List of Figures

View Image Figure 1:
Diagram of the convective engine for supernova explosions.
View Image Figure 2:
Accretion rates of different mass stars. The more massive stars have higher accretion rates and are, hence, harder to explode. Figure 1 from Fryer [97].
View Image Figure 3:
Supernova explosion energies (dotted lines) based on simulation (solid circles) and observation (solid dot of SN 1987A) as a function of progenitor mass. The binding energy of the envelop (material beyond the 3M ⊙ core) rises dramatically at 20M ⊙ (solid line). This fast rise with mass and the decline based on explosion simulations of the energies from the convective engine mean that even if the errors in these estimates are large, the likely dividing line between neutron star and black hole formation can be determined fairly accurately. Figure 1 of Fryer & Kalogera [109].
View Image Figure 4:
Fate of massive stars as a function of mass and metallicity. Figure 1 from Heger et al. [136].
View Image Figure 5:
Explosion energy as a function of launch time of the supernova shock for four differently-massed stars assuming the energy is stored in the convective region. The energy is then limited by the ram pressure of the infalling stellar material. Note that it is difficult to make a strong explosion after a long delay. For more details, see [99] and Fryer et al. (in preparation).
View Image Figure 6:
Left-hand panel: Evolution of the core-collapse supernova rate with redshift. The dashed line shows the intrinsic total supernova rate derived from the star formation density. The supernova rate that can be recovered by optical searches is shown in light gray, and is compared with the data points from Cappellaro et al. [44] (squares) and Dahlen et al. [59] (circles). Right-hand panel: Fraction of CC SNe that are not present in the optical and near-IR searches as a function of redshift. (Figure 2 of Mannucci et al. [193]; used with permission.)
View Image Figure 7:
Six snapshots in time of the convection in the collapse of a 23M ⊙ star. The plot displays slices of the data in the x-z plane. The vectors denote direction and magnitude of the particle motion. The colors denote entropy. The convection is far from symmetric, but we do not get the single-sided downflows seen in many recent 2-dimensional calculations. Figure 4 of [116].
View Image Figure 8:
Images of the gas entropy (red is higher than the equilibrium value, blue is lower) illustrate the instability of a spherical standing accretion shock. This model has γ = 4∕3 and is perturbed by placing overdense rings into the infalling preshock gas. The shock is kept stalled by using a cooling function. Note that with the scaling for a realistic supernova model, the last image on the right corresponds to 300 ms. These simulations are axisymmetric, forcing a reflection symmetry about the vertical axis. (Figure 6 of [21]; used with permission.)
View Image Figure 9:
Mean angular momenta vs. mass for both merged stars just after the merger and at collapse. The thick solid line at the top of the graph is the angular momentum just after merger. Dotted lines correspond to different mappings of the 3-dimensional merger calculation into the 1-dimensional stellar evolution code. We also plotted the angular momentum for material at the innermost stable circular orbit for a non-rotating black hole vs. mass (thin solid line). Figure 5 of [104].
View Image Figure 10:
Type I waveform (quadrupole amplitude AE2 20 as a function of time) from one of Zwerger and Müller’s [350] simulations of a collapsing polytrope. The vertical dotted line marks the time at which the first bounce occurred. (Figure 5d of [350]; used with permission.)
View Image Figure 11:
Type II waveform (quadrupole amplitude AE2 20 as a function of time) from one of Zwerger and Müller’s [350] simulations of a collapsing polytrope. The vertical dotted line marks the time at which bounce occurred. (Figure 5a of [350]; used with permission.)
View Image Figure 12:
Type III waveform (quadrupole amplitude E2 A 20 as a function of time) from one of Zwerger and Müller’s [350] simulations of a collapsing polytrope. The vertical dotted line marks the time at which bounce occurred. (Figure 5e of [350]; used with permission).
Watch/download Movie Figure 13: (mpeg-Movie; 11557 KB)
Movie: The evolution of the regular collapse model A3B2G4 of Dimmelmeier et al. [67]. The left frame contains the 2D evolution of the logarithmic density. The upper and lower right frames display the evolutions of the gravitational wave amplitude and the maximum density, respectively.
Watch/download Movie Figure 14: (mpeg-Movie; 10308 KB)
Movie: Same as Movie 13, but for rapid collapse model A3B2G5 of Dimmelmeier et al. [67].
Watch/download Movie Figure 15: (mpeg-Movie; 12174 KB)
Movie: Same as Movie 13, but for multiple collapse model A2B4G1 of Dimmelmeier et al. [67].
Watch/download Movie Figure 16: (mpeg-Movie; 8722 KB)
Movie: Same as Movie 13, but for rapid, differentially-rotating collapse model A4B5G5 of Dimmelmeier et al. [67].
View Image Figure 17:
The gravitational waveform (including separate matter and neutrino contributions) from the collapse simulations of Burrows and Hayes [37]. The curves plot the GW amplitude of the source as a function of time. (Figure 3 of [37]; used with permission.)
View Image Figure 18:
The gravitational waveform for matter contributions from the asymmetric collapse simulations of Fryer et al. [107]. The curves plot the GW amplitude of the source as a function of time. (Figure 3 of [107]; used with permission.)
View Image Figure 19:
Convective instabilities inside the proto neutron star in the 2D simulation of Müller and Janka [208]. The evolutions of the temperature (left panels) and logarithmic density (right panels) distributions are shown for the radial region 15 – 95 km. The upper and lower panels correspond to times 12 and 21 ms, respectively, after the start of the simulation. The temperature values range from 2.5 × 1010 to 1.8 × 1011 K. The values of the logarithm of the density range from 10.5 to 13.3 g cm–3. The temperature and density both increase as the colors change from blue to green, yellow, and red. (Figure 7 of [208]; used with permission.)
