The main goal of this research is to discover the composition of matter at supra-nuclear density, which, in turn, would allow us to map in a more complete way the phase diagram of matter under extreme conditions. A few fundamental questions wait to be answered:

• At which baryonic densities do quarks start to deconfine? Is there at all a deconfinement critical density?
• Is Witten’s hypothesis about the absolute stability of strange quark matter realized in compact stars?
• Are supernova explosions and gamma-ray bursts associated to phase transitions in dense matter?

These questions are deeply connected with another problem: at which densities can strange hadrons be produced and what is their impact on the equation of state of matter? The solution of this problem has become extremely urgent after the discovery of compact stars having a mass of at least two solar masses: the so-called “hyperon puzzle” has to do with the difficulties in explaining the stability of very massive stars while taking into account the production of strange hadrons, as requested by the present laboratory data. The solution of this problem could indicate that the interaction of strange hadrons is deeply different from what is known at the moment or that deconfined quarks appear at least in the most massive stars.

Objectives and envisaged achievements
There exist long-standing collaborations between the components of our research group. This fact allows us to propose common effective strategies for facing the following research themes.

• Nuclear Three Body Forces (TBFs) are required to ensure a realistic saturation point of nuclear matter within the Bruckner Hartree Fock approach and provide a major contribution to the nuclear EoS at high density, relevant for NS physics. A reliable and consistent theoretical approach is thus needed, in particular for confident predictions regarding the high-density EoS. A variety of nuclear interactions will be used, also derived in the framework of Chiral Effective Field Theory. See CT and PI sections.
• Hyperons and Delta resonances in NSs. This is one of the main research theme. It will be addressed by using non-relativistic and relativistic approaches, the former having the advantage of being connected with scattering data, the latter allowing to discuss the formation and the role of Delta resonances. See CT, FE, PI.
• Quarks in compact stars. They can either appear only in the core of a Hybrid Star (HS) or compose almost the entire Strange Star (SS). New approaches to the dynamics of quarks will be used (Dyson-Schwinger eq., chiral models) and the possible existence of new phases, such as the Crystalline Color Superconducting (CCSC) one, will be explored. The conditions for the realization of Witten’s hypothesis will be investigated. See CT, FE, LNGS.
• Superfluidity, superconductivity, cooling and glitches. The groups of CT and of LNS have a long experience in studying these problems. In particular LNS will investigate clustering phenomena which can affect the thermodynamics and the transport properties of the crust. MI will keep developing realistic descriptions of glitches, whose properties are strictly linked with the formation of a superfluid/superconductive phases in the crust and in the core of the star. See CT, LNS, MI.
• Gravitational waves and explosive phenomena. We plan to collaborate with groups studying hydrodynamical simulations of the rapid rotation and of the merger of two neutron stars in order to provide the link between the GW emission and the EoS and to study the relevance of the EoS in explosive phenomena as GRBs and SNe. In particular we will study matter at finite temperature and in conditions of neutrino trapping. The sistematic study of the rotational properties of matter can constitute a fundamental tool to discriminate between the possible EoSs. See CT, FE, PI, LNS.

The main subjects that the IS intends to develop can be summarized as follows.

Catania

• BHF EOS of High-Density (Hyper)-Nuclear Matter at Zero and Finite Temperature: We plan to continue our studies within the BHF formalism, in particular focusing on the effect of TBF, and the inclusion of hyperons with newly available potentials.
• Microscopic Nuclear TBF, Hyperon-Nucleon and Hyperon-Hyperon Potentials: We are constantly improving the microscopic meson-exchange model of TBF, compatible with modern nucleon-nucleon potentials.
• Hybrid Stars and the Hadron-Quark Phase Transition with Different Quark Models: We plan to continue our study of these objects employing different quark models (Dyson-Schwinger model, Field Correlator model, ...) in combination with our hadronic BHF EoS.
• Simulation of Gravitational Wave Emission from Protoneutron Stars: We plan to extend our previous studies of stellar oscillations with our finite-temperature EoS to more realistic dynamical simulations of NS formation.
• Microscopic Energy Density Functional for the NS Crust: We intend to complete the work on the universal BHF energy density functional. Future developments are the inclusion of the effective mass in the functional, in order to be able to describe also the quadrupole giant resonance, and the further reduction of parameters, in particular by extracting the spin-orbit strength from many-body calculations in nuclear matter. We plan also to develop further, within the same scheme, the study of the NS crust.
• Cooling of NS Matter: The computation of cooling processes in NS matter requires several microscopic input information, like Urca reaction matrix elements, effective masses, pairing gaps, etc. We intend to study these aspects in the BHF & BCS formalisms, in view of future data on NS cooling, which will strongly constrain our theoretical models.

