98.1 | 97.0 |
| fb | 4deg175vel | 11 882 | 66.0 | 79.9 | 59.8 | 12 389 | 29.5 | 63.6 | 26.5 | 11 793 | 31.8 | 49.8 | 24.7 |
| fb | 4deg200vel | 14 127 | 34.7 | 77.6 | 33.8 | 13 732 | 36.3 | 70.8 | 33.2 | 12 205 | 39.9 | 69.2 | 36.4 |
| fb | 4deg225vel | 16 477 | 28.8 | 83.9 | 28.6 | 16 812 | 27.4 | 71.0 | 25.7 | 16 276 | 25.6 | 56.9 | 21.0 |
| fb | 4deg250vel | 11 858 | 38.3 | 87.0 | 38.1 | 12 016 | 48.9 | 92.2 | 48.9 | 11 330 | 45.0 | 85.3 | 44.4 |
| fb | 6deg175vel | 6284 | 97.6 | 86.7 | 85.6 | 7730 | 42.3 | 67.5 | 37.1 | 8245 | 27.4 | 41.9 | 18.3 |
| fb | 6deg200vel | 6205 | 97.9 | 95.2 | 93.7 | 7730 | 38.8 | 65.0 | 33.0 | 7337 | 31.5 | 56.4 | 24.9 |
| fb | 6deg225vel | 8659 | 98.7 | 94.7 | 93.8 | 8213 | 85.4 | 82.1 | 73.5 | 8509 | 57.4 | 60.1 | 40.7 |
| fb | 6deg250vel | 4970 | 94.3 | 96.0 | 91.4 | 5067 | 77.4 | 62.0 | 50.3 | No data, galaxies left model volume | |||
| fb | 8deg175vel | 4522 | 96.2 | 93.1 | 91.0 | 5129 | 80.9 | 84.3 | 73.5 | 4815 | 74.2 | 76.5 | 63.4 |
| Average | 75.2 | 89.4 | 71.5 | 56.5 | 75.8 | 50.0 | 47.9 | 66.0 | 41.2 | ||||
| mp | 2.5deg050vel | 66 917 | 32.8 | 12.7 | 6.9 | 62 262 | 23.9 | 27.4 | 10.8 | 63 893 | 14.8 | 28.2 | 6.2 |
| mp | 2.5deg100vel | 81 684 | 44.9 | 23.9 | 16.2 | 82 953 | 31.2 | 17.7 | 7.4 | 81 788 | 25.9 | 27.2 | 7.5 |
| mp | 5deg050vel | 64 938 | 38.4 | 24.9 | 16.6 | 60 115 | 29.0 | 17.8 | 7.9 | 64 109 | 24.3 | 28.9 | 6.9 |
| mp | 5deg100vel | 86 824 | 86.1 | 68.5 | 63.5 | 82 448 | 77.8 | 58.5 | 51.1 | 81 435 | 75.9 | 59.9 | 50.4 |
| mp | 7.5deg100vel | 93 940 | 82.6 | 82.3 | 74.6 | 80 454 | 89.1 | 74.6 | 70.9 | 77 768 | 74.0 | 53.9 | 47.0 |
| mp | 10deg100vel | 83 850 | 89.8 | 90.0 | 85.7 | 72 029 | 77.1 | 74.3 | 64.0 | 68 751 | 65.2 | 53.2 | 43.4 |
| Average | 62.4 | 50.4 | 43.9 | 54.7 | 45.0 | 35.3 | 46.7 | 41.9 | 26.9 | ||||
| mr | 2.5deg050vel | 69 336 | 27.8 | 72.8 | 25.9 | 65 802 | 25.7 | 45.9 | 18.3 | 72 171 | 25.7 | 43.1 | 17.2 |
| mr | 2.5deg100vel | 80 994 | 42.1 | 53.0 | 29.1 | 78 535 | 21.6 | 41.7 | 13.4 | 78 556 | 22.9 | 45.2 | 15.5 |
| mr | 5deg050vel | 64 109 | 30.8 | 62.8 | 25.3 | 61 710 | 25.3 | 46.7 | 16.9 | 64 159 | 20.9 | 45.3 | 14.5 |
| mr | 5deg100vel | 72 679 | 22.9 | 42.8 | 15.7 | 61 278 | 19.7 | 34.2 | 10.6 | 59 795 | 23.1 | 41.1 | 15.3 |
| mr | 7.5deg100vel | 70 490 | 56.5 | 4.3 | 3.3 | 51 645 | 41.1 | 36.3 | 18.4 | 49 391 | 17.4 | 19.4 | 4.4 |
| mr | 10deg100vel | 75 431 | 32.8 | 36.2 | 18.8 | 60 248 | 16.2 | 28.4 | 6.9 | 61 157 | 7.9 | 13.8 | 0.9 |
| Average | 35.5 | 45.3 | 19.7 | 24.9 | 38.9 | 14.1 | 19.6 | 34.6 | 11.3 | ||||
