Engineering topics

Tohline, Joel E.

Publications and source records attributed to Tohline, Joel E..

9 records

NASA NTRS1995

A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 1: Axisymmetric form

We analyze previous results on the stability of uniformly and differentialy rotating, self-gravitating, gaseous and stellar, axisymmetric systems to derive a new stability criterion for the appearance of torodial, m = 2 intermediate or I-modes and bar modes. In the process, we demonstrate that the bar modes in stellar systems and the m = 2 I-modes in gaseous systems have many common physical characteristics and only one substantial difference: because of the anisotropy of the stress tensor, dynamical instability sets in at lower rotation in stellar systems. This difference is reflected also in the new stability criterion. The new stability parameter alpha equals (T(sub J))/(absolute value of W) is formulated first for uniformly rotating systems and is based on the angular momentum content rather than on the energy content of a system. (T(sub J) is defined as ((L)(Omega(sub J)))/2; L is the total angular momentum; Omega(sub J) is the Jeans frequency introduced by self-gravity; and W is the total gravitational potential energy.) For stability of stellar systems alpha less than or equal to 0.254-0.258 while alpha less than or equal to 0.341-0.354 for stability of gaseous systems. For uniform rotation, one can write alpha = ((ft)/2)(exp 1/2), where t is defined as T/(absolute value of W), T is the total kinetic energy due to rotation, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. Equivalently, alpha equals t/(chi), where chi is defined as Omega/Omega(sub J) and Omega is the rotation frequency. Using these forms, alpha can be extended to and calculated for a variety of differentially rotating, gaseous and stellar, axisymmetric disk and spheroidal models whose equilibrium structures and stability characteristics are known. In this paper, we also estimate alpha for gaseous torodial models and for stellar disk systems embedded in an inert or responsive 'halo.' We find that the new stability criterion holds equally well for all these previously published axisymmetric models.

Christodoulou, Dimitris M.↗

NASA NTRS1995

A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 2: Nonaxisymmetric form

We have previously introduced the parameter alpha as an indicator of stability to m = 2 nonaxisymmetric modes in rotating, self-gravitating, axisymmetric, gaseous (alpha less than or approximately equal to 0.34) and stellar (alpha less than or approximately equal to 0.25) systems. This parameter can be written as alpha = (ft/2)(exp 1/2), where t is defined as T/(absolute value of W), T is the total rotational kinetic energy, W is the total gravitational potential energy, and f is a function characteristic of the topology/connectedness and the geometric shape of a system. In this paper, we extend the stability criterion to nonaxisymmetric equilibrium systems by determining empirically the appropriate form of the function f for ellipsoids and elliptical disks and cylinders. We test the validity of this extension of the stability indicator alpha by considering its predictions for previously published, gaseous and stellar, nonaxisymmetric models. The formulation and critical values account accurately for the stability properties of m =2 modes in gaseous Riemann S-type ellipsoids (including the Jacobi and Dedekind ellipsoids) and elliptical Riemann disks as well as in stellar elliptical Freeman disks and cylinders: all these systems are dynamically stable except the stellar elliptical Freeman disks that exhibit a relatively small region of m = 2 dynamical instability. A partial disagreement in the case of stellar Freeman ellipsoids in maximum rotation may be due to the fact that the region of instability has not been previously determined with sufficient accuracy.

Christodoulou, Dimitris M.↗

NASA NTRS1995

Structural Stability and gamma-Transitions

In this work, we review some new discoveries and physical interpretations that concern the secular and dynamical instabilities and the associated structural changes in rotating, self-gravitating, incompressible fluids. For such fluids, we have been able to examine in depth and to understand physically a variety of classic results. Here we discuss the structural stability and the lambda-transitions of astrophysical fluids. We conclude with a summary of all the different types of lambda-transitions found in the course of our investigation and with a discussion of the implications of our results for superfluids, catastrophes, thermodynamical phase transitions, and the breaking of symmetry and topology.

Christodoulou, Dimitris M.↗

NASA NTRS1994

The stability of thick, self-gravitating disks in protostellar systems

Using numerical hydrodynamics techniques, we perform a nonlinear stability analysis of accretion disk systems that contain thick, self-gravitating disks. The systems are initially represented by a point mass M(sub c) at the center and a geometrically thick, axisymmetric disk of mass M(sub d) that supports uniform specific angular momentum and obeys an n = 3/2, polytropic equation of state. The equilibrium disk structure is uniquely defined upon the specification of two key dimensionless system parameters: M(sub d)/M(sub c) and T/absolute value of W (the ratio of rotational kinetic energy if the disk to the gravitational potential energy of the system). The focus of this work is on the identification of systems within this two-dimensional parameter space that are marginally unstable toward the development of nonaxisymmetric distortions. The geometric form and relative pattern speed of the disk's distortion as well as the likelihood of disk fragmentation as a result of such instabilities is examined, particularly in the context of protostellar systems. The value of T/absolute value of W at which thick disks first become dynamically unstable to nonaxisymmetric distortions is found to vary significantly with the mass ratio of the accertion disk system. Nonaxisymmetric eigenmodes with four distinctly different characters are identified in systems with mass ratios in the range 0.2 less than or equal to (M(sub d)/M(sub c)) less than or equal to 5.

