Prolate Model Research Articles

Alignment and morphology of elliptical galaxies: the influence of the cluster tidal field

We investigate two possible effects of the tidal field induced by a spherical cluster on its elliptical galaxy members: the modification of the ellipticity of a spherical galaxy and the isophotal alignment in the cluster radial direction of a misaligned prolate galaxy. Numerical N-body simulations have been performed for radial and circular galactic orbits. The properties of the stars' zero--velocity surfaces in the perturbed galaxies are explored briefly, and the adiabaticity of the galaxy to the external field is discussed. For a choice of parameters characteristic of rich clusters we find that the induced ellipticity on a spherical galaxy is below or close to the detectability level. But we find that the tidal torque can result in significant isophotal alignment of the galaxies' major axis with the cluster radial direction if the galaxy is outside the cluster core radius. The time required for the alignment is very short compared with the Hubble time. A significant increase in the ellipticity of the outer isophotes of the prolate model is also found, but with no observable isophotal twisting. Our main prediction is an alignment segregation of the elliptical galaxy population according to whether their orbits lie mostly outside or inside the cluster core radius. These results also suggest that galactic alignment in rich clusters is not incompatible with a bottom-up galaxy formation scenario.

Self-similar Collapse of Axisymmetric Systems

view Abstract Citations (17) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Self-similar Collapse of Axisymmetric Systems Ryden, Barbara S. Abstract Self-similar solutions are found for the collisionless collapse of axisymmetric density perturbations in an Einstein-de Sitter universe. At large radii, the isodensity contours of the model perturbations are assumed to be oblate spheroids (with axis ratios 3/5) or prolate spheroids (with axis ratios 5/3). The spherically averaged density profiles of the oblate and prolate models are similar to those of spherically symmetric models with the same asymptotic density slope; the main difference is that the nonspherical models have a shallower density profile in the central regions. The self-similar collisionless solutions do not show "pancakes" or "needles"; that is, the axis ratios in the inner regions are not much more extreme than those in the outer regions. One of the models examined, which is oblate at large radii, is prolate at smaller radii. Publication: The Astrophysical Journal Pub Date: November 1993 DOI: 10.1086/173365 Bibcode: 1993ApJ...418....4R Keywords: COSMOLOGY: THEORY; COSMOLOGY: LARGE-SCALE STRUCTURE OF UNIVERSE full text sources ADS |

On the true shapes of galaxies

We analyse the distribution of axial ratios of images in the APM Bright Galaxy Survey (APMBGS). The sample analysed contains a total of 20399 galaxies (2135 ellipticals, 4782 SOS, 13482 spirals). For these objects the APM survey provides homogeneous measurements of image characteristics with great accuracy. We apply analytic inversion to infer the true distribution of axial ratios for oblate and prolate models. We also apply Monte Carlo techniques to explore triaxial models. For elliptical galaxies, we find that neither pure oblate nor pure prolate models can satisfactorily account for the observed distribution of apparent axial ratios, since the derived solutions for the distribution of true axial ratios become significantiy negative for q > 0.9. We consider triaxial models in which the true axial ratios b/a and c/a of galaxies are selected from Gaussian distributions. Models with |$\langle(b-c)/(a-c)\rangle\simeq0.6$| provide a good fit to the observed distribution of axial ratios. We analyse possible variations of the intrinsic flattening of ellipticals depending on low and high local density environments. We find that the projected distributions of axial ratios of high and low local density environment ellipticals are remarkably similar. We therefore see no evidence in the data that the environment has significantly affected the shapes of early-type galaxies. For spiral galaxies, pure oblate models fail to reproduce the distribution of observed axial ratios, but consistent fits can be obtained with nearly oblate models with thickness |$c/a\simeq0.2$| and ellipticity |$b/a\simeq 0.9$|⁠. The distributions in this model are very similar to the classical oblate solution of Sandage, Freeman & Stokes. The inferred slight triaxiality could be due to the presence of substructure in discs, or may reflect truly triaxial potentials in spirals.