Column descriptions. Type: type of interaction. Either a fly-by with the infalling disc in prograde orientation (fb), or a merger with the infalling disc in prograde (mp) or retrograde (mr) orientation. Model: name of the model or simulation. To show the evolution of the models, the following data are given for three different time steps in each model, except when stated otherwise. N: number of angular momentum directions to draw realizations from. fΔ: fraction of realizations fulfilling the clustering criterion (having a spherical standard distance of no more than 35.°4, the value for the MW satellites). fd: fraction of realizations fulfilling the direction criterion (having an average angular momentum direction pointing no further away from the equator than 9.°4, the value for the MW satellites). fboth: fraction of realizations fulfilling both criteria. They are shown in italic to ease the comparison of the different columns.
4:1 mass ratio tidal models and resulting fractions of realizations fulfilling the criteria.
| Type | Model | N | Time step 5 Gyr | fboth (per cent) | N | Time step 7.5 Gyr | fboth (per cent) | N | Time step 10 Gyr | fboth (per cent) | |||
| fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | ||||||||
| fb | 2deg200vel | 1045 | 99.4 | 99.9 | 99.3 | 1136 | 98.4 | 99.3 | 98.0 | 1084 | 98.3 | 98.1 | 97.0 |
| fb | 4deg175vel | 11 882 | 66.0 | 79.9 | 59.8 | 12 389 | 29.5 | 63.6 | 26.5 | 11 793 | 31.8 | 49.8 | 24.7 |
| fb | 4deg200vel | 14 127 | 34.7 | 77.6 | 33.8 | 13 732 | 36.3 | 70.8 | 33.2 | 12 205 | 39.9 | 69.2 | 36.4 |
| fb | 4deg225vel | 16 477 | 28.8 | 83.9 | 28.6 | 16 812 | 27.4 | 71.0 | 25.7 | 16 276 | 25.6 | 56.9 | 21.0 |
| fb | 4deg250vel | 11 858 | 38.3 | 87.0 | 38.1 | 12 016 | 48.9 | 92.2 | 48.9 | 11 330 | 45.0 | 85.3 | 44.4 |
| fb | 6deg175vel | 6284 | 97.6 | 86.7 | 85.6 | 7730 | 42.3 | 67.5 | 37.1 | 8245 | 27.4 | 41.9 | 18.3 |
| fb | 6deg200vel | 6205 | 97.9 | 95.2 | 93.7 | 7730 | 38.8 | 65.0 | 33.0 | 7337 | 31.5 | 56.4 | 24.9 |
| fb | 6deg225vel | 8659 | 98.7 | 94.7 | 93.8 | 8213 | 85.4 | 82.1 | 73.5 | 8509 | 57.4 | 60.1 | 40.7 |
| fb | 6deg250vel | 4970 | 94.3 | 96.0 | 91.4 | 5067 | 77.4 | 62.0 | 50.3 | No data, galaxies left model volume | |||
| fb | 8deg175vel | 4522 | 96.2 | 93.1 | 91.0 | 5129 | 80.9 | 84.3 | 73.5 | 4815 | 74.2 | 76.5 | 63.4 |
| Average | 75.2 | 89.4 | 71.5 | 56.5 | 75.8 | 50.0 | 47.9 | 66.0 | 41.2 | ||||
| mp | 2.5deg050vel | 66 917 | 32.8 | 12.7 | 6.9 | 62 262 | 23.9 | 27.4 | 10.8 | 63 893 | 14.8 | 28.2 | 6.2 |
| mp | 2.5deg100vel | 81 684 | 44.9 | 23.9 | 16.2 | 82 953 | 31.2 | 17.7 | 7.4 | 81 788 | 25.9 | 27.2 | 7.5 |
