Hadron-quark phase transitions in hybrid stars and core-collapse supernovae

Extreme temperatures and densities in core-collapse supernovae and one of their possible remnants, the so-called neutron stars, are likely to favor the appearance of new degrees of freedom such as hyperons and/or quark matter.
This work is dedicated to the investigation of the hadron-quark phase transition in core-collapse supernovae and cold neutron stars.
To this day, only a couple of supernova equations of state that consider quark matter have been developed and none of them fulfills the observational 2 M_sun neutron star mass constraint [...].
The phase transition from hadronic to quark matter can have an interesting impact on the post-bounce evolution of core-collapse supernovae: The phase transition is able to induce a collapse of the protoneutron star which ultimately can trigger an explosion, as shown in spherically-symmetric simulations [...]. So far, this scenario has not been investigated in multi-dimensional core-collapse supernova simulations.
In the first part of this work, we analyze cold hybrid stars (Hybrid stars are neutron stars that contain quark matter.) by the means of a systematic parameter scan for the phase transition properties.
The hadronic phase is described by the state-of-the-art supernova equation of state HS(DD2) and the quark phase by an equation of state with a constant speed of sound (CSS).
Choosing a quark matter speed of sound of c_{QM}^2=1/3, we find promising cases which meet the 2 M_sun criterion and are interesting for core-collapse supernova explosions. We show that the very simple CSS equation of state is transferable into the well-known thermodynamic bag model, important for application in core-collapse simulations.
Additionally, the occurrence of reconfinement and multiple phase transitions is discussed.
The influence of hyperons in our parameter scan is studied as well. 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_{QM}^2=1/3 can increase the maximum mass only if reconfinement is suppressed or if quark matter is absolutely stable.
The systematic parameter study is completed with an analogous analysis using c_{QM}^2=1, the maximum value to be still consistent with special relativity. The higher speed of sound leads to more parameter configurations consistent with the 2 M_sun criterion. Increasing the speed of sound to c_{QM}^2>1/3 is therefore an interesting case which increases the possibilities when constructing a future hybrid supernova equation of state.
On the basis of the best guess configuration obtained in the parameter scan for c_{QM}^2=1/3, we construct the new hybrid supernova equation of state BASQUARK. BASQUARK uses HS(DD2) for the hadronic part and a bag model to describe quark matter. The detailed analysis of BASQUARK with the sophisticated spherical supernova code AGILE-BOLTZTRAN shows an explosion for a 15 M_sun progenitor. Hence, BASQUARK is the first hybrid supernova equation of state that fulfills the 2 M_sun neutron star constraint and is known to trigger an explosion in spherical symmetry.
The second part of this work is dedicated to the analysis of BASQUARK in the 3D core-collapse supernova code ELEPHANT. To ensure an effective analysis at late post-bounce times without consuming a vast amount of computational resources, we develop a new method called the spherical restart method. This method allows us to perform a separate spherical AGILE-IDSA simulation, which is computationally very cheap, map its profile into ELEPHANT, and continue the simulation in three dimensions. The method shows that the obtained 3D profiles imitate well the profiles obtained in a consistently run simulation.
If the collapse behavior of ELEPHANT up to bounce is considered in AGILE-IDSA, the spherical restart method is able to reproduce profiles that are on spherical average almost identical to such, obtained in consistently run ELEPHANT simulations.
This allows the opportunity to increase the resolution for more detailed investigations.
Finally, we apply BASQUARK in ELEPHANT and use a 15 M_sun and a 40 M_sun progenitor. Both progenitors explode in spherical symmetry due to the phase-transition induced collapse of the protoneutron star.
In initial tests, ab-intio calculations with ELEPHANT are executed with a low resolution of 2 km to proceed fast to the relevant post-bounce times.
Both progenitors ultimately explode due to oscillations of the protoneutron star which are probably an artifact of the low resolution. This mechanism is not expected at higher resolution.
The 15 M_sun progenitor does not show any indication of a collapse of the protoneutron star, but seems to be powered by the delayed-neutrino driven mechanism.
In turn, the 40 M_sun progenitor shows indications of a failed collapse of the protoneutron star.
By the use of the spherical restart method, the simulation is spherically restarted before the suspected collapse, using a resolution of 2 km, 1 km, and 500 m.
The 2 km run indicates once more collapse features, but fails due to stability issues caused by the low resolution.
Using a resolution of 1 km ultimately shows a collapse of the protoneutron star which results in the explosion of the star. 500 m resolution confirms the results using 1 km resolution and additionally helped the convection to develop. This is the first time, a phase-transition induced collapse and the succeeding explosion is simulated in a three-dimensional core-collapse supernova. We find that resolution is crucial for a correct description of quark matter in the center of the protoneutron star. In the near future, neutrino-quark rates and the IDSA treatment have to be investigated in more detail.
The results obtained with BASQUARK in ELEPHANT are preliminary yet. Nevertheless, this work opens the door into the new field of multi-dimensional core-collapse supernova simulations that consider quark matter and gives some clear indications on the subjects to be investigated in the future.