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Register a new userN-MODY: a code for collisionless N-body simulations in modified Newtonian dynamics
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Pasquale Londrillo
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We describe the numerical code N-MODY, a parallel particle-mesh code for collisionless N-body simulations in modified Newtonian dynamics (MOND). N-MODY is based on a numerical potential solver in spherical coordinates that solves the non-linear MOND field equation, and is ideally suited to simulate isolated stellar systems. N-MODY can be used also to compute the MOND potential of arbitrary static density distributions. A few applications of N-MODY indicate that some astrophysically relevant dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter.
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We describe some results obtained with N-MODY, a code for N-body simulations of collisionless stellar systems in modified Newtonian dynamics (MOND). We found that a few fundamental dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter. In particular, violent relaxation, phase mixing and galaxy merging take significantly longer in MOND than in Newtonian gravity, while dynamical friction is more effective in a MOND system than in an equivalent Newtonian system with dark matter.
We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f_0. Our method uses importance sampling to find the sampling DF f_s that minimizes the mean-square formal errors in a given set of projections of the DF f_0. The result is a multi-mass N-body realization of the galaxy model in which ``interesting regions of phase-space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher-mass particles. As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N-body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor ~100 reduction in the variance in the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N-body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N-body simulations closer to the collisionless ideal.
The N-body problem has become one of the hottest topics in the fields of computational dynamics and cosmology. The large dynamical range in some astrophysical problems led to the use of adaptive time steps to integrate particle trajectories, however, the search of optimal strategies is still challenging. We quantify the performance of the hierarchical time step integrator Hamiltonian Splitting (HamSp) for collisionless multistep simulations. We compare with the constant step Leap-Frog (LeapF) integrator and the adaptive one (AKDK). Additionally, we explore the impact of different time step assigning functions. There is a computational overhead in HamSp however there are two interesting advantages: choosing a convenient time-step function may compensate and even turn around the efficiency compared with AKDK. We test both reversibility and time symmetry. The symmetrized nature of the HamSp integration is able to provide time-reversible integration for medium time scales and overall deliver better energy conservation for long integration times, and the linear and angular momentum are preserved at machine precision. We address the impact of using different integrators in astrophysical systems. We found that in most situations both AKDK and HamSp are able to correctly simulate the problems. We conclude that HamSp is an attractive and competitive alternative to AKDK, with, in some cases, faster and with better energy and momentum conservation. The use of recently discussed Bridge splitting techniques with HamSp may allow to reach considerably high efficiency.
We describe a novel N-body code designed for simulations of the central regions of galaxies containing massive black holes. The code incorporates Mikkolas algorithmic chain regularization scheme including post-Newtonian terms up to PN2.5 order. Stars moving beyond the chain are advanced using a fourth-order integrator with forces computed on a GRAPE board. Performance tests confirm that the hybrid code achieves better energy conservation, in less elapsed time, than the standard scheme and that it reproduces the orbits of stars tightly bound to the black hole with high precision. The hybrid code is applied to two sample problems: the effect of finite-N gravitational fluctuations on the orbits of the S-stars; and inspiral of an intermediate-mass black hole into the galactic center.
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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