| mp | 5deg050vel | 64 938 | 38.4 | 24.9 | 16.6 | 60 115 | 29.0 | 17.8 | 7.9 | 64 109 | 24.3 | 28.9 | 6.9 |
| mp | 5deg100vel | 86 824 | 86.1 | 68.5 | 63.5 | 82 448 | 77.8 | 58.5 | 51.1 | 81 435 | 75.9 | 59.9 | 50.4 |
| mp | 7.5deg100vel | 93 940 | 82.6 | 82.3 | 74.6 | 80 454 | 89.1 | 74.6 | 70.9 | 77 768 | 74.0 | 53.9 | 47.0 |
| mp | 10deg100vel | 83 850 | 89.8 | 90.0 | 85.7 | 72 029 | 77.1 | 74.3 | 64.0 | 68 751 | 65.2 | 53.2 | 43.4 |
| Average | 62.4 | 50.4 | 43.9 | 54.7 | 45.0 | 35.3 | 46.7 | 41.9 | 26.9 | ||||
| mr | 2.5deg050vel | 69 336 | 27.8 | 72.8 | 25.9 | 65 802 | 25.7 | 45.9 | 18.3 | 72 171 | 25.7 | 43.1 | 17.2 |
| mr | 2.5deg100vel | 80 994 | 42.1 | 53.0 | 29.1 | 78 535 | 21.6 | 41.7 | 13.4 | 78 556 | 22.9 | 45.2 | 15.5 |
| mr | 5deg050vel | 64 109 | 30.8 | 62.8 | 25.3 | 61 710 | 25.3 | 46.7 | 16.9 | 64 159 | 20.9 | 45.3 | 14.5 |
| mr | 5deg100vel | 72 679 | 22.9 | 42.8 | 15.7 | 61 278 | 19.7 | 34.2 | 10.6 | 59 795 | 23.1 | 41.1 | 15.3 |
| mr | 7.5deg100vel | 70 490 | 56.5 | 4.3 | 3.3 | 51 645 | 41.1 | 36.3 | 18.4 | 49 391 | 17.4 | 19.4 | 4.4 |
| mr | 10deg100vel | 75 431 | 32.8 | 36.2 | 18.8 | 60 248 | 16.2 | 28.4 | 6.9 | 61 157 | 7.9 | 13.8 | 0.9 |
| Average | 35.5 | 45.3 | 19.7 | 24.9 | 38.9 | 14.1 | 19.6 | 34.6 | 11.3 | ||||
| Type | Model | N | Time step 5 Gyr | fboth (per cent) | N | Time step 7.5 Gyr | fboth (per cent) | N | Time step 10 Gyr | fboth (per cent) | |||
| fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | fΔ (per cent) | fd (per cent) | ||||||||
| fb | 2deg200vel | 1045 | 99.4 | 99.9 | 99.3 | 1136 | 98.4 | 99.3 | 98.0 | 1084 | 98.3 | 98.1 | 97.0 |
| fb | 4deg175vel | 11 882 | 66.0 | 79.9 | 59.8 | 12 389 | 29.5 | 63.6 | 26.5 | 11 793 | 31.8 | 49.8 | 24.7 |
| fb | 4deg200vel | 14 127 | 34.7 | 77.6 | 33.8 | 13 732 | 36.3 | 70.8 | 33.2 | 12 205 | 39.9 | 69.2 | 36.4 |
| fb | 4deg225vel | 16 477 | 28.8 | 83.9 | 28.6 | 16 812 | 27.4 | 71.0 | 25.7 | 16 276 | 25.6 | 56.9 | 21.0 |
| fb | 4deg250vel | 11 858 | 38.3 | 87.0 | 38.1 | 12 016 | 48.9 | 92.2 | 48.9 | 11 330 | 45.0 | 85.3 | 44.4 |
| fb | 6deg175vel | 6284 | 97.6 | 86.7 | 85.6 | 7730 | 42.3 | 67.5 | 37.1 | 8245 | 27.4 | 41.9 | 18.3 |
| fb | 6deg200vel | 6205 | 97.9 | 95.2 | 93.7 | 7730 | 38.8 | 65.0 | 33.0 | 7337 | 31.5 | 56.4 | 24.9 |
| fb | 6deg225vel | 8659 | 98.7 | 94.7 | 93.8 | 8213 | 85.4 | 82.1 | 73.5 | 8509 | 57.4 | 60.1 | 40.7 |
| fb | 6deg250vel | 4970 | 94.3 | 96.0 | 91.4 | 5067 | 77.4 | 62.0 | 50.3 | No data, galaxies left model volume | |||
| fb | 8deg175vel | 4522 | 96.2 | 93.1 | 91.0 | 5129 | 80.9 | 84.3 | 73.5 | 4815 | 74.2 | 76.5 | 63.4 |
