Results Of N-body Simulations Research Articles

Effect of discretization choices when modeling the thermo-chemical history of the accreting core

Different discretizations methods applied to models of core/mantle segregations are tested (single stage, multistage accretion, results of N-body simulations) in order to test the sensitivity of the thermo-chemical coupling to the type of discretization used. We found that while single stage and large discretization of segregation steps yield very different core temperature, multistage models of accretion and core mantle segregation, at least for the model presented in this paper, tend to yield similar results, whether it is for the light element concentrations or the final temperature of the core. As long as a magma ocean existence throughout the entire process of core/mantle segregation is posited, and that only the impactor's masses of metal and silicate are re-equilibrated at each step, the degree of discretization of continuous model does not matter as long as it encompasses more than 10 steps of calculations.

Positive Lynden-Bell derivative as a ticket to the bar trap?

ABSTRACT We have translated the results of N-body simulations of one barred model into the language of action variables and frequencies. Using this language, we analysed the behaviour of all orbits in the model on a large time-scale at the stage of a mature bar. We show that the orbits join the bar while preserving their adiabatic invariant, which takes into account the three-dimensional structure of the orbits. This allows us to apply the concept of the Lynden-Bell derivative for each of these orbits and trace how the sign of the derivative changes; i.e. how asynchronous changes in angular momentum Lz and orbital precession rate Ωpr (normal orbital mode) change to synchronous (abnormal mode). The transition to the abnormal mode occurs when Ωpr reaches the angular velocity of the pattern Ωp, after which the orbit becomes stuck in the bar trap. All this happens against the background of secular changes in actions (Lz decreases, JR and Jz increase). At the same time, corotating particles near two stable Lagrange points are also subject to secular changes in their actions. They increase Lz and drift to the periphery, shifting corotation outwards. We also show that a change in the orbital mode from normal to abnormal and the trapping of orbits in a bar are possible only when the bar speed decreases with time, regardless of what is causing the bar to slow down. Our findings clarify and expand the picture of bar formation and evolution in numerical models.

Born to Be Wide: The Distribution of Wide Binaries in the Field and Soft Binaries in Clusters

Most stars, binaries, and higher-multiplicity systems are thought to form in stellar clusters and associations that later dissociate. Very wide binaries can be easily disrupted in clusters due to dynamical evaporation (soft binaries) and/or tidal disruption by the gravitational potential of the cluster. Nevertheless, wide binaries are quite frequent in the field, where they can sometimes play a key role in the formation of compact binaries and serve as tools to study key physical processes. Here we use analytic tools to study the dynamical formation of soft binaries in clusters and their survival as field binaries following cluster dispersion. We derive the expected properties of very wide binaries both in clusters and in the field. We analytically derive their detailed distributions, including the wide binary fraction as a function of mass in different cluster environments, binary mass functions and mass ratios, and the distribution of their orbital properties. We show that our calculations agree well in most aspects with the results of N-body simulations but show some different binary fraction dependence on the cluster mass. We find that the overall fraction of wide binaries scales as , where N ⋆ is the size of the cluster, even for non-equal-mass stars. More massive stars are more likely to capture wide companions, with most stars above 5 M ⊙ likely to capture at least one stellar companion, and formation of triples is found to be frequent.

Long-term Evolution of Warps in Debris Disks—Application to the Gyr-old System HD 202628

We present the results of N-body simulations meant to reproduce the long-term effects of mutually inclined exoplanets on debris disks, using the HD 202628 system as a proxy. HD 202628 is a Gyr-old solar-type star that possesses a directly observable, narrow debris ring with a clearly defined inner edge and nonzero eccentricity, hinting at the existence of a sculpting exoplanet. The eccentric nature of the disk leads us to examine the effect on it over Gyr timescales from an eccentric and inclined planet, placed on its orbit through scattering processes. We find that, in systems with dynamical timescales akin to that of HD 202628, a planetary companion is capable of completely tilting the debris disk. This tilt is preserved over the Gyr age of the system. Simulated observations of our models show that an exoplanet around HD 202628 with an inclination misalignment ≳10° would cause the disk to be observably diffuse and broad, which is inconsistent with Atacama Large Millimeter Array (ALMA) observations. With these observations, we conclude that, if there is an exoplanet shaping this disk, it likely had a mutual inclination of less than 5° with the primordial disk. The conclusions of this work can be applied either to debris disks appearing as narrow rings (e.g., Fomalhaut and HR 4796) or to disks that are vertically thick at ALMA wavelengths (e.g., HD 110058).

