Self-gravitating Fluid Systems Research Articles

Methods for relativistic self-gravitating fluids: from binary neutron stars to black hole-disks and magnetized rotating neutron stars

The cataclysmic observations of event GW170817, first as gravitational waves along the inspiral motion of two neutron stars, then as a short \(\gamma \)-ray burst, and later as a kilonova, launched the era of multimessenger astronomy, and played a pivotal role in furthering our understanding on a number of longstanding questions. Numerical modeling of such multimessenger sources is an important tool to understand the physics of compact objects and, more generally, the physics of matter under extreme conditions. In this review we present a unified view of various techniques used to obtain equilibrium and quasiequilibrium solutions for three astrophysically relevant relativistic, self-gravitating fluid systems: Binary neutron stars, black hole-disks, and magnetized rotating neutron stars. These solutions are necessary not only for modeling such compact objects, but equally important, for providing self-consistent initial data in numerical relativity simulations. Instead of presenting the full details of the formulations and numerical algorithms, we focus on painting the broadbrush picture of the methods developed to address these problems, and facilitate future work in the area.

Anisotropic generalization of well-known solutions describing relativistic self-gravitating fluid systems: an algorithm

We present an algorithm to generalize a plethora of well-known solutions to Einstein field equations describing spherically symmetric relativistic fluid spheres by relaxing the pressure isotropy condition on the system. By suitably fixing the model parameters in our formulation, we generate closed-form solutions which may be treated as an anisotropic generalization of a large class of solutions describing isotropic fluid spheres. From the resultant solutions, a particular solution is taken up to show its physical acceptability. Making use of the current estimate of mass and radius of a known pulsar, the effects of anisotropic stress on the gross physical behaviour of a relativistic compact star is also highlighted.

Self-gravitating fluid systems and galactic dark matter

We study gravitational collapse with anisotropic pressures, whose end stage can mimic space-times that are seeded by galactic dark matter. To this end, we identify a class of space-times (with conical defects) that can arise out of such a collapse process, and admit stable circular orbits at all radial distances. These have a naked singularity at the origin. An example of such a space-time is seen to be the Bertrand space-time discovered by Perlick, that admits closed, stable orbits at all radii. Using relativistic two- fluid models, we show that our galactic space-times might indicate exotic matter, i.e one of the component fluids may have negative pressure for a certain asymptotic fall off of the associated mass density, in the Newtonian limit. We complement this analysis by studying some simple examples of Newtonian two-fluid systems, and compare this with the Newtonian limit of the relativistic systems considered.

FAST: A Fully Asynchronous Split Time-Integrator for a Self-Gravitating Fluid

Abstract We describe a new algorithm for the integration of self-gravitating fluid systems using SPH method. We split the Hamiltonian of a self-gravitating fluid system into the gravitational potential and others (kinetic and internal energies), and used different time-steps for their integrations. The time integration was done in the way similar to that used in the mixed-variable or multiple stepsize symplectic schemes. We performed three test calculations. The first test was spherical collapse, and the second test was an explosion. As the third test, we also performed a realistic test, in which the initial model was taken from a simulation of merging galaxies. In all test calculations, we found that the number of time-steps for gravitational interaction were reduced by nearly an order of magnitude when we adopted our integration method. In the case of the realistic test, in which the dark-matter potential dominates the total system, the total calculation time was significantly reduced. The simulation results were almost the same as those of simulations with the ordinary individual time-step method. Our new method has achieved good performance without sacrificing the accuracy of the time integration.

Linear Gravitational Instability of Filamentary and Sheetlike Molecular Clouds with Magnetic Fields

We study the linear evolution of small perturbations in self-gravitating fluid systems with magnetic fields. We consider wave-like perturbations to nonuniform filamentary and sheet-like hydrostatic equilibria in the presence of a uniform parallel magnetic field. Motivated by observations of molecular clouds that suggest substantial nonthermal (turbulent) pressure, we adopt equations of state that are softer than isothermal. We numerically determine the dispersion relation and the form of the perturbations in the regime of instability. The form of the dispersion relation is the same for all equations of state considered, for all magnetic field strengths, and for both geometries examined. We demonstrate the existence of a fastest growing mode for the system and study how its characteristics depend on the amount of turbulence and the strength of the magnetic field. Generally, turbulence tends to increase the rate and the length scale of fragmentation. While tending to slow the fragmentation, the magnetic field has little effect on the fragmentation length scale until reaching some threshold, above which the length scale decreases significantly. Finally, we discuss the implications of these results for star formation in molecular clouds.

