| GENERAL RELATIVISTIC BACK REACTION |
Physical Scenario:
Gravitational wave induced secular instabilities were first discovered by
Chandrasekhar (1970). In his Physical Review letter, Chandrasekhar
demonstrated that gravitational radiation reaction (GRR) could induce
nonaxisymmetric kelvin l=m=2 bar mode instabilies
in uniformly rotating, incompressible, fluid configurations. Extending this
work, Friedman & Schutz (1978) showed that all rotating, self-gravitating
fluid equilibrium states are secularly unstable to nonaxisymmetric
GRR-driven instabilities, independent of the rotation rate.
GRR-driven instabilities result from the speed-of-light retardation which
occurs between the interactions of different parts of a star rotating
relativistically. In such a system, the equality of action-reaction forces
found in Newtonian systems is violated. This violation results in net
self-forces which can do work and change the body's energy. Since all
fundamental physical field theories are conservative, the energy lost by
the body as a result of these retardation self-forces, or reaction forces,
produces gravitational radiation (Schutz 1986).
Studies have shown (Bonazzola et al. 1996; Lai & Shapiro 1995; Schutz 1986)
that viscosity, either
physical or numerical, may compete with GRR and stabalize the star.
Bonazzola et al. (1996) have shown that in the most severe cases, viscosity
can stabalize the star up to the dynamcial stability point.
By modeling neutron stars as uniformly rotating polyropes with
indicies ranging between 0.5 and 1.0, Imamura et al. (1985) have
shown that the secular instability for the m=2 mode is located at
approximately 0.31c while the pear and quadrupole modes
lie within the values of approximately 0.23-0.26c,
respectively, for the range of indicies studied. The work presented here
focuses on the inclusion of the general relatistic back reaction into the
SPH hydrodynamical equations and its effect on the system dynamics of
pre-collapsed stellar cores.
GRR-driven instabilities result from the speed-of-light retardation which occurs between the interactions of different parts of a star rotating relativistically. In such a system, the equality of action-reaction forces found in Newtonian systems is violated. This violation results in net self-forces which can do work and change the body's energy. Since all fundamental physical field theories are conservative, the energy lost by the body as a result of these retardation self-forces, or reaction forces, produces gravitational radiation (Schutz 1986).
Studies have shown (Bonazzola et al. 1996; Lai & Shapiro 1995; Schutz 1986) that viscosity, either physical or numerical, may compete with GRR and stabalize the star. Bonazzola et al. (1996) have shown that in the most severe cases, viscosity can stabalize the star up to the dynamcial stability point. By modeling neutron stars as uniformly rotating polyropes with indicies ranging between 0.5 and 1.0, Imamura et al. (1985) have shown that the secular instability for the m=2 mode is located at approximately 0.31c while the pear and quadrupole modes lie within the values of approximately 0.23-0.26c, respectively, for the range of indicies studied. The work presented here focuses on the inclusion of the general relatistic back reaction into the SPH hydrodynamical equations and its effect on the system dynamics of pre-collapsed stellar cores.
Results:
-
Results are pending. This work is currently being prepared for
publication (Houser 2000).
These simulations were performed on Sun Ultra Workstation's at the
Harvard-Smithsonian
Center for
Astrophysics and at the Massachusetts
Institute of Technology.
-
This work was supported by the NSF Cooperative Agreement No. PHY-9603177 in
support of LIGO's Visitor's Program.
References:
Chandrasekhar, S., Phys. Rev. Lett., 24, 611.
Bonazzola, S., Frieben, J. & Gourgoulhon, E. 1996,
Astrophys. J., 460, 379.
Friedman, J.L. & Schutz, B.F. 1978, Astrophys. J.,
222, 281.
Houser, J.L. 2000, in preparation.
Imamura, J., Friedman, J., & Durisen, R. 1985, Astrophys.
J., 294, 474.
Lai, D. & Shapiro, S. 1995, Astrophys J., 442,
259.
Schutz, B. 1986, in Dynamical Spacetimes and Numerical
Relativity, edited by J. Centrella (Cambridge University
Press, New York).
Bonazzola, S., Frieben, J. & Gourgoulhon, E. 1996, Astrophys. J., 460, 379.
Friedman, J.L. & Schutz, B.F. 1978, Astrophys. J., 222, 281.
Houser, J.L. 2000, in preparation.
Imamura, J., Friedman, J., & Durisen, R. 1985, Astrophys. J., 294, 474.
Lai, D. & Shapiro, S. 1995, Astrophys J., 442, 259.
Schutz, B. 1986, in Dynamical Spacetimes and Numerical Relativity, edited by J. Centrella (Cambridge University Press, New York).