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Abstract Binary neutron star mergers can produce extreme magnetic fields, some of which can lead to strong magnetar-like remnants. While strong magnetic fields have been shown to affect the dynamics of outflows and angular momentum transport in the remnant, they can also crucially alter the properties of nuclear matter probed in the merger. In this work, we provide a first assessment of the latter, determining the strength of the pressure anisotropy caused by Landau-level quantization and the anomalous magnetic moment. To this end, we perform the first numerical relativity simulation with a magnetic polarization tensor and a magnetic-field-dependent equation of state using a new algorithm we present here, which also incorporates a mean-field dynamo model to control the magnetic field strength present in the merger remnant. Our results show that—in the most optimistic case—corrections to the anisotropy can be in excess of 10% and are potentially largest in the outer layers of the remnant. This work paves the way for a systematic investigation of these effects. 

For densities beyond nuclear saturation, there is still a large uncertainty in the equations of state (EoSs) of dense matter that translate into uncertainties in the internal structure of neutron stars. The MUSES Calculation Engine provides a free and open-source composable workflow management system, which allows users to calculate the EoSs of dense and hot matter that can be used, e.g., to describe neutron stars. For this work, we make use of two MUSES EoS modules, i.e., Crust Density Functional Theory and Chiral Mean Field model, with beta-equilibrium with leptons enforced in the Lepton module, then connected by the Synthesis module using different functions: hyperbolic tangent, generalized Gaussian, bump, and smoothstep. We then calculate stellar structure using the QLIMR module and discuss how the different interpolating functions affect our results. 

We study in detail the influence of different chemical potentials (baryon, electric charge, strange, and neutrino) on how and how fast a free gas of quarks in the zero-temperature limit reaches the conformal limit. We discuss the influence of non-zero masses, the inclusion of leptons, and different constraints, such as charge neutrality, zero-net strangeness, and fixed lepton fraction. We also investigate for the first time how the symmetry energy of the system under some of these conditions approaches the conformal limit. We find that the inclusion of all quark masses (even the light ones) can produce different results depending on the chemical potential values or constraints assumed. A positive or negative deviation of 10% from the pressure of free massless quarks with the same chemical potential was found to take place as low as μB=77 to as high as 48,897 MeV. This illustrates the fact that the “free” or conformal limit is not a unique description. Finally, we briefly discuss what kind of corrections are expected from perturbative QCD as one goes away from the conformal limit. 

At high density, matter is expected to undergo a phase transition to deconfined quark matter. Although the density at which it happens and the strength of the transition are still largely unknown, we can model it to be in agreement with known experimental data and reliable theoretical results. We discuss how deconfinement in dense matter can be affected by both by temperature and by strong magnetic fields within the Chiral Mean Field (CMF) model. To explore different dependencies in our approach, we also explore how deconfinement can be affected by the assumption of different degrees of freedom, different vector coupling terms, and different deconfining potentials, all at zero temperature. Both zero-net-strangeness and isospin-symmetric heavy-ion collision matter and beta-equilibrated charge-neutral matter in neutron stars are discussed. 

We explore the Quantum Chromodynamics (QCD) phase diagram's complexities, including quark deconfinement transitions, liquid-gas phase changes, and critical points, using the chiral mean-field (CMF) model that is able to capture all these features. We introduce a vector meson renormalization within the CMF framework, enabling precise adjustments of meson masses and coupling strengths related to vector meson interactions. Performing a new fit to the deconfinement potential, we are able to replicate recent lattice QCD results, low energy nuclear physics properties, neutron star observational data, and key phase diagram features as per modern constraints. This approach enhances our understanding of vector mesons' roles in mediating nuclear interactions and their impact on the equation of state, contributing to a more comprehensive understanding of the QCD phase diagram and its implications for nuclear and astrophysical phenomena.