Publications of the Astronomical Society of Australia (PASA), Vol. 34, e067, 19 pages (2017). © Astronomical Society of Australia 2017; published by Cambridge University Press. doi:10.1017/pasa.2017.63 The State of Matter in Simulations of Core-Collapse supernovae—Reflections and Recent Developments Tobias Fischer1,10, Niels-Uwe Bastian1, David Blaschke1,2,3, Mateusz Cierniak1, Matthias Hempel4, Thomas Klähn5, Gabriel Martínez-Pinedo6,7, William G. Newton8, Gerd Röpke3,9 and Stefan Typel7,6 1Institute of Theoretical Physics, University of Wroclaw, Pl. M. Borna 9, 50-204 Wroclaw, Poland 2Bogoliubov Laboratory for Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia 3National Research Nuclear University (MEPhI), Kashirskoe shosse 31, 115409 Moscow, Russia 4Department of Physics, University of Basel, Klingelbergstrasse 82, 4058 Basel, Switzerland 5Department of Physics and Astronomy, California State University Long Beach, 250 Bellflower Boulevard, Long Beach, California 90840-9505, USA 6GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany 7Institut für Kernphysik, Technische Universität Darmstadt, Schlossgartenstraße 9, 64289 Darmstadt, Germany 8Department of Physics and Astronomy, Texas A&M University-Commerce, Commerce, TX 75429, USA 9Institut für Physik, Universität Rostock, Albert-Einstein Straße 23–24, 18059 Rostock, Germany 10Email: fi[email protected] (RECEIVED July 28, 2017; ACCEPTED November 22, 2017) Abstract In this review article, we discuss selected developments regarding the role of the equation of state in simulations of core- collapse supernovae. There are no first-principle calculations of the state of matter under supernova conditions since a wide range of conditions is covered, in terms of density, temperature, and isospin asymmetry. Instead, model equation of state are commonly employed in supernova studies. These can be divided into regimes with intrinsically different degrees of freedom: heavy nuclei at low temperatures, inhomogeneous nuclear matter where light and heavy nuclei coexist together with unbound nucleons, and the transition to homogeneous matter at high densities and temperatures. In this article, we discuss each of these phases with particular view on their role in supernova simulations. Keywords: supernovae: general – equation of state – neutrinos 1 INTRODUCTION heavy nuclei together with unbound nucleons, and homo- geneous matter at high temperatures and densities. In this The state of matter at the interior of core-collapse super- article, we reflect on the role of the EOS in core-collapse novae as well as in the core of proto-neutron stars (PNS) supernovae explored in spherically symmetric simulations. can reach extreme conditions, in terms of temperatures up To this end, accurate three-flavour Boltzmann neutrino trans- to several 1011 K(1.16 × 1010K 1 MeV), densities in port, developed by Mezzacappa & Bruenn (1993b, 1993a, excess of normal nuclear matter density and large isospin 1993c), is employed in the fully self-consistent general rel- asymmetry. The associated supernova phase diagram, i.e. the ativistic radiation-hydrodynamics framework of Liebendör- thermodynamic conditions obtained during a core-collapse fer et al. (2004). In general, accurate neutrino transport is supernova, is shown in Figure 1(a) for a selected exam- essential for the prediction of the neutrino signal for core- ple simulation. Central densities and maximum tempera- collapse supernova events, as was observed from SN1987A tures may vary on the order of 10–20% depending on the (cf. Bionta et al. 1987; Hirata et al. 1988) which marked a stellar progenitor. The EOS for supernova simulations must benchmark for current supernova modelling. The latter al- cover such an extended three-dimensional domain illustrated ready confirmed that neutrinos from the next galactic event in Figure 1(a), where presently first-principle EOS are not will be the potentially observable signal, from which we will available. Instead, model EOS are being developed for su- learn not only details about the stellar explosion but also about pernova studies. These combine several domains with differ- the state of matter at the supernova interior which is hidden ent degrees of freedom, e.g., heavy nuclei at low tempera- otherwise, e.g., for electromagnetic radiation by the stellar tures, inhomogeneous nuclear matter composed of light and mantle. 1 Downloaded from https://www.cambridge.org/core. IP address: 170.106.35.76, on 26 Sep 2021 at 12:27:55, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pasa.2017.63 2 Fischer et al. Figure 1. Supernova phase diagram (colour coding is due to the electron fraction Ye) in graph (a) and space-time diagram of the supernova evolution (colour coding is due to the entropy per baryon) in graph (b), both obtained from the spherically symmetric core-collapse supernova simulation of the massive progenitor star of 18 M published in Fischer (2016a). (a) Temperature-density domain of a supernova evolution. (b) Space-time diagram of the supernova evolution. 