1. Purpose and Objectives of the Leave

This sabbatical leave will provide an opportunity for me to become immersed in several specific research activities at an educational institution that offers a rich tradition of academic excellence and a stimulating research environment, but where I will be uninterrupted by regular classroom teaching duties and the numerous regular committee assignments that have become associated with my daily routine at LSU. My primary objectives are:

1. To gain a much better appreciation of the variety and quality of astronomical data that is being collected by millimeter-wave radio telescope arrays in connection with ongoing star formation processes in the solar neighborhood of our Galaxy and in external galaxies.

2. To better understand the connection between the models of (Newtonian) self-gravitating fluid systems that have been constructed in recent years by students in my group at LSU and the models of relativistic systems that may be used effectively to decipher the complex properties of gravitational wave signals that are expected to be detected by LIGO instrumentation.

3. To expand considerably the amount of technical material that is included in the online, graduate-level textbook entitled, "The Structure, Stability, and Dynamics of Self-Gravitating Systems," that I have been developing over the past few years at LSU.

In connection with objective #1, my expectation is that modern data from millimeter arrays can be used to critically evaluate the physical significance of numerical models of star forming clouds that have been constructed in recent years by my research group and that a firm understanding of such data will play a critical role in defining my future research directions at LSU. Objective #2 has emerged as a direct consequence of the construction of the LIGO site near Livingston, Louisiana, within an hour's drive of the LSU campus. Should the modeling expertise developed within my group at LSU prove to be sufficiently complementary to ongoing modeling efforts that are directly connected with LIGO, I will seriously consider expanding the research efforts of my group to include the investigation of astrophysical problems that are directly related with LIGO activities.

2. Outline of Proposed Activities

A significant portion of my research activities over the past 15 years at LSU have been focused on the development of tools (primarily in the form of efficient numerical algorithms) that will permit astronomers to accurately model the structure, stability, and dynamical evolution of rapidly rotating, (Newtonian) self-gravitating astrophysical fluid systems. Through continuous funding from the astronomy division of the National Science Foundation (NSF), much of this work has been conducted with the expressed desire to obtain a better understanding of the processes by which stars form in galaxies. Since 1987, seven students have completed their doctoral dissertation research under my direction at LSU. (A brief account of each student's research accomplishments and present place of employment can be obtained online at http://www.phys.lsu.edu/faculty/tohline/students.info.html) At present, five additional LSU students are working closely with me on dissertation projects.

In recent years, my group's modeling efforts have been primarily aimed at answering the question, "Why do stars tend to form in pairs?" This has been in response to recent observational investigations of the frequency of occurrence of pre-main-sequence binary stars which have reinforced earlier suspicions that ''binary formation is the primary branch of the star-formation process'' (Mathieu 1994). More specifically, we have focused on adiabatic (as opposed to isothermal) phases of protostellar cloud evolution in an effort to understand how binary stars with relatively short (fraction of a year to a few hundred years) orbital periods form.

Because rapidly rotating, gaseous disks appear to frequently (if not always!) accompany protostellar objects and very young stars, we also have attempted to understand (a) how circumstellar and/or circumbinary disks form in association with and interact with nascent stars; and (b) to what extent the binary star formation process depends on the existence of a disk of significant mass (cf., Woodward, Tohline, and Hachisu 1994; Andalib, Tohline, and Christodoulou 1997).

Most significantly, using two quite independent modeling techniques, my group recently has demonstrated that it is possible to construct dynamically stable, self-gravitating configurations with highly nonaxisymmetric structures (for example, ellipsoidal and dumbbell-shaped objects) out of highly compressible gases such as the gases that comprise protostellar clouds. These nonaxisymmetric configurations rotate coherently as though they were solid objects, but in reality they exhibit strongly differential (sometimes supersonic) internal motions. In many respects these objects appear to be compressible analogs of the family of incompressible ellipsoids with internal motions that were discovered by Riemann over a century ago (see Chandrasekhar 1969 for a thorough review of Riemann's incompressible figures of equilibrium). As we have argued in a paper presented recently at the "Numerical Astrophysics 1998" conference in Tokyo (Tohline, Cazes, and Cohl 1998), proof of the existence of these dynamically stable nonaxisymmetric models permits us to resurect the "fission hypothesis of binary star formation." (The text of this conference paper, along with several animation sequences illustrating the dynamical properties of our nonaxisymmetric equilibrium models is available online as an html document at the following URL: //www.phys.lsu.edu/astro/nap98/bf.final.html) That is, it now seems likely that isolated, rotating protostellar gas clouds can evolve slowly through a sequence of more and more distorted equilibrium configurations until they spontaneously break into a pair of self-gravitating structures that are in orbit about one another.

