4.7 Explosions
4.7.1 Gamma-ray bursts
4.7 Explosions
Chemically-homogeneously evolving single stellar models have been proposed to be long-duration gamma-ray burst progenitors, since they may fulfill the collapsar criterion: their fast-rotating cores can retain significant amount of angular momentum until the moment of the collapse, so an accretion disc forms around the central black hole. This set-up, called a collapsar, is thought to lead to a lGRB explosion (Yoon and Langer, 2005; Woosley and Heger,2006). To decide if a given stellar model is a collapsar progenitor or not, the angular momentum distribution of the stellar model needs to be compared to the critical angular momentum corresponding to the last stable orbit around a Kerr-black-hole (Yoon and Langer, 2005; Woosley and Heger,2006). In case the angular momentum of the star is higher than that of the last stable orbit, an accretion-disc can be maintained after the core-collapse, and two jets, facilitating the gamma-ray production, can form. Our models in the mass-range of 13-133 M
fulfill the angular momentum criterion. This, however, does not necessarily mean that they all produce lGRBs, as discussed below.
13 14 15 16 17 18 19 20
0 5 10 15 20
log j [cm2 /s]
Total mass [M⊙]
M = 20 M⊙ vini = 450 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
Figure 4.14. Distribution of the specific angular momentum inside the stellar model with Mini=20 M
and vini=450 km s−1. Models corresponding to four evolutionary stages are plotted: the zero-age main-sequence (ZAMS), the terminal-age main-sequence (TAMS), the end of core-helium-burning (He-exhaustion) and the end of the calculation at core-carbon-exhaustion (End). Since the model is not spherical due to fast rotation, and since the accretion disc supporting the collapsar-formation should form around the equator, the angular momentum at the equator is plotted for the end of the calculation (End equator). The specific angular momentum corresponding to the last stable orbit (lso) around a rotating Kerr-black-hole is represented by the line marked with jKerr,lso. This model fulfills the angular momentum constrain of the collapsar scenario, as significant parts of the stellar core retain enough angular momentum to form an accretion disc around the central black hole.
Fig.4.14shows the angular momentum distribution in the final model with an initial mass of 20 M. It does fulfill the above criterion: not only the material around the equator is above the critical limit, but most of the stellar model is. This model has a CO-core of 13.55 M at the end of the computation, as seen in Fig.4.15. The core contains a total angular mometum of 5.6·1051erg·s. The temperature in the core is 9.5·108K, which means that there is carbon-burning going on. In the remaining time until the iron-core formation and core-collapse, which
4.7 Explosions
-8 -7 -6 -5 -4 -3 -2 -1 0
0 5 10 15 20
Abundances(logmassfraction)
Total mass [M⊙]
Mi = 20 M⊙ vi = 450 km/s Tc8 = 14.131 t = 12.0 Myr
HeH C
N O
20Ne
21Ne
22Ne
23Na
Figure 4.15. Composition of the last computed model of the sequence with Mini=20 M and vini=450 km s−1. Isotopes of the elements indicated by the key legend are shown with coloured lines (except for hydrogen since the model is hydrogen-deficient at this late evolutionary stage). Vertical black line marks the surface. The core temperature is 1.4·109K, and has exhausted from the core (see green line). The total mass of the CO-core is 13.55 M.
is around 3 yr, the mass-loss and the consequent angular momentum loss are 0.0009 M and 3·1049erg·s, respectively (with the mass-loss rate of 3.05·10−4Myr−1, rotational velocity of 2582 km s−1and radius of 0.62 Rin the last computed model, cf. Tables4.1and4.3). Since the angular momentum to be lost until the iron core formation is not significant (two orders of magnitude lower than the total amount of angular momentum in the last computed model), the angular momentum distribution at the moment of the core-collapse can be fairly estimated by that at the onset of carbon-burning.
Our other models in the initial mass-range of 13-131 M behave similarly to that shown in Figs.4.14and4.15. Table4.2provides information on their rotational velocity and their total angular momentum at several evolutionary stages. We present the plots of their angular momentum distribution in Figs.4.16–4.17. The models with initial masses of 13-131 Mall rotate faster than the critical limit for collapsar formation.
