Triaxial Galaxy Research Articles

A Second Integral of Motion in a Triaxial Galaxy

We construct a formal second integral of motion in a bisymmetrical potential field describing the motion on the plane of symmetry of a triaxial galaxy. We also check the constancy of the second integral adding higher-order terms which are found using a computer program.

Preferred orbit planes in triaxial galaxies. I - Tumbling about a principal axis

Preferred orbit planes in triaxial galaxies. I - Tumbling about a principal axis

On the oscillations and the stability of stellar systems

view Abstract Citations (26) References (23) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the oscillations and the stability of stellar systems Vandervoort, P. O. Abstract The oscillations and the stability of a rotating, axisymmetric galaxy are investigated with the aid of a stellar-dynamical form to the tensor virial equations of the second order. The method requires the use of a representation of small perturbations in stellar systems in terms of a Lagrangian displacement in the six-dimensional phase space of a single star. The modes of oscillation fall into three groups: three pairs of toroidal modes, one of which becomes unstable at a sufficiently high angular momentum; four pairs of transverse shear modes, all of which appear to be stable in cases of practical interest; and two pairs of pulsation modes which are stable in oblate stellar systems. A connection is established between certain triaxial figures of equilibrium in stellar systems and the stable toroidal and transverse shear modes in axisymmetric stellar systems. One implication of that connection is that, in some cases, the figure of a triaxial galaxy can rotate about an axis which does not coincide with a principal axis of the configuration. Publication: The Astrophysical Journal Pub Date: October 1983 DOI: 10.1086/161388 Bibcode: 1983ApJ...273..511V Keywords: Barred Galaxies; Celestial Mechanics; Dynamic Stability; Galactic Structure; Stellar Oscillations; Stellar Systems; Equations Of Motion; Galactic Rotation; Harmonic Oscillation; Lagrangian Equilibrium Points; Maclaurin Series; Many Body Problem; Tensor Analysis; Virial Theorem; Astrophysics full text sources ADS |

Stellar and gaseous dynamics of triaxial galaxies

A variety of analytic means for examining the existence and stability of orbit families in triaxial potentials which approximate the potential fields of triaxial galaxies are presented. A particular class of potentials which possess three exact integrals of motion is analyzed. This potential is chosen because of its resemblance to the potential used by Schwarzschild (1979) to produce an equilibrium model of a triaxial stellar figure. The properties of a potential based on an expansion about the core region is explored, including the potential and the resulting integrals of motion for the 1-1-1 resonance and the stability of periodic orbits. The Galerkin method is used to solve for the resonant orbits to first order. New features of the central regions of galaxies are discussed, particularly the possibility of the formation of stable equilibrium tilted disks, the structure of the Spindle galaxy, and implications for enhanced fueling of gas into the central engine of active galaxies.

Stellar orbits in a triaxial galaxy. I - Orbits in the plane of rotation

Stellar orbits in a triaxial galaxy. I - Orbits in the plane of rotation

Dust and Gas in Triaxial Galaxies

There are many reasons to consider the dynamics of triaxial galaxies. Elliptical galaxies are not rotationally flattened (Illingworth, this conference) and their isophotal profiles are often twisted. N-body simulations of collapse have produced a number of final state figures which are triaxial. Even those still skeptical will have to grant that barred spirals (a category which seems to include the Galaxy) are certainly not axisymmetric.

A numerical experiment on the equilibrium and stability of a rotating galactic bar

A self-consistent, three-dimensional numerical experiment is performed on an N-body system whose initial state is a realization of a certain theoretical model of a rotating triaxial galaxy. The model is a stellar-dynamical counterpart of a uniformly rotating polytrope of index equal to 0.5. The aim of the experiment is to study the equilibrium of the system and, in particular, to test its stability. The experimental system behaves in the mean like a realization of the theoretical model for at least seven crossing times. The principal departure of the system from equilibrium is an oscillation which is identified as a radial pulsation. There is no indication in its behavior that the system is unstable with respect to anu mode with an e-folding time shorter than or of the order of two crossing times. Certain changes that occur in the state of the system are interpreted, with the aid of the theoretical model, as secular changes which result from a slight failure of our numerical methods to conserve the mass, energy, and angular momentum of the system; these effects are small enough that they do not vitiate the experiment on a dynamical time scale.

