3.4 Core-collapse supernovae from stars above 20 solar masses: Massive star collapse

In the absence of winds, as the stellar mass approaches 20M ⊙, the explosion energy predicted by engine models decreases while the binding energy of these stars increases (recall Figure 3View Image). As this happens, more and more material from the stellar mantle falls back onto the newly formed neutron star. Roughly at 20M ⊙, so much material falls back that the mass of the compact remnant exceeds the maximum neutron star mass and ultimately collapses to form a black hole. However, note that Heger et al. [136] argue that, at solar metalliciety, many massive stars lose so much mass in their winds that they will form neutron stars, not black holes (recall Figure 4View Image).

The formation of a black hole opens up an entirely new set of physics in the stellar collapse. Material continues to accrete onto the black hole after its formation. The angular momentum of material in a star tends to increase with increasing radius of the star (Figure 9View Image). For rapidly-rotating stars, the angular momentum of the accreting material will ultimately be sufficiently high to hang up in a disk. Astronomers have argued that energy generation in this accretion disk (either through magnetic field generation or neutrino emission) may drive Gamma-Ray Bursts [242, 189, 244, 250Jump To The Next Citation Point]. As we shall see below, these black hole accretion disks also open up new possibilities for GW emission.

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 [104Jump To The Next Citation Point].

3.4.1 Massive star collapse: Evolution

The evolution of a massive star collapse begins identically to lesser mass stars. In general, it is likely that the core bounces just as in normal core-collapse supernovae [90, 97Jump To The Next Citation Point, 296, 295].10 The bounce shock stalls as in normal supernovae. The primary exception are the low metallicity (< 10 −4Z⊙) stars in the 140 – 260M ⊙ range that produce pair-instability supernovae [114Jump To The Next Citation Point]. These stars explode completely leaving no remnant behind. We will ignore these stars in the rest of our discussion.

These massive stars are much less likely to revive the stalled shock. Although the region above the proto neutron star is convective, the convective engine is unable to quickly drive an explosion (recall Section 3.1). In such cases, low-mode instabilities (e.g., SASI, see Section 3.1.2) are more likely to dominate the convection. If the shock is revived at all, the explosion is weaker than normal supernovae. Considerable material begins to fall back within 1 – 2 s of the explosion with accretion rates nearly at −1 1M ⊙ s [190, 347, 100Jump To The Next Citation Point]. This accretion may lead to additional convection and possible further outbursts [105, 100]. With both the SASI and the accretion convection, these stars are likely to have more asymmetric convection than normal core-collapse supernovae (beneficial for GW emission).

Ultimately, the mass accretion causes the proto neutron star to collapse down to a black hole [55, 54]. After the collapse, a disk forms around the black hole if the star’s angular momentum is sufficiently high. Magnetic dynamos in the disk, or neutrino emission, might lead to an additional explosion. Indeed, this is the mechanism behind the collapsar GRB [219, 333].

Massive stars might avoid the collapse to a black hole if strong magnetar-like fields can be produced in the dense environment produced when the above engine fails [35, 175, 2Jump To The Next Citation Point, 3, 6, 329].

3.4.2 Rates of massive star collapse

The rate of massive star collapse can be determined by the same method used to determine the normal supernova rate: multiplying the star formation rate times the fraction of stars above ∼ 20M ⊙. The uncertainties in such a calculation lie in determining the lower limit for black hole formation (determined by theory, and bolstered by observations), the power in the initial mass function and the star formation rate (both beyond theory at this point). As with core collapse, the latter two quantities dominate the errors in this rate estimate. Fryer & Kalogera [109] argue that between 10 – 40% of all massive stars above 10M ⊙ (those that are likely to form bright core-collapse supernovae and contribute to the observed supernova rate) form black holes. This answer depends primarily on their prescription for winds and the initial mass function. The fraction is likely to be lower at low-redshift but increase with increasing redshift as winds remove less mass from the star, allowing more stars to form black holes.

Unfortunately, there are no direct observational estimates for the black-hole–formation rate. If we assume this collapse is the primary scenario for the production of long-duration GRBs we can estimate a lower limit for the black-hole–formation rate (and estimate the formation rate of fast-rotating systems). This value is roughly 0.1 – 0.01% the total core-collapse supernova rate.

3.4.3 Gravitational waves from massive stars

For most massive stars, the GW signal will be similar to normal core-collapse supernovae. Massive stars above 300M ⊙ are likely to have much stronger signals than normal core-collapse supernovae, but they will only occur at high redshift.

Bounce: For the lower-mass range of these stars, the signal is unlikely to be demonstrably different than normal core-collapse supernovae.

Post-Bounce and Convection: Because the convective phase in these massive stars persists longer than normal supernovae, it can develop strong low-mode activity. Such convective cycles produce the strongest GWs, so we might expect stronger GWs from this convective phase for massive stars than for any other stellar collapse scenario. Fryer et al. [115Jump To The Next Citation Point] also found that bar instabilities could develop in ∼ 300M ⊙ stars.

Black Hole Formation: The initial black-hole formation and the subsequent accretion leads to a perturbed geometry of the black hole, initially distorting it. This distortion causes the hole to “ring” in distinct harmonics as gravitational radiation removes the perturbation and the black hole settles into a stationary Kerr state.

Disk Fragmentation: Depending upon the angular momentum profile, the mass in the disk can be large enough that self-gravity can drive instabilities and induce fragmentation.

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