Analytical potentials for barred galaxies

view Abstract Citations (30) References (8) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Analytical Potentials for Barred Galaxies Long, Kevin ; Murali, Chigurupati Abstract We present simple, analytical, prolate, and triaxial potential-density pairs in three dimensions. The potentials are convolutions of the density of a thin "needle" with a softened potential; the density is everywhere positive. Each choice of softening model and needle density generates a family of models that vary between the extremes of a needle and a sphere. With appropriate choices of the needle density and softening model, the potential can be found in terms of elementary functions. The softening potential need not be spherically symmetric; triaxial models can be constructed in this way. We derive a prolate model that reduces to the Plummer sphere and a triaxial model that reduces to the Miyamoto-Nagai disk. Formulae are given for the forces and projected surface densities. Publication: The Astrophysical Journal Pub Date: September 1992 DOI: 10.1086/171764 Bibcode: 1992ApJ...397...44L Keywords: Astronomical Models; Barred Galaxies; Celestial Mechanics; Galactic Structure; Gravitational Fields; Potential Theory; Ellipsoids; Prolateness; Quadrupoles; Astrophysics; GALAXIES: KINEMATICS AND DYNAMICS full text sources ADS |

Equilibrium stellar systems with spindle singularities

Equilibrium sequences of axisymmetric Newtonian clusters that tend toward singular states are constructed. The distribution functions are chosen to be of the form f = f(E, Jz). The numerical method then determines the density and gravitational potential self-consistently to satisfy Poisson's equation. For the prolate models, spindle singularities arise from the depletion of angular momentum near the symmetry axis. While the resulting density enhancement is confined to the region near the axis, the influence of the spindle extends much further out through its tidal gravitational field. Centrally condensed prolate clusters may contain strong-field regions even though the spindle mass is small and the mean cluster eccentricity is not extreme. While the calculations performed here are entirely Newtonian, the issue of singularities is an important topic in general relativity. Equilibrium solutions for relativistic star clusters can provide a testing ground for exploring this issue. The methods used in this paper for building nonspherical clusters can be extended to relativistic systems.

Stability of nonrotating stellar systems. II - Prolate shell-orbit models

Stability of nonrotating stellar systems. II - Prolate shell-orbit models

Spheroidal galaxy models with anisotropic stresses

A method for finding the kinematical properties of galaxy models without the explicit construction of distribution functions is presented. For any axisymmetric mass density generated by a Stackel potential, an ansatz is introduced for the stress tensor, which enables a unique solution of the equations of stellar hydrodynamics to be deduced. The methods are used to find velocity ellipsoids for oblate and prolate Kuzmin-Kutuzov models. It is found that the velocity ellipsoids can be rounder for flatter systems, which illustrates the limitations of the virial equations

Models of elliptical galaxies: NGC 3379, 4261, 4278 and 4472

Summary We investigate whether the observed kinematics and surface photometry for the elliptical E1/E2 galaxies NGC 3379, 4261, 4278 and 4472 can be modelled under the assumptions of (i) axisyrnmetry, (ii) a distribution function of the form f = f (E, Lz,) and (iii) constant mass-to-light ratio. The methods used are an extension of the work of Binney, Davies & Illingworth (Paper I). Models satisfying the above assumptions fit the observations of all four galaxies remarkably well. For all galaxies, the rotation curves rule out isotropic velocity dispersion tensors. However, an excellent fit to the data can usually be obtained by including a measure velocity of anisotropy. Only in the case of NGC 4472 do the velocity dispersion profiles suggest that the radial and vertical dispersions are decoupled and thus the distribution function depends upon a third integral. In NGC 4278 the rotation velocity changes sign at R ⋍ 30 arcsec. Such behaviour is allowed by our models, but since it is associated with a large isophote twist, it is likely that it indicates a triaxial figure. We have developed a prolate model for NGC 4261 which accurately predicts the kinematics, although the comparison is limited to the rms line-of-sight velocities. We investigate how the predicted kinematics vary as a galaxy’s isophotes are varied from ‘boxy’ to ‘discy’ in shape merely by deforming the bulge rather than introducing a thin disc. A discy model rotates faster on the major axis than the equivalent boxy system, but the effect is too small to account for Bender’s suggested correlation of (v/σ)* with disciness (which exhibits a large scatter). In boxy galaxies the rotation velocity falls more slowly away from the equatorial plane than in the equivalent discy galaxies.

Instabilities of Slowly Rotating Galaxies

The location of instabilities in flattened, pressure-supported stellar systems is discussed. Oblate, prolate, and triaxial models of slowly rotating galaxies is examined. The role of instabilities in explaining the structure of observed galaxies is briefly considered. 47 refs.

