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3.1 Collapse scenario

UpdateJump To The Next Update Information Stars with mass greater than ~ 8- 10 M o . will undergo core collapse at the end of their thermonuclear burning life cycles. The gravitational energy released during the collapse is believed to be the power source behind a large subset of supernovae (for reviews, see [8Jump To The Next Citation Point23Jump To The Next Citation Point7981143]). Core collapse SNe include Types II and Ib/Ic. SNe Ib/Ic are distinguished from Type II SNe by the absence of hydrogen in their spectra. SNe Ib/Ic are thought to result from the collapse of the cores of massive stars that have lost their hydrogen envelopes (and possibly part of their helium envelopes) by stellar winds or by mass transfer. The SN Ib/Ic progenitors that lose their outer envelopes via stellar winds are known as Wolf-Rayet stars and have initial masses >~~ 30Mo. [108Jump To The Next Citation Point266]; those that undergo mass loss via mass transfer in binaries can have progenitor masses as low as 12 Mo . [194].

If the stellar mass is less than ~ 20- 25Mo. [78Jump To The Next Citation Point89Jump To The Next Citation Point86Jump To The Next Citation Point108Jump To The Next Citation Point], 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 40 -50 Mo . are thought to collapse directly to black holes without producing a supernova explosion [78Jump To The Next Citation Point108Jump To The Next Citation Point]. 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 [262Jump To The Next Citation Point]. 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 20 Mo . and are likely to produce supernovae and, at least initially, neutron stars, not black holes [89Jump To The Next Citation Point108]. If the progenitor’s mass is in the range 20 - 25 <~ M <~ 40 -50 Mo ., the entire star is not ejected in the SN explosion. More than 2Mo . 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 40- 50 Mo . lower limit for direct black hole formation) are uncertain because the progenitor mass dependence of the neutrino explosion mechanism (see below) is unknown [103178].

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 [71Jump To The Next Citation Point]. 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 [71Jump To The Next Citation Point]. 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 [71Jump To The Next Citation Point170Jump To The Next Citation Point]. The maximum velocity of the outer regions of the core reaches ~ 7 × 104 km s-1. It takes just 1 s for an earth-sized core to collapse to a radius of 50 km [8Jump To The Next Citation Point].

The inward collapse of the core is halted by nuclear forces when its central density rc is 2 - 10 times the density of nuclear material [13Jump To The Next Citation Point12]. 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 E > 1051 erg (supplied by the binding energy of the nascent neutron star), then the remainder of the star can be ejected in about 20 ms [8Jump To The Next Citation Point]. 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 (M <~ 1.35Mo., derived from a very low mass progenitor) and a large portion of the collapse proceeds homologously [23Jump To The Next Citation Point173Jump To The Next Citation Point]. Inclusion of general relativistic effects in collapse simulations can increase the success of the prompt mechanism in some cases [13237].

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 100 -200 km. 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 [302925724259258]. However, their 1-dimensional simulations and those of others had difficulty producing energies high enough to match observations [53Jump To The Next Citation Point36131]. 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 [112Jump To The Next Citation Point].

Observations of SN 1987a show that significant mixing occurred during this supernovae (see Arnett et al. [8Jump To The Next Citation Point] 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 10 - 100 ms after bounce) due to the presence of negative lepton and energy gradients [173Jump To The Next Citation Point]. This has been confirmed by both 2D and 3D simulations [11242132173Jump To The Next Citation Point16778Jump To The Next Citation Point83Jump To The Next Citation Point128130Jump To The Next Citation Point197Jump To The Next Citation Point91Jump To The Next Citation Point8526Jump To The Next Citation Point39Jump To The Next Citation Point92Jump To The Next Citation Point80Jump To The Next Citation Point212Jump To The Next Citation Point253]. 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 [173Jump To The Next Citation Point]. The “hot bubble” region above the surface of the neutron star also has been shown to be convectively unstable [53235491Jump To The Next Citation Point]. 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 [168130Jump To The Next Citation Point197Jump To The Next Citation Point39] and this problem is far from solved. But progress not only in neutrino transport, but in understanding new features in the convection [26Jump To The Next Citation Point43Jump To The Next Citation Point75] some including the effect of magnetic fields is leading to new ideas about the supernova mechanism [3Jump To The Next Citation Point]. 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 [83Jump To The Next Citation Point116Jump To The Next Citation Point122Jump To The Next Citation Point121Jump To The Next Citation Point] 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 [130Jump To The Next Citation Point]. 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 [172553Jump To The Next Citation Point]. 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 [122121], 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 [26Jump To The Next Citation Point212Jump To The Next Citation Point43Jump To The Next Citation Point] to rotation(e.g.,[83Jump To The Next Citation Point]) to asymmetric collapse [41Jump To The Next Citation Point80Jump To The Next Citation Point]. 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 [83Jump To The Next Citation Point], implicitly assuming that the asymmetries are driving by rotation.

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