1.1. Supernova phenomenology Marek 2015;Lentzetal.2015; Roberts et al. 2016). However, in the framework of multi-dimensional simulations, accurate PNS are the central object of core-collapse supernovae. The Boltzmann neutrino transport cannot be employed due to the latter are being triggered from the initial implosion of the stel- current computational limitations. Instead, approximate neu- lar core of stars more massive than about 8 M. The core col- trino transport schemes are commonly used, whose range of lapse proceeds until normal nuclear matter density is reached, applicability is currently being debated (cf. Sumiyoshi et al. when nuclei dissolve into homogeneous matter. The highly 2015). Another issue of multi-dimensional supernova simu- repulsive nature of the short-range nuclear force balances lations with approximate neutrino transport may be related to gravity such that the core bounces back with the formation of the rather sparse neutrino phase-space resolution used, again, a hydrodynamics shock wave which propagates quickly out due to the current computational limitations. of the stellar core, as illustrated in Figure 1(b) (thick solid Besides the aforementioned three scenarios for the onset green line). The shock stalls at around 100–200 km due to of the supernova explosion, another mechanism was discov- the continuous photodisintegration of infalling heavy nuclei ered by Sagert et al. (2009) due to the phase transition at high from above and the launch of the νe-burst associated with the densities from ordinary nuclear matter to the quark gluon shock propagation across the neutrinosphere of last scattering plasma. The latter was being treated within the simple but (see thick dashed green line in Figure 1(b)). Consequently, powerful thermodynamic bag model. During the phase tran- the shock turns into an accretion front. sition, a large amount of latent heat is released in a highly The supernova explosion, i.e., the revival of the shock wave dynamical fashion, which in turn triggers the onset of the and the subsequent ejection of the stellar mantle that sur- supernova explosion even in spherically symmetric simula- rounds the PNS, is due to the liberation of energy from the tions (for details, see also Fischer et al. 2011). Moreover, it PNS interior to a thin layer of accumulated material at the leaves an observable millisecond burst in the neutrino sig- PNS surface (for recent reviews, cf. Janka et al. 2007; Janka nal (for details, see Dasgupta et al. 2010). These milestones 2012). Several scenarios have been explored. Besides the demonstrate the sensitivity of EOS uncertainties related to magneto-rotational mechanism of LeBlanc & Wilson (1970) our understanding of core-collapse supernovae and suffice (for recent works, cf. Takiwaki, Kotake, & Sato 2009;Win- the need of a more elaborate understanding of the EOS at teler et al. 2012; Mösta et al. 2014, 2015) and the dumping high densities including better constraints in particular. of sound waves developed by Burrows et al. (2006)—yet Once the supernova explosion proceeds, mass accretion not confirmed by other groups—the neutrino-heating mech- ceases at the PNS surface and the nascent PNS deleptonises anism of Bethe & Wilson (1985) has been demonstrated to via the emission of neutrinos of all flavors on a timescale on lead to supernova explosions for a variety of massive pro- the order of 10–30 s. This phase of the supernova evolution genitor stars (cf. Müller, Janka, & Marek 2012; Takiwaki, is mildly independent from details of the explosion mech- Kotake, & Suwa 2012; Bruenn et al. 2013; Melson, Janka, & anism. This has been explored in Fischer et al. (2010) and PASA, 34, e067 (2017) doi:10.1017/pasa.2017.63 Downloaded from https://www.cambridge.org/core. IP address: 170.106.35.76, on 26 Sep 2021 at 12:27:55, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/pasa.2017.63 The State of Matter in Simulations of Core-Collapse Supernovae – Reflections and Recent Developments 3 Hüdepohl et al. (2010) within the first self-consistent dynam- ables: temperature T, rest-mass density ρ (or baryon number 2 ical simulations based on accurate three-flavour Boltzmann density, nB ), and electron fraction Ye. With increasing den- neutrino transport in spherical symmetry. These aforemen- sity, these nuclei become heavier while their abundance de- tioned studies confirmed that the PNS settles into a quasi- creases simultaneously. At normal nuclear matter density, ρ0 14 −3 −3 static state (Pons et al. 1999) with a wind outflow devel- ࣃ 2.5 × 10 gcm (n0 ࣃ 0.15 fm ), as well as above tem- oping from the PNS surface. This happens once the accre- peratures of about 5–10 MeV, nuclei dissolve at the liquid– tion funnels are quenched during the explosion phase and gas phase transition into homogeneous nuclear matter com- convection/SASI in the gain region cease. posed of quasi-free nucleons (for details, cf.