| Average | 75.2 | 89.4 | 71.5 | 56.5 | 75.8 | 50.0 | 47.9 | 66.0 | 41.2 | ||||
| mp | 2.5deg050vel | 66 917 | 32.8 | 12.7 | 6.9 | 62 262 | 23.9 | 27.4 | 10.8 | 63 893 | 14.8 | 28.2 | 6.2 |
| mp | 2.5deg100vel | 81 684 | 44.9 | 23.9 | 16.2 | 82 953 | 31.2 | 17.7 | 7.4 | 81 788 | 25.9 | 27.2 | 7.5 |
| mp | 5deg050vel | 64 938 | 38.4 | 24.9 | 16.6 | 60 115 | 29.0 | 17.8 | 7.9 | 64 109 | 24.3 | 28.9 | 6.9 |
| mp | 5deg100vel | 86 824 | 86.1 | 68.5 | 63.5 | 82 448 | 77.8 | 58.5 | 51.1 | 81 435 | 75.9 | 59.9 | 50.4 |
| mp | 7.5deg100vel | 93 940 | 82.6 | 82.3 | 74.6 | 80 454 | 89.1 | 74.6 | 70.9 | 77 768 | 74.0 | 53.9 | 47.0 |
| mp | 10deg100vel | 83 850 | 89.8 | 90.0 | 85.7 | 72 029 | 77.1 | 74.3 | 64.0 | 68 751 | 65.2 | 53.2 | 43.4 |
| Average | 62.4 | 50.4 | 43.9 | 54.7 | 45.0 | 35.3 | 46.7 | 41.9 | 26.9 | ||||
| mr | 2.5deg050vel | 69 336 | 27.8 | 72.8 | 25.9 | 65 802 | 25.7 | 45.9 | 18.3 | 72 171 | 25.7 | 43.1 | 17.2 |
| mr | 2.5deg100vel | 80 994 | 42.1 | 53.0 | 29.1 | 78 535 | 21.6 | 41.7 | 13.4 | 78 556 | 22.9 | 45.2 | 15.5 |
| mr | 5deg050vel | 64 109 | 30.8 | 62.8 | 25.3 | 61 710 | 25.3 | 46.7 | 16.9 | 64 159 | 20.9 | 45.3 | 14.5 |
| mr | 5deg100vel | 72 679 | 22.9 | 42.8 | 15.7 | 61 278 | 19.7 | 34.2 | 10.6 | 59 795 | 23.1 | 41.1 | 15.3 |
| mr | 7.5deg100vel | 70 490 | 56.5 | 4.3 | 3.3 | 51 645 | 41.1 | 36.3 | 18.4 | 49 391 | 17.4 | 19.4 | 4.4 |
| mr | 10deg100vel | 75 431 | 32.8 | 36.2 | 18.8 | 60 248 | 16.2 | 28.4 | 6.9 | 61 157 | 7.9 | 13.8 | 0.9 |
| Average | 35.5 | 45.3 | 19.7 | 24.9 | 38.9 | 14.1 | 19.6 | 34.6 | 11.3 | ||||
Column descriptions. Type: type of interaction. Either a fly-by with the infalling disc in prograde orientation (fb), or a merger with the infalling disc in prograde (mp) or retrograde (mr) orientation. Model: name of the model or simulation. To show the evolution of the models, the following data are given for three different time steps in each model, except when stated otherwise. N: number of angular momentum directions to draw realizations from. fΔ: fraction of realizations fulfilling the clustering criterion (having a spherical standard distance of no more than 35.°4, the value for the MW satellites). fd: fraction of realizations fulfilling the direction criterion (having an average angular momentum direction pointing no further away from the equator than 9.°4, the value for the MW satellites). fboth: fraction of realizations fulfilling both criteria. They are shown in italic to ease the comparison of the different columns.
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