Wave Motions in Molecular Clouds: Results in Two Dimensions

We study the linear evolution of small perturbations in self-gravitating fluid systems in two spatial dimensions; we consider both cylindrical and cartesian (i.e., slab) geometries. The treatment is general, but the application is to molecular clouds. We consider a class of equations of state which heuristically take into account the presence of turbulence; in particular, we consider equations of state which are {\it softer} than isothermal. We take the unperturbed cloud configuration to be in hydrostatic equilibrium. We find a class of wave solutions which propagate along a pressure supported cylinder (or slab) and have finite (trapped) spatial distributions in the direction perpendicular to the direction of propagation. Our results indicate that the dispersion relations for these two dimensional waves have similar forms for the two geometries considered here. Both cases possess a regime of instability and a fastest growing mode. We also find the (perpendicular) form of the perturbations for a wide range of wavelengths. Finally, we discuss the implications of our results for star formation and molecular clouds. The mass scales set by instabilities in both molecular cloud filaments and sheets are generally much larger than the masses of stars. However, these instabilities can determine the length scales for the initial conditions for protostellar collapse.

Phase-Transition Theory of Instabilities. III. The Third-Harmonic Bifurcation on the Jacobi Sequence and the Fission Problem

In Papers I and II, we have used a free-energy minimization approach that stems from the Landau-Ginzburg theory of phase transitions to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Here we investigate the secular and dynamical 3rd-harmonic instabilities that appear first on the Jacobi sequence of incompressible zero- vorticity ellipsoids. Poincare found a bifurcation point on the Jacobi sequence where a 3rd-harmonic mode becomes neutral. A sequence of pear-shaped equilibria branches off at this point but stands at higher energies. Therefore, the Jacobi ellipsoids remain secularly and dynamically stable. Cartan found that dynamical 3rd-harmonic instability also sets in at the Jacobi-pear bifurcation. We find that Cartan's instability leads to differentially rotating objects and not to uniformly rotating pear-shaped equilibria. We demonstrate that the pear-shaped sequence exists at higher energies and at higher rotation relative to the Jacobi sequence. The Jacobi ellipsoid undergoes fission on a secular time scale and a short-period binary is produced. The classical fission hypothesis of binary-star formation of Poincare and Darwin is thus feasible.

Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and lambda -Transitions

view Abstract Citations (8) References (55) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and lambda -Transitions Christodoulou, Dimitris M. ; Kazanas, Demosthenes ; Shlosman, Isaac ; Tohline, Joel E. Abstract We use a free-energy minimization approach to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In this paper, we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two cases are very similar in the framework of phase transitions. It has been conjectured (Hachisu & Eriguchi 1983) that third-order phase transitions, manifested as smooth bifurcations in the angular momentum-rotation frequency plane, may occur on the Maclaurin sequence at the bifurcation point of the axisymmetric one-ring sequence and on the Jacobi sequence at the bifurcation point of the dumbbell-binary sequence. We show that these transitions are forbidden when viscosity maintains uniform rotation. The uniformly rotating one-ring/dumbbell equilibria close to each bifurcation point and their neighboring uniformly rotating nonequilibrium states have higher free energies than the Maclaurin/Jacobi equilibria of the same mass and angular momentum. These high-energy states act as free-energy barriers preventing the transition of spheroids/ellipsoids from their local minima to the free-energy minima that exist on the low rotation frequency branch of the one-ring/binary sequence. At a critical point, the two minima of the free-energy function are equal, signaling the appearance of a first-order phase transition. This transition can take place beyond the critical point only nonlinearly if the applied perturbations contribute enough energy to send the system over the top of the barrier (and if, in addition, viscosity maintains uniform rotation). In the angular momentum-rotation frequency plane, the one-ring and dumbbell-binary sequences have the shape of an "inverted S" and two corresponding turning points each. Because of this shape, the free-energy barrier disappears suddenly past the higher turning point, leaving the spheroid/ellipsoid on a saddle point but also causing a "catastrophe" by permitting a "secular" transition toward a one-ring/binary minimum energy state. This transition appears as a typical second-order phase transition, although there is no associated sequence bifurcating at the transition point (cf. Christodoulou et al. 1995a). Irrespective of whether a nonlinear first-order phase transition occurs between the critical point and the higher turning point or an apparent second-order phase transition occurs beyond the higher turning point, the result is fission (i.e., "spontaneous breaking" of the topology) of the original object on a secular timescale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric torus, and the Jacobi ellipsoid becomes a binary. The presence of viscosity is crucial since angular momentum needs to be redistributed for uniform rotation to be maintained. We strongly suspect that the "secular catastrophe" is the dynamical analog of the notorious λ-transition of liquid 4He because it appears as a "second-order" phase transition with infinite "specific heat" at the point where the free-energy barrier disappears suddenly. This transition is not an elementary catastrophe. In contrast to this case, a "dynamical catastrophe" takes place from the bifurcation point to the lower branch of the Maclaurin toroid sequence because all conservation laws are automatically satisfied between the two equilibrium states. Furthermore, the free-energy barrier disappears gradually, and this transition is part of the elementary cusp catastrophe. This type of "λ-transition" is the dynamical analog of the Bose-Einstein condensation of an ideal Bose gas. The phase transitions of the dynamical systems are briefly discussed in relation to previous numerical simulations of the formation and evolution of protostellar systems. Some technical discussions concerning related results obtained from linear stability analyses, the breaking of topology, and the nonlinear theories of structural stability and catastrophic morphogenesis are included in an appendix. Publication: The Astrophysical Journal Pub Date: June 1995 DOI: 10.1086/175807 arXiv: arXiv:astro-ph/9504062 Bibcode: 1995ApJ...446..485C Keywords: GALAXIES: KINEMATICS AND DYNAMICS; GALAXIES: STRUCTURE; INSTABILITIES; STARS: FORMATION; STARS: ROTATION; Astrophysics E-Print: 34 pages, postscript, compressed,uuencoded. 7 figures available in postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd /shlosman/paper2 mget *.ps.Z). To appear in ApJ full text sources arXiv | ADS | Related Materials (3) Part 1: 1995ApJ...446..472C Part 3: 1995ApJ...446..500C Part 4: 1995ApJ...446..510C

Phase-Transition Theory of Instabilities. IV. Critical Points on the Maclaurin Sequence and Nonlinear Fission Processes