Шаровые скопления, захваченные баром Млечного Пути

Equations of motion are integrated backwards in time by 5 Gyr for thirty globular clusters from the central parts of the Milky Way. We considered two models of the potential, one, which is obtained by fitting the velocity curve of the Milky Way, and the second one, which is based on the results of N-body simulations. Obtained orbits were studied within the approach of spectral dynamics: main frequency of oscillations fx and fR were calculated for each of the orbits. Our analysis showed that six of the studied gloubular clusters (NGC 6266, NGC 6642, Terzan 1, Terzan 2, Terzan 4, and Terzan 5) have frequencies ratios fR/fx ≈ 2, that is, they can support the bar in the considered models.

Gravothermal Solutions of SIDM Halos: Mapping from Constant to Velocity-dependent Cross Section

The scale-free gravothermal fluid formalism has long proved effective in describing the evolution of self-interacting dark matter halos with a constant dark matter particle cross section. However, whether the gravothermal fluid solutions match numerical simulations for velocity-dependent cross-section scenarios remains untested. In this work, we provide a fast mapping method that relates the constant-cross-section gravothermal solution to models with arbitrary velocity dependence in the cross section. We show that the gravothermal solutions after mapping are in good agreement with Arepo N-body simulation results. We illustrate the power of this approach by applying this fast mapping method to a halo hosting a low-surface-brightness galaxy, UGC 128. We show that this fast mapping method can be used to constrain free parameters in a physically motivated cross-section model and illustrate the parameter space favored by the rotation curve measurement.

N-BODY SIMULATIONS: ADVANTAGES AND PROBLEMS

The N-body simulations method is widely used in astrophysics and cosmology. The article briefly lists its advantages, disadvantages and possible errors. It is concluded that the results of computer simulation not only cannot replace the data of astronomical observations, but also are not a sufficient reason to reject new hypotheses that do not have other drawbacks, other than the discrepancy between their conclusions and the results of N-body simulations.

Constraints on star formation in NGC 2264

ABSTRACT We quantify the spatial distribution of stars for two subclusters centred around the massive/intermediate-mass stars S Mon and IRS 1/2 in the NGC 2264 star-forming region. We find that both subclusters have neither a substructured nor a centrally concentrated distribution according to the $\mathcal {Q}$-parameter. Neither subcluster displays mass segregation according to the ΛMSR ratio, but the most massive stars in IRS 1/2 have higher relative surface densities according to the ΣLDR ratio. We then compare these quantities to the results of N-body simulations to constrain the initial conditions of NGC 2264, which are consistent with having been dense ($\tilde{\rho } \sim 10^4$ M⊙ pc−3), highly substructured and subvirial. These initial conditions were also derived from a separate analysis of the runaway and walkaway stars in the region, and indicate that star-forming regions within 1 kpc of the Sun likely have a broad range of initial stellar densities. In the case of NGC 2264, its initial stellar density could have been high enough to cause the destruction or truncation of protoplanetary discs and fledgling planetary systems due to dynamical encounters between stars in the early stages of its evolution.

The mean free path approximation and stellar collisions in star clusters: numerical exploration of the analytic rates and the role of perturbations on binary star mergers

ABSTRACTIn this paper, we compute predictions for the number of stellar collisions derived from analytic models based on the mean free path (MFP) approximation and compare them to the results of N-body simulations. Our goal is to identify the cluster conditions under which the MFP approximation remains valid. Adopting a range of particle numbers (100 ≤ N ≤ 5000) and different combinations of particle masses and radii, we explore three different channels leading to stellar collisions, all of which are expected to occur in realistic stellar environments. At high densities, binaries form from isolated three-body interactions of single stars. Hence, we consider collisions between single stars and collisions involving binary stars, after they form in our simulations. For the latter, we consider two channels for mergers, namely direct stellar collisions during chaotic single–binary interactions and perturbation-driven mergers of binaries due to random walks in eccentricity approaching unity. In the densest systems considered here, a very massive object is formed at the cluster centre, causing local stellar orbits to become increasingly Keplerian and the assumptions going into our analytic model to break down. Before reaching this limit, we obtain excellent agreement between our theoretical predictions and the simulations: The analytic rates are typically accurate to within one standard deviation for the entire parameter space considered here, but the agreement is best for short integration times. Our results have direct implications for blue straggler formation in dense star clusters, and stellar mergers in galactic nuclei hosting massive black holes.

Homogeneous vs Biased IGM: Impact on Reionization

This paper considers the impact of large scale biasing of the IGM on reionization. The two simplest but extreme scenarios for IGM biasing are: an unbiased IGM which has a constant density and an IGM with density equal to the collapsed matter density. In this work, the relationship between the IGM density and the collapsed matter density is defined through an IGM bias parameter. The two extreme scenarios of homogeneous and perfectly biased IGM are produced for two extreme values of this bias parameter. It is found that, for the same level of reionization (i.e., for same global neutral hydrogen fraction). one could get very different 21 cm brightness temperature distributions for different values of this bias parameter. These distributions could give an order of magnitude more or less power as compared to the uniform case. It is also found that there exists a critical value for the IGM bias parameter for which there could be a near washout of the structure in the 21 cm brightness temperature distribution (i.e., zero power or a nearly uniform 21 cm brightness temperature distribution). To address the problem, a new method of generating 21 cm brightness temperature maps is used. The method uses the results of n-body simulations and then employs ray tracing to obtain the 21 cm brightness temperature maps. Towards the end, a prescription for the IGM bias parameter is given. This is derived within the framework of the Press-Schechter theory.