Ferrara

We have suggested the possible co-existence of two families of compact stars: hadronic stars with small radii and not too large masses and very massive quark stars (PRD89 (2014) 043014). In this context, we plan to study the following problems:

• Equation of state of hadronic matter. We will extend our relativistic mean-field model (with nucleons, hyperons and deltas) to the case of finite temperature and finite neutrino chemical potential in order to study the temporal evolution of protoneutron stars. We will include also the finite width of the Δ-isobars by considering fluctuations of the effective particle mass.
• Investigation of the conditions for the birth of quark stars. In the two-families scenario, hadronic stars and quark stars coexist. It is important to establish how the quark star branch can be populated and to establish under which conditions the amount of strangeness present in the core of the hadronic star is high enough to trigger the conversion to a quark star. Also, in some specific conditions the formation of the quark star could happen during a long GRB event. The neutrino emission associated with the energy released by the conversion could lead to a new episode of prompt emission (within the protomagnetar model) which could possibly explain the cases of double bursts (such as GRB110709B).
• Phenomenological implications of the two families scenario and impact on the astrophysics of compact stellar objects. A remarkable implication of the two families scenario is that stars with masses between about 1.35 and 1.5 Msun could be either hadronic or quark stars. That would lead to a unique signature in the distribution of the masses and of the moment of inertia of compact stars that we plan to investigate through a population synthesis analysis on isolated stars and stars in binary systems. Our predictions will be tested in the near future e.g. by using the data collected by the Square Kilometer Array.
• Merger of two compact stars. In the merger of two hadronic stars, an intermediate stage during which a quark star is formed is unavoidable with the two-families scenario. The jump from the hadronic to the quark family could have an imprint on the gravitational waves signal which will be for the first time studied by means of a state of the art code for the numerical simulations of compact stars merger. These studies will have important implications for the proto-magnetar model for short GRBs.

LNGS

• Regarding compact stellar objects, we have studied the torsional oscillations of strange stars with an inner core of CFL phase, a crystalline color superconducting crust (CCSC) and an external crust of nuclear matter (NM). We have shown that this peculiar structure can support torsional oscillations of very large amplitude. The most intriguing aspect is that the shear strain has a radial dependence with a maximum much closer to the star surface than in standard neutron stars, showing a peculiar breaking pattern. With this in mind we plan to extend our studies concerning strange stars with a nuclear crust to the rotating case. We will investigate the stable configurations in the presence of CCSC matter in the interior of the star and the maximum rotational velocity supported by the structure.
• Concerning the high-energy neutrinos (HEN), we studied the impact of neutrino oscillations uncertainties at the energy scale of 100 TeV. This is the range of the observed signals detected by IceCube during the last year. We tested the hypothesis of non-radiative neutrino decay using the latest IceCube data. We plan to investigate the astrophysical sources of these HEN starting from the diffuse component due to the interaction of cosmic rays with the Galactic gas.
• Finally, within the large collaboration involving gravitational waves detectors, i.e. Ligo and Virgo, and neutrinos detectors, i.e. LVD, Borexino and IceCube, we started developing a Monte Carlo describing all the neutrino detectors involved in the network and all the features known of the two different signals expected, including their correlations. We also started the data exchange for joint analysis of Neutrinos and Gravitational Waves emitted by Core Collapse Supernovae. We plan to characterize the noise of the neutrino detectors and to identify a way to disentangle poor signals from the background.