Via such a model of binary star formation, evolution is driven by slow cooling and associated slow contraction of the cloud. Because such an evolution would occur over many dynamical times, it is conceivable that protostellar clouds can be "caught" during such a phase of their evolution and that their structural properties can be observed using millimeter-wave radio telescope arrays. (By contrast, if short period binary systems form through direct "Jeans" fragmentation, the binary formation process will happen within only a few dynamical times -- too quickly for this critical phase of cloud evolution to be studied observationally.)

3. Location of Leave

My plans are to base my sabbatical leave activities on the campus of the California Institute of Technology (Caltech) in Pasadena, California. In concert with my planned research activities, described above, I will have two primary academic contacts at Caltech:

• Kip Thorne, J.Willard Gibbs Professor of Theoretical Physics; and
• Anneila I. Sargent, Professor of Astronomy and Director of Caltech's Owens Valley Radio Observatory.

Movie1

Quicktime (5,907K)

Employing a significantly improved finite-difference simulation code and improved spatial resolution (128³ grid zones), we recently have repeated the simulation that was first reported in Durisen et al. (1986). Movie1 shows the nonlinear development of the two-armed, spiral-mode instability. The evolution is shown in the inertial reference frame and covers 20 central initial rotation periods. Each frame of Movie1 displays four nested isodensity contours at r/r_max = 0.8, 0.4, 0.04, and 0.004. Via the trailing spiral structure, gravitational torques are able to effectively redistribute angular momentum on a dynamical time scale; a relatively small amount of material is shed into an equatorial disk (this disk material is not visible in Movie1 because r_disk < 0.004 r_max); and the central object (containing most of the initial object's mass) settles down into a new equilibrium configuration. Clearly, evolution to a binary star system as suggested by the classical fission hypothesis does not occur. It is primarily because simulations of this type have not produced a binary star system that the classical fission hypothesis has lost favor within the star formation community over the past decade (Bodenheimer et al. 1993).

This work has been supported, in part, by the U.S. National Science Foundation through grant AST-9528424 and, in part, by grants of high-performance-computing time at the San Diego Supercomputer Center and through the PET program of the NAVOCEANO DoD Major Shared Resource Center in Stennis, MS.

4. Alternate Plans (in case original plans are not accomplished)

5. Travel Plans

Movie2 Quicktime (5,747K)

Movie3 Quicktime (3,376K)

6. Compensation

I do not expect to receive any compensation from sources other than the LSU System while on leave.

7. Courses to be Taken

I do not expect to audit any formal courses or to take any courses for academic credit while I am on leave.

8. Scholarly Standing and Benefit to the University

Andalib (1998) recently has developed a self-consistent-field technique that can be used to

Movie4

Quicktime (6,927K)

construct equilibrium models of infinitesimally thin, self-gravitating gaseous disks with (a) compressible equations of state, (b) nonaxisymmetric structures, and (c) nontrivial internal motions. By demanding that the disks have uniform vortensity (defined as the ratio of vorticity to mass density), Andalib has successfully constructed equilibrium disks with polytropic indices 0 < n < 1.3 and minor-to-major axis ratios in the range 0.06 < b/a < 0.80. Movie4 illustrates the internal flow of four of Andalib's compressible disks with nonaxisymmetric structures: one with fully retrograde internal motions (R); one with fully prograde internal motions (P); one with vortices sandwiched between separate regions of prograde and retrograde flow (V); and a common-envelope binary (dumbbell-shaped) configuration (D).

The similarity between the flow illustrated in Movie2 and the flow in Andalib's model P (Movie4) is striking. Apparently Andalib's model provides a good 2D analog of th