User:Tohline/Appendix/Ramblings/Hadley and Imamura Supplementary Database

Supplementary Dataset Generated by Hadley & Imamura Collaboration

Introduction

Using numerical hydrodynamic techniques, the Hadley & Imamura collaboration — see especially Paper I and Paper II — has studied the dynamical development of nonaxisymmetric instabilities in toroidal configurations that have a range of "star-to-disk" mass ratios and a wide variety of (initially axisymmetric) geometric structures. We have begun to analyze the results of these numerical simulations in the context of what is known, analytically, about normal modes of oscillation and nonaxisymmetric instabilities in massless Papaloizou-Pringle tori. On the analytic side, our focus has been on the very informative stability analysis published by Blaes (1985).

This brief appendix is provided primarily to support our accompanying discussion of the "Characteristics of Unstable Eigenvectors in Self-Gravitating Tori;" especially the subsection of that chapter in which some results from the Hadley & Imamura collaboration are directly compared to the analytic analysis by Blaes (1985). In addition to the relatively small number of individual models whose unstable eigenvectors have been described in the published literature — see especially the three papers listed below — Hadley and Imamura have stored digital results from a very large number of model simulations in an online Stardisks repository. We greatly appreciate being granted permission (explicitly by K. Z. Hadley) to access this data repository and to post this link so that other researchers may study the accumulated data as well.

Specifics of Database

The initial, axisymmetric toroidal configuration that is associated with each simulation is uniquely characterized by the following set of physical parameters:

• <math>~n</math> … Polytropic index • <math>~q</math> … Power-law index characterizing angular velocity profile • <math>~M_*/M_\mathrm{disk}</math> … Star-to-disk (i.e., star-to-torus) mass ratio • <math>~r_-/r_+</math> … Ratio of inner-to-outer edge of the torus, in its equatorial plane

In addition to specifying these four parameters, the Hadley & Imamura collaboration also tag each evolution with an integer value of <math>~m</math>, to identify the nonaxisymmetric mode that was observed to be fastest growing. For example, following the "star-disk models" link that appears at the top of the category list on the home page of the Stardisks repository will bring you to a page that provides active links to 32 separate model categories, such as:

				In order to go directly to the identified page …
	<math>~(n, q, m)</math>	<math>~=</math>	<math>~(1.5, 1.0, 1)</math>	click this link
	<math>~(n, q, m)</math>	<math>~=</math>	<math>~(1.5, 1.75, 3)</math>	click this link
Most relevant here    ➠	<math>~(n, q, m)</math>	<math>~=</math>	<math>~(1.5, 2.0, 2)</math>	click this link
	<math>~(n, q, m)</math>	<math>~=</math>	<math>~(2.5, 1.5, 2)</math>	click this link

See Also

• Hadley & Imamura collaboration:
  • Paper I: K. Hadley & J. N. Imamura (2011, Astrophysics and Space Science, 334, 1-26), "Nonaxisymmetric instabilities in self-gravitating disks.   I. Toroids" — In this paper, Hadley & Imamura perform linear stability analyses on fully self-gravitating toroids; that is, there is no central point-like stellar object and, hence, <math>~M_*/M_d = 0.0</math>.
  • Paper II: K. Z. Hadley, P. Fernandez, J. N. Imamura, E. Keever, R. Tumblin, & W. Dumas (2014, Astrophysics and Space Science, 353, 191-222), "Nonaxisymmetric instabilities in self-gravitating disks.   II. Linear and quasi-linear analyses" — In this paper, the Imamura & Hadley collaboration performs "an extensive study of nonaxisymmetric global instabilities in thick, self-gravitating star-disk systems creating a large catalog of star/disk systems … for star masses of <math>~0.0 \le M_*/M_d \le 10^3</math> and inner to outer edge aspect ratios of <math>~0.1 < r_-/r_+ < 0.75</math>."
  • Paper III: K. Z. Hadley, W. Dumas, J. N. Imamura, E. Keever, & R. Tumblin (2015, Astrophysics and Space Science, 359, article id. 10, 23 pp.), "Nonaxisymmetric instabilities in self-gravitating disks.   III. Angular momentum transport" — In this paper, the Imamura & Hadley collaboration carries out nonlinear simulations of nonaxisymmetric instabilities found in self-gravitating star/disk systems and compares these results with the linear and quasi-linear modeling results presented in Papers I and II.

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