ROTATION RATE









Physical Scenario:



Numerical simulations have been performed of the dynamical instability in rapidly rotating stellar cores modeled as n=0.5 polytropes with rotation rates of approximately 0.42c, 0.44c, 0.46c, 0.47c and 0.49c, where c is the speed of light in a vacuum. A 3D SPH code was used to evolve the self-gravitating fluid using a purely Newtonian gravitational field. The gravitational radiation was calculated using the quadrupole approximation with the effects of the general relativistic back-reaction omitted. Each model consisted of N=12000 particles and used a new rotational cooling method to create the initial equilibrium SPH state (Houser 1998).

Since it is uncertain at what point during the collapse phase a stellar core may go unstable, this work investigates a variety of rotation rates. The work presented here targets the effect of rotation on the dynamics and gravitational radiation of stiff (n=0.5) polytropic models, which approximate stellar cores that have collapsed to near neutron-star densities.











Results:



Depending on the initial rotation rate of the core, either an m=2 or m=3 mode will dominate the early stages of the core deformation. The model which rotates at approximately 0.42c (which is dynamically stable by secularly unstable) showed little physical change throughout its evolution. In all models that were dynamicaly unstable, the growth of the bar mode eventually dominates the global structure producing trailing spiral arms which transport angular momentum into the surrounding envelope.

As the rotation of the model is increased to 0.42c, which it is just over the threshold of the dynamical stability point, an instability develops and sheds mass in the form of a very weak two-armed spiral. As the models become more unstable, the strength and exponential growth period of the odd modes increases.

The m=1 and m=3 modes appear to grow during core recontraction for models which surpass 0.46c. As was found by Bonnell (1994), this suggests that these modes may be generated via gravitational torques which result from the bar mode. During the re-contraction, the formation of a quadrupole structure, previously called the ``antibar'' (Houser 1998), occurred in models rotating less than approximately 0.46c. As the rotation rate approaches 0.47c, the dominance of the odd modes early in the evolution becomes significant. As rotation is increased to 0.49c, the odd modes dominate all aspects of the evolution.

The gravitational waveform profiles appear to be sensitive to rotation rate. The amplitude of the primary burst as well as the frequency of the waves increase with increasing rotation. However, the duration of the burst decreases. Although the frequency of the waves is independent of observing angle, the amplitude is not. Its magnitude appears to decrease by approximately 50% as the observing angle is varied from zero to 90 degrees. The energy spectrum is also sensitive to the rotation rate of the core; the location and strength of the peak amplitude depends on the initial rotation rate as well as the duration of the signal.

The detectability of a rotationally unstable core will depend critically on the fraction of rest-mass energy converted into gravitational waves during the event. This study examines the effect of the rotation rate on the gravitational wave signature which arises from a dynamical instability. In the physical scenarios examined, the core was assumed to be 1.4 Solar Masses and to have collapsed to near neutron-star densities size and density of n=0.5 and 10-20 km, respectively. The gravitational wave quantities are particularly sensitive to rotation rates. If the core collapses to a radius of approximately 10 km prior to the onset of a dynamical instability then it is likely that such an event out to the Local Group will be detected by the broad-band interferometers. However, if the dynamical instability occurs at about 20 km, the frequency of the gravitational radiation will lie outside the range of the broad-band interferometers.



These simulations were performed on an Sun Ultra Workstation at the Harvard-Smithsonian Center for Astrophysics.







MPEG MOVIES: 0.44c, 0.46c, 0.47c, and 0.49c





NOTE: The movie shown consist of the projection of approximately 12,000 "fluid" elements or ``particles'' onto the xy plane. In these movies, the axis of rotation is the z axis.



For more information, please see: Houser 1998.





This work was supported by the LIGO's Visitor's Program under NSF Cooperative Agreement No. PHY-9603177.









References:

Bonnell, I.A. 1994, Mon. Not. R. Astron. Soc., 269, 837.

Houser, J.L. 1998, Mon. Not. R. Astron. Soc., 299, 1069.

Tohline, J.E., Durisen, R.H., & McCollough, M. 1985, Astrophys. J., 298, 220.