Context. Modeling core-collapse supernovae (SNe) with neutrino transport in three dimensions (3D) requires tremendous computing resources and some level of approximation. We present a first comparison study of core-collapse SNe in 3D with different physics approximations and hydrodynamics codes. Aims. The objective of this work is to assess the impact of the hydrodynamics code, approximations for the neutrino, gravity treatments, and rotation on the simulation of core-collapse SNe in 3D. Methods. We use four different hydrodynamics codes in this work (ELEPHANT, FLASH, fGR1, and SPHYNX) in combination with two different neutrino treatments, the isotropic diffusion source approximation (IDSA) and two-moment M1, and three different gravity treatments (Newtonian, 1D General Relativity correction, and full General Relativity). Additional parameters discussed in this study are the inclusion of neutrino-electron scattering via a parametrized deleptonization and the influence of rotation. Results. The four codes compared in this work include Eulerian and fully Lagrangian (smoothed particle hydrodynamics) codes for the first time. They show agreement in the overall evolution of the collapse phase and early post-bounce within the range of 10% (20% in some cases). The comparison of the different neutrino treatments highlights the need to further investigate the antineutrino luminosities in IDSA, which tend to be relatively high. We also demonstrate the requirement for a more detailed heavy-lepton neutrino leakage. When comparing with a full General Relativity code, including an M1 transport method, we confirm the influence of neutrino-electron scattering during the collapse phase, which is adequately captured by the parametrized deleptonization scheme. Also, the effective general relativistic potential reproduces the overall dynamic evolution correctly in all Newtonian codes. Additionally, we verify that rotation aids the shock expansion and estimate the overall angular momentum losses for each code in rotating scenarios.

A phase transition to quark matter can lead to interesting phenomenological consequences in corecollapse supernovae, e.g., triggering an explosion in spherically symmetric models. However, until now, this explosion mechanism was only shown to be working for equations of state that are in contradiction with recent pulsar mass measurements. Here, we identify that this explosion mechanism is related to the existence of a third family of compact stars. For the equations of state investigated, the third family is only pronounced in the hot, early stages of the protocompact star and absent or negligibly small at zero temperature and thus represents a novel kind of third family. This interesting behavior is a result of unusual thermal properties induced by the phase transition, e.g., characterized by a decrease of temperature with increasing density for isentropes, and can be related to a negative slope of the phase transition line in the temperature-pressure phase diagram.

The hadron-quark phase transition in core-collapse supernovae (CCSNe) has the potential to trigger explosions in otherwise nonexploding models. However, those hybrid supernova equations of state (EOS) shown to trigger an explosion do not support the observational 2 M ⊙ neutron star maximum mass constraint. In this work, we analyze cold hybrid stars by the means of a systematic parameter scan for the phase transition properties, with the aim to develop a new hybrid supernova EOS. The hadronic phase is described with the state-of-the-art supernova EOS HS(DD2), and quark matter by an EOS with a constant speed of sound (CSS) of c 2 QM ¼ 1=3. We find promising cases which meet the 2 M ⊙ criterion and are interesting for CCSN explosions. We show that the very simple CSS EOS is transferable into the wellknown thermodynamic bag model, important for future application in CCSN simulations. In the second part, the occurrence of reconfinement and multiple phase transitions is discussed. In the last part, the influence of hyperons in our parameter scan is studied. Including hyperons no change in the general behavior is found, except for overall lower maximum masses. In both cases (with and without hyperons) we find that quark matter with c 2 QM ¼ 1=3 can increase the maximum mass only if reconfinement is suppressed or if quark matter is absolutely stable.

Our long-term goal is to develop a new supernova equation of state that meets the observational 2 M ⊙ neutron star constraint and that includes quark matter. In this work, we perform a parameter scan to systematically investigate the hadron-quark phase transition in cold neutron stars using the state-of-the-art supernova equation of state HS(DD2) for the hadronic phase. We find neutron star configurations with maximum masses above 2 M ⊙ and even above the maximum mass of HS(DD2). Our results show good agreement with other parameter scans.

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