view Abstract Citations (9) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Phase-Transition Theory of Instabilities. IV. Critical Points on the Maclaurin Sequence and Nonlinear Fission Processes Christodoulou, Dimitris M. ; Kazanas, Demosthenes ; Shlosman, Isaac ; Tohline, Joel E. Abstract We use a free-energy minimization approach to describe in simple and clear physical terms the secular and dynamical instabilities as well as the bifurcations along equilibrium sequences of rotating, self-gravitating fluid systems. Our approach is fully nonlinear and stems from the Ginzburg-Landau theory of phase transitions. In the final paper of this series, we examine higher than second-harmonic disturbances applied to Maclaurin spheroids, the corresponding bifurcating sequences, and their relation to nonlinear fission processes. The triangle and ammonite sequences bifurcate from the two third-harmonic neutral points on the Maclaurin sequence, while the square and one-ring sequences bifurcate from two of the three known fourth-harmonic neutral points. The one-ring sequence has been analyzed in Christodoulou et al. (1995b). In the other three cases, secular instability does not set in at the corresponding bifurcation points because the sequences stand and terminate at higher energies relative to the Maclaurin sequence. Consequently, an anticipated (numerically unresolved) third-order phase transition at the ammonite bifurcation and numerically resolved second-order phase transitions at the triangle and square bifurcations are strictly forbidden. Furthermore, the ammonite sequence exists at higher rotation frequencies as well and is similar in every respect to the pear-shaped sequence that has been analyzed in Christodoulou et al. (1995c). There is no known bifurcating sequence at the point of third-harmonic dynamical instability. This point represents a discontinuous λ-transition of type 3 that brings a Maclaurin spheroid on a dynamical timescale directly to the binary sequence while the original symmetry and topology are broken in series. The remaining fourth-harmonic neutral point also appears to be related to a type-3 λ-transition which however takes place from the lower turning point of the one-ring sequence toward the starting point and then on toward the stable branch of the three-fluid-body (triple) sequence. A third type-3 λ-transition, taking place from the one-ring sequence toward the starting point and then on toward the stable branch of the four-fluid-body (quadruple) sequence, is also discussed. The two-ring sequence bifurcates from the axisymmetric sixth-harmonic neutral point on the Maclaurin sequence also toward higher energies initially but eventually turns around and proceeds to lower energies relative to the Maclaurin sequence. The point where the two sequences have equal energies represents a fourth type of λ-transition which is not preceded by a first-order phase transition. This type-4 λ-transition results in double fission on a secular timescale: a Maclaurin spheroid breaks into two coaxial axisymmetric tori that rotate uniformly and with the same frequency. Finally, our nonlinear approach easily identifies resonances between the Maclaurin sequence and various multi-fluid-body sequences that cannot be detected by linear stability analyses. Resonances appear as first-order phase transitions at points where the energies of the two sequences are nearly equal but the lower energy state belongs to one of the multi-fluid-body sequences. Three nonlinear resonances leading to the turning points of the binary, triple, and quadruple sequences are described. Publication: The Astrophysical Journal Pub Date: June 1995 DOI: 10.1086/175809 arXiv: arXiv:astro-ph/9505101 Bibcode: 1995ApJ...446..510C Keywords: GALAXIES: FORMATION; STARS: BINARIES: GENERAL; HYDRODYNAMICS; INSTABILITIES; STARS: FORMATION; Astrophysics E-Print: 23 pages, postscript, compressed, uuencoded. Figs. (6) available by anonymous ftp from ftp://asta.pa.uky.edu/shlosman/paper4/ , get *.ps.Z). To appear in ApJ full text sources arXiv | ADS | Related Materials (3) Part 1: 1995ApJ...446..472C Part 2: 1995ApJ...446..485C Part 3: 1995ApJ...446..500C

General analytic results for nonlinear waves and solitons in molecular clouds

We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a 'charge density' q(rho); this quantity replaces the density on the right-hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This 'no-charge' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We study nonlinear wave motions for Jeans-type theories (where q(rho) = rho-rho(sub 0)) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also study wave motions for molecular clouds threaded by magnetic fields and show how the allowed range of wavelengths is affected by the field strength. Since the gravitational force in one spatial dimension does not fall off with distance, we consider two classes of models with more realistic gravity: Yukawa potentials and a pseudo two-dimensional treatment. We study the allowed types of wave behavior for these models. Finally, we discuss the implications of this work for molecular cloud structure. We argue that molecular clouds can support a wide variety of wave motions and suggest that stationary waves (such as those considered in this paper) may have already been observed.

The equilibrium of a galactic bar. II - Stellar-dynamical counterparts of the s-type Riemann ellipsoids

The family of triaxial stellar systems described in Paper I of this series is generalized to include, in addition to the previous dependence on Jacobi's integral, a dependence of the distribution function on a second isolating integral of the motion of a star in the prevailing gravitational field. The second integral is approximated with the aid of a model of the stellar orbits which is valid in the absence of important resonances and which should be accurate in the systems of relatively small central concentration on which this investigation concentrates. The new stellar systems are stellar-dynamical counterparts of the classical S-type Riemann ellipsoids well known in the study of self-gravitating fluid systems, and, within the framework of stellar dynamics, they are also three-dimensional counterparts of the elliptical disks studied by Freeman and by Hunter. The Riemann-like stellar systems form an extensive family, and they exhibit a rich interplay of effects of the rotations of their triaxial figures and effects of the dependence of their distribution functions on the second integral of the motion. The family includes stellar-dynamical counterparts of the classical Maclaurin spheroids, Jacobi ellipsoids, and Dedekind ellipsoids. The study of triaxial, Riemann-like systems is related to the study ofmore » bar modes of oscillation in corresponding axisymmetric, Maclaurin-like systems. On the basis of this relationship, it is shown that an axisymmetric stellar system having the structure of a uniformly rotating polytrope of index n = 0.5 is dynamically unstable with respect to a bar mode if the ratio of the rotational kinetic energy to the magnitude of the gravitational potential energy exceeds 0.166.« less