Evolution of progenitor stars of Type Ibc supernovae and long gamma-ray bursts
S.-C. Yoon, N. Langer, M. Cantiello, S.E. Woosley, G.A. Glatzmaier
aa r X i v : . [ a s t r o - ph ] J a n Massive Stars as Cosmic EnginesProceedings IAU Symposium No. 250, 2008F. Bresolin, P.A. Crowther & J. Puls, eds. c (cid:13) Evolution of progenitor stars of Type Ibcsupernovae and long gamma-ray bursts
S.-C. Yoon , N. Langer , M. Cantiello , S. E. Woosley , and G. A.Glatzmaier Department of Astronomy & Astrophysics, University of California, Santa CruzHigh Street, Santa Cruz, CA 95064, USA Astronomical Institute, Utrecht University, Utrecht, The Netherlands3 Department of Earth & Planetary Sciences, University of California, Santa CruzHigh Street, Santa Cruz, CA 95064, USA
Abstract.
We discuss how rotation and binary interactions may be related to the diversity oftype Ibc supernovae and long gamma-ray bursts. After presenting recent evolutionary modelsof massive single and binary stars including rotation, the Tayler-Spruit dynamo and binaryinteractions, we argue that the nature of SNe Ibc progenitors from binary systems may notsignificantly differ from that of single star progenitors in terms of rotation, and that most longGRB progenitors may be produced via the quasi-chemically homogeneous evolution at sub-solarmetallicity. We also briefly discuss the possible role of magnetic fields generated in the convectivecore of a massive star for the transport of angular momentum, which is potentially importantfor future stellar evolution models of supernova and GRB progenitors.
1. Introduction
Rotation influences not only the evolution of massive stars, but also their supernova(SN) explosions (Maeder & Meynet 2000; Heger, Langer & Woosley 2000). In particu-lar, recently many asymmetric supernovae with unusually large energy (broad-lined SNeor hypernovae) have been discovered (e.g. Mazzali et al. 2007), which shows evidencefor rapidly rotating progenitors. The most spectacular example may be long gamma-raybursts (GRBs), which are generally believed to be produced by deaths of some massivestars retaining extremely large angular momenta in their cores ( j > ∼ cm s − ;Woosley 1993; MacFadyen & Woosley 1999; see, however, Dessart et al. 2008). Inter-estingly, such energetic core-collapse events seem to only occur in Wolf-Rayet (WR) stars:all of the broad-lined SNe/Hypernovae and the supernovae associated with long GRBshave been observationally identified as Type Ic (see Woosley & Bloom 2006 for a re-view). This raises the question which WR stars can produce broad-lined SNe Ic or longGRBs while most WR stars die as normal SNe Ibc. Here we present recent evolutionarymodels of massive stars that include binary interactions and the transport of chemicalspecies and angular momentum via rotationally induced hydrodynamic instabilities andmagnetic torques, and discuss how rotation and binary interactions may be related tothe diversity of SNe Ibc and long GRBs.
2. Single star models
Redistribution of angular momentum and chemical species in a rotating star occurs byrotationally induced hydrodynamic instabilities and magnetic torques (See Talon 2007for a review). Eddington-Sweet circulations, shear instability and Goldreich-Schubert-Fricke instability among others have been considered in previous non-magnetic models1 Yoon et al.
Figure 1.
Mean specific angular momentum of the star and the innermost 1 . ⊙ and 3 . ⊙ as a function of the evolutionary time for 18 M ⊙ (left panel) and 60 M ⊙ (right panel) models.The time span for the helium core contraction is marked by the color shade as indicated by thelabel. (Maeder & Meynet 2000; Heger, Langer & Woosley 2000; Hirschi, Meynet & Maeder2004), and the so-called Tayler-Spruit dynamo (Spruit 2002) has been implemented inrecent magnetic models (e.g. Heger, Woosley & Spruit 2005; Maeder & Meynet 2005;Yoon & Langer 2005). In non-magnetic models, it is shown that the buoyancy due tothe chemical gradient at the interface between the core and the envelope largely prohibitsthe considered rotationally induced hydrodynamic instabilities from transporting angularmomentum. The amount of angular momentum retained in the core at the pre-supernovastage is thus close to its initial value even at solar metallicity (Heger, Langer & Woosley2000; Hirschi, Meynet & Maeder 2004). Most massive stars are predicted to die with anenough amount of angular momentum in the cores to produce long GRBs via formationof millisecond magnetars or collapsar (i.e., j > ∼ cm s − ), given that a large frac-tion of young massive stars in our Galaxy and Small/Large Magellanic Clouds are rapidrotators (e.g. Maeder & Meynet 2000; Mokiem et al. 2006; Hunter et al. 2008). On theother hand, in magnetic models adopting the Tayler-Spruit dynamo the core is effectivelyspun down by magnetic torques, and the predicted spin rates of white dwarfs and youngneutron stars are smaller by two orders of magnitude than those from non-magnetic mod-els, which can better explain observations (Heger, Woosley & Spruit 2005; Suijs et al.2008).Fig. 1 shows the evolution of the core angular momentum in the magnetic modelsequences with M init = 18 M ⊙ & v rot , init = 144 km s − , and 60 M ⊙ & v rot , init =186 km s − . In the sequence with M init = 18 M ⊙ , the core loses a significant amount of an-gular momentum during the helium core contraction phase where a strong degree of differ-ential rotation between the core and the envelope appears. A similar effect is also observedduring the CO core contraction phase. In the sequence with M init = 60 M ⊙ , spinning-down of the core during He-core contraction becomes less significant as the star loses thehydrogen envelope, which leads to a smaller moment of inertia of the envelope. However,the core is further spun down by loss of mass due to LBV/WR winds during core He burn-ing. At the neon burning stage, both stars retain a similar amount of angular momentumin their cores as shown in Fig. 1. In fact, the calculations by Yoon, Langer & Norman(2006) show that magnetic models give < j . > ≃ ... × cm s − for different initialmetallicities, masses and rotational velocities, implying that most massive stars includingType Ibc progenitors should die with a similar amount of core angular momentum. Thisconclusion remains the same even for binary stars, as discussed below.An exception is the case for the so-called chemically homogeneous evolution. If the ini-tial rotational velocity is exceptionally high and if metallicity is sufficiently low, chemicalmixing by Eddington-Sweet circulations may occur on a time scale even smaller than volution of SNe Ibc & GRB progenitors Figure 2.
Final fate of our rotating massive star models at four different metallicities ( Z =0.004, 0.002, 0.001, & 0.00001), in the plane of initial mass and initial fraction of the Keplerianvalue of the equatorial rotational velocity. The solid line divides the plane into two parts, wherestars evolve quasi-chemically homogeneous above the line, while they evolve into the classicalcore-envelope structure below the line. The dotted-dashed lines bracket the region of quasi-ho-mogeneous evolution where the core mass, core spin and stellar radius are compatible with thecollapsar model for GRB production (absent at Z=0.004). To both sides of the GRB productionregion for Z = 0.002 and 0.001, black holes are expected to form inside WR stars, but the corespin is insufficient to allow GRB production. For Z = 0.00001, the pair-instability might occurto the right side of the GRB production region, although the rapid rotation may shift the pairinstability region to larger masses. The dashed line in the region of non-homogeneous evolutionseparates Type II supernovae (SN II; left) and black hole (BH; right) formation, where the min-imum mass for BH formation is simply assumed to be 30 M ⊙ . From Yoon, Langer & Norman(2006). the nuclear time scale. Quasi-homogeneity of the chemical composition of a star is thusensured on the main sequence and the star is gradually transformed into a massive WRstar, avoiding the giant phase that would result in strong braking down of the core. Allof the necessary conditions for producing long GRBs – massive core to make a blackhole, removal of hydrogen envelope and retention of a large amount of angular momen-tum in the core – thus can be fulfilled by this type of evolution (Yoon & Langer 2005;Woosley & Heger 2006). This chemically homogeneous evolution scenario (CHES) fa-vors low metallicity environment for producing long GRBs (Fig. 2) and predicts a higherratio of GRB to SN rate at higher redshift, which should be tested by future observations(Yoon, Langer & Norman 2006; cf. Kistler et al. 2007).
3. Binary star models
A significant fraction of SNe Ibc may be produced in close binary systems (e.g.Podsiadlowski, Joss & Hsu 1992). An example is given in Fig. 3 that shows the evolutionof of the primary star in a close binary system with P init = 4 days, M primary , init = 18 M ⊙ ,and M secondary , init = 17 M ⊙ . Both stars are tidally synchronized early on the main se-quence. Once the primary star fills the Roche-lobe radius, it loses about 7 M ⊙ duringthe Case A mass transfer phase, and additional 3 . ⊙ later during the Case AB mass Yoon et al. Figure 3.
