tokens: difference in realization may cause a bigger difference in the mass evolution (however, still very small) than using the same realization but with a different code. Figure 7. Comparison of models performed with different N -body codes. The blue and orange lines are the differences in the remaining bound masses between models 18 and 19 on one hand (performed with φ grape and ph4 , respectively) and 17 on the other (performed with nbody6++ ). The light green lines are similarly the differences between models 17A and 17B on one hand and 17 on the other that only differ in random seed. These models are in our weak tidal field eccentric orbit and have N = 10 5 stars. No gravitational softening was used. The small and seemingly random residuals indicate that there is no systematic difference in these models. Despite the differences between nbody6++ , φ grape , and ph4 , we find that the evolution of N = 10 5 clusters in weak tidal fields is nearly identical from one code to the next. 3.3 Softened models Gravitational softening is a technique to ease the computation of N -body simulation. In ‘Plummer’-type softening, the gravitational force between two bodies is modified from ∼ r −2 to ∼( r 2 + a 2 ) −1 , where a is called the softening length. For r ≫ a , the modified force approaches the true Newtonian force, but otherwise it approaches a constant. This hinders the formation of bound systems on scales ≤ a which otherwise have small time-steps and are difficult to integrate unless a regularization technique is used. Modifying the gravitational force in such a way has implications for hyperbolic encounters as well, the effect is decreasing the Coulomb logarithm and thus increasing of the two-body relaxation time. 3.3.1 Model with <italic>N</italic> = 10<sup>5</sup> Model 22 is the softened equivalent of model 17 presented in Section 3.1 . The two models evolve in a very similar way, and most quantities (total mass-loss, Lagrange radii) match when 17 is ‘slowed down’ by a factor of 1.18. Between 0.2 and 5 Gyr (roughly the time of the core collapse), model 17 experiences 461 kicks and 8593 sweeps, while model 22 experiences 129 kicks and 6620 sweeps. The softer potential causes a significant reduction in the number of kicks (as expected given the treatment of close encounters) and a moderate reduction in the number of sweeps. 3.3.2 Model with <italic>N</italic> = 10<sup>6</sup> Model 6 is the softened equivalent of model 1 presented in Section 3.1 . It behaves unexpectedly. While it is similar to model 1 , one would expect a somewhat lower mass-loss rate due to the gravitational softening, as seen when comparing models 22 and 17 . However, the result is the opposite. The difference in kick rate is especially stark: Between 0.2 and 5 Gyr, model 1 experiences 558 kicks and 14 530 sweeps, while model 6 experiences 5369 kicks and 16 607 sweeps. This ∼tenfold increase in the kick rate (as opposed to a decrease by a factor of 3.6 when softening is added in
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