Tailoring triaxial N-body models via a novel made-to-measure method

The made-to-measure N -body method slowly adapts the particle weights of an N -body model, whilst integrating the trajectories in an assumed static potential, until some constraints are satisfied, such as optimal fits to observational data. I propose a novel technique for this adaption procedure, which overcomes several limitations and shortcomings of the original method. The capability of the new technique is demonstrated by generating realistic N -body equilibrium models for dark matter haloes with prescribed density profile, triaxial shape and slowly outwardly growing radial velocity anisotropy.     

Multimass schemes for collisionless N-body simulations

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 multimass 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 of ∼100 reduction in the variance at 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.     

Multimass spherical structure models for N-body simulations

We present a simple and efficient method to set up spherical structure models for N -body simulations with a multimass technique. This technique reduces by a substantial factor the computer run time needed in order to resolve a given scale as compared to single-mass models. It therefore allows to resolve smaller scales in N -body simulations for a given computer run time. Here, we present several models with an effective resolution of up to  1.68 × 10⁹  particles within their virial radius which are stable over cosmologically relevant time-scales. As an application, we confirm the theoretical prediction by Dehnen that in mergers of collisionless structures like dark matter haloes always the cusp of the steepest progenitor is preserved. We model each merger progenitor with an effective number of particles of approximately 10⁸ particles. We also find that in a core–core merger the central density approximately doubles whereas in the cusp–cusp case the central density only increases by approximately 50 per cent. This may suggest that the central regions of flat structures are better protected and get less energy input through the merger process.     

Influence of a stellar cusp on the dynamics of young stellar discs and the origin of the S-stars in the Galactic Centre

Observations of the Galactic Centre show evidence of one or two disc-like structures of very young stars orbiting the central supermassive black hole within a distance of a few 0.1 pc. A number of analyses have been carried out to investigate the dynamical behaviour and consequences of these discs, including disc thickness and eccentricity growth as well as mutual interaction and warping. However, most of these studies have neglected the influence of the stellar cusp surrounding the black hole, which is believed to be one to two orders of magnitude more massive than the disc(s).
By means of N -body integrations using our bhint code, we study the impact of stellar cusps of different compositions. We find that although the presence of a cusp does have an important effect on the evolution of an otherwise isolated flat disc, its influence on the evolution of disc thickness and warping is rather mild in a two-disc configuration. However, we show that the creation of highly eccentric orbits strongly depends on the graininess of the cusp (i.e. the mean and maximum stellar masses). While Chang recently found that full cycles of Kozai resonance are prevented by the presence of an analytic cusp, we show that relaxation processes play an important role in such highly dense regions and support short-term resonances. We thus find that young disc stars on initially circular orbits can achieve high eccentricities by resonant effects also in the presence of a cusp of stellar remnants, yielding a mechanism to create S-stars and hypervelocity stars.
Furthermore, we discuss the underlying initial mass function (IMF) of the young stellar discs and find no definite evidence for a non-canonical IMF.     

The Adaptive TreePM: an adaptive resolution code for cosmological N-body simulations

Cosmological N -body simulations are used for a variety of applications. Indeed progress in the study of large-scale structures and galaxy formation would have been very limited without this tool. For nearly 20 yr the limitations imposed by computing power forced simulators to ignore some of the basic requirements for modelling gravitational instability. One of the limitations of most cosmological codes has been the use of a force softening length that is much smaller than the typical interparticle separation. This leads to departures from collisionless evolution that is desired in these simulations. We propose a particle-based method with an adaptive resolution where the force softening length is reduced in high-density regions while ensuring that it remains well above the local interparticle separation. The method, called the Adaptive TreePM (ATreePM), is based on the TreePM code. We present the mathematical model and an implementation of this code, and demonstrate that the results converge over a range of options for parameters introduced in generalizing the code from the TreePM code. We explicitly demonstrate collisionless evolution in collapse of an oblique plane wave. We compare the code with the fixed resolution TreePM code and also an implementation that mimics adaptive mesh refinement methods and comment on the agreement and disagreements in the results. We find that in most respects the ATreePM code performs at least as well as the fixed resolution TreePM in highly overdense regions, from clustering and number density of haloes to internal dynamics of haloes. We also show that the adaptive code is faster than the corresponding high-resolution TreePM code.     