Do ultracompact dwarf galaxies form monolithically or as merged star cluster complexes?

ABSTRACT Some ultracompact dwarf galaxies (UCDs) have elevated observed dynamical V-band mass-to-light (M/LV) ratios with respect to what is expected from their stellar populations assuming a canonical initial mass function (IMF). Observations have also revealed the presence of a compact dark object in the centres of several UCDs, having a mass of a few to 15 per cent of the present-day stellar mass of the UCD. This central mass concentration has typically been interpreted as a supermassive black hole, but can in principle also be a subcluster of stellar remnants. We explore the following two formation scenarios of UCDs: (i) monolithic collapse and (ii) mergers of star clusters in cluster complexes as are observed in massively starbursting regions. We explore the physical properties of the UCDs at different evolutionary stages assuming different initial stellar masses of the UCDs and the IMF being either universal or changing systematically with metallicity and density according to the integrated Galactic IMF theory. While the observed elevated M/LV ratios of the UCDs cannot be reproduced if the IMF is invariant and universal, the empirically derived IMF that varies systematically with density and metallicity shows agreement with the observations. Incorporating the UCD-mass-dependent retention fraction of dark remnants improves this agreement. In addition, we apply the results of N-body simulations to young UCDs and show that the same initial conditions describing the observed M/LV ratios reproduce the observed relation between the half-mass radii and the present-day masses of the UCDs. The findings thus suggest that the majority of UCDs that have elevated M/LV ratios could have formed monolithically with significant remnant-mass components that are centrally concentrated, while those with small M/LV values may be merged star cluster complexes.

Signature of a cosmic string wake at z=3

In this paper, we describe the results of N-body simulation runs, which include a cosmic string wake of tension Gμ= 4 × 10−8 on top of the usual Λ CDM fluctuations. To obtain a higher resolution of the wake in the simulations compared to previous work, we insert the effects of the string wake at a lower redshift and perform the simulations in a smaller volume. A curvelet analysis of the wake and no-wake maps is applied, indicating that the presence of a wake can be extracted at a three-sigma confidence level from maps of the two-dimensional dark matter projection down to a redshift of z=3.

Gaia’s detectability of black hole–main sequence star binaries formed in open clusters

Abstract Black hole–main sequence star (BH–MS) binaries are one of the targets of future data releases of the astrometric satellite Gaia. They are supposed to be formed in two main sites: a galactic field and star clusters. However, previous work has never predicted the number of BH–MS binaries originating in the latter sites. In this paper we estimate the number of BH–MS binaries formed in open clusters and detectable with Gaia based on the results of N-body simulations. By considering interstellar extinction in the Milky Way and observational constraints, we predict that ∼10 BH–MS binaries are observable. We also find that chemical abundance patterns of companion MSs will help us to identify the origin of the binaries as star clusters. Such MSs are not polluted by outflows of the BH progenitors, such as stellar winds and supernova ejecta. Chemical anomalies might be a good test to confirm the origin of binaries with relatively less massive MSs (≲5 M⊙), short orbital periods (∼1.5 yr), and higher eccentricities (e ≳0.1).

On the existence of exotic matter in classical Newtonian mechanics

According to Newton’s law of gravitation, the force between two particles depends upon their inertial, as well as their active and passive gravitational masses. For ordinary matter, all three of these are equal and positive. We consider here the more general case where these quantities are equal in magnitude for a given particle but can differ in sign. The resulting set of possible interactions allows each particle type to be assigned to one of precisely four different classes, and the results of N-body simulations show that the corresponding dynamics can give rise to a fairly rich spectrum of possible outcomes, some of which are familiar from nature at various scales. Total energy and momentum are conserved by all of these interactions if the definitions of momentum and kinetic and potential energy are suitably generalized.

Towards an improved model of self-interacting dark matter haloes

We discuss the relation between the strength of the self-interaction of dark matter particles and the predicted properties of the inner density distributions of dark matter haloes. We present the results of N-body simulations for 28 galaxy cluster sized haloes performed with the same initial conditions for cold dark matter and for self-interacting dark matter with cross-sections ranging from 0.1 to 10 cm2/g. We provide a simple phenomenological description of these results and compare them to the semi-analytical model typically used in the literature. We find that some of the assumptions made in this model are not satisfied in the simulations. We identify the reasons for this disagreement and improve the semi-analytical model correspondingly. We discuss how simulation results can be properly compared with observations and in particular how quantities like the core radius and the inner dark matter surface density depend on the self-interaction cross-section.

