If the stellar mass is less than [78
, 89
, 86
, 108
], it is believed that the star will produce
a strong supernova, leaving behind a neutron star remnant. This section studies the gravitational waves
produced during the stellar collapse and supernova explosion mechanism. Without mass loss, stars above
are thought to collapse directly to black holes without producing a supernova
explosion [78
, 108
]. If rotating, the collapsing stars may form an accretion disk around their black hole
core. One of the leading models for long-duration gamma-ray bursts (the “collapsar” engine) argues that the
energy extracted from the disk or the black hole spin can drive a relativistic jet [262
]. We will discuss these
collapsars and their resultant gravitational waves further in Section 4. However, if we include the
effects of winds, these stars lose much of their mass through winds during their nuclear-burning
lifetimes. Their fate will be closer to that of a
and are likely to produce supernovae and,
at least initially, neutron stars, not black holes [89
, 108]. If the progenitor’s mass is in the
range
, the entire star is not ejected in the SN explosion. More
than
will fall back onto the nascent neutron star and lead to black hole formation.
These objects also produce a variant of the collapsar engine for gamma-ray bursts (GRBs).
Although the discussion of GW production from the collapse and supernova explosion phase will be
discussed in this section, the GWs produced during the fallback and black hole accretion disk phase
will be discussed in Section 4. Note that the limits on the progenitor masses quoted in this
paragraph (especially the
lower limit for direct black hole formation) are uncertain
because the progenitor mass dependence of the neutrino explosion mechanism (see below) is
unknown [103, 178].
The massive iron cores of SN II/Ib/Ic progenitors are supported by both thermal and electron
degeneracy pressures. The density and temperature of such a core will eventually rise, due
to the build up of matter consumed by thermonuclear burning, to the point where electron
capture and photodissociation of nuclei begin. Dissociation lowers the photon and electron
temperatures and thereby reduces the core’s thermal support [71]. Electron capture reduces the
electron degeneracy pressure. One or both of these processes will trigger the collapse of the
core. The relative importance of dissociation and electron capture in instigating collapse is
determined by the mass of the star [71
]. The more massive the core, the bigger is the role played by
dissociation.
Approximately 70% of the inner portion of the core collapses homologously and subsonically. The outer
core collapses at supersonic speeds [71, 170
]. The maximum velocity of the outer regions of the core
reaches
. It takes just
for an earth-sized core to collapse to a radius of
[8
].
The inward collapse of the core is halted by nuclear forces when its central density is 2 - 10 times
the density of nuclear material [13
, 12]. The core overshoots its equilibrium position and bounces. A shock
wave is formed when the supersonically infalling outer layers hit the rebounding inner core. If the inner core
pushes the shock outwards with energy
(supplied by the binding energy of the nascent
neutron star), then the remainder of the star can be ejected in about
[8
]. This so-called “prompt
explosion” mechanism has been succesful numerically only when a very soft supra-nuclear equation of state
is used in conjunction with a relatively small core (
, derived from a very low mass
progenitor) and a large portion of the collapse proceeds homologously [23
, 173
]. Inclusion of general
relativistic effects in collapse simulations can increase the success of the prompt mechanism in some
cases [13, 237].
Both dissociation of nuclei and electron capture can reduce the ejection energy, causing the prompt
mechanism to fail. The shock will then stall at a radius in the range . Colgate and
White [55] suggested that energy from neutrinos emitted by the collapsed core could revive the stalled
shock. (See Burrows and Thompson [44] for a review of core collapse neutrino processes.) However, their
simulations did not include the physics necessary to accurately model this “delayed explosion” mechanism.
Wilson and collaborators were the first to perform collapse simulations with successful delayed
ejections [30, 29, 257, 24, 259, 258]. However, their 1-dimensional simulations and those of others had
difficulty producing energies high enough to match observations [53
, 36, 131]. It was not until Herant and
collaborators modelled the collapse and bounce phase with neutrino-transport in 2-dimensions that
convection began to be accepted as a necessary puzzle piece in understanding the supernova explosion
mechanism [112
].
Observations of SN 1987a show that significant mixing occurred during this supernovae (see
Arnett et al. [8] for a review). Such mixing can be attributed to nonradial motion resulting from
fluid instabilities. Convective instabilities play a significant role in the current picture of the
delayed explosion mechanism. The outer regions of the nascent neutron star are convectively
unstable after the shock stalls (for an interval of
after bounce) due to the presence
of negative lepton and energy gradients [173
]. This has been confirmed by both 2D and 3D
simulations [112, 42, 132, 173
, 167, 78
, 83
, 128, 130
, 197
, 91
, 85, 26
, 39
, 92
, 80
, 212
, 253].
Convective motion is more effective at transporting neutrinos out of the proto-neutron star than is diffusion.
Less than 10% of the neutrinos emitted by the neutron star need to be absorbed and converted to kinetic
energy for the shock to be revived [173
]. The “hot bubble” region above the surface of the neutron star also
has been shown to be convectively unstable [53, 23, 54, 91
]. Janka and Müller have demonstrated that
convection in this region only aids the explosion if the neutrino luminosity is in a narrow region [133]. Some
simulations that include advanced neutrino transport methods have cast doubt on the ability of convection
to ensure the success of the delayed explosion mechanism [168, 130
, 197
, 39] and this problem is far from
solved. But progress not only in neutrino transport, but in understanding new features in the
convection [26
, 43
, 75] some including the effect of magnetic fields is leading to new ideas about the
supernova mechanism [3
]. We will discuss the effects of this new physics on the GW signal at the end of
this section.
In addition to the mixing seen in SN 1987a, observations of (i) polarization in the spectra of several core
collapse SNe, (ii) jets in the Cas A remnant, and (iii) kicks in neutron stars suggest that supernovae are
inherently aspherical (see [8, 3, 116
, 122
, 121
] and references therein). Note that these asphericities could
originate in the central explosion mechanism itself and/or the mechanism(s) for energy transfer between the
core and ejecta [130
]. If due to the mechanism itself, these asymmetries may provide clues into the true
engine behind supernova explosions. Already, the observations partly motivated the multi-dimensional
studies of convection in the delayed explosion mechanism as well as work on magnetic field
engines [17, 255, 3
]. Observations have also driven the work on jets and collapsars 4. Höflich et
al. [116] have argued that low velocity jets stalled inside SN envelopes can account for the
observed asymmetries. Hungerford and collaborators have argued that the asymmetries required
are not so extreme [122, 121], arguments that have now been confirmed [138]. This debate is
crucial to our understanding of the supernova mechanism. If jets are required, magnetic field
mechanisms are the likely source of the asymmetry. If jets are not required, the convective engine can
produce asymmetries via a number of channels from low mode convection [26
, 212
, 43
] to
rotation(e.g.,[83
]) to asymmetric collapse [41
, 80
]. Most GW emission calculations of stellar collapse
have focused on the collapse of rotating, massive stars with rotation periods at least as high as
those assumed by Fryer & Heger [83
], implicitly assuming that the asymmetries are driving by
rotation.
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