However, starting with the model of Mini=59 M, some parts of the stellar core of our most massive models enter the regime of pair-instability. As we shall show in Sect.4.7.4, the models in the initial mass range of Mini=59 M–Mini=77 M are predicted to undergo pulsational pair-instability, which means that although they do eventually form an iron-core, they may lose their high angular momentum due to pulsation-induced mass-loss. As for the more massive models, they are predicted to explode as a pair-instability supernovaebefore a hydrostatic iron-core could even form. Therefore, the most massive collapsar progenitor amongst our models is the one with Mini=45 M.
13 14 15 16 17 18 19 20
0 2 4 6 8 10 12 14
log j [cm2 /s]
Total mass [M⊙] M = 13 M⊙ vini = 450 km/s
ZAMS TAMS End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 5 10 15 20 25
log j [cm2 /s]
Total mass [M⊙] M = 23 M⊙ vini = 500 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 5 10 15 20 25 30
log j [cm2 /s]
Total mass [M⊙] M = 26 M⊙ vini = 350 km/s
ZAMS TAMS End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 5 10 15 20 25 30 35 40 45 log j [cm2 /s]
Total mass [M⊙] M = 45 M⊙ vini = 500 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 10 20 30 40 50 60
log j [cm2 /s]
Total mass [M⊙] M = 59 M⊙ vini = 300 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 10 20 30 40 50 60 70
log j [cm2 /s]
Total mass [M⊙] M = 67 M⊙ vini = 275 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
Figure 4.16. Distribution of the specific angular momentum inside the stellar models indicated by the title of every figure. Models corresponding to four evolutionary stages are plotted: the zero-age main-sequence (ZAMS), the terminal-age main-sequence (TAMS), the end of core-helium-burning (He-exhaustion) and the end of the calculation (End). Since the models are not spherical due to fast rotation, and since the accretion disc supporting the collapsar-formation should form around the equator, also the angular momentum at the equator is plotted for the end of the calculation (End equator). The specific angular momentum corresponding to the last stable orbit (lso) around a rotating Kerr-black-hole is represented by the line marked with jKerr,lso. For details, see Sect.4.7.1.
4.7 Explosions
13 14 15 16 17 18 19 20
0 10 20 30 40 50 60 70
log j [cm2 /s]
Total mass [M⊙] M = 67 M⊙ vini = 300 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 10 20 30 40 50 60 70 80 log j [cm2 /s]
Total mass [M⊙] M = 77 M⊙ vini = 500 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 10 20 30 40 50 60 70 80 90 log j [cm2 /s]
Total mass [M⊙] M = 88 M⊙ vini = 275 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 20 40 60 80 100 120 140 log j [cm2 /s]
Total mass [M⊙] M = 131 M⊙ vini = 600 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
13 14 15 16 17 18 19 20
0 20 40 60 80 100 120 140 160 180 log j [cm2/s]
Total mass [M⊙] M = 172 M⊙ vini = 350 km/s
ZAMS TAMS He-exh End End equator jKerr,lso
Figure 4.17. The same as Fig.4.16, but for another models as indicated by the title of every figure.
Magnetars
Another promising scenario for the origin of long-duration GRBs is the proto-magnetar model.
As opposed to the collapsar scenario where the central object is a black hole, the magnetar model supposes a fast rotating, magnetized proto-neutron-star as the powering engine of the jet (Metzger et al.,2011). For this to happen in our model, their supernova explosion should not ’fail’, but produce a successful outgoing shock and a (rotating) neutron star in the center (MacFadyen and Woosley,1999; MacFadyen et al.,2001). In the context of our models, it is possible that they form lGRBs via the proto-magnetar model.
It is not straightforward to decide whether our models destined to become ’failed’ supernovae and collapsars, or successful supernovae and magnetars, since our simulations have been stopped before an iron-core formed. We will come back to this question in Sect.4.7.3. It is indeed an important question, not necessarily from the point of view of lGRB formation (after all, both scenarios predict lGRBs), but from the point of view of superluminous supernovae, as explained below.