Why does Einasto profile index n∼ 6 occur so frequently?

We consider the behavior of spherically symmetric Einasto halos composed of gravitating particles in the Fokker-Planck approximation. This approach allows us to consider the undesirable influence of close encounters in the N-body simulations more adequately than the generally accepted criteria. The Einasto profile with index n ≈ 6 is a stationary solution of the Fokker-Planck equation in the halo center. There are some reasons to believe that the solution is an attractor. Then the Fokker-Planck diffusion tends to transform a density profile to the equilibrium one with the Einasto index n ≈ 6. We suggest this effect as a possible reason why the Einasto index n ≈ 6 occurs so frequently in the interpretation of N-body simulation results. The results obtained cast doubt on generally accepted criteria of N-body simulation convergence.

The detection rates of merging binary black holes originating from star clusters and their mass function

Abstract Advanced LIGO (Laser Interferometer Gravitational Wave Observatory) observations achieved the first detection of the gravitational wave, which was from a merging binary black hole (BBH). In the near future, more merger events will be observed, and the mass distribution of them will become available. The mass distribution of merger events reflects the evolutionary path of BBHs: dynamical formation in dense star clusters or common envelope evolution from primordial binaries. In this paper, we estimate the detection rate of merging BBHs which dynamically formed in dense star clusters by combining the results of N-body simulations, modeling of globular clusters, and cosmic star-cluster formation history. We estimate that the merger rate density in the local universe within the redshift of 0.1 is 13–57 Gpc−3 yr−1. We find that the detection rate is 0.23–4.6 per year for the current sensitivity limit and that it would increase to 5.1–99 per year for the designed sensitivity which will be achieved in 2019. The distribution of merger rate density in the local universe as a function of redshifted chirp mass has a peak close to the low-mass end. The chirp mass function of the detected mergers, on the other hand, has a peak at the high-mass end, but is almost flat. This difference is simply because the detection range is larger for more massive BBHs.

TheGaia-ESO Survey: Structural and dynamical properties of the young cluster Chamaeleon I

The young (~2 Myr) cluster Chamaeleon I is one of the closest laboratories to study the early stages of star cluster dynamics in a low-density environment. We studied its structural and kinematical properties combining parameters from the high-resolution spectroscopic survey Gaia-ESO with data from the literature. Our main result is the evidence of a large discrepancy between the velocity dispersion (sigma = 1.14 \pm 0.35 km s^{-1}) of the stellar population and the dispersion of the pre-stellar cores (~0.3 km s^{-1}) derived from submillimeter observations. The origin of this discrepancy, which has been observed in other young star clusters is not clear. It may be due to either the effect of the magnetic field on the protostars and the filaments, or to the dynamical evolution of stars driven by two-body interactions. Furthermore, the analysis of the kinematic properties of the stellar population put in evidence a significant velocity shift (~1 km s^{-1}) between the two sub-clusters located around the North and South main clouds. This result further supports a scenario, where clusters form from the evolution of multiple substructures rather than from a monolithic collapse. Using three independent spectroscopic indicators (the gravity indicator $\gamma$, the equivalent width of the Li line, and the H_alpha 10\% width), we performed a new membership selection. We found six new cluster members located in the outer region of the cluster. Starting from the positions and masses of the cluster members, we derived the level of substructure Q, the surface density \Sigma and the level of mass segregation $\Lambda_{MSR}$ of the cluster. The comparison between these structural properties and the results of N-body simulations suggests that the cluster formed in a low density environment, in virial equilibrium or supervirial, and highly substructured.

Testing the imprint of nonstandard cosmologies on void profiles using Monte Carlo random walks

Using a Monte Carlo random walks of a log-normal distribution, we show how to qualitatively study void properties for non-standard cosmologies. We apply this method to an f(R) modified gravity model and recover the N-body simulation results of (Achitouv et al. 2016) for the void profiles and their deviation from GR. This method can potentially be extended to study other properties of the large scale structures such as the abundance of voids or overdense environments. We also introduce a new way to identify voids in the cosmic web, using only a few measurements of the density fluctuations around random positions. This algorithm allows to select voids with specific profiles and radii. As a consequence, we can target classes of voids with higher differences between f(R) and standard gravity void profiles. Finally we apply our void criteria to galaxy mock catalogues and discuss how the flexibility of our void finder can be used to reduce systematics errors when probing the growth rate in the galaxy-void correlation function.

Suppression of type I migration by disk winds

Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw < 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths.