Dynamics Of Stellar Systems Research Articles

Gargantuan chaotic gravitational three-body systems and their irreversibility to the Planck length

ABSTRACT Chaos is present in most stellar dynamical systems and manifests itself through the exponential growth of small perturbations. Exponential divergence drives time irreversibility and increases the entropy in the system. A numerical consequence is that integrations of the N-body problem unavoidably magnify truncation and rounding errors to macroscopic scales. Hitherto, a quantitative relation between chaos in stellar dynamical systems and the level of irreversibility remained undetermined. In this work, we study chaotic three-body systems in free fall initially using the accurate and precise N-body code Brutus, which goes beyond standard double-precision arithmetic. We demonstrate that the fraction of irreversible solutions decreases as a power law with numerical accuracy. This can be derived from the distribution of amplification factors of small initial perturbations. Applying this result to systems consisting of three massive black holes with zero total angular momentum, we conclude that up to 5 per cent of such triples would require an accuracy of smaller than the Planck length in order to produce a time-reversible solution, thus rendering them fundamentally unpredictable.

Stellar kinematics in the IC 348 cluster

In 30 - 40s of the last century Viktor Ambartsumian has published several studies on the kinematics and dynamics of stellar systems. The scientific issues of these papers not only remain relevant up to nowadays, but also are of key importance for the construction of the generalized theory of star formation. The launch of the Gaia spacecraft on December 19, 2013, opens up new horizons in the study of young stellar systems origin and evolution. The accuracy of astrometric measurements (the typical uncertainty is about 0.04 - 0.7 mas for the positions and parallaxes, and about 0.05 - 1.2 mas yr-1 for the proper motions), undoubtedly, will allow lifting the possibilities of study the kinematics and dynamics of star-forming regions to a new level. We focus our present research on the young (∼ 2 - 3Myr) stellar cluster IC 348. It has a complex structure, which includes the older compact core and the younger subgroup in the vicinity of HH 211 outflow. Based on the Gaia DR2 data, we considered the kinematic properties of both the cluster as a whole and its subgroups. We found that special velocity dispersion significantly exceeds the virial velocity dispersion and, therefore, the IC 348 stellar cluster is a supervirial or gravitationally unbound system.

Dynamical equivalence, the origin of the Galactic field stellar and binary population, and the initial radius–mass relation of embedded clusters

Abstract In order to allow a better understanding of the origin of Galactic field populations, dynamical equivalence of stellar-dynamical systems has been postulated by Kroupa and Belloni et al. to allow mapping of solutions of the initial conditions of embedded clusters such that they yield, after a period of dynamical processing, the Galactic field population. Dynamically equivalent systems are defined to initially and finally have the same distribution functions of periods, mass ratios and eccentricities of binary stars. Here, we search for dynamically equivalent clusters using the mocca code. The simulations confirm that dynamically equivalent solutions indeed exist. The result is that the solution space is next to identical to the radius–mass relation of Marks & Kroupa, $\left( r_{\rm h}/{\rm pc} \right)= 0.1^{+0.07}_{-0.04}{\, } \left( M_{\rm ecl}/{\rm M}_{\odot } \right)^{0.13\pm 0.04}$. This relation is in good agreement with the observed density of molecular cloud clumps. According to the solutions, the time-scale to reach dynamical equivalence is about 0.5 Myr which is, interestingly, consistent with the lifetime of ultra-compact H ii regions and the time-scale needed for gas expulsion to be active in observed very young clusters as based on their dynamical modelling.

Incorporating post-Newtonian effects inN-body dynamics

The increasing role of general relativity in the dynamics of stellar systems with central massive black holes and in the evolution of hierarchical triple systems inspires a close examination of how post-Newtonian effects are incorporated into N-body dynamics. The majority of approaches incorporate relativity by adding to the Newtonian N-body equations the standard two-body post-Newtonian terms for a given star around the black hole or for the close binary in a triple system. We argue that, for calculating the evolution of such systems over timescales comparable to the relativistic pericenter advance timescale, it is essential to include "cross terms" in the equations of motion. These are post-Newtonian terms that represent a coupling between the potential of the central black hole and the potential due to other stars in the system. For hierarchical triple systems, these are couplings between the potential of the inner binary and that of the distant third body. Over pericenter precession timescales, the effects of such terms can actually be "boosted" to amplitudes of Newtonian order. We write down the post-Newtonian N-body equations of motion including a central black hole in a truncated form that includes all the relevant cross terms, in a format ready to use for numerical implementation. We do the same for hierarchical triple systems, and illustrate explicitly the effects of cross terms on the orbit-averaged equations of evolution for the orbit elements of the inner binary for the special case where the third body is on a circular orbit. We also describe the inspiration for this investigation: the motion of a test body about a central body with a Newtonian quadrupole moment, including the relativistic pericenter advance, whose correct solution for the conserved total Newtonian energy requires including PN cross terms between the mass monopole and quadrupole potentials.

ENHANCED ACCRETION RATES OF STARS ON SUPERMASSIVE BLACK HOLES BY STAR-DISK INTERACTIONS IN GALACTIC NUCLEI

We investigate the dynamical interaction of a central star cluster surrounding a super-massive black hole and a central accretion disk. The dissipative force acting on stars in the disk leads to an enhanced mass flow towards the super-massive black hole and to an asymmetry in the phase space distribution due to the rotating accretion disk. The accretion disk is considered as a stationary Keplerian rotating disk, which is vertically extended in order to employ a fully self-consistent treatment of stellar dynamics including the dissipative force originating from star-gas ram pressure effects. The stellar system is treated with a direct high-accuracy N-body integration code. A star-by-star representation, desirable in N-body simulations, cannot be extended to real particle numbers yet. Hence, we carefully discuss the scaling behavior of our model with regard to particle number and tidal accretion radius. The main idea is to find a family of models for which the ratio of two-body relaxation time and dissipation time (for kinetic energy of stellar orbits) is constant, which then allows us to extrapolate our results to real parameters of galactic nuclei. Our model is derived from basic physical principles and as such it provides insight into the role of physical processes in galactic nuclei, but it should be regarded as a first step towards more realistic and more comprehensive simulations. Nevertheless, the following conclusions appear to be robust: the star accretion rate onto the accretion disk and subsequently onto the super-massive black hole is enhanced by a significant factor compared to purely stellar dynamical systems neglecting the disk. This process leads to enhanced fueling of central disks in active galactic nuclei and to an enhanced rate of tidal stellar disruptions. [Abridged]

Spherically averaging ellipsoidal galaxy clusters in X-ray and Sunyaev-Zel’dovich studies - I. Analytical relations

This is the first of two papers investigating the deprojection and spherical averaging of ellipsoidal galaxy clusters. We specifically consider applications to hydrostatic X-ray and Sunyaev-Zel'dovich (SZ) studies, though many of the results also apply to isotropic dispersion-supported stellar dynamical systems. Here we present analytical formulas for galaxy clusters described by a gravitational potential that is a triaxial ellipsoid of constant shape and orientation. For this model type we show that the mass bias due to spherically averaging X-ray observations is independent of the temperature profile, and for the special case of a scale-free logarithmic potential, there is exactly zero mass bias for any shape, orientation, and temperature profile. The ratio of spherically averaged intracluster medium (ICM) pressures obtained from SZ and X-ray measurements depends only on the ICM intrinsic shape, projection orientation, and H_0, which provides another illustration of how cluster geometry can be recovered through a combination of X-ray and SZ measurements. We also demonstrate that Y_SZ and Y_X have different biases owing to spherical averaging, which leads to an offset in the spherically averaged Y_SZ - Y_X relation. A potentially useful application of the analytical formulas presented is to assess the error range of an observable (e.g., mass, Y_SZ) accounting for deviations from assumed spherical symmetry, without having to perform the ellipsoidal deprojection explicitly. Finally, for dedicated ellipsoidal studies, we also generalize the spherical onion peeling method to the triaxial case for a given shape and orientation.

Equilibrium of stellar dynamical systems in the context of the Vlasov–Poisson model

This short review is devoted to the problem of the equilibrium of stellar dynamical systems in the context of the Vlasov–Poisson model. In a first part we will review some classical problems posed by the application of the Vlasov–Poisson model to the astrophysical systems like globular clusters or galaxies. In a second part we will recall some recent numerical results which may give us some quantitative hints about the equilibrium state associated to those systems.

Collisional Dynamics of Stellar Systems in the Northern and Southern Coalsack Regions

The visual interstellar extinction in the Northern and Southern Coalsack regions is estimated from a photographic survey of proper motion and B, V photometry of 6 × 104 stars as faint as apparent magnitude 14 over a field of view of 6° × 6° in each region. Each cloud is located at a distance of about 160 ± 50 pc from the Sun and exceeds the mean interstellar extinction by more than 0.7 ± 0.1 mag. Galactic plane orbits of 103 stars located at the same distance of 160 ± 50 pc from the Sun in these regions show a semimajor axis of 8.45 ± 0.15 kpc and a mean inclination of 03 ± 02 over the Galactic plane, suggesting a mean impact parameter of 9 ± 3 pc with diffuse clouds of relative velocity on the order of 4 ± 1 km s-1. The weak distant encounter of stars with the cold neutral medium can be explained by a mean mass of about 2500 ± 1250 M⊙ for the gas and dust content in order to account for the diffusion of stellar orbits. A mean displacement of 0012 ± 0001 yr-1 of the western limb of the Southern Coalsack is estimated in the northwest direction and permits a search for strong close stellar encounters. The transfer of angular momentum between the interstellar medium and the scattering of stellar orbits resulting from the encounters suggests a dissipation rate of (2.0 ± 0.7) × 10-4 M⊙ yr-1, leading to an equipartition time of 12 ± 4 Myr. A spin rate of 0.25 ± 0.05 km s-1 pc-1 of the diffuse clouds in the Southern Coalsack is measured and interpreted as the result of the perturbation induced by stellar systems during flyby encounters with a crossing time of 3 Myr, suggesting a cloud core radius of 1 pc.

Populating Stellar Orbits inside a Rotating, Gaseous Bar

In an effort to understand better the formation and evolution of barred galaxies, we have examined the properties of equatorial orbits in the effective potential of one specific model of a rapidly rotating, steady state gasdynamical bar that has been constructed via a self-consistent hydrodynamical simulation. At a given value of the Jacobi constant, roughly half of all test particles (stars) that are injected into the equatorial plane of this potential follow quasi-ergodic orbits; most regular prograde orbits have an overall bow tie shape; and some trace out trajectories that resemble the x4 family of regular, retrograde orbits. The bow tie orbits appear to be related to the 4/1 orbit family discussed by Contopoulous in 1988, but particles moving along a bow tie orbit pass very close to the center of the bar twice each orbit. Unlike the barlike configurations that previously have been constructed using dissipationless, N-body simulation techniques, the effective potential of our gasdynamical bar is very shallow and generally does not support the x1 family of orbits. If primordial galaxies evolve to a rapidly rotating barlike configuration before a significant amount of star formation has taken place and then stars form from the gas that makes up the bar, the initial stellar distribution function should consist of orbits that are (1) supported by the gaseous barlike potential and (2) restricted to have initial conditions dictated by the gasdynamics of the bar. With this restriction hypothesis in mind, we propose that stellar dynamical systems that form from gaseous bars will have characteristics that differ significantly from systems that form from a bisymmetric instability in an initially axisymmetric stellar system. Since bow tie orbits are preferred over x1 orbits, for example, such systems should have a more boxy or peanut shape when seen face-on; there will be a mechanism for funneling material more directly into the center of the galaxy; and, near the galaxy center, stars may appear to move along retrograde trajectories.

The birth of gravitational evolutionary dynamics of stellar systems (from Th. wright to w. herschel)

Abstract Th. Wright, I. Kant and I. H. Lambert used well-known ideas about the structure and dynamics of the Solar system as a basis of their concepts of the stellar Universe. W. Herschel discovered the main features of the true, non-hierarchical large-scale structure of the Universe. He was also a pioneer of stellar dynamics with its new statistical laws and also of the theory of dynamical evolution in stellar systems at different scales.

Adiabatic invariants in stellar dynamics. 2: Gravitational shocking

A new theory of gravitational shocking based on time-dependent perturbation theory shows that the changes in energy and angular momentum due to a slowly varying disturbance are not exponentially small for stellar dynamical systems in general. It predicts significant shock heating by slowly varying perturbations previously thought to be negligible according to the adiabatic criterion. The theory extends the scenarios traditionally computed only with the impulse approximation and is applicable to a wide class of disturbances. The approach is applied specifically to the problem of disk shocking of star clusters.

Adiabatic invariants in stellar dynamics. 1: Basic concepts

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results that precisely define the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause significant evolution stellar dynamical systems even if its time scale is longer than any internal orbital time scale. This additional 'heating' may have serious implications for the evolution of star clusters and dwarf galaxies which are subject to long-term environmental forces. The mathematical developments leading to these results are reviewed, and the conditions for applicability to and further implications for stellar systems are discussed. Companion papers present a computational method for a general time-dependent disturbance and detailed example.

Dynamical friction from fluctuations in stellar dynamical systems

view Abstract Citations (28) References (20) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dynamical Friction from Fluctuations in Stellar Dynamical Systems Bekenstein, Jacob D. ; Maoz, Eyal Abstract A test particle traveling through a collisionless gravitating background suffers a dissipative drag force known as dynamical friction. This paper develops a theory of the interaction of the test particle with the stochastic force of the background. The Chandrasekhar formula for the friction and the heating of the particle by background fluctuations is derived in a unified way. This new approach shows that dynamical friction fits into the generic fluctuation-dissipation relation. It also readily suggests the modifications that would be required to treat dynamical friction and heating in an inhomogeneous background, as well as in the presence of initial correlations between background particles. Publication: The Astrophysical Journal Pub Date: May 1992 DOI: 10.1086/171260 Bibcode: 1992ApJ...390...79B Keywords: Celestial Mechanics; Energy Dissipation; Friction Drag; Stellar Motions; Autocorrelation; Equipartition Theorem; Momentum Transfer; Stochastic Processes; Astrophysics; CELESTIAL MECHANICS; STELLAR DYNAMICS full text sources ADS |

Gravothermal Oscillations

Stellardynamical systems are modelled by gaseous spheres. The properties of an isothermal equilibrium configuration with a central singularity are discussed in the context of post-collapse evolution. For the numerical calculations heating effects are taken into account. Evolution towards the equilibrium configuration is monotonically only if much energy is delivered from hardening processes of binary stars. Since the equilibrium configuration is gravo-thermally unstable a minute emission of energy is sufficient to turn gravothermal contraction into gravothermal expansion. In such case equilibrium is approached by oscillations of the core.

The Harvard summer school in astronomy

Professional astronomy in the 1920s and 1930s was a science in transition. Modern relativistic cosmologies were born, and three major areas of modern physics became central to progress in astronomy: quantum mechanics, nuclear physics and relativity. The old empirical and quantitative methods of spectroscopic astronomy, methods that generated vast amounts of systematic knowledge of the spectra of the Sun and stars and the dynamics of stellar systems, were being supplemented by rational and quantitative methods. These new techniques promised to reveal not only the compositions of the Sun and stars, their sources of energy and their ages, but also the origin and ultimate fate of the universe.

Six collapses

view Abstract Citations (71) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Six collapses. Miller, R. H. ; Smith, B. F. Abstract The self-consistent dynamical development of six stellar systems, started from rotating spherical configurations, has been studied by means of a fully three-dimensional n-body integration. The six examples had different initial angular velocities and velocity dispersions. All settled down into prolate bars rotating about a short axis within two initial rotation periods. The bars are long-lived, robust, and stable. Bars are the natural form toward which rapidly rotating stellar dynamical systems develop, instead of the flattened axisymmetric disks that had been expected. The early stages of each collapse are reasonably well described by a theoretical model according to which a collapse passes through a sequence of rigidly rotating, uniform-density spheroids. The first significant departures from spheroidal form were axisymmetric in all cases. Rings formed in some examples, sheets in others, with transition cases between these extremes. Nonaxisymmetric forms developed from these intermediate stages. Publication: The Astrophysical Journal Pub Date: January 1979 DOI: 10.1086/156745 Bibcode: 1979ApJ...227..407M Keywords: Astronomical Models; Galactic Evolution; Galactic Structure; Gravitational Collapse; Self Consistent Fields; Stellar Systems; Astrodynamics; Many Body Problem; Stellar Motions; Astrophysics; Collapse:Stellar Systems; Galaxies:Dynamics; Galaxies:Evolution; Galaxies:Rotation; Galaxies:Structure full text sources ADS |

Dynamics of Relativistic Stellar Systems

Relativistic stellar-dynamical systems and their possible occurrence in nature are discussed. Features of the equilibrium models that have been constructed for spherical star clusters in general relativity are delineated. The results of studies of the stability of relativistic spherical clusters are reviewed. It is noted that the results, while not conclusive, indicate that realistic spherical clusters are stable against gravitational collapse if their central redshifts zc ≲ 0.55 and unstable if zc ≳ 0.55. More work is needed on this and other problems.

On using entropy arguments to study the evolution and secular stability of spherical stellar-dynamical systems

view Abstract Citations (31) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On using entropy arguments to study the evolution and secular stability of spherical stellar-dynamical systems. Ipser, J. R. Abstract The appropriateness of using the notion of Boltzmann-entropy maxima to develop criteria for the secular stability of Newtonian stellar-dynamical systems is studied. Our interest in entropy maxima leads to consideration of the general problem of finding those self-bounded, spherical, equilibrium star clusters for which the phase-space integral of any chosen function of the distribution function and the mass of a star has a maximum or minimum value. When compared with all neighboring configurations having the same energy and stars, a spherical equilibrium cluster is a local maximum or minimum if and only if its distribution function is of a certain specified form, the cluster has an isotropic velocity distribution, and the isentropic gas sphere with the same distribution of density and pressure is dynamically stable to adiabatic spherical perturbations. A specialization reveals that no realistic spherical clusters can be local entropy-maxima. Hence in general it is incorrect to invoke secular-stability criteria which say that evolution preferentially takes a cluster to a state of locally maximum entropy. Also discussed are the possible implications of this result for arguments that spherical clusters may in some cases become secularly unstable to a gravothermal catastrophe involving rapid evolution to an extreme core-halo structure. In another specialization of the theorem, the integrals maximized by polytropic clusters are constructed. Subject headings: globular clusters - stellar dynamics Publication: The Astrophysical Journal Pub Date: October 1974 DOI: 10.1086/153181 Bibcode: 1974ApJ...193..463I Keywords: Dynamic Stability; Entropy; Long Term Effects; Star Clusters; Stellar Evolution; Stellar Motions; Astronomical Models; Boltzmann Transport Equation; Distribution Functions; Dynamic Models; Extremum Values; Polytropic Processes; Secular Variations; Thermodynamic Equilibrium; Astrophysics full text sources ADS |

Numerical experiments concerning isolated and non-isolated stellar systems

A brief review is given of the principal methods used to deal with the dynamics of stellar systems, mostly star clusters, which are nearly all, at least partly, relaxed with respect to stellar encounters; particular stress is laid upon the direct numerical integration of the N-body problem.

On the Statistics of Stellar Dynamical Systems.

view Abstract Citations References (4) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the Statistics of Stellar Dynamical Systems. Miller, R. H. Abstract The phase space ( space) is divided into cells with at most one occupant per cell by the pair correlation recently reported. The exclusion leads to a statistics similar to the Fermi-Dirac statistics. The cell size (analog of the Planck constant) depends on the total energy and on the number of particles, becoming large in systems with many particles. When values appropriate to the Galaxy are inserted into the empirical forms suggested by the numerical experiments, no degeneracy is indicated. Publication: The Astrophysical Journal Pub Date: March 1972 DOI: 10.1086/151385 Bibcode: 1972ApJ...172..685M full text sources ADS |