View Image Figure 20:
Quadrupole amplitudes AE220 [cm] from convective instabilities in various models of [208]. The upper left panel is the amplitude from a 2D simulation of proto neutron star convection. The other three panels are amplitudes from 2D simulations of hot bubble convection. The imposed neutrino flux in the hot bubble simulations increases from the top right model through the bottom right model. (Figure 18 of [208]; used with permission.)
Watch/download Movie Figure 21: (gif-Movie; 15979 KB)
Movie: Isosurface of material with radial velocities of 1000 km s–1 for three different simulation resolutions. The isosurface outlines the outward moving convective bubbles. The open spaces mark the downflows. Note that the upwelling bubbles are large and have very similar size scales to the two-dimensional simulations. From Fryer & Warren [112].
Watch/download Movie Figure 22: (avi-Movie; 4081 KB)
Movie: The oscillation of the proto neutron star caused by downstreams in the SASI-induced convective region above the proto neutron star. From Burrows et al. [40].
View Image Figure 23:
A comparison between the GW amplitude h(f) for various sources and the LIGO-II sensitivity curve based on the analytic estimates from FHH [106]. See the text for details regarding the computations of h. The SNe sources at 10 Mpc; and the Population III sources at a luminosity distance of ∼ 50 Gpc. Secular bar-mode sources are identified with an (s), dynamical bar modes with a (d). This assumes strong bar modes exist, which has not been demonstrated robustly.
Watch/download Movie Figure 24: (mov-Movie; 9566 KB)
Movie: Evolution of a secular bar instability, see Ou et al. [236] for details.
View Image Figure 25:
β and instability growth time versus mass in the proto black hole formed in the collapse of a 300M ⊙ star at bounce (dotted line) and just prior to black-hole formation (solid line). Figure 10 of [115].
View Image Figure 26:
The GW signal from convection in a proto neutron star. The top panel shows the GW quadrupole amplitude AE220 as a function of time for both the convective mass flow (thick line) and anisotropic neutrino emission (thin line). The combined spectral energy distribution of the quadrupole radiation for both sources is shown in the middle figure, with just the neutrino component alone in the bottom panel. Note that although the quadrupole amplitude for the neutrino emission is much higher, it varies slower than the mass motions. Hence, it only dominates the signal at low frequencies. (Figures from [209]; used with permission.)
View Image Figure 27:
Detection limits of TAMA, first LIGO, advanced LIGO, and Large-scale Cryogenic Gravitational wave Telescope (LCGT) with the expected GW spectrum obtained from the numerical simulations. The left panel shows the GW spectrum contributed from neutrinos (solid) and from the matter (dashed) in a rotating model with − 1 Ω = 4 rad s imposed initially on a 15M ⊙ progenitor model. In the right panel, the open circles and the pluses represent the amplitudes of hν,eq with the characteristic frequencies of νeq for the models with the cylindrical and the shell-type rotation profiles, respectively. Under the frequency of ν eq, the GWs from the neutrinos dominate over those from the matter contributions. From the panel, it is seen that the GWs from neutrinos dominate over the ones from the matter in a lower frequency (f ≤ 100 Hz). Note that the source is assumed to be located at the distance of 10 kpc. (Figures from [166]; used with permission.)
View Image Figure 28:
The gravitational waveform for neutrino contributions from the asymmetric collapse simulations of Fryer et al. [107]. The curves plot the product of the GW amplitude to the source as a function of time. (Figures from [107]; used with permission.)
View Image Figure 29:
The matter density in the equatorial plane of the rapidly-rotating collapsar simulation, 0.44 s after collapse. The spiral wave forms near the center of the collapsar 0.29 s after collapse and moves outward through the star. (Figure 4 of [250]; used with permission.)
View Image Figure 30:
A comparison between the GW amplitude h (f) for various sources and the LISA noise curve. See the text for details regarding the computations of h. The SMS sources are assumed to have masses of ∼ 106M ⊙ and be located at a luminosity distance of 50 Gpc. The bar-mode source is a dynamical bar mode.
View Image Figure 31:
Meridional plane density contours from the SMS collapse simulation of Saijo, Baumgarte, Shapiro, and Shibata [259]. The contour lines denote densities ρ = ρc × d(1−i∕16), where ρc is the central density. The frames are plotted at (t∕tD, ρc, d) = (a) (5.0628 × 10–4, 8.254 × 10–9, 10–7), (b) (2.50259, 1.225 × 10–4, 10–5), (c) (2.05360, 8.328 × 10–3, 5.585 × 10–7), (d) (2.50405, 3.425 × 10–2, 1.357 × 10–7). Here t, tD, and M0 are the time, dynamical time (∘ --3---- = R e∕M, where Re is the initial equatorial radius and M is the mass), and rest mass. (Figure 15 of [259]; used with permission.)
View Image Figure 32:
GW signals from matter motions in the bounce and convection phases of stellar collapse. These limits and estimates have not changed from the previous publication of this Living Reviews article [111]. Uncertainties in the estimates still allow variations within an order of magnitude of these results. The LIGO and advanced LIGO sensitivities are included for reference. The limits are not upper limits of a single signal, but upper limits of all possible signals (varying the conditions of the collapse). This figure does not represent a single signal.
View Image Figure 33:
GW signals from asymmetric neutrino emission in the bounce and convection phases of stellar collapse. These limits and estimates have not changed from the previous publication of this Living Reviews article [111]. Uncertainties in the estimates still allow variations within an order of magnitude of these results. The LIGO and advanced LIGO sensitivities are included for reference. The limits are not upper limits of a single signal, but upper limits of all possible signals (varying the conditions of the collapse). This figure does not represent a single signal.