Human plasma fibronectin structure probed by steady-state fluorescence polarization: evidence for a rigid oblate structure

In order to more clearly define the structure of human plasma fibronectin (PFn) under physiologic buffer conditions, we determined the mean harmonic rotational relaxation times (rho H) of PFn and the thrombin-derived 190/170-kDa PFn fragment using steady-state fluorescence polarization. These measurements utilized the long lifetime emission (tau = 1.2 X 10(-7) S) exhibited by 1-pyrenebutyrate, which had been covalently attached to amino groups at random sites on the PFn subunit. Our data analysis assumed that two independent processes depolarize the fluorescence exhibited by the dansylcadaverine and 1-pyrenebutyrate conjugates of PFn: (A) rapid (rho H less than 10(-9) S) "thermally-activated" localized rotational motion of the protein side chains bearing the fluorescent probe [Weber, G. (1952) Biochem. J. 51, 145-154] and (B) slow (rho H approximately 10(-6) S) temperature-independent global rotational motion of the whole PFn molecule. Since only the rho H associated with the latter process is a true hydrodynamic parameter (i.e., sensitive to size and/or shape of the PFn molecule), we utilized isothermal polarization measurements to discriminate against the interfering signal arising from "thermally activated" probe rotation. The rho H (4.4 +/- 0.9 microseconds) derived from an experiment in which pyrene-PFn fluorescence polarization was monitored as a function of sucrose concentration at constant temperature is 7 (+/- 1.4) times longer than that predicted for an equivalent hydrated sphere. We propose that "thermally activated" probe rotation gives rise to the nearly 100-fold shorter PFn rho H values previously reported in the literature. Consequently, our data exclude all previous models which invoke segmental flexibility of the PFn peptide backbone. The simplest hydrodynamic model supported by our fluorescence data is an oblate ellipsoid with an axial ratio of 15:1. All prolate models can be unambiguously excluded by this result. We estimate that the disk-shaped PFn molecule has a diameter and thickness of 30 and 2 nm, respectively. Electron microscopy of negatively stained PFn specimens on carbon also showed PFn to have a compact rounded structure. The much faster rotational relaxation rate of the pyrene-190/170-kDa PFn fragment (rho H = 0.92 +/- 0.11 microseconds) compared to pyrene-PFn indicated that this monomeric PFn fragment, like native PFn, had an oblate shape under physiologic buffer conditions.

Orbital contributions to the stability of triaxial galaxies

view Abstract Citations (14) References (36) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Orbital Contributions to the Stability of Triaxial Galaxies de Zeeuw, Tim ; Schwarzschild, Martin Abstract Goodman's indicator is employed to investigate the stability of perfect ellipsoids, which are prototypical nonrotating triaxial galaxy models. The contributions of the individual stellar orbits to the indicator are presented for three specific adiabatic perturbations, which change the axis ratios of the ellipsoids but leave the density profile invariant. It is found that for barlike perturbations, in which one axis is elongated and another is compressed, box orbits are predominantly destabilizing, while outer long-axis tubes are invariably stabilizing. Short-axis tubes and inner long-axis tubes may be both stabilizing and destabilizing. These results for the contributions by individual orbits have been combined with Statler's (1987) results for the distribution functions of self-consistent perfect ellipsoid models. This combination, though still numerically insecure, permits tentative estimates of Goodman's indicator for these models, with the following results. The occurrence of a bar instability appears to be confirmed for triaxial models in which box orbits are heavily occupied. Nearly prolate models seem to suffer from the same instability. In strongly elongated triaxial models nearly all orbits are stabilizing, so that these systems are likely to be stable against barlike perturbations, in agreement with recent N-body simulations. The results for an adiabatic perturbation in which all three axes of the ellipsoid are changed in the same direction indicate--but by no means prove-- the existence of a possible core instability. Publication: The Astrophysical Journal Pub Date: October 1989 DOI: 10.1086/167883 Bibcode: 1989ApJ...345...84D Keywords: Computational Astrophysics; Galactic Structure; Stellar Orbits; Astronomical Models; Density Distribution; Ellipsoids; Many Body Problem; Perturbation Theory; Astrophysics; GALAXIES: INTERNAL MOTIONS; GALAXIES: STRUCTURE; STARS: STELLAR DYNAMICS full text sources ADS |