LNS

• Extension of the Brueckner theory (Induced Interaction Theory). We plan to work on extensions of the nuclear matter Brueckner theory towards the introduction of long- range correlations (core polarization) in the nuclear effective interaction. The induced interaction theory, already extended to asymmetric nuclear matter (PRC 93, 044329 (2016)), will be further developed beyond the Landau limit, and the residual interaction in the spin-singlet and spin-triplet two-body channels will be calculated. The screening and antiscreening on the Cooper pairs will be investigated for the 1S0 proton superfluid state and 3PF2 neutron superfluid state, both supposed to exist in neutron stars. The corresponding energy gaps will be applied to the present models of neutron-star cooling.
• Clustering phenomena in neutron stars. Low-density clustering phenomena are predicted to occur in the inner crust of a neutron star and along the supernova explosion process. Clusterization effects are expected to modify significantly the thermodynamical features of the stellar matter and to influence neutrino scattering processes, which are one of the main sources of cooling. We plan to investigate the impact of such a clustered structure on specific heat and on neutrino scattering cross sections. The sensitivity of the results to the adopted nuclear effective interaction (and nuclear EoS), as well as to the pairing strength, will be also analyzed.
• Weak interaction in nuclear systems. Charge exchange processes will be studied in the framework of the induced interaction theory either in the determination of the neutrino mean free path in neutron-stars and in the calculation of nuclear matrix elements in double beta-decay. We also plan to investigate possible analogies with charge exchange mechanisms induced by heavy-ion collisions.

Milano

In the last few years, we concentrated on the theory of Pulsar Glitches which may be a direct evidence for the presence of bulk nucleon superfluidity in their interior. At the microscopic level, we have completed our study to determine the mesoscopic vortex-lattice interaction which is responsible for pinning the vorticity to the star's inner crust and thence for the accumulation and storage of angular momentum to be release at the glitch. We plan to extend this numerical model in order to study the mesoscopic interaction between neutron vortices and magnetic fluxtubes in the core. This is crucial in the presence of type II proton superconductivity, since such an interaction could pin the vorticity also in the core, with clear observational signatures. We also plan to extend our existing work based on the Local Density approximation to study the profile of the vortex-nucleus pinning interaction, a crucial but still unknown quantity for realistic simulations of vortex dynamics. At the level of macroscopic observable physics, we have developed a new consistent analytical formalism in the framework of two-fluid hydrodynamics to treat the mixed spherical (the pulsar) and cylindrical (the vortices) symmetry of the glitch problem. This extends our "snowplow model" for pulsar glitches as a general mechanism to store vorticity; General Relativity and realistic equations of state for dense matter are implemented and we have accounted for the effect of entrainment in the neutron and proton superfluids. We are now developing a hydrodynamical code based on this formalism and we plan to use the model to study the effect of pulsar masses on the glitch amplitude: in particular, we will compare the results of the extended snowplow model and of the hydrodynamical code to observations of frequent glitchers, in an attempt to give a unified description of the glitch phenomenon. Preliminary results based on the available reservoir of angular momentum show a remarkable correlation between strength of the glitcher and pulsar mass.

Pisa

• Equation of state of nuclear matter and structure of Neutron Stars. We will perform ab initio calculations of the equation of state (EoS) of symmetric nuclear matter (NM), pure neutron matter and beta-stable nuclear matter within the Brueckner-Harthree-Fock (BHF) approach using nuclear interactions recently derived in the framework of the chiral effective field theory (ChEFT). We will extend this study by using the recent chiral interaction with Delta-isobar intermediate states (Piarulli et al., Phys. Rev. C 91 (2015) 024003) to calculate the EoS of nuclear matter. We will next make use of these EoS models to calculate the structure of non-rotating as well as rapidly-rotating Neutron Stars (NS) in General Relativity (GR).
• Hyperons in dense matter, hyperonic three-body interactions (YTBIs), “hyperon puzzle”. We will perform systematic calculations of hyperonic matter EoS and NS structure using the recent ChEFT interactions developed by the Julich-Bonn-Munich group, and using the BHF approach. An alternative method to attach these problems consist in the development of hyperonic three-body interactions based on meson exchange theory. To this end we will extend the work of (Logoteta et al., NPA 914 (2013)) where the first model of two-meson exchange YNN interaction has been developed. We will use these EoSs to calculate: (i) properties of hyperon stars and looking for a possible solution of the hyperon puzzle based on YTBIs; (ii) rapidly spinning hyperon stars in GR to study the role of the presence of hyperons and particularly of YTBIs on the mass-shed frequency, moment of inertia and other stellar properties.
• Equation of state of nuclear/hyperonic matter at finite temperature and proto-NSs. We will next make two further advances, calculating the EoS at finite-T for matter with trapped neutrinos, which allow us to calculate properties of non-rotating and fast-spinning proto-NSs and proto-hyperon stars.