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Two aspects of our recent N-body studies of star clusters are presented: (1) What impact does mass segregation and selective mass loss have on integrated photometry? (2) How well compare results from N-body simulations using NBODY4 and STARLAB/KIRA?
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We use N-body simulations to examine whether a characteristic turnaround radius, as predicted from the spherical collapse model in a $rm {Lambda CDM}$ Universe, can be meaningfully identified for galaxy clusters, in the presence of full three-dimensional effects. We use The Dark Sky Simulations and Illustris-TNG dark-matter--only cosmological runs to calculate radial velocity profiles around collapsed structures, extending out to many times the virial radius $R_{200}$. There, the turnaround radius can be unambiguously identified as the largest non-expanding scale around a center of gravity. We find that: (a) Indeed, a single turnaround scale can meaningfully describe strongly non-spherical structures. (b) For halos of masses $M_{200}>10^{13}M_odot$, the turnaround radius $R_{ta}$ scales with the enclosed mass $M_{ta}$ as $M_{ta}^{1/3}$, as predicted by the spherical collapse model. (c) The deviation of $R_{ta}$ in simulated halos from the spherical collapse model prediction is insensitive to halo asphericity. Rather, it is sensitive to the tidal forces due to massive neighbors when such are present. (d) Halos exhibit a characteristic average density within the turnaround scale. This characteristic density is dependent on cosmology and redshift. For the present cosmic epoch and for concordance cosmological parameters ($Omega_m sim 0.7$; $Omega_Lambda sim 0.3$) turnaround structures exhibit an average matter density contrast with the background Universe of $delta sim 11$. Thus $R_{ta}$ is equivalent to $R_{11}$ -- in a way analogous to defining the virial radius as $R_{200}$ -- with the advantage that $R_{11}$ is shown in this work to correspond to a kinematically relevant scale in N-body simulations.
We have performed fully self-consistent $N$-body simulations of star clusters near the Galactic center (GC). Such simulations have not been performed because it is difficult to perform fast and accurate simulations of such systems using conventional methods. We used the Bridge code, which integrates the parent galaxy using the tree algorithm and the star cluster using the fourth-order Hermite scheme with individual timestep. The interaction between the parent galaxy and the star cluster is calculate with the tree algorithm. Therefore, the Bridge code can handle both the orbital and internal evolutions of star clusters correctly at the same time. We investigated the evolution of star clusters using the Bridge code and compared the results with previous studies. We found that 1) the inspiral timescale of the star clusters is shorter than that obtained with traditional simulations, in which the orbital evolution of star clusters is calculated analytically using the dynamical friction formula and 2) the core collapse of the star cluster increases the core density and help the cluster survive. The initial conditions of star clusters is not so severe as previously suggested.
We use direct $N$-body calculations to study the evolution of the unusually extended outer halo globular cluster Palomar 4 (Pal~4) over its entire lifetime in order to reproduce its observed mass, half-light radius, velocity dispersion and mass function slope at different radii. We find that models evolving on circular orbits, and starting from a non-mass segregated, canonical initial mass function (IMF) can reproduce neither Pal 4s overall mass function slope nor the observed amount of mass segregation. Including either primordial mass segregation or initially flattened IMFs does not reproduce the observed amount of mass segregation and mass function flattening simultaneously. Unresolved binaries cannot reconcile this discrepancy either. We find that only models with both a flattened IMF and primordial segregation are able to fit the observations. The initial (i.e. after gas expulsion) mass and half-mass radius of Pal~4 in this case are about 57000 M${odot}$ and 10 pc, respectively. This configuration is more extended than most globular clusters we observe, showing that the conditions under which Pal~4 formed must have been significantly different from that of the majority of globular clusters. We discuss possible scenarios for such an unusual configuration of Pal~4 in its early years.
Gravitational N-body simulations, that is numerical solutions of the equations of motions for N particles interacting gravitationally, are widely used tools in astrophysics, with applications from few body or solar system like systems all the way up to galactic and cosmological scales. In this article we present a summary review of the field highlighting the main methods for N-body simulations and the astrophysical context in which they are usually applied.
We describe a major upgrade of a Monte Carlo code which has previously been used for many studies of dense star clusters. We outline the steps needed in order to calibrate the results of the new Monte Carlo code against $N$-body simulations for large $N$ systems, up to $N=200000$. The new version of the Monte Carlo code (called MOCCA), in addition to the features of the old version, incorporates the direct Fewbody integrator (Fregeau et al. 2004) for three- and four-body interactions, and a new treatment of the escape process based on Fukushige & Heggie (2000). Now stars which fulfil the escape criterion are not removed immediately, but can stay in the system for a certain time which depends on the excess of the energy of a star above the escape energy. They are called potential escapers. With the addition of the Fewbody integrator the code can follow all interaction channels which are important for the rate of creation of various types of objects observed in star clusters, and ensures that the energy generation by binaries is treated in a manner similar to the $N$-body model. There are at most three new parameters which have to be adjusted against $N$-body simulations for large $N$: two (or one, depending on the chosen approach) connected with the escape process, and one responsible for the determination of the interaction probabilities. The values adopted for the free parameters have at most a weak dependence on $N$. They allow MOCCA to reproduce $N$-body results with reasonable precision, not only for the rate of cluster evolution and the cluster mass distribution, but also for the detailed distributions of mass and binding energy of binaries. Additionally, the code can follow the rate of formation of blue stragglers and black hole - black hole binaries.
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