Triaxial scale-free models of highly flattened elliptical galaxies with and without massive halos

view Abstract Citations (49) References (21) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Triaxial Scale-free Models of Highly Flattened Elliptical Galaxies with and without Massive Halos Levison, Harold F. ; Richstone, Douglas O. Abstract Two sets of dynamical models of triaxial elliptical galaxies with isothermal potentials, one nearly oblate and the other nearly prolate, have been constructed in order to better understand the range of possible dynamical properties of triaxial galaxies. It is found, as expected, that the position angle of maximum rotation in both potentials can be at any position angle with respect to the projected major axis of the model. More surprisingly, it is found that almost oblate models can be constructed that only rotate along their minor axes and that almost prolate models can be constructed with only major axis rotation. The almost oblate models have larger major axis rotation that the almost prolate models, while the almost prolate models have larger minor axis rotation. The most startling finding is that in most models the position angle of zero rotation is not perpendicular to the position angle of maximum rotation. Publication: The Astrophysical Journal Pub Date: March 1987 DOI: 10.1086/165079 Bibcode: 1987ApJ...314..476L Keywords: Astronomical Models; Elliptical Galaxies; Galactic Structure; Halos; Angular Momentum; Dynamic Models; Mass To Light Ratios; Oblate Spheroids; Astrophysics; GALAXIES: INTERNAL MOTIONS; GALAXIES: STRUCTURE full text sources ADS | data products SIMBAD (3) NED (2)

Evidence of a shape transition in even-A Ge isotopes.

Cross-section and vector-analyzing-power measurements have been carried out for /sup 70,72,74,76/Ge(darrow ,d) at E/sub d/ = 8 and 16 MeV, (darrow,d') 2/sup +/ at E/sub d/ = 16 MeV, and (parrow,p) and (parrow,p') 2/sup +/ at E/sub p/ = 11.5 MeV. Exploratory measurements of /sup 70,72,74/Ge(darrow,d) at E/sub d/ = 6 MeV have also been performed. The elastic analyzing-power data for A = 70,72 are nearly identical, as are those for A = 74,76, and a sudden decrease in the amplitude of A/sub y/ occurs in going from A = 72 to 74. The inelastic-scattering data also show near identity for the A = 70,72 target nuclei as well as for A = 74,76, with characteristic changes occurring between A = 72 and 74. Coupled-channels calculations have been performed for all four isotopes using a macroscopic form factor employing both vibrational and rotational models. It is found that the anomalous behavior of the elastic-scattering data at E/sub d/ = 16 MeV and at E/sub p/ = 11.5 MeV is by itself not indicative of ground-state shape, but only shows the effects of target excitation on elastic scattering. The 2/sup +/ inelastic-scattering data, however, can be explained only if a vibrationalmore » model is assumed for /sup 70,72/Ge and a prolate symmetric rotational model is assumed for /sup 74,76/Ge. These results are indicative of a shape transition between /sup 72/Ge and /sup 74/Ge, consistent with the conclusions drawn from transfer-reaction measurements.« less

Molecular theory for fluids modelled with gaussian overlap potentials

In recent years it has become evident that molecular shape is an important factor in determining the equation of state and structure of molecular fluids. In formulating a molecular theory of the equation of state it is important to use a model for the molecular interactions which adequately includes the effect of shape but at the same time is computationally simple. The Gaussian overlap potential can be used effectively to model systems of highly non-spherical shape while retaining the simplicity of a single site potential. The model is applicable to both oblate and prolate molecules. We present calculations, using thermodynamic perturbation theory and Monte Carlo simulations, of the thermodynamic properties and structure of fluids of molecules interacting with a Gaussian overlap potential. Both oblate and prolate molecules are considered. The perturbation theory is based on an extension of the Weeks-Chandler-Andersen theory to orientation dependent potentials, and uses a Mayer-function expansion about a spherically averaged reference potential to compute the structure of the hard core reference system. Results are presented for a prolate model with a length to breadth ratio similar to nitrogen and an oblate model with a length to breadth ratio similar to that of benzene. The predictions of the perturbation theory are compared with the computer simulation results. The theory predicts the structural features of the fluids quite accurately except for the most anisotropic system at high density. The thermodynamic properties of the prolate system are given quite accurately by the theory but for the oblate system, which is more anisotropic, the agreement is less satisfactory.

