Relativistic equations of state at finite temperature

Abstract

In this work we study the effects of temperature on the equations of state within a relativistic model, with the inclusion of the baryons of the octet over a wide range of densities. We compare the results of the equation of state, effective mass and strangeness fraction for the TM1, NL3 and GL sets of parameters. MotivationA neutron star is born after the gravitational collapse of the core of a very massive star. We briefly summarize the evolution process as follows: when massive stars in late stages of evolution (supergiants) come to a stage that thermal energy no longer bears the weight of the outer layers, gravity attracts the denser regions to the centre of the supergiant, and since thermal pressure is lower and lower as it cools, gravitational collapse comes next. Now with a denser and hotter core, the star starts fusing elements (beginning with hydrogen into helium, at T ∼ 10 7 K), spending most of its life in this stage until the core contracts to form a white dwarf. Inverse beta decay lowers the high pressure provided by the relativistic eletrons in the core and it collapses. This core implosion takes about 0.5 seconds. The infalling material rebounce on the core, meets the decompression wave and ejects all but the core which cools, comes to an equilibrium composition of neutrons, protons, hyperons and leptons and is then called a neutron star. In [1] the authors study the equations of state (EOS) for cold neutron stars in a ThomasFermi framework, with the presence of the baryonic octet. In this work we study the effects of finite temperature on the EOS considering the presence of the hyperons of the octet. We work in the framework of the relativistic nonlinear . We study the behaviour of the effective mass curves of baryons with these three parameter sets at different temperatures and densities, whilst performing the calculations through a wide range of baryonic densities (at least up to ∼6.0 times the saturation density). We also investigate the strangeness fraction at finite temperature for the parameter sets used in this work and finally draw our conclusions. The NLWM at Finite TemperatureThe Lagrangian density in the model reads:whereand g νB = χ vB g v , g ρB = χ ρB g ρ and g sB = χ sB g s are the coupling constants of baryon "B " to the mesons; M B * = M B − g sB φ, M B is the mass of baryon "B ", m v , m ρ and m s are the masses of the mesons. From the Euler-Lagrange formalism we obtain the equa-

Consistent nonadditive approach and nuclear equation of state

“…However, we are investigating the nonadditive effects on the QHD-I, as originally developed in [1][2][3]. QHD-I has been used in the calculations of nuclear matter and finite nuclei (See [7] and references therein), as well as in the astrophysics context to describe the properties of nuclear matter in compact stars [8][9][10][11][12][13][14]. In this regard, some improvements and extensions of the model have been made to make it more suitable for neutron and proto-neutron stars calculations [8][9][10][11][12][13][14].…”

Head on collision of shock and breaking waves in degenerate hadronic plasmas

“…The baryon field ψ, the neutral scalar meson field φ and the neutral vector meson field V μ with the respective couplings and masses are the minimal degree of freedom. The equation of state is obtained using the mean-field approximation (Serot and Walecka 1986;Furnstahl 2004;Serot 2004;Fukushima and Sasaki 2013). The meson fields are considered as classical fields:…”

“…We can use the classical approximation, if the following conditions are met: 1) the baryonic sources are intense, 2) their coupling to the meson field are strong and 3) the infinite nuclear matter is static, homogeneous and isotropic. Based on calculations done in Serot and Walecka (1986), Furnstahl (2004), Serot (2004), Fukushima and Sasaki (2013), the following equations of motion are obtained:…”

“…The energy density is obtained by inserting M * into Eq. (13) as the following power series of the baryon density (Serot and Walecka 1986;Espindola and Menezes 2002;Santos and Menezes 2004) …”