Neutron Stars (NSs) are extremely compact objects, in wich matter reaches extreme conditions that are inaccessible by Earth-based experiments. To improve the present understanding of the properties of NS matter encoded the Equation of State (EOS)--that is, the relation linking pressure and energy density--one has to resort largely to the astrophysical data that are being collected by the rapidly evolving multimessenger astronomy. Gravitational waves (GWs) from a binary NS merger were first detected in event GW170817, and the upcoming third generation of GW detectors are even more promising. Moreover, missions aimed at studying the NS radius, such as NICER, have already provided measurements that point to a bright future. In general, matter in the inner region of a cold NS can be modelled as a charge-neutral perfect fluid consisting of nucleons and leptons in beta equilibrium, in which strong interactions dominate nucleon-nucleon forces. It has been also pointed out, however,that a phase transition to more exotic forms of matter, leading to the appearance of, e.g., strange baryons or even deconfined quarks, could eventually take place in the innermost region of massive NSs.
In order to study these two scenarios, we plan to (i) develop a novel EOS of nuclear matter--obtained from a microscopic dynamical model using the formalism of Correlated Basis Functions (CBF)--and (ii) investigate how a physically motivated quark extension would be connected to it. We will adopt a fully Bayesian framework to constrain the properties of both phases using astrophysical data. Thermal effects, relevant in the merger and post-merger stages of NS cohalescence, will be also studied using a suitable generalisation of the formalism.
The ultimate goal of NS astrophysics is to understand the EOS of ultradense matter. To do so, we must count with astrophysical data and a reliable description of nuclear matter to be able to connect all the information. A lot of work has been carried out using parametric models for the EOS, for example piecewise polytropes or the spectral representation. LIGO analyses are indeed based on the spectral representation of several EOSs due to the limitation of computational resources. At first, they are obviously useful because they can give us a general understanding about the phenomena we are dealing with, but if we want to infer the real EOS, at a given point we should start assuming microscopic models instead of parametric ones. Our goal here is exactly to provide a satisfying microscopic description of the physics behind the EOS constraints at the state-of-the-art level.
Fasano et al.[10] have done a remarkable work on constraining the NS EOS combining GW and EM observations and assuming a parametric representation. In the light of this first work, Maselli et al. [12] have extended the analysis now to a widely used microscopic model with a clear interpretation of the influence of the three-body force on the stellar observables. Their results clearly show an exciting scenario to constrain the three-body force, a key ingredient in the nuclear EOS, for the near future with more GW and EM detections. Moreover, they show how powerful is the combination of finding a robust microscopic EOS and using statistical analysis to infer direct physical quantities.
Based on this previous experience, our proposal within the present project is to study the relativistic boost corrections on the effective interaction EOS, explained in the last section, and analysing the role of the three-body force in this new model. Also, we want to explore the possibility of a phase transition to deconfined quark matter inside the core of NSs, leading to new observables and a new interesting physics. Our idea is always to keep track of the microphysics involved and using the astrophysical data to integrate over any free parameter in our assumptions. Doing that, we are able to get important information on characteristics of our EOSs and align our discoveries with the fast evolving data acquisition scenario we are living in. Through precise microscopic calculations, natio- nal and international collaborations and a heavy statistical analysis, we will be able to significantly constrain part of the NS physics. Moreover, we have just started our studies together as one can see by the recently submitted paper [18], where we extend the results of Maselli et al. [12] to the specific case of Quasi Normal Modes of compact objects.
All the work that has been carried out by our group at Sapienza has focused on the inspiral phase of Binary NS mergers or on isolated NSs, however for the third generation of GW detectors, we also expect to get information by the merger and the postmerger phases in coalescences. So, as our ultimate goal of this project, we want to generalise our results of cold stars to warm stars by constructing a warm EOS, similarly to what has been done by Camelio et al. [6]. We aim to describe the EOS in the postmerger phase, which is currently one of the main challenges in the field, so if we are able to have clear control over the most important physical parameters in our model, we can go towards a unified description of a microscopic EOS for all phases in a coalescence. This would represent a large step for the NS community.