The Equation of State (EoS) of strongly interacting cold and hot ultra-dense QCD matter remains a major challenge in the field of nuclear astrophysics. With the advancements in measurements of neutron star masses, radii, and tidal deformabilities, from electromagnetic and gravitational wave observations, neutron stars play an important role in constraining the ultra-dense QCD matter EoS. In this work, we present a novel method that exploits deep learning techniques to reconstruct the neutron star EoS from mass-radius (M-R) observations. We employ neural networks (NNs) to represent the EoS in a model-independent way, within the range of ∼1-7 times the nuclear saturation density. The unsupervised Automatic Differentiation (AD) framework is implemented to optimize the EoS, so as to yield through TOV equations, an M-R curve that best fits the observations. We demonstrate that this method works by rebuilding the EoS on mock data, i.e., mass-radius pairs derived from a randomly generated polytropic EoS. The reconstructed EoS fits the mock data with reasonable accuracy, using just 11 mock M-R pairs observations, close to the current number of actual observations.

We investigate gross properties of merger components and remnant in GW170817 using equations of state (EoSs) within the finite temperature field theoretical models. We also adopt finite temperature equations of state in the density dependent hadron field theory such as DD2 EoS and Banik, Hempel and Bandyopadhyay (BHB) EoS involving Λ hyperons interacting via Φ meson popularly known as BHBΛφ EoS. Properties of merger components are studied using zero temperature EoSs. Particularly we investigate tidal deformabilities and radii of merger components in light of GW170817. An analytical expression relating the radius of merger components and the combined tidal deformability is obtained for binary neutron star masses in the range 1.1M ⊙ M 1.6M ⊙ . The upper bound on the tidal deformability gives the upper bound on the radius of merger components 13 km. Next the role of finite temperature on the merger remnant is explored. In this case, we investigate the gravitational and baryon mass, radius, Kepler frequency and moment of inertia of the rigidly rotating remnant for different EoSs at fixed entropy per baryon. The remnant radius is enlarged due to thermal effects compared with the zero temperature case. Consequently it is found that the Kepler frequency is much lower at higher entropy per baryon than that of the case at zero temperature.

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