Retrograde closed orbits in a rotating triaxial potential

view Abstract Citations (106) References (7) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Retrograde closed orbits in a rotating triaxial potential Heisler, J. ; Merritt, D. ; Schwarzschild, M. Abstract Four closed periodic orbit sequences are determined numerically, and their stability is investigated by the standard Floquet method, for the case of a specific, triaxial rotating potential. The sequences comprise (1) stable anomalous orbits that are tipped to the long axis which they circle, so that they also circle the short rotation axis, (2) unstable, anomalous orbits circling the intermediate axis, otherwise behaving like (1), (3) stable, normal retrograde orbits lying in the equatorial plane, which become unstable against perpendicular perturbations in Binney's instability strip, and (4) Z-axis orbits lying on the rotation axis, which, although stable in their inner section, become unstable to perturbations parallel to the intermediate axis farther out, and to the long axis farther out still. The entire set contains one composite sequence which is stable over the entire energy range, consisting of the outer section of the normal retrograde orbits, the sequence of the anomalous orbits, and the inner section of the Z-axis orbits. It is suggested that the composite sequence may be relevant to the dynamics of gas masses captured by rotating triaxial galaxies. Publication: The Astrophysical Journal Pub Date: July 1982 DOI: 10.1086/160100 Bibcode: 1982ApJ...258..490H Keywords: Axes Of Rotation; Floquet Theorem; Galactic Rotation; Orbit Calculation; Orbit Perturbation; Galactic Structure; Gas Dynamics; Astrophysics full text sources ADS |

On the stability of Schwarzschild's triaxial galaxy model

The numerical model for a triaxial galaxy constructed by Schwartzschild (1979) has been tested by means of fully self-consistent three-dimensional n-body numerical experiments that use a representation of this model to start the integration. The integration, study models, initial load, and correcting potential of the experiment are detailed. Preliminary checks included density values, potential values, and integration in potential of an ideal model. The results showed some particle loss and no significant shape change. The model is rugged and robust, and no growing disturbances with growth rate in excess of 0.5 per crossing time could be detected. Runs were done at 50 percent excess halo and with tube orbits reversed.

A stationary and a slowly rotating model of a triaxial elliptical galaxy

A stationary and a slowly rotating model of a triaxial elliptical galaxy

On the nonexistence of three-dimensional tube orbits around the intermediate axis in a triaxial galaxy model

view Abstract Citations (81) References (3) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS On the nonexistence of three-dimensional tube orbits around the intermediate axis in a triaxial galaxy model. Heiligman, G. ; Schwarzschild, M. Abstract A specific triaxial model for a galaxy was previously investigated by numerical methods. In that investigation tube orbits around the major axis (X), as well as tube orbits around the minor axis (Z), had been found, but no tube orbit around the intermediate axis (Y) had been encountered. The present paper shows, again by numerical methods, that Y-tube orbits nearly certainly do not exist in the adopted model. Instead, a new family of 'shell orbits' has been found. The existence of X- and Z-tube orbits and the replacement of Y-tube orbits by shell orbits are made understandable by a numerical determination of the stability or instability, respectively, of the relevant two-dimensional closed resonance orbits in the three symmetry planes of the model. Publication: The Astrophysical Journal Pub Date: November 1979 DOI: 10.1086/157449 Bibcode: 1979ApJ...233..872H Keywords: Astronomical Models; Dynamic Stability; Galactic Structure; Orbit Perturbation; Stellar Motions; Astrodynamics; Orbital Elements; Orbital Resonances (Celestial Mechanics); Resonance; Three Dimensional Motion; Astronomy; Galaxies:Internal Motions; Galaxies:Structure full text sources ADS |

On the rotation of elliptical galaxies

The tensor virial theorem is applied to models of early-type galaxies. First the theorem is applied to rotating elliptical galaxies whose constant-density surfaces are similar ellipsoids. A relationship is obtained between the observed rotations and the forms of generally triaxial galaxies. By applying the results of Robert (1962) to the evaluation of the components of the Chandrasekhar tensor which occurs in this relationship, it is found that the form of a galaxy that lacks global velocity anisotropy uniquely determines the ratio of its rotational and random kinetic energies independently of the radial density profile of that galaxy. A distribution of three-dimensional prolate spheroids is derived which accounts for the observed distribution of ellipticities reported by Sandage, Freeman, and Stokes (1970). This is then used to derive curves giving the expected frequency of occurrence of galaxies of given rotational velocities for each of a number of different apparent elongations on the sky. It is found that if elliptical galaxies are prolate, there should be little correlation between apparent ellipticity and rotation velocity.