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==Introduction==
Using numerical hydrodynamic techniques, the [[#See_Also|Hadley & Imamura collaboration]] — see especially [http://adsabs.harvard.edu/abs/2011Ap%26SS.334....1H Paper I] and [http://adsabs.harvard.edu/abs/2014Ap%26SS.353..191H 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 [[User:Tohline/Apps/PapaloizouPringleTori#Massless_Polytropic_Tori|''massless'' Papaloizou-Pringle tori]].  On the analytic side, our focus has been on the very informative stability analysis published by [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)].
Using numerical hydrodynamic techniques, the [[#See_Also|Hadley & Imamura collaboration]] — see especially [http://adsabs.harvard.edu/abs/2011Ap%26SS.334....1H Paper I] and [http://adsabs.harvard.edu/abs/2014Ap%26SS.353..191H 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 [[User:Tohline/Apps/PapaloizouPringleTori#Massless_Polytropic_Tori|''massless'' Papaloizou-Pringle tori]].  On the analytic side, our focus has been on the very informative stability analysis published by [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B Blaes (1985)].




This brief appendix is provided primarily to support our accompanying discussion of the "[[User:Tohline/Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]];" especially the [[User:Tohline/Apps/ImamuraHadleyCollaboration#Comparison_with_Results_from_the_Imamura_.26_Hadley_Collaboration|subsection of that chapter]] in which some results from the Hadley & Imamura collaboration are directly compared to the analytic analysis by [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B 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 [[#See_Also|three papers listed below]] — Hadley and Imamura have stored digital results from a very large number of model simulations in an [http://pages.uoregon.edu/khadley/ 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.
This brief appendix is provided primarily to support our accompanying discussion of the "[[User:Tohline/Apps/ImamuraHadleyCollaboration#Characteristics_of_Unstable_Eigenvectors_in_Self-Gravitating_Tori|Characteristics of Unstable Eigenvectors in Self-Gravitating Tori]];" especially the [[User:Tohline/Apps/ImamuraHadleyCollaboration#Comparison_with_Results_from_the_Imamura_.26_Hadley_Collaboration|subsection of that chapter]] in which some results from the Hadley & Imamura collaboration are directly compared to the analytic analysis by [http://adsabs.harvard.edu/abs/1985MNRAS.216..553B 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 [[#See_Also|three papers listed below]] — Hadley and Imamura have stored digital results from a very large number of model simulations in an [http://pages.uoregon.edu/khadley/ 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:
<table align="left" cellpadding="5" border="0">
<tr><td align="left">
<table border="0" cellpadding="5" align="left">
<tr>
  <td align="center"><font size="+2">&bull;</font></td>
  <td align="left"><math>~n</math></td>
  <td align="center">&hellip;</td>
  <td align="left">Polytropic index</td>
</tr>
<tr>
  <td align="center"><font size="+2">&bull;</font></td>
  <td align="left"><math>~q</math></td>
  <td align="center">&hellip;</td>
  <td align="left">Power-law index characterizing angular velocity profile</td>
</tr>
<tr>
  <td align="center"><font size="+2">&bull;</font></td>
  <td align="left"><math>~M_*/M_\mathrm{disk}</math></td>
  <td align="center">&hellip;</td>
  <td align="left">Star-to-disk (''i.e.'', star-to-torus) mass ratio</td>
</tr>
<tr>
  <td align="center"><font size="+2">&bull;</font></td>
  <td align="left"><math>~r_-/r_+</math></td>
  <td align="center">&hellip;</td>
  <td align="left">Ratio of inner-to-outer edge of the torus, in its equatorial plane</td>
</tr>
</table>
</td></tr>
</table>


=See Also=
=See Also=

Revision as of 20:26, 3 June 2016

Supplementary Dataset Generated by Hadley & Imamura Collaboration

Whitworth's (1981) Isothermal Free-Energy Surface
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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

See Also


Whitworth's (1981) Isothermal Free-Energy Surface

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