scholarly journals l = 1: Weinberg’s weakly damped mode in an N-body model of a spherical stellar system

2020 ◽  
Author(s):  
Douglas C Heggie ◽  
Philip G Breen ◽  
Anna Lisa Varri
Keyword(s):  
Distribution Function ◽  
Initial Conditions ◽  
Stellar System ◽  
Power Spectra ◽  
Monte Carlo Sampling ◽  
Stellar Systems ◽  
Prominent Feature ◽  
Body Model ◽  
Perturbative Solution ◽  
The Matrix

Abstract Spherical stellar systems such as King models, in which the distribution function is a decreasing function of energy and depends on no other invariant, are stable in the sense of collisionless dynamics. But Weinberg showed, by a clever application of the matrix method of linear stability, that they may be nearly unstable, in the sense of possessing weakly damped modes of oscillation. He also demonstrated the presence of such a mode in an N-body model by endowing it with initial conditions generated from his perturbative solution. In the present paper we provide evidence for the presence of this same mode in N-body simulations of the King W0 = 5 model, in which the initial conditions are generated by the usual Monte Carlo sampling of the King distribution function. It is shown that the oscillation of the density centre correlates with variations in the structure of the system out to a radius of about 1 virial radius, but anticorrelates with variations beyond that radius. Though the oscillations appear to be continually reexcited (presumably by the motions of the particles) we show by calculation of power spectra that Weinberg’s estimate of the period (strictly, 2π divided by the real part of the eigenfrequency) lies within the range where the power is largest. In addition, however, the power spectrum displays another very prominent feature at shorter periods, around 5 crossing times.

scholarly journals Variable Stars and Problems of Stellar Formation

1957 ◽  
Vol 3 ◽  
pp. 111-115 ◽  
Author(s):  
B. V. Kukarkin
Keyword(s):  
Initial Conditions ◽  
Stellar System ◽  
Variable Stars ◽  
Stellar Systems ◽  
Stellar Formation ◽  
Evolutionary Paths ◽  
Different Origin

The possibility of discovering phenomenologically similar objects either located in different stellar systems, or in totally different (according to their origin and age) parts of some complex stellar system (as, for instance, our Galaxy) is of extreme importance. The detection of such objects permits us to confirm that, in spite of different initial conditions and evolutionary paths, stars of quite different origin pass in the course of their evolution through the same stages.

scholarly journals Brownian motion of black holes in stellar systems with non-Maxwellian distribution of the field stars

2006 ◽  
Vol 2 (S238) ◽  
pp. 427-428
Author(s):  
Isabel Tamara Pedron ◽  
Carlos H. Coimbra-Araújo
Keyword(s):  
Black Holes ◽  
Black Hole ◽  
Distribution Function ◽  
Brownian Motion ◽  
Random Walk ◽  
Brownian Particle ◽  
Stellar System ◽  
Stellar Systems ◽  
Massive Black Hole ◽  
Nearby Stars

AbstractA massive black hole at the center of a dense stellar system, such as a globular cluster or a galactic nucleus, is subject to a random walk due gravitational encounters with nearby stars. It behaves as a Brownian particle, since it is much more massive than the surrounding stars and moves much more slowly than they do. If the distribution function for the stellar velocities is Maxwellian, there is a exact equipartition of kinetic energy between the black hole and the stars in the stationary state. However, if the distribution function deviates from a Maxwellian form, the strict equipartition cannot be achieved.The deviation from equipartition is quantified in this work by applying the Tsallis q-distribution for the stellar velocities in a q-isothermal stellar system and in a generalized King model.

scholarly journals The Dynamical Evolution of Young Open Clusters

1985 ◽  
Vol 113 ◽  
pp. 463-465
Author(s):  
Michael Margulis ◽  
Charles J. Lada ◽  
David Dearborn
Keyword(s):  
Potential Function ◽  
Molecular Clouds ◽  
Initial Conditions ◽  
Stellar System ◽  
Dynamical Evolution ◽  
Mass Function ◽  
Open Clusters ◽  
Stellar Systems ◽  
Spherically Symmetric ◽  
Star Forming

Using numerical N-body calculations we have simulated the dynamical evolution of young clusters as they emerge from molecular clouds. Starting with initially virialized systems of stars and gas we follow the evolution of these systems from the time immediately after the stars have formed in a cloud until a time long after all the residual star-forming gas has been dispersed. In the models stellar systems were composed of 50, and in some cases 100, stars and these stars were represented as point masses. The stellar mass function followed a power law with an index of −2.5 and ranged over two decades in mass (Scalo 1978). Gas in the models was represented as an extra term in the gravitational potential function governing stellar motions, and was set to follow a density distribution corresponding to a spherically symmetric Plummer potential function (Plummer 1911). Starting with these initial conditions, stellar motions were then integrated and evolution of each stellar system was followed as gas was dispersed from the vicinity of the stars as a function of time.

