R. H. Durisen

Dynamic fission instabilities in rapidly rotating n = 3/2 polytropes - A comparison of results from finite-difference and smoothed particle hydrodynamics codes

The effectiveness of three different hydrodynamics models is evaluated for the analysis of the effects of fission instabilities in rapidly rotating, equilibrium flows. The instabilities arise in nonaxisymmetric Kelvin modes as rotational energy in the flow increases, which may occur in the formation of close binary stars and planets when the fluid proto-object contracts quasi-isostatically. Two finite-difference, donor-cell methods and a smoothed particle hydrodynamics (SPH) code are examined, using a polytropic index of 3/2 and ratios of total rotational kinetic energy to gravitational energy of 0.33 and 0.38. The models show that dynamic bar instabilities with the 3/2 polytropic index do not yield detached binaries and multiple systems. Ejected mass and angular momentum form two trailing spiral arms that become a disk or ring around the central remnant. The SPH code yields the same data as the finite difference codes but with less computational effort and without acceptable fluid constraints in low density regions. Methods for improving both types of codes are discussed. 68 references.

Chondrule-forming Shock Fronts in the Solar Nebula: A Possible Unified Scenario for Planet and Chondrite Formation

Chondrules are millimeter-sized spherules found throughout primitive chondritic meteorites. Flash heating by a shock front is the leading explanation of their formation. However, identifying a mechanism for creating shock fronts inside the solar nebula has been difficult. In a gaseous disk capable of forming Jupiter, the disk must have been marginally gravitationally unstable at and beyond Jupiters orbit. We show that this instability can drive inward spiral shock fronts with shock speeds of up to ~10 km s-1 at asteroidal orbits, sufficient to account for chondrule formation. The mixing and transport of solids in such a disk, combined with the planet-forming tendencies of gravitational instabilities, results in a unified scenario linking chondrite production with gas giant planet formation.

Hydraulic/Shock Jumps in Protoplanetary Disks

In this paper, we describe the nonlinear outcome of spiral shocks in protoplanetary disks. Spiral shocks, for most protoplanetary disk conditions, create a loss of vertical force balance in the postshock region and result in rapid expansion of the gas perpendicular to the disk midplane. This expansion has characteristics similar to hydraulic jumps, which occur in incompressible fluids. We present a theory to describe the behavior of these hybrids between shocks and hydraulic jumps (shock bores) and then compare the theory to three-dimensional hydrodynamics simulations. We discuss the fully three-dimensional shock structures that shock bores produce and discuss possible consequences for disk mixing, turbulence, and evolution of solids.

Linear and nonlinear dynamic stability of rotating n = 3/2 polytropes

A three-dimensional hydrodynamic computer program has been used to study the growth of nonaxisymmetric structure in rapidly rotating, n = 3/2 polytropes whose initial axisymmetric equilibria were constructed with the Ostriker-Mark, self-consistent field method. Differentially rotating models were studied, whose initial ratios t of rotational to gravitational potential energy were t = 0.28, 0.30, 0.33, and 0.35. An open, two-armed, trailing spiral pattern, rather than a coherent bar mode, has been found to grow dynamically in all models with t at least 0.30. The results of the investigation support the reliability of both the tensor virial equation (TVE) analysis of such systems and the computer simulation itself. The 3D code can be used with confidence to study the dynamical growth of nonaxisymmetric structure into the nonlinear amplitude regime. 25 references.

