The Nonlinear Development of Instabilities in Rotating Stars and Binary Star Systems

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

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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

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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

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Movies

http://baton.phys.lsu.edu/tohline/LSUAEI.movies.html

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Principal Governing Equations

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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

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Regions of Instability & Possible Evolutions

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Regions of Instability & Possible Evolutions

Movie #1 & Movie #2[Dynamical Barmode]

http://http://

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Regions of Instability & Possible Evolutions

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Hanford Observatory

LivingstonObservatory

Laser Interferometer Gravitational-wave Observatory (LIGO)

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Principal Governing Equations

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GR for (Dedekind) f-mode

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GR for (Dedekind) f-model = m = 2

5th derivative!

c5

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FGR for (Rossby) r-mode

[Lindblom, Tohline & Vallisneri (2001, 2002)]

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FGR for (Rossby) r-mode

[Lindblom, Tohline & Vallisneri (2001, 2002)]

(l = m = 2)

c7 !

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r-mode amplitude vs. time

[Lindblom, Tohline & Vallisneri (2001, 2002)]

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r-mode amplitude vs. time

[Lindblom, Tohline & Vallisneri (2001, 2002)]

Movie #3

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r-mode velocity field

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r-mode amplitude vs. time

[Lindblom, Tohline & Vallisneri (2001, 2002)]

Movie #4

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Neutron Star’s Angular Momentum, Erot, & Mass

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Sample Binaries

Exa

mpl

e B

inar

y S

yste

ms

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Roche Potential for Unequal-Mass Binary

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Sample Binaries

Exa

mpl

e B

inar

y S

yste

ms

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Movie #5 (top)

Movie #6 (side)

Movie #7 (vectors)