List of Footnotes

1 Note that some stars in M = 100– 500M ⊙ mass range may not collapse at all, but rather explode in a pair-instability supernovae [136Jump To The Next Citation Point].
2 Currently, there are major discussions on the details of the drive in the convection above the proto neutron star. Instabilities can be driven by the post–bounce-shock entropy profile, neutrino heating, or the standing accretion shock instability (SASI). Similarly, debate surrounds the magnitude of the entropy/lepton driven convection within the proto neutron star.
3 Müller & Janka [208Jump To The Next Citation Point] did not specifically describe what they used, but any standard derivative discretization would work, e.g., ∂Φ ∕∂r = (Φk+1 − Φk −1)∕(rk+1 − rk−1).
4 The term “proto black hole” is used to describe the large (above 50M ⊙) core produced in the collapse of a massive star. Because of high entropies, the core does not collapse down to nuclear densities but collapses straight to a black hole, never producing a compact proto neutron star at nuclear densities.
5 Our models of these collapsing cores are also sensitive to the numerical modeling of the physics as well as uncertainties in the physics, both leading to the current variety in results between different simulations.
6 In accretion, Rayleigh–Taylor instabilities occur due to entropy gradients in the envelope set up by accretion [101Jump To The Next Citation Point]. In a supernova engine, where the proto neutron star is hot, neutrino heating can also produce entropy gradients [140Jump To The Next Citation Point].
7 These different supernova types are thought to differ primarily based on the envelope left on the star at collapse, not based on a different collapse mechanism: type II supernovae still have a hydrogen envelope, whereas type Ib/c SNe have lost their hydrogen, and for the type Ic SNe, most of its helium, envelopes.
8 Fryer & Young [116Jump To The Next Citation Point] have pointed out that current simulations are likely to be under-resolved and predict less vigorous convection than what should happen in nature: see also [41, 70]. In general, models of convective instabilities suggest that high resolution (above 5123 zones) across a convective cell is required to resolve convection accurately (e.g., [243]). If such constraints from the turbulence community are correct, the current grid-based simulations in core collapse (e.g., Marek & Janka [195Jump To The Next Citation Point]) remain under-resolved.
9 Neutrino emission is tied to electron spin, which is made anisotropic by strong magnetic fields [170, 120].
10 The possible exception is extremely massive stars above ∼ 300M ⊙. Fryer et al. [114Jump To The Next Citation Point, 217, 218] found that such stars may have enough entropy and angular momentum to alter the “bounce” density (and mass) considerably. These stars form proto black holes and collapse to a black hole shortly after the initial bounce with no supernova explosion whatsoever.
11 This “softening” of the equation of state has been studied for three decades [322].
12 Even the more pessimistic/realistic estimates of the rate of neutron-star mergers predict that such a detection will occur within a few years of operation.