The type of collapsing star and the explosion mechanism both determine what sources of GWs can occur in a stellar collapse. Before we discuss the different collapses individually and the detailed simulations, let’s discuss some of the basics behind stellar collapse and core-collapse supernovae. In this review, the term “stellar collapse” refers to any stellar system that collapses down to a neutron star or black hole. These stellar systems are produced by many different scenarios, but they can be loosely grouped into two categories:
For both classes of stellar collapse, the core is supported by a combination of thermal and degeneracy pressures. When the mass is too great for these pressures to support the star/core, it begins to compress and heat up. The compression leads to electron capture, neutrino emission, and ultimately, dissociation of the elements. Electron capture reduces the support from degeneracy pressure while Urca processes and dissociation of elements remove thermal support. With less support, the core compresses further, accelerating the rate of electron capture and dissociation, ultimately leading to a runaway implosion. This collapse continues until the matter reaches nuclear densities and the formation of a proto neutron star, or, in the case of massive stars above , a proto black hole 4.
In stellar collapse, it is the structure (density, entropy, rotation) of the core that determines whether a black hole or neutron star is formed5 For those stellar collapses that form neutron stars, the structure of the star just beyond the collapsed core is critical in defining the fate of the system. As the collapsed material reaches nuclear densities, nuclear forces and neutron degeneracy pressure halt the collapse and send a bounce shock out through the star. For nearly all systems, this bounce shock stalls. The shock can be revived by neutrinos leaked from the core depositing their energy above the proto neutron star. This is the basis of the neutrino-driven supernova mechanism [56, 19].
Over the past 15 years, scientists studying the supernova engine have focused on convection above the proto neutron star as a crucial piece of physics needed to unlock powerful supernova explosions (Figure 1). To drive an explosion, the convective engine must overcome the ram pressure at the top of the convective region caused by the infalling star [36, 140, 97, 156, 211]. The infalling material creates a cap or lid on top of the convective engine that must be blown off to produce an explosion. The strength of this “lid” is a function of the infalling accretion rate. Fryer  used this simple picture and the varying accretion rates of different stars (Figure 2) to determine the fate of massive stars. A supernova occurs if the engine can blow off the lid.
Using this simplified picture, Fryer and collaborators [97, 109, 136] were able to estimate the fate of massive stars. Fryer and Kalogera  outlined three fates for the star: neutron-star formation, black-hole formation through fallback after a weak supernova explosion, and prompt (or direct) black-hole formation where no supernova explosion is launched. The “prompt” or “direct” name has led to some confusion. These systems still initially form a proto neutron star. However, they are unable to throw off the infalling lid and thus they collapse down to a black hole without launching a supernova shock. Very massive (above ) stars might collapse directly to a black hole without the formation of a proto neutron star and without the bounce associated with this formation [115, 217, 218]. But rotation can allow the formation of a proto black hole . Because the binding energy of the star rises so quickly with stellar mass as the explosion energy goes down, the line dividing proto–neutron-star and black-hole formation can be determined fairly accurately (Figure 3). Of course, stellar winds will affect the stellar structure and also this fate (Figure 4).
One can take this one step further. If the energy of the explosion is stored in the convective region, one can estimate the maximum energy of the explosion based on the infalling accretion rate. The pressure in this convective region is 
This picture does not change even if the standing accretion shock instability contributes to the convective instabilities. Many of the recent simulations have focused on the SASI and it is worth reviewing how it effects the basic convective picture of supernovae. This instability was originally discussed in the context of white-dwarf and neutron-star accretion in scenarios under the assumption that the accretion envelope was stable to Rayleigh–Taylor instabilities . Asymmetries and strong Rayleigh–Taylor convection in actual models  coupled with the long predicted growth times for the SASI ( 3 s ) in neutron star accretion, led the accretion community to limit such instabilities to late times. Blondin et al.  introduced this instability into the core-collapse supernovae by setting up conditions that were stable to Rayleigh–Taylor instabilities to study the SASI. In this case, SASI dominates and, as Blondin et al.  found, can produce low-mode convection.
There are two dominant questions currently under discussion with regard to this instability. First, how dominant is SASI when entropy gradients do exist? Recall, the analytic estimates of the SASI were originally derived under the assumption that the envelope is Rayleigh–Taylor stable  and in neutron-star fallback; simulations argue that Rayleigh–Taylor instabilities dominate6. Low-mode convection is not a sure indicator of the SASI, as Rayleigh–Taylor instabilities also predict a growth toward low modes ). Second, is the SASI driven by an advective-acoustic instability or is it simply an acoustic instability? Blondin and collaborators, who first mentioned the possibility of advected vortices in the supernova context, later argued for an acoustic scenario . Answering these question has spawned a great deal of both simulation and analytic theory work [38, 39, 82, 81, 94, 93, 92, 116, 195, 196, 229, 264, 263, 164, 336].
Our analysis of explosion energy holds regardless of the dominant instability or the cause of that instability if the assumption that the energy is stored in the convective region remains true. In such a case, it is difficult to construct a strong explosion from a mechanism that has a long delay. But other sources of energy exist. The neutron star itself can store energy in oscillations to add to the explosion energy [40, 39]. Fallback may also drive additional explosions [101, 100]. We will study both of these in more detail below. This has repercussions on the explosion engine and the resultant GW mechanisms.
Alternative mechanisms for the core-collapse supernova mechanism exist, most notably the magnetic-field mechanism [175, 299, 2, 3, 6, 35, 61, 62, 265]. The idea here is that magnetic fields strengthened in the collapse and subsequent convection (especially if the star is rotating rapidly) will drive an explosion. How the magnetic fields affect the GW signal will depend on how and when the magnetic field develops. For most magnetic-field generation schemes, the field grows after the bounce of the core, and signal from the collapse/bounce phase (and indeed some of the convective phase) from supernovae will be the same whether the mechanism is this alternate magnetic-field driven mechanism or the standard convective engine. For some magnetar models, the magnetic field develops after the launch of a weak, convectively-driven explosion . In such a case, the GW signal will be identical to the convective-driven mechanism.
Finally, if the core collapses to a black hole and the infalling material has enough angular momentum to prevent its infall directly into the event horizon, explosions might be produced. An accretion disk forms and, either through the wind-up of magnetic fields or neutrino annihilation above the disk, an explosion may result. This type of explosion has been posited as the engine behind GRBs [219, 333]. The association of GRBs with supernova-like outbursts has argued strongly for a massive-star origin for at least long-duration GRBs [335, 117].
In this section, we review the various progenitors of core collapse, describing their physical properties, its occurrence rate, evolution, and likely GW emission mechanisms. Rather than follow the order of progenitor mass, we first discuss the fate of stars in the range, the likely progenitors for core-collapse supernovae. These are the most-studied gravitational-collapse systems. We then discuss the AIC of white dwarfs and the very similar collapse of stars in the range. We then move upwards in mass studying massive, very massive () and supermassive () stars.
Living Rev. Relativity 14, (2011), 1
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