Prepared October 5, 1998

Joel E. Tohline, Professor

Louisiana State University
Department of Physics & Astronomy, 202 Nicholson Hall,
Baton Rouge, LA 70803-4001 U.S.A.

Through this document, I am requesting permission from the LSU Board of Supervisors to take one full semester of sabbatical leave at full pay during the Spring semester of the year 2000.

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 properties of gravitational wave signals that are expected to be detected by LIGO (The Laser Interferometer Gravitational-Wave Observatory) 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 to LIGO activities.

2. Outline of Proposed Activities

a.) Background

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.

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.

Details: Because the dynamical time associated with a given protostellar cloud tdyn ~ [Grmean]-1/2, where rmean is the mean mass density of the cloud material, and, according to Kepler's 3rd law, orbital periods are approximately 3tdyn, one can readily ascertain from which cloud structures various short period binary systems will form. For example, a rotationally flattened region of a protostellar gas cloud with a mean number density of molecular hydrogen nH2 ~ 1011 cm-3 -- that is, a mean mass density of 3 x 10-13 gm cm-3 -- potentially can give birth to a binary system with an orbital period of about six hundred years; see the following table for other examples. For systems containing on the order of a few solar masses of material, the linear diameter D of the corresponding region of the protostellar cloud (or the approximate separation of the binary system that is formed from such a cloud), and the typical velocity of rotationally supported cloud material vrot are also easily estimated.
nH2 rmean Porb D vrot
[cm-3] [gm cm-3] [years] [AU] [km s-1]
--------- --------------- --------- --------- ---------
1011 3 x 10-13 600 200 5
1013 3 x 10-11 60 50 12
1016 3 x 10-8 2 0.7 50

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 objects, dumbbell-shaped objects, and common-envelope binaries) 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 often 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 resurrect 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: // 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-type" 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.)

b.) Objective #1

Observational data from arrays of millimeter-wave radio telescopes now provide sufficient spatial resolution and signal-to-noise to permit mapping of the structure and dynamical properties of star-forming gas clouds with linear scales approaching the size of our own solar system (cf., Sargent & Welch 1993; Ohashi et al. 1997). Hence, there is an opportunity to directly compare the properties of my group's most recent models with the observed properties of star-forming clouds having comparable scales. One of the most productive facilities of this type is the Owens Valley Millimeter Array which is operated by CalTech as part of the larger Owens Valley Radio Observatory (OVRO). As Director of the OVRO, Anneila Sargent leads a strong radio astronomy group at CalTech whose efforts are largely focused on studies of star forming regions in our Galaxy.

By spending an extended period of time interacting with this radio astronomy group at CalTech, I expect to gain a much better appreciation of the variety and quality of data that is being collected in connection with ongoing star formation processes in the solar neighborhood of our Galaxy as well as in extragalactic systems. While on leave, I plan to modify my group's current (generally adiabatic) modeling algorithms to incorporate radiative transfer techniques that will permit us to produce spatially resolved surface brightness and velocity maps from our dynamical models for comparison with the observations. Having gained a much better appreciation of the type (eg., mass, number density, and linear scale) of system that can be well studied with maturing millimeter-wave arrays, I will understand better on what types of systems my group should focus its future dynamical modeling efforts upon my return to LSU.

c.) Objective #2

Although directed primarily toward a better understanding of how binary star systems are formed, most of my group's recent modeling efforts have been of a sufficiently general nature that they also can provide insight into the structural and stability properties of other self-gravitating systems, such as galaxies or highly evolved binary systems with or without accompanying accretion disks. In connection with highly evolved, compact stars or compact binary systems that might give rise to observable levels of gravitational radiation, for example, my group recently has made two significant contributions ( New et al. 1995; New & Tohline 1997; see also New 1996). The second of these papers, in particular, reports on an extensive set of numerical calculations in which the relative stability of close, equal-mass binary stars having a wide variety of different equations of state was carefully examined.