On the number of young stellar discs in the Galactic Centre

Observations of the Galactic Centre show evidence of disc-like structures of very young stars orbiting the central supermassive black hole within a distance of a few 0.1 pc. While it is widely accepted that about half of the stars form a relatively flat disc rotating clockwise on the sky, there is a substantial ongoing debate on whether there is a second, counter-clockwise disc of stars.
By means of N -body simulations using our bhint code, we show that two highly inclined stellar discs with the observed properties cannot be recognized as two flat circular discs after 5 Myr of mutual interaction. Instead, our calculations predict a significant warping of the two discs, which we show to be apparent among the structures observed in the Galactic Centre. While the high eccentricities of the observed counter-clockwise orbits suggest an eccentric origin of this system, we show the eccentricity distribution in the inner part of the more massive clockwise disc to be perfectly consistent with an initially circular disc in which stellar eccentricities increase due to both non-resonant and resonant relaxation.
We conclude that the relevant question to ask is therefore not whether there are two discs of young stars, but whether there were two such discs to begin with.     

N-body simulations for testing the stability of triaxial galaxies in MOND

We perform a stability test of triaxial models in Modified Newtonian Dynamics (MOND) using N -body simulations. The triaxial models considered here have densities that vary with   r ⁻¹  in the centre and   r ⁻⁴  at large radii. The total mass of the model varies from 10⁸ to  10¹⁰ M_⊙  , representing the mass scale of dwarfs to medium-mass elliptical galaxies, respectively, from deep MOND to quasi-Newtonian gravity. We build triaxial galaxy models using the Schwarzschild technique, and evolve the systems for 200 Keplerian dynamical times (at the typical length-scale of 1.0 kpc). We find that the systems are virial overheating, and in quasi-equilibrium with the relaxation taking approximately 5 Keplerian dynamical times (1.0 kpc). For all systems, the change of the inertial (kinetic) energy is less than 10 per cent (20 per cent) after relaxation. However, the central profile of the model is flattened during the relaxation and the (overall) axis ratios change by roughly 10 per cent within 200 Keplerian dynamical times (at 1.0 kpc) in our simulations. We further find that the systems are stable once they reach the equilibrium state.     

grommet: an N-body code for high-resolution simulations of individual galaxies

This paper presents a fast, economical particle-multiple-mesh N -body code optimized for large- N modelling of collisionless dynamical processes, such as black hole wandering or bar–halo interactions, occurring within isolated galaxies. The code has been specially designed to conserve linear momentum. Despite this, it also has variable softening and an efficient block-time-step scheme: the force between any pair of particles is calculated using the finest mesh that encloses them both (respecting Newton's third law) and is updated only on the longest time-step of the two (which conserves momentum). For realistic galaxy models with   N ≳ 10⁶  , it is faster than the fastest comparable tree code by factors ranging from ∼2 (using single time-steps) to ∼10 (multiple time-steps in a concentrated galaxy).     

Limits on initial mass segregation in young clusters

Mass segregation is observed in many star clusters, including several that are less than a few Myr old. Time-scale arguments are frequently used to argue that these clusters must be displaying primordial segregation, because they are too young to be dynamically relaxed. Looking at this argument from the other side, the youth of these clusters and the limited time available to mix spatially distinct populations of stars can provide constraints on the amount of initial segregation that is consistent with current observations. We present n -body experiments testing this idea, and discuss the implications of our results for theories of star formation. For system ages less than a few crossing times, we show that star formation scenarios predicting general primordial mass segregation are inconsistent with observed segregation levels.