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Register a new userMOCCA Code for Star Cluster Simulations - II. Comparison with N-body Simulations
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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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Direct $N$-body simulations of star clusters are accurate but expensive, largely due to the numerous $mathcal{O} (N^2)$ pairwise force calculations. To solve the post-million-body problem, it will be necessary to use approximate force solvers, such as tree codes. In this work, we adapt a tree-based, optimized Fast Multipole Method (FMM) to the collisional $N$-body problem. The use of a rotation-accelerated translation operator and an error-controlled cell opening criterion leads to a code that can be tuned to arbitrary accuracy. We demonstrate that our code, Taichi, can be as accurate as direct summation when $N> 10^4$. This opens up the possibility of performing large-$N$, star-by-star simulations of massive stellar clusters, and would permit large parameter space studies that would require years with the current generation of direct summation codes. Using a series of tests and idealized models, we show that Taichi can accurately model collisional effects, such as dynamical friction and the core-collapse time of idealized clusters, producing results in strong agreement with benchmarks from other collisional codes such as NBODY6++GPU or PeTar. Parallelized using OpenMP and AVX, Taichi is demonstrated to be more efficient than other CPU-based direct $N$-body codes for simulating large systems. With future improvements to the handling of close encounters and binary evolution, we clearly demonstrate the potential of an optimized FMM for the modeling of collisional stellar systems, opening the door to accurate simulations of massive globular clusters, super star clusters, and even galactic nuclei.
Stellar tidal streams are sensitive tracers of the properties of the gravitational potential in which they orbit and detailed observations of their density structure can be used to place stringent constraints on fluctuations in the potential caused by, e.g., the expected populations of dark matter subhalos in the standard cold dark matter paradigm (CDM). Simulations of the evolution of stellar streams in live $N$-body halos without low-mass dark-matter subhalos, however, indicate that streams exhibit significant perturbations on small scales even in the absence of substructure. Here we demonstrate, using high-resolution $N$-body simulations combined with sophisticated semi-analytic and simple analytic models, that the mass resolutions of $10^4$--$10^5,rm{M}_{odot}$ commonly used to perform such simulations cause spurious stream density variations with a similar magnitude on large scales as those expected from a CDM-like subhalo population and an order of magnitude larger on small, yet observable, scales. We estimate that mass resolutions of $approx100,rm{M}_{odot}$ ($approx1,rm{M}_{odot}$) are necessary for spurious, numerical density variations to be well below the CDM subhalo expectation on large (small) scales. That streams are sensitive to a simulations particle mass down to such small masses indicates that streams are sensitive to dark matter clustering down to these low masses if a significant fraction of the dark matter is clustered or concentrated in this way, for example, in MACHO models with masses of $10$--$100,rm{M}_{odot}$.
Star clusters form via clustering star formation inside molecular clouds. In order to understand the dynamical evolution of star clusters in their early phase, in which star clusters are still embedded in their surrounding gas, we need an accurate integration of individual stellar orbits without gravitational softening in the systems including both gas and stars, as well as modeling individual stars with a realistic mass function. We develop a new tree-direct hybrid smoothed particle hydrodynamics/N-body code, ASURA+BRIDGE, in which stars are integrated using a direct N-body scheme or PeTar, a particle-particle particle-tree scheme code, without gravitational softening. In ASURA+BRIDGE, stars are assumed to have masses randomly drawn from a given initial mass function. With this code, we perform star-cluster formation simulations starting from molecular clouds without gravitational softening. We find that artificial dense cores in star-cluster centers due to the softening disappear when we do not use softening. We further demonstrate that star clusters are built up via mergers of smaller clumps. Star clusters formed in our simulations include some dynamically formed binaries with the minimum semi-major axes of a few au, and the binary fraction is higher for more massive stars.
The first detections of black hole - neutron star mergers (GW200105 and GW200115) by the LIGO-Virgo-Kagra Collaboration mark a significant scientific breakthrough. The physical interpretation of pre- and post-merger signals requires careful cross-examination between observational and theoretical modelling results. Here we present the first set of black hole - neutron star simulations that were obtained with the numerical-relativity code BAM. Our initial data are constructed using the public LORENE spectral library which employs an excision of the black hole interior. BAM, in contrast, uses the moving-puncture gauge for the evolution. Therefore, we need to ``stuff the black hole interior with smooth initial data to evolve the binary system in time. This procedure introduces constraint violations such that the constraint damping properties of the evolution system are essential to increase the accuracy of the simulation and in particular to reduce spurious center-of-mass drifts. Within BAM we evolve the Z4c equations and we compare our gravitational-wave results with those of the SXS collaboration and results obtained with the SACRA code. While we find generally good agreement with the reference solutions and phase differences $lesssim 0.5$ rad at the moment of merger, the absence of a clean convergence order in our simulations does not allow for a proper error quantification. We finally present a set of different initial conditions to explore how the merger of black hole neutron star systems depends on the involved masses, spins, and equations of state.
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.
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