As mentioned in § 2a, above, my group recently has demonstrated that it is possible to construct dynamically stable, self-gravitating configurations with highly nonaxisymmetric structures out of compressible gases. If scaled to the size of compact stars, such long-lived nonaxisymmetric configurations would produce significant, luminous sources of gravitational radiation. We are anxious to gain a better understanding of the connection between (Newtonian) models of this type and models of relativistic systems that may be detectable by LIGO instrumentation. Under Kip Thorne's direction, CalTech is widely recognized as the home base for one of the world's leading theory groups whose efforts are directed largely toward models of LIGO sources. By participating in the activities of this group on a regular basis while on leave, I should be able to achieve this second objective. Upon my return to LSU, I should be in a good position to decide whether an expansion of my group's activities in this direction will be of value to the LIGO scientific community.

d.) Objective #3

Over the past few years I have been investing a considerable amount of time developing an extensive, technical web-based document that covers the extremely broad topic of "The Structure, Stability, and Dynamics of Self-Gravitating Systems." ( My objective is to gather into a single source: much of the classical literature on the structural and stability properties of rotating, incompressible fluids that has been reviewed by Chandrasekhar (1969); much of the work on the stability of rotating stars that was presented by Tassoul (1978) two decades ago; and an overview of numerical models that have contributed to our understanding of the nonlinear development of instabilities in such systems over the past 20 years. A web-based document (as opposed to a printed textbook) is particularly appealing when presenting recent numerical developments because the reader can be given direct access to existing numerical tools, and animation sequences (or Java applets) can be called upon to illustrate clearly the behavior of time-evolving, dynamical systems.

Although I have already invested a great deal of time laying out the structural elements of this web-based document and have written a good deal of the introductory material, the "meat" of the subject has yet to be presented in a satisfactory manner. (Surprisingly, the document already has received some publicity; it was featured on the cover and in an "Internet Goldmine" article in the 1998 July/August issue of Computers in Physics.) During this proposed sabbatical leave, I expect to find many uninterrupted hours during which the primary text of this web-based document can be written and supporting utilities developed. Although my hope is that the astrophysical community at large will find this technical document to be of value in a variety of different contexts, my primary motivation for developing the document is to provide a modern resource to graduate students at LSU who wish to push forward the frontiers of knowledge in this field. I also expect the document to serve as a primary resource for the graduate-level astrophysics course (ASTR 7741) that is offered on a regular basis to physics students at LSU.

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:

As documented by the accompanying letters from Professors Sargent and Thorne, I have been invited to participate in activities associated with both of their research programs in an effort to develop a more complete understanding of how the numerical, fluid dynamic simulations currently being performed by my group at LSU relate to (a) high-resolution radio observations of newly forming stars both inside and outside the solar neighborhood of our Galaxy that are being acquired with OVRO instruments, and (b) efforts that are underway to predict the luminosity and spectral signature of strong sources of gravitational radiation that will be detectable by LIGO. Professor Sargent have assured me that office space will be provided on the CalTech campus from which my research activities may comfortably be based, and that I will have opportunities to visit the OVRO.

4. Compensation

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

5. References

Andalib, S. W., J.E. Tohline, & D.M. Christodoulou. (1997). The Astrophysical Journal Supplement, 108, 471-487.

Chandrasekhar, S. (1969), Ellipsoidal Figures of Equilibrium. Yale University Press, New Haven, CT, U.S.A.

Mathieu, R.D. (1994), Ann. Rev. Astr. Ap., 32, p. 465

Ohashi, N., Hayashi, M., Ho, P.T.P., Momose, M., Tamura, M., Hirano, N., and Sargent A.I. (1997). The Astrophysical Journal, 488, 317.

New, K.C.B. (1996), Instabilities in and Gravitational Radiation from Compact Stars and Compact Binary Systems, Ph.D. Dissertation, Louisiana State University

New, K.B.C., Chanmugam, G., Johnson, W.W., and Tohline, J.E. (1995), The Astrophysical Journal, 450, p. 757

New, K.B.C. and Tohline, J.E. (1997), The Astrophysical Journal, 490, p. 311

Sargent, A.i., and Welch, W.J (1993), Ann. Rev. Astr. Ap., 31, p. 297

Tassoul, J.-L. (1978), Theory of Rotating Stars. Princeton University Press, Princeton, NJ, U.S.A.

Tohline, J.E., Cazes, J.E., and Cohl, H.S (1998), in Proceedings of the Conference, Numerical Astrophysics 1998, in press.

Woodward, J. W., J. E. Tohline, and I. Hachisu. (1994). The Astrophysical Journal, 420, 247-267.

6. Resume

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