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2.3 GW emission mechanisms

UpdateJump To The Next Update Information During AIC, emission of GWs will occur if the infall of matter is aspherical. The convective time is likely to be brief, so it is unlikely that post-bounce convection will produce GWs. However, GWs will also be produced if the collapsing star or neutron star remnant develops rotational or pulsational instabilities [226227235Jump To The Next Citation Point252254]. These include global rotational mode, r-mode, f-mode, and fragmentation instabilities.

Global rotational instabilities in fluids arise from non-axisymmetric modes ±imf e, where m = 2 is known as the “bar-mode” [239Jump To The Next Citation Point6Jump To The Next Citation Point]. It is convenient to parameterize a system’s susceptibility to these modes by the stability parameter b = Trot/ |W |. Here, Trot is the rotational kinetic energy and W is the gravitational potential energy. Dynamical rotational instabilities, driven by Newtonian hydrodynamics and gravity, develop on the order of the rotation period of the object. For the uniform-density, incompressible, uniformly rotating MacLaurin spheroids, the dynamical bar-mode instability sets in at bd ~~ 0.27. For differentially rotating fluids with a polytropic equation of state, numerical simulations have determined that the stability limit bd ~~ 0.27 is valid for initial angular momentum distributions that are similar to those of MacLaurin spheroids [221Jump To The Next Citation Point63162125192Jump To The Next Citation Point118248]. If the object has an off-center density maximum, bd could be as low as 0.10 [247Jump To The Next Citation Point260Jump To The Next Citation Point192Jump To The Next Citation Point49Jump To The Next Citation Point]. General relativity may enhance the dynamical bar-mode instability by slightly reducing bd [223209]. Secular rotational instabilities are driven by dissipative processes such as gravitational radiation reaction and viscosity. When this type of instability arises, it develops on the timescale of the relevant dissipative mechanism, which can be much longer than the rotation period (e.g., [225]. The secular bar-mode instability limit for MacLaurin spheroids is bs ~~ 0.14.

In an attempt to reduce these high rotation requirements, there has been increasing work studying bar-mode instabilities driven by dynamical sheer in differentially rotating neutron stars. Sheer instabilities excite the co-rotating f-mode. If viscous forces don’t damp this instability altogether, it is possible that this instability can occur for bd-values as low as ~ 0.01 for stars with a large degree of differential rotation.

In rotating stars, gravitational radiation reaction drives the r-modes toward unstable growth [577]. In hot, rapidly rotating neutron stars, this instability may not be suppressed by internal dissipative mechanisms (such as viscosity and magnetic fields) [152]. If not limited, the dimensionless amplitude a of the dominant (m = 2) r-mode will grow to order unity within ten minutes of the formation of a neutron star rotating with a millisecond period. The emitted GWs carry away angular momentum, and will cause the newly formed neutron star to spin down over time. The spindown timescale and the strength of the GWs themselves are directly dependent on the maximum value amax to which the amplitude is allowed to grow [153Jump To The Next Citation Point154Jump To The Next Citation Point]. Originally, it was thought that amax ~ 1. Later work indicated that amax may be > 3 [153Jump To The Next Citation Point236213154Jump To The Next Citation Point]. Some research suggests that magnetic fields, hyperon cooling, and hyperon bulk viscosity may limit the growth of the r-mode instability, even in nascent neutron stars [1361352012021541511026] (significant uncertainties remain regarding the efficacy of these dissipative mechanisms). Furthermore, a study of a simple barotropic neutron star model by Arras et al. [9] suggests that multimode couplings could limit amax to values « 1. If amax is indeed « 1 (see also [97]),UpdateJump To The Next Update Information GW emission from r-modes in collapsed remnants is likely undetectable. For the sake of completeness, an analysis of GW emission from r-modes (which assumes amax ~ 1) is presented in the remainder of this paper. However, because it is quite doubtful that amax is sizeable, r-mode sources are omitted from figures comparing source strengths and detector sensitivities and from discussions of likely detectable sources in the concluding section.

There is some numerical evidence that a collapsing star may fragment into two or more orbiting clumps [96Jump To The Next Citation Point]. If this does indeed occur, the orbiting fragments would be a strong GW source.

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