Table 2.
Integration result for the various braids.
| Model | E | tperi | tL | tstable | N | fBSS | f4S | fBB | fTS | Stability |
|---|---|---|---|---|---|---|---|---|---|---|
| Figure-8 | −1.29 | 6.33 | ≲3 ⋅ 104 | > 105 | 4380 | 0.833 | 0.079 | 0.064 | 0.025 | Linear stable |
| Model A | −2.08 | 5.99 | ≳3 ⋅ 104 | > 105 | 4175 | 0.817 | 0.078 | 0.083 | 0.022 | Linear stable |
| I.A.4i.c.(0.5) | −1.00 | 19.01 | ≲2 ⋅ 102 | ≲40 | 3624 | 0.877 | 0.055 | 0.037 | 0.031 | Unstable |
![]() |
−1.26 | 83.85 | ∼104 | ≲9 ⋅ 104 | 3020 | 0.803 | 0.094 | 0.064 | 0.039 | Marginally stable |
Notes. Integrations were performed using the fourth-order Hermite predictor corrector for 104 N-body time units with a time-step parameter of η = 0.01, and with outputs every 0.1 time unit. The first column identifies the interaction, followed by the braid’s total energy in N-body units [mass⋅(length/time)2], and the period of one complete orbit. The Lyapunov timescale (fourth column) was calculated by introducing a small perturbation (of 10−5) in the x-coordinate of the first particle. The fifth column gives tstable, the integration time over which we could determine that the system remained stable with a maximum integration time of tstable = 104. Note that we classify
as marginally stable, discussed in Sect. 4.1. The following column gives the number of experiments calculated while varying min, the impact parameter and relative encounter velocity. The last 4 columns give the fraction of interaction that leads to the various outcomes (marginalized over vin, min, and din), binary-single-single (BSS), four single stars (4S), binary-binary (BB), and triple-single (TS).
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