scholarly journals The anisotropy of the power spectrum in periodic cosmological simulations

2021 ◽  
Vol 503 (4) ◽  
pp. 5638-5645
Author(s):  
Gábor Rácz ◽  
István Szapudi ◽  
István Csabai ◽  
László Dobos
Keyword(s):  
Dark Matter ◽  
Power Spectrum ◽  
Large Scale ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Power Spectra ◽  
Cosmological Simulations ◽  
Spherical Collapse ◽  
Lower Amplitude ◽  
Hydrodynamical Simulations

ABSTRACT The classical gravitational force on a torus is anisotropic and always lower than Newton’s 1/r2 law. We demonstrate the effects of periodicity in dark matter only N-body simulations of spherical collapse and standard Lambda cold dark matter (ΛCDM) initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations is a consequence of the missing large-scale modes and the equally important smaller periodic forces. The effect is most significant when the largest mildly non-linear scales are comparable to the linear size of the simulation box, as often is the case for high-resolution hydrodynamical simulations. Spherical collapse morphs into a shape similar to an octahedron. The anisotropic growth distorts the large-scale ΛCDM dark matter structures. We introduce the direction-dependent power spectrum invariant under the octahedral group of the simulation volume and show that the results break spherical symmetry.

scholarly journals Scalar and tensor perturbations in DHOST bounce cosmology

2021 ◽  
Vol 2021 (11) ◽  
pp. 045
Author(s):  
Mian Zhu ◽  
Amara Ilyas ◽  
Yunlong Zheng ◽  
Yi-Fu Cai ◽  
Emmanuel N. Saridakis
Keyword(s):  
Scale Invariance ◽  
Initial Conditions ◽  
Power Spectra ◽  
Thermal Fluctuations ◽  
Spectral Indices ◽  
Vacuum Fluctuations ◽  
Perfect Agreement ◽  
Expansion Phase ◽  
Contraction Phase ◽  
Tensor Perturbations

Abstract We investigate the bounce realization in the framework of DHOST cosmology, focusing on the relation with observables. We perform a detailed analysis of the scalar and tensor perturbations during the Ekpyrotic contraction phase, the bounce phase, and the fast-roll expansion phase, calculating the power spectra, the spectral indices and the tensor-to-scalar ratio. Furthermore, we study the initial conditions, incorporating perturbations generated by Ekpyrotic vacuum fluctuations, by matter vacuum fluctuations, and by thermal fluctuations. The scale invariance of the scalar power spectrum can be acquired introducing a matter contraction phase before the Ekpyrotic phase, or invoking a thermal gas as the source. The DHOST bounce scenario with cosmological perturbations generated by thermal fluctuations proves to be the most efficient one, and the corresponding predictions are in perfect agreement with observational bounds. Especially the tensor-to-scalar ratio is many orders of magnitude within the allowed region, since it is suppressed by the Hubble parameter at the beginning of the bounce phase.

scholarly journals Phenomenological Implications of Modified Loop Cosmologies: An Overview

2021 ◽  
Vol 8 ◽  
Author(s):  
Bao-Fei Li ◽  
Parampreet Singh ◽  
Anzhong Wang
Keyword(s):  
Initial Conditions ◽  
Scale Effects ◽  
Hybrid Approach ◽  
Planck Scale ◽  
Power Spectra ◽  
Big Bang ◽  
Hamiltonian Constraint ◽  
Hybrid Approaches ◽  
Effective Dynamics ◽  
The Big Bang

In this paper, we first provide a brief review of the effective dynamics of two recently well-studied models of modified loop quantum cosmologies (mLQCs), which arise from different regularizations of the Hamiltonian constraint and show the robustness of a generic resolution of the big bang singularity, replaced by a quantum bounce due to non-perturbative Planck scale effects. As in loop quantum cosmology (LQC), in these modified models the slow-roll inflation happens generically. We consider the cosmological perturbations following the dressed and hybrid approaches and clarify some subtle issues regarding the ambiguity of the extension of the effective potential of the scalar perturbations across the quantum bounce, and the choice of initial conditions. Both of the modified regularizations yield primordial power spectra that are consistent with current observations for the Starobinsky potential within the framework of either the dressed or the hybrid approach. But differences in primordial power spectra are identified among the mLQCs and LQC. In addition, for mLQC-I, striking differences arise between the dressed and hybrid approaches in the infrared and oscillatory regimes. While the differences between the two modified models can be attributed to differences in the Planck scale physics, the permissible choices of the initial conditions and the differences between the two perturbation approaches have been reported for the first time. All these differences, due to either the different regularizations or the different perturbation approaches in principle can be observed in terms of non-Gaussianities.

scholarly journals On the Role of Chaos and Instability in the Evolution of Nonlinear Nonstationary Stellar Systems

1993 ◽  
Vol 132 ◽  
pp. 39-44
Author(s):  
S.N. Nuritdinov
Keyword(s):  
Stationary State ◽  
Chaotic Motion ◽  
Stellar System ◽  
Stellar Systems

AbstractThe role of chaos and instability in evolution of nonlinear, non-stationary stellar system have been discussed. It is possible to distinguish between the only two different cases (i) strongly non-stationary stage when we have the violent relaxation accompanied by the compulsive mixing (ii) weakly non-stationary state or quasilinear case, when the quasidiffusion mixing takes place. In case (i), the chaos and chaotic motion g stars play very important role and in case (ii) the role of any type of instability is important.

scholarly journals Rotation and Flattening of Globular Clusters

1985 ◽  
Vol 113 ◽  
pp. 285-296 ◽  
Author(s):  
S. Michael Fall ◽  
Carlos S. Frenk
Keyword(s):  
Angular Momentum ◽  
Internal Rotation ◽  
Globular Clusters ◽  
Pressure Support ◽  
Initial Conditions ◽  
Anisotropic Pressure ◽  
Stellar Systems ◽  
Galactic Globular Clusters

Pease and Shapley (1917) first remarked on the apparent flattening of several Galactic globular clusters, a view that has been confirmed by many subsequent studies. Tidal stresses, internal rotation, and velocity anisotropies can cause deviations from sphericity in stellar systems. In general, we might expect globular clusters to have some angular momentum at the time of formation and, if they collapsed from flattened initial conditions, to have anisotropic pressure support. Since the velocity distributions within the clusters can be altered by a variety of internal and external processes, their shapes are expected to evolve. In this article, we review the methods for measuring ellipticities and the results that have emerged from such studies. Our main purpose, however, is to discuss the processes that determine the shapes of globular clusters and the ways in which they change with time.

scholarly journals Comparing approximate methods for mock catalogues and covariance matrices II: power spectrum multipoles

2019 ◽  
Vol 485 (2) ◽  
pp. 2806-2824 ◽  
Author(s):  
Linda Blot ◽  
Martin Crocce ◽  
Emiliano Sefusatti ◽  
Martha Lippich ◽  
Ariel G Sánchez ◽  
...  
Keyword(s):  
Growth Rate ◽  
Distribution Function ◽  
Power Spectrum ◽  
Probability Distribution Function ◽  
Initial Conditions ◽  
Covariance Matrices ◽  
Full Density ◽  
Model Parameters ◽  
Approximate Methods ◽  
Parameter Constraints

ABSTRACT We study the accuracy of several approximate methods for gravitational dynamics in terms of halo power spectrum multipoles and their estimated covariance matrix. We propagate the differences in covariances into parameter constraints related to growth rate of structure, Alcock–Paczynski distortions, and biasing. We consider seven methods in three broad categories: algorithms that solve for halo density evolution deterministically using Lagrangian trajectories (ICE–COLA, pinocchio, and peakpatch), methods that rely on halo assignment schemes on to dark matter overdensities calibrated with a target N-body run (halogen, patchy), and two standard assumptions about the full density probability distribution function (Gaussian and lognormal). We benchmark their performance against a set of three hundred N-body simulations, running similar sets of approximate simulations with matched initial conditions, for each method. We find that most methods reproduce the monopole to within $5{{\ \rm per\ cent}}$, while residuals for the quadrupole are sometimes larger and scale dependent. The variance of the multipoles is typically reproduced within $10{{\ \rm per\ cent}}$. Overall, we find that covariances built from approximate simulations yield errors on model parameters within $10{{\ \rm per\ cent}}$ of those from the N-body-based covariance.

scholarly journals The Dynamical Evolution of Young Clusters and Associations

1986 ◽  
Vol 7 ◽  
pp. 481-488 ◽  
Author(s):  
Robert D. Mathieu
Keyword(s):  
Star Formation ◽  
Formation Process ◽  
Initial Conditions ◽  
Dynamical Evolution ◽  
Short Review ◽  
Stellar Systems ◽  
Galactic Field ◽  
Dynamical State ◽  
Orbital Mixing ◽  
Formation Efficiency

A young cluster or association bears the imprint of the conditions at its birth for perhaps ten million years, after which the initial conditions are lost to either dilution in the galactic field or erasure by orbital mixing and stellar encounters. In its youngest years, however, the dynamical state of the system can provide valuable information concerning the structure and energetics of the parent gas, the star-formation efficiency and the star-formation process itself. This short review discusses recent theoretical and observational progress in the study of the very youngest of stellar systems.

Sign in / Sign up

Export Citation Format

Share Document