![Page 1: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/1.jpg)
8/27/03 LSU - AEI Astrophysics 1
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
![Page 2: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/2.jpg)
8/27/03 LSU - AEI Astrophysics 2
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
![Page 3: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/3.jpg)
8/27/03 LSU - AEI Astrophysics 3
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
![Page 4: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/4.jpg)
8/27/03 LSU - AEI Astrophysics 4
Movies
http://baton.phys.lsu.edu/tohline/LSUAEI.movies.html
![Page 5: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/5.jpg)
8/27/03 LSU - AEI Astrophysics 5
Principal Governing Equations
![Page 6: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/6.jpg)
8/27/03 LSU - AEI Astrophysics 6
Numerical Simulations
• Initial Models: Self-Consistent-Field Technique
• Explicit Time-Integration
• Finite-Difference Scheme– Uniform, Cylindrical Lattice
[typically, 1283 - 2563]
– Rotating Frame
– van Leer Advection
• Heterogeneous Computing Environment SuperMike: LSU’s 1024-processor, 2.2
TeraFlop Supercomputer
![Page 7: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/7.jpg)
8/27/03 LSU - AEI Astrophysics 7
Regions of Instability & Possible Evolutions
![Page 8: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/8.jpg)
8/27/03 LSU - AEI Astrophysics 8
Regions of Instability & Possible Evolutions
Movie #1 & Movie #2[Dynamical Barmode]
http://http://
![Page 9: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/9.jpg)
8/27/03 LSU - AEI Astrophysics 9
Regions of Instability & Possible Evolutions
![Page 10: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/10.jpg)
8/27/03 LSU - AEI Astrophysics 10
Hanford Observatory
LivingstonObservatory
Laser Interferometer Gravitational-wave Observatory (LIGO)
![Page 11: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/11.jpg)
8/27/03 LSU - AEI Astrophysics 11
![Page 12: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/12.jpg)
8/27/03 LSU - AEI Astrophysics 12
Principal Governing Equations
![Page 13: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/13.jpg)
8/27/03 LSU - AEI Astrophysics 13
GR for (Dedekind) f-mode
![Page 14: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/14.jpg)
8/27/03 LSU - AEI Astrophysics 14
GR for (Dedekind) f-model = m = 2
5th derivative!
c5
![Page 15: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/15.jpg)
8/27/03 LSU - AEI Astrophysics 15
FGR for (Rossby) r-mode
[Lindblom, Tohline & Vallisneri (2001, 2002)]
![Page 16: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/16.jpg)
8/27/03 LSU - AEI Astrophysics 16
FGR for (Rossby) r-mode
[Lindblom, Tohline & Vallisneri (2001, 2002)]
(l = m = 2)
c7 !
![Page 17: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/17.jpg)
8/27/03 LSU - AEI Astrophysics 17
r-mode amplitude vs. time
[Lindblom, Tohline & Vallisneri (2001, 2002)]
![Page 18: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/18.jpg)
8/27/03 LSU - AEI Astrophysics 18
r-mode amplitude vs. time
[Lindblom, Tohline & Vallisneri (2001, 2002)]
Movie #3
![Page 19: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/19.jpg)
8/27/03 LSU - AEI Astrophysics 19
r-mode velocity field
![Page 20: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/20.jpg)
8/27/03 LSU - AEI Astrophysics 20
r-mode amplitude vs. time
[Lindblom, Tohline & Vallisneri (2001, 2002)]
Movie #4
![Page 21: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/21.jpg)
8/27/03 LSU - AEI Astrophysics 21
Neutron Star’s Angular Momentum, Erot, & Mass
![Page 22: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/22.jpg)
8/27/03 LSU - AEI Astrophysics 22
Sample Binaries
Exa
mpl
e B
inar
y S
yste
ms
![Page 23: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/23.jpg)
8/27/03 LSU - AEI Astrophysics 23
Roche Potential for Unequal-Mass Binary
![Page 24: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/24.jpg)
8/27/03 LSU - AEI Astrophysics 24
Sample Binaries
Exa
mpl
e B
inar
y S
yste
ms
![Page 25: The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems](https://reader036.vdocuments.us/reader036/viewer/2022062409/5681499a550346895db6dd70/html5/thumbnails/25.jpg)
8/27/03 LSU - AEI Astrophysics 25
Movie #5 (top)
Movie #6 (side)
Movie #7 (vectors)