The orientation of gas disks in tumbling prolate galaxies

In Paper I, it has been suggested that dissipative processes coupled with the differential precession of particle orbits will cause gas flowing in a static spheroidal galaxy to settle into a preferred plane of the galaxy--namely, the equatorial plane of the spheroid. In this paper, we discuss the existence of preferred planes for gas which flows into a tumbling, prolate spheroidal (barlike) galaxy. We argue that this type of galaxy exhibits three different dynamical regions and that the preferred plane into which the gas will settle is not the same in all three regions. In particular, while gas in the outermost region of the galaxy aligns its orbital angular momentum vector with the spin axis of the tumbling bar, gas in the innermost region will align its angular momentum vector in a direction orthogonal to that axis, along the major axis of the bar. An analytic determination of the orientation of preferred planes in the case of a weak bar supports this picture. We suggest that NGC 2685 is an example of a galaxy in which orthogonally oriented disks have been observed. A dynamical classification scheme is outlined that encompasses all prolate elliptical galaxies and, perhaps, many barred spiral galaxiesmorexa0» as well.«xa0less

Preferred orbit planes in the gravitational field of a tumbling spheroidal galaxy

The orientation and kinematics of gas disks may provide clues concerning the true three-dimensional shapes of elliptical galaxies. This paper describes a simple, analytic method for determining the preferred planes into which gas will settle by dissipative differential precession in a slightly nonspherical, nonstatic potential. In particular, we thoroughly analyze precession of circular orbits in the external potential of a slightly prolate spheroidal mass that is tumbling about a short axis. This provides a crude model for barred spiral galaxies as well as for prolate elliptical galaxies. For small radial distances from the center, the preferred planes correspond to orbits in the equatorial plane of the spheroid; at large radial distances, they correspond to orbits in the principal plane perpendicular to the tumble axis. Inner and outer gas disks can thus be orthogonal to one another, as is occasionally observed in real galaxies. The transition with radius between these preferred orbital orientations is mapped out in detail and is found to be smooth for gas in orbits that are retrograde with respect to the tumble direction. Our results agree with work by others on the existwence, orientation, and stability of periodic orbits in triaxial potentials. Simple physical interpretations of ourmorexa0» analytic solutions are provided. Depending on the source and injection geometry of the gas and on the nature of dissipation in the gas, the orbital dynamics could lead to enhanced, or even catastrophic, radial inflow and to steady-state warped structures.«xa0less

An Update on Binary Formation by Rotational Fission

During the 1980s, numerical simulations showed that dynamic growth of a barlike mode in initially axisymmetric, equilibrium protostars does not lead to prompt binary formation, i.e., fission. Instead, such evolutions usually produce a dynamically stable, spinning barlike configuration. In recent years, this result has been confirmed by numerous groups using a variety of different hydrodynamical tools, and stability analyses have convincingly shown that fission does not occur in such systems because gravitational torques cause nonlinear saturation of the mode amplitude. Other possible routes to fission have been much less well scrutinized because they rely upon a detailed understanding of the structure and stability of initially nonaxisymmetric structures and/or evolutions that are driven by secular, rather than dynamic processes. Efforts are underway to examine these other fission scenarios. 1. Relevant Results up through the 1980s In the context of binary star formation, fission is the hypothetical process by which a rotating, equilibrium protostellar core becomes unstable to the spontaneous growth of nonaxisymmetric structure which, when fully developed, causes it to break into two or more pieces. This concept dates back over 100 years to stability analyses which showed that rapidly rotating, axisymmetric fluid configurations are unstable to the growth of an ellipsoidal or barlike structure (Chandrasekhar 1969; Tassoul 1978; Durisen & Tohline 1985). For example, dynamic instability of a barlike distortion occurs when the ratio of rotational to gravitational potential energy TjlWI ~ 0.27. When T/IWI ~ 0.14, axisymmetric systems can evolve to lower energy, barlike configurations in the presence of dissipative mechanisms (e.g., viscosity or gravitational radiation). In this case, evolution proceeds on a secular time scale that is long compared to the dynamic time scale. Early stability analyses were unable to determine whether these types of instabilities would ultimately lead to fission due to the difficulty of modeling nonlinear-amplitude figure distortions for realistic fluids. In the 1980s, the development of 3D hydrodynamics codes and advances in computing technologies made it possible to study the linear and nonlinear