Woodward, John W.↗

NASA NTRS1990

The formation phase of the solar nebula

Hydrodynamical calculations of the collapse of an axisymmetric, rotating protostellar cloud, with radiation transport and without magnetic fields, are presented. The collapse is assumed to start from a centrally condensed sphere of radius 5 x 10 to the 15th cm, a mean density of 4 x 10 to the -15th g/cu cm, a total mass of 1 solar mass, and a total angular momentum of 10 to the 53rd g sq cm per sec. The numerical grid is chosen to resolve the region of disk formation between 1 and 60 AU from the center. Frequency-dependent radiative transfer calculations show how the emergent spectrum of the structure depends upon viewing angle with respect to the rotation axis and how the observed isophotal contours should depend on wavelength and viewing angle. The central part of the protostar, interior to 1 AU, is not resolved numerically but is modeled approximately. At the end of the calculation, this region is found to have a mass of 0.6 solar mass and a ratio of rotational to gravitational energy of about 0.4, sufficiently large to be unstable to nonaxisymmetric perturbations. Although the disk is gravitationally stable according to the local Toomre criterion, the nonaxisymmetric structure in the center is likely to lead to angular momentum transport.

Bodenheimer, Peter↗

NASA NTRS1988

Tilted-ring models of the prolate spiral galaxies NGC 5033 and 5055

Observations of the kinematics of H I in the disks of spiral galaxies have shown that isovelocity contours often exhibit a twisted pattern. The shape of a galaxy's gravitational potential well (whether due to luminous matter or dark matter) can be determined from the direction of the twist. If this twist is a manifestation of the precession of a nonsteady-state disk, it is shown that the twists of NGC 5033 and 5055 imply an overall prolate shape, with the major axis of the potential well aligned along the rotation axis of the disk. Therefore, the luminous disks of these galaxies must be embedded in dark halos that are prolate spheroids or prolatelike triaxial figures.

Christodoulou, Dimitris M.↗

NASA NTRS1988

Star formation via the phase transition of an adiabatic gas

An analytic model based on a second-order accurate global virial analysis is used to describe two stable equilibrium states for rotating gas clouds: a pressure-supported, diffuse state and a rotationally supported, compact state. Diffuse and compact equilibrium sequences are identified along which slow, secular evolution of a gas cloud can occur. A virial analysis provides analytic expressions for the limiting masses of gas clouds at points of dynamical instability. The minimum mass below which external triggers of any amplitude cannot effectively induce star formation is identified for adiabatic gas clouds. It is suggested that fluctuations in the ISM of some galaxies may actually cause star formation to proceed primarily via a phase transition, rather than via the classical Jeans instability.

Tohline, Joel E.↗

NASA NTRS1987

The crucial role of cooling in the making of molecular clouds and stars

The role that velocity or pressure fluctuations in the H I clouds medium can play in initiating compression of sub-Jeans mass diffuse clouds is outlined. The frequently discussed idea is reviewed that substantial overpressures arising in the warm, medium and/or highly supersonic compressions of H I clouds can push sub-Jeans mass clumps to densities where gravity can take over and complete the star formation process. A nonequilibrium model is used to analyze the impact of external disturbances on gas clouds, and estimates of the required disturbance amplitudes are substantially reduced from previous estimates based on equilibrium arguments. The results reveal that a cloud which cools under compression is particularly sensitive to mild disturbances from its environment. Furthermore, the specific energy required to trigger effective compressions in a cooling medium is nearly independent of the cloud's mass. It is proposed that mildly nonlinear disturbances play a primary role in the formation of molecular cloud and stars.

Tohline, Joel E.↗

NASA NTRS1987

Linear and nonlinear dynamic instability of rotating polytropes

A three-dimensional hydrodynamic computer program is used to study the growth of nonaxisymmetric structures in rapidly rotating, self-gravitating polytropes. Models with polytropic index n = 0.8, 1.0, 1.3, 1.5, and 1.8 are studied. The initially axisymmetric equilibria are constructed by the Ostriker-Mark self-consistent-field method. The nonaxisymmetric pattern that develops out of low-amplitude random noise is a two-armed spiral with a well-defined pattern speed and growth rate which closely match properties of the toroidal mode predicted from the linear, second-order tensor-virial equation. A Fourier analysis of each polytrope's azimuthal density distribution shows that, even in the linear amplitude regime, higher-order angular patterns also develop exponentially in time. The higher-order patterns ultimately move in synchronization with the broad two-armed spiral, creating a narrow two-armed spiral. As the polytropic index is decreased, a more open and centrally more barlike pattern develops.

Williams, Harold A.↗