Character of ‘prolate’ galaxies

It is still not known whether elliptical galaxies are oblate, prolate or triaxial. The prototype prolate galaxy NGC2685 has a rapid observed stellar rotation rate around the projected minor axis. It is shown that a steady figure, exactly prolate model can have no such rotation, and that a nearly prolate model fails by a factor of 7. The galaxy is suggested to be oblate with gas disk that is the wreck of a dwarf companion.

The surface brightness-axis ratio relation as a test of intrinsic shapes of elliptical galaxies

view Abstract Citations (30) References (13) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The surface brightness-axis ratio relation as a test of intrinsic shapes of elliptical galaxies Olson, D. W. ; de Vaucouleurs, G. Abstract The relation between apparent ellipticity and surface brightness for a sample of 112 normal, noninteracting, bright elliptical galaxies in the Second Reference Catalogue is used as a test of their intrinsic shapes. The observed trend is consistent with that expected from geometric projection effects for oblate spheroids, when it is assumed that intrinsic surface brightness, as viewed down the symmetry axis, is independent of the intrinsic axis ratio. Prolate models for elliptical galaxies cannot be ruled out, however, if the ad hoc hypothesis is made that a correlation strong enough to dominate the projection effects exists between intrinsic flattening and surface brightness. Publication: The Astrophysical Journal Pub Date: October 1981 DOI: 10.1086/159260 Bibcode: 1981ApJ...249...68O Keywords: Brightness Distribution; Elliptical Galaxies; Flattening; Galactic Structure; Astronomical Models; Axes (Reference Lines); Oblate Spheroids; Prolate Spheroids; Spectrophotometry; Surface Properties; Astrophysics full text sources ADS | data products NED (112)

PROLATE ELLIPSOLIDAL BAG MODEL FOR THE HADRON WITH HEAVY QUARKNIUM

The static prolate ellipsolidal bag model is discussed in this paper, and it is compared with the spherical bag model and the string-like bag model. The relations between the ellipsolid shape and the energy and 2d, the separation between quarks, are obtained. The cases for B=0 and σ=0 are discussed respectively.

Dynamical Modeling of Elliptical Galaxies - Part Two - Numerical Prolate Models

view Abstract Citations (13) References (11) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Dynamical Modeling of Elliptical Galaxies - Part Two - Numerical Prolate Models Lake, G. Abstract The analytical solutions of Paper I are generalized using the self-consistent field method. These prolate models are constructed using only two integrals of motion, the energy (E) and the angular momentum about the axis of symmetry, (LZ). They are the first models with flattening greater than E4 which possess elliptical isophotes and realistic density profiles. The singularity in the surface brightness which characterized the models of Paper I has been removed by smoothing the extreme suppression of LZ. The new models (like those of Paper I) still show a sharp rise in the velocity dispersion at the center. This feature is due to the strongly anisotropic velocity dispersions, rather than the existence of a supermassive object. Publication: The Astrophysical Journal Pub Date: January 1981 DOI: 10.1086/158574 Bibcode: 1981ApJ...243..121L full text sources ADS |

Dynamical modeling of elliptical galaxies. I - Analytical prolate models. II - Numerical prolate models

Self-consistent models are constructed for prolate elliptical galaxies. Using only two integrals of motion, the energy E and the angular momentum about the axis of symmetry (L/sub z/), analytical solutions are derived. In projection they resemble the spindle-shaped galaxies NGC 3115 and 7332. The flattening of these systems arises from a suppression of the angular momentum about the long axis. The models have a logarithmic singularity in the central surface brightness and exhibit a strong peak in the central velocity dispersion, thus providing another example of the effect of anisotropic velocity dispersion on the observed properties of the central regions of galaxies.

The shape of myosin subfragment-1. A equivalent oblate ellipsoid model based on hydrodynamic properties.

The molecular weights of the two heads of myosin subfragment-1, S-1(A1) and S-1(A2), based on sedimentation equilibrium are 120 000 and 110 000. Hydrodynamically, the two heads are indistinguishable, with intrinsic viscosity, [eta], of 0.064-0.065 dL/g and sedimentation coefficient, s(0)20,w, of 5.8 S. Together with the rotational correlation time taken from the literature (235 ns), all three hydrodynamic properties can be better fitted with an equivalent oblate ellipsoid of revolution than a prolate model. The width of the equatorial axis of the ellipsoid is about 135 A (the axial ratio is about 6). Probably, the S-1(A1) and S-1(A2) molecules have a half-doughnutlike or a flattened pearlike shape rather than an elongated one.