Until recently, such simulations had been published only for nearly spherical collapse. The
spherical simulations of Shapiro and Teukolsky [220] produced collapse evolutions that were nearly
homologous. In this case, the collapse time is roughly the free-fall time at the horizon
The amplitude of this burst signal can be roughly estimated in terms of the star’s quadrupole
moment
There are two possible aspherical collapse outcomes that can be discussed. The first outcome is direct
collapse to a SMBH. In this case, will be on the order of one near the horizon. Thus, according to
Equation 8
, the peak amplitude of the GW burst signal will be
Alternatively, the star may encounter the dynamical bar mode instability prior to complete collapse.
Baumgarte and Shapiro [16] have estimated that a uniformly rotating SMS will reach
when
. The frequency of the quasiperiodic gravitational radiation emitted by the bar can be
estimated in terms of its rotation frequency to be
The collapse of a uniformly rotating SMS has been investigated with post-Newtonian hydrodynamics, in
3+1 dimensions, by Saijo, Baumgarte, Shapiro, and Shibata [208]. Their numerical scheme used a
post-Newtonian approximation to the Einstein equations, but solved the fully relativistic hydrodynamics
equations. Their initial model was an
polytrope.
The results of Saijo et al. (confirmed in conformally flat simulations [207]Update) indicate that the collapse of a uniformly rotating SMS is coherent (i.e., no fragmentation
instability develops). The collapse evolution of density contours from their model is shown in
Figure 19
. Although the work of Baumgarte and Shapiro [16
] suggests that a bar instability
should develop prior to BH formation, no bar development was observed by Saijo et al. They
use the quadrupole approximation to estimate a mean GW amplitude from the collapse itself:
, for a
star located at a distance of
. Their estimate for
at
the time of BH formation is
. This signal would be detectable with LISA (see
Figure 18
).
|
![]() |
http://www.livingreviews.org/lrr-2003-2 |
© Max Planck Society and the author(s)
Problems/comments to |