Whether this supernova explosion is produced by the burning of this CO white dwarf into nickel (type Ia Supernova) or by the “Accretion Induced Collapse” (AIC) of the white dwarf down to a neutron star (making these objects relevant to this review) depends upon the accretion rate onto this white dwarf. Nomoto & Kondo  summarized the fate of an accreting white dwarf presented as a function of its initial mass and the accretion rate. When material accretes, it ignites. And the fate of the accreting white dwarf both depends on this ignition process (does the accreting material explode as a nova, ejecting matter, or does it burn less explosively, accreting onto the white dwarf) and also the ultimate ignition of the accreting white dwarf itself. Heat inflow ignites white dwarfs with masses below about at low densities, causing thermonuclear explosions. AICs are only produced in stars with masses below in one of two categories:
At this time, stellar modelers do not expect that Nature produces that many CO white dwarfs with initial masses above [287, 241]. The most massive white dwarfs are probably formed as ONe white dwarfs from stars above – see Section 3.3. So this class of AIC formation is likely to be rare. But high accretion rates are expected in a very important, and perhaps common, event: the merger of two white dwarfs (generally a He or CO white dwarf merging with a CO white dwarf). Most current simulations predict that this merger process is very rapid, arguing that the more-massive white dwarf will tidally disrupt and accrete its companion in a very short time. Such a rapid process suggests high accretion rates, arguing that most mergers produce AICs. However, there are a number of uncertainties in such calculations and no other mechanism produces a sufficiently high rate to explain the occurrence of type Ia supernovae, so we cannot rule out that these mergers produce thermonuclear supernovae instead of AICs.
Thus far, no outburst from the AIC of a white dwarf has been observed. Given that the outburst is expected to be very dim because the shock heating is negligible and the predicted 56Ni yields are all low ( [102, 161, 61]), the lack of observed AICs does not place firm upper limits on the AIC rate.
Theoretical estimates of the rate of AICs are also quite uncertain. If we accept the conclusions of Nomoto & Kondo , the AIC rate may be well above the type Ia supernova rate ( 10–2 y–1 in a Milky-Way–sized galaxy). This result depends upon a number of assumptions in the accretion process in these binary systems and the true rate of AICs could be many orders of magnitude lower than this value. Studies of binary mass transfer [198, 199, 16, 270, 126, 203, 72, 342] and white dwarf accretion  are both becoming more accurate. As they are coupled with stellar evolution models of these systems, our understanding of the rate of AICs should become more accurate as well.
Alternatively, one can use observed features of AIC explosions to constrain the AIC rate. Fryer  argued that the neutron-rich ejecta from an AIC limits their rate to 10–4 y–1. More recent results, which eject a smaller fraction of neutron-rich material, may loosen this limit by 1 order of magnitude [161, 61].
As a white dwarf accretes material up to the Chandrasekhar limit, it will begin to compress. As it does, it heats up and, in principle, can ignite explosive burning. But the URCA process cooling (electron capture followed by a beta decay, which leads to the emission of two neutrinos, which escape and cool the system, see Couch & Arnett  for a summary) on nuclei can allow the white dwarf to cool enough that the burning does not generate enough energy to disrupt the white dwarf. When the white dwarf becomes sufficiently dense, the material is dissociated and the collapse proceeds in a very similar manner to that of a “standard” core-collapse supernova. The core proceeds through a runaway collapse that ends when nuclear forces and neutron degeneracy pressure halt the collapse, causing a “bounce”. Especially in the case of a white dwarf/white dwarf merger, the accretion phase just prior to collapse is likely to spin up the core and these are almost certainly the most rapidly-rotating core-collapse models.
The structure of AIC cores is very similar to the structure of low-mass stars, and a large set of simulations of both have been conducted in the past few decades [142, 11, 334, 102, 63, 61]. The latest simulations [63, 61] use progenitors including rotation [341, 339]. The shock stalls in AICs, just as in standard core-collapse supernovae, but there is no stellar envelope with which to prevent further accretion and the explosion is quickly revived (hence there will be little convective overturn). The cooling neutron star could well develop instabilities (both to convection and to bar modes). If magnetic fields develop, additional outflows can occur.
Due to the lack of convection, AICs may only have a subset of the GW sources that we see in core-collapse supernovae. However, AICs have the potential to be much faster rotating, which may make them strong GW sources.
Bounce: The potentially high-rotation in AICs mean that the bounce signal in these systems could be quite large. The primary source of this emission is the rapidly changing quadrupole moment in the matter as the asymmetries evolve (Section 4.1), although we cannot rule out a strong signal from asymmetric neutrino emission (Section 4.4).
In the Neutron Star: Convection in the cooling neutron star could produce GW emission. But more likely, due to the strong rotation, bar-mode instabilities can become important in these collapsed systems (Section 4.3).
Living Rev. Relativity 14, (2011), 1
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