Left panel
Evolution of the internal structure of the primary star in a binary system of M primary , init = 18 M ⊙ , M secondary , init = 17 M ⊙ and P init = 4 days, from zero age main sequenceto neon burning. Right panel
Mean specific angular momentum of the innermost 1 . ⊙ and3 . ⊙ of the primary star considered in the left panel as a function of time. The time spanfor Case A or Case AB mass transfer phase is marked by the color shades as indicated by thelabels. transfer phase, becoming a 4 M ⊙ WR star. The core loses angular momentum mostlyduring these Case A and AB mass transfer phases as shown in Fig. 3. The amount ofangular momentum in the core at the neon burning stage turns out to be very similarto those in single star models (see Fig. 1). In fact, we find that mean specific angu-lar momentum of the innermost 1 . ⊙ at the final evolutionary stage of a primarystar in a binary system does not change much according to different initial parameters(primary mass, mass ratio and orbital separation): it remains within a narrow range of2 ... . × cm s − regardless of the detailed history of binary interactions, as longas the tidal synchronization is not unusually strong (Yoon, Woolsey & Langer 2008, inprep.). This implies that the nature of most binary star progenitors of SNe Ibc may notmuch differ from that of single star progenitors, in terms of rotation.The evolution of secondary stars has not yet been well understood. In particular,it sensitively depends on the uncertain efficiency of semi-convection whether the massaccreting star may be rejuvenated or not (Braun & Langer 1995). If a rather large semi-convection parameter is adopted, rejuvenation can significantly weaken the chemicalgradient between the hydrogen burning core and the envelope, in favor of rotationallyinduced chemical mixing. As the secondary is spun up to the critical rotation by massaccretion, even the chemically homogeneous evolution can be occasionally induced ifmetallicity is sufficiently low and if the secondary is not strongly spun down by the tidalsynchronization after the mass accretion phase (Cantiello et al. 2007). The secondarywill eventually die as a GRB after traveling from a few to several hundreds PCs away,if the binary system is unbound due to the supernova kick as a result of the explosionof the primary. This scenario may explain the recent observational evidence that someGRBs are produced in runaway stars (Hammer et al. 2006).Other types of binary interactions may also lead to formation of rapidly rotating WRstars to produce long GRBs. Tidal spinning-up of a WR star in a compact binary systemwith a neutron star or a black hole companion (Brown et. al. 2000; Izzard, Ramirez-Ruiz & Tout2004; van Putten, M.H.P.M. 2004; van den Heuvel & Yoon 2007) and merger of two he-lium cores in a common evenlope (Fryer & Heger 2005) have been recently suggestedamong others. It remains uncertain, however, that such binary systems could explain theobserved GRB rate. For example, recent stellar evolution models by Detmers, Langer & Podsiadlowski(2008) show that a merger of the WR star with the compact object, which is not sup-posed to produce a classical long GRB, is the most likely outcome in the former case. volution of SNe Ibc & GRB progenitors Figure 4.
Mean radial fields B r ( r, θ ) on the meridional plane in a 12 M ⊙ rotating star on themain sequence in a MHD simulation with a 3-D anelastic code (Glatzmaier 1984). The adoptedangular velocity is 10 − Rad s − . The inner region of r × cm ( r . Further detailed evolutionary models are certainly needed for observationally testingdifferent evolutionary scenarios (e.g. van Marle et al. 2008). On the other hand, it ispuzzling why no GRB-associated SNe Ib have been observed yet while most GRB pro-genitor scenarios predict their existence (e.g. Yoon, Langer & Norman 2006). Within theCHES, this puzzle might be solved if one considered anisotropic mass loss, as discussedin Meynet & Maeder (2007).
4. Concluding remarks
Our stellar evolution models including the Tayler-Spruit dynamo indicate that mostSNe Ibc progenitors should explode with a similar amount of angular momentum in theircores, regardless of their single or binary star origin. This is due to the self-regulationarynature of the Tayler-Spruit dynamo. Loss of the hydrogen envelope due to stellar winds ormass transfer results in both removal of angular momentum from the core and weakeningof the core braking by the extended hydrogen enveloped due to magnetic torques, andvice versa. Therefore, most different pre-supernova evolutionary paths may not contributemuch to the diversity of Type Ibc supernovae in terms of core angular momentum,although different iron core masses, and thus different spin rates of young neutron starsmay result (Heger, Woosley & Spruit 2005). GRB progenitors, which require unusuallylarge angular momenta, may undergo the chemically homogeneous evolution, which maynot be unusual at low metallicity. On the other hand, recent observations indicate thatnot all broad-lined SNe Ic are associated with long GRBs (e.g. Modjaz et al. 2008), whichneeds a theoretical explanation in future work.Although the predicted spin rates of the stellar remnants from the magnetic models areconsistent with observations, the validity of the Tayler-Spruit dynamo has been recentlyquestioned by several authors (Denissenkov & Pinsonneault 2007; Zahn, Brun & Mathis Yoon et al.2008). Furthermore, we might have ignored potentially important physical ingredients insimulating the evolution of rotating massive stars. These include gravity waves (Townsendin this volume), and magnetic fields generated by the convective core. For instance, ourrecent 3-D simulations with an anelastic magnetohydrodynamics code (Glatzmaier 1984)show that the strength of poloidal fields generated in the convective core in a young mas-sive star may amount to several thousand Gauss on average (Fig. 4), and its influence onthe transport processes might be comparable to what the Tayler-Spruit dynamo predicts.This issue will be addressed in Yoon, Woosely & Glatzmaier (2008, in prep.).This work was, in part, supported by the DOE Program for Scientific Discovery throughAdvanced Computing and NASA.
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