1. 8/27/03LSU - AEI Astrophysics1 The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems Joel E. Tohline & Juhan Frank Kevin Pearson Shangli Ou, Mario D’Souza, Ravi Kopparapu, Vayu Gokhale (Hopefully: Xiaomeng Peng & Ilsoon Park) Former students: Kim New; John Cazes, Howard Cohl, Patrick Motl, Eric Barnes

2. 8/27/03LSU - AEI Astrophysics2 Recent Focus Isolated, rotating stars –Dynamical, barmode instability –(Secular) barmode instability in young Neutron Stars –(Secular) r-mode instability in young Neutron Stars Binary star systems (late stages of evolution) –Tidal instability (stiff equations of state) –Mass-transferring instabilities Formation of binary stars

3. 8/27/03LSU - AEI Astrophysics3 Recent Focus Isolated, rotating stars –Dynamical, barmode instability –(Secular) barmode instability in young Neutron Stars –(Secular) r-mode instability in young Neutron Stars Binary star systems (late stages of evolution) –Tidal instability (stiff equations of state) –Mass-transferring instabilities Formation of binary stars

4. 8/27/03LSU - AEI Astrophysics4 Movies http://baton.phys.lsu.edu/tohline/LSUAEI.movies.html

5. 8/27/03LSU - AEI Astrophysics5 Principal Governing Equations

6. 8/27/03LSU - AEI Astrophysics6 Numerical Simulations Initial Models: Self- Consistent-Field Technique Explicit Time-Integration Finite-Difference Scheme –Uniform, Cylindrical Lattice [typically, 128 3 - 256 3 ] –Rotating Frame –van Leer Advection Heterogeneous Computing Environment SuperMike: LSU’s 1024-processor, 2.2 TeraFlop Supercomputer

7. 8/27/03LSU - AEI Astrophysics7 Regions of Instability & Possible Evolutions

8. 8/27/03LSU - AEI Astrophysics8 Regions of Instability & Possible Evolutions Movie #1 & Movie #2 [Dynamical Barmode] http://

9. 8/27/03LSU - AEI Astrophysics9 Regions of Instability & Possible Evolutions

10. 8/27/03LSU - AEI Astrophysics10 Hanford Observatory Livingston Observatory Laser Interferometer Gravitational-wave Observatory (LIGO)

11. 8/27/03LSU - AEI Astrophysics11

12. 8/27/03LSU - AEI Astrophysics12 Principal Governing Equations

13. 8/27/03LSU - AEI Astrophysics13  GR for (Dedekind) f-mode

14. 8/27/03LSU - AEI Astrophysics14  GR for (Dedekind) f-mode l = m = 2 5 th derivative! c5c5

15. 8/27/03LSU - AEI Astrophysics15 F GR for (Rossby) r-mode [Lindblom, Tohline & Vallisneri (2001, 2002)]

16. 8/27/03LSU - AEI Astrophysics16 F GR for (Rossby) r-mode [Lindblom, Tohline & Vallisneri (2001, 2002)] (l = m = 2) c 7 !

17. 8/27/03LSU - AEI Astrophysics17 r-mode amplitude vs. time [Lindblom, Tohline & Vallisneri (2001, 2002)]

18. 8/27/03LSU - AEI Astrophysics18 r-mode amplitude vs. time [Lindblom, Tohline & Vallisneri (2001, 2002)] Movie #3

19. 8/27/03LSU - AEI Astrophysics19 r-mode velocity field

20. 8/27/03LSU - AEI Astrophysics20 r-mode amplitude vs. time [Lindblom, Tohline & Vallisneri (2001, 2002)] Movie #4

21. 8/27/03LSU - AEI Astrophysics21 Neutron Star’s Angular Momentum, E rot, & Mass

22. 8/27/03LSU - AEI Astrophysics22 Sample Binaries Example Binary Systems

23. 8/27/03LSU - AEI Astrophysics23 Roche Potential for Unequal-Mass Binary

24. 8/27/03LSU - AEI Astrophysics24 Sample Binaries Example Binary Systems

25. 8/27/03LSU - AEI Astrophysics25 Movie #5 (top) Movie #6 (side) Movie #7 (vectors)