### Abstract

We propose a new method of investigating nonlinear dynamics focusing on the physical phenomena of rotating stars in Newtonian gravity which appear in secu- lar timescale. Since acoustic waves normally interact with the surrounding material in dynamical timescale, we need a special technique to achieve secular timescale in dynamical approach. We particularly focus on r-mode instability and construct a nu- merical scheme of killing the effect of acoustic wave by imposing an anelastic condition at every timestep. Although we only explain the rotating star in Newtonian gravity here, this technique can be also applied to relativistic gravitation (conformally at approximation in general relativity). Boundary condition for solving pressure Poisson equation and future extension from the anelastic conditions are also discussed.

Original language | English |
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Title of host publication | Proceedings of the 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011 |

Publisher | Kyoto University |

Pages | 104-107 |

Number of pages | 4 |

Publication status | Published - 2011 |

Externally published | Yes |

Event | 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011 - Sendai Duration: 2011 Sep 26 → 2011 Sep 29 |

### Other

Other | 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011 |
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City | Sendai |

Period | 11/9/26 → 11/9/29 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Proceedings of the 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011*(pp. 104-107). Kyoto University.

**Dynamical approaches for secular instabilities in rotating stars.** / Saijo, Motoyuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011.*Kyoto University, pp. 104-107, 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011, Sendai, 11/9/26.

}

TY - GEN

T1 - Dynamical approaches for secular instabilities in rotating stars

AU - Saijo, Motoyuki

PY - 2011

Y1 - 2011

N2 - We propose a new method of investigating nonlinear dynamics focusing on the physical phenomena of rotating stars in Newtonian gravity which appear in secu- lar timescale. Since acoustic waves normally interact with the surrounding material in dynamical timescale, we need a special technique to achieve secular timescale in dynamical approach. We particularly focus on r-mode instability and construct a nu- merical scheme of killing the effect of acoustic wave by imposing an anelastic condition at every timestep. Although we only explain the rotating star in Newtonian gravity here, this technique can be also applied to relativistic gravitation (conformally at approximation in general relativity). Boundary condition for solving pressure Poisson equation and future extension from the anelastic conditions are also discussed.

AB - We propose a new method of investigating nonlinear dynamics focusing on the physical phenomena of rotating stars in Newtonian gravity which appear in secu- lar timescale. Since acoustic waves normally interact with the surrounding material in dynamical timescale, we need a special technique to achieve secular timescale in dynamical approach. We particularly focus on r-mode instability and construct a nu- merical scheme of killing the effect of acoustic wave by imposing an anelastic condition at every timestep. Although we only explain the rotating star in Newtonian gravity here, this technique can be also applied to relativistic gravitation (conformally at approximation in general relativity). Boundary condition for solving pressure Poisson equation and future extension from the anelastic conditions are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=84887491320&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887491320&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84887491320

SP - 104

EP - 107

BT - Proceedings of the 21st Workshop on General Relativity and Gravitation in Japan, JGRG 2011

PB - Kyoto University

ER -