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We study the structure of neutron stars in $f(R)$ gravity theories with perturbative constraints. We derive the modified Tolman-Oppenheimer-Volkov equations and solve them for a polytropic equation of state. We investigate the resulting modifications to the masses and radii of neutron stars and show that observations of surface phenomena alone cannot break the degeneracy between altering the theory of gravity versus choosing a different equation of state of neutron-star matter. On the other hand, observations of neutron-star cooling, which depends on the density of matter at the stellar interior, can place significant constraints on the parameters of the theory.Keywords:
Degeneracy (biology)
There are various cosmological models with polytropic equation of state associated to dark energy. Polytropic EoS has important applications in astrophysics, therefore a study of it on cosmological framework continues to be interesting. From the other hand, there are various forms of interactions phenomenologically involved into the darkness of the universe able to solve important cosmological problems. This is a motivation for us to perform a phase space analysis of various cosmological scenarios where non linear interacting polytropic gas models are involved. Dark matter is taken to be a pressureless fluid.
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The structure of neutron stars is determined by the equation of state of dense matter in their interiors. Brief review of the equation of state from neutron star surface to its center is presented. Recent discovery of two two-solar-mass pulsars puts interesting constraints on the poorly known equation of state of neutron-star cores for densities greater than normal nuclear matter density. Namely, this equation of state has to be stiff enough to yield maximum allowable mass of neutron stars greater than two solar masses. There are many models of neutron stars cores involving exclusively nucleons that satisfy this constraint. However, for neutron-star models based on recent realistic baryon interaction, and allowing for the presence of hyperons, the hyperon softening of the equation of state yields maximum masses significantly lower than two solar masses. Proposed ways out from this "hyperon puzzle" are presented. They require a very fine tuning of parameters of dense hadronic matter and quark matter models. Consequences for the mass-radius relation for neutron stars are illustrated. A summary of the present situation and possible perspectives/challenges, as well as possible observational tests, are given.
Solar mass
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In this article, we have presented the anisotropic stars by taking a modified polytropic equation of state (pr = k ρ1+1/n − α, where k and α are constants) in the framework of the Korkina-Orlyanskii spacetime. In this study, we have discussed four different models as: (A) n = 1 (Bose–Einstein Condensate (BEC) neutron liquid), (B) n = 2, (C) n = 3/2 (Non-relativistic neutron gas, (D) n = 3 (Ultra relativistic Fermi-gas). Moreover, we have tested several physical properties for each model. To compare the stiffness of these four models, we have plotted the M − R curves, M − I curves and compression modulus. As per the M − R curves, the equation of state can hold maximum mass when the polytropic index in 2 and minimum mass when n = 1 (BEC neutron liquid). Further, the ultra relativistic Fermi gas (n = 3) can also hold more Mmax than its non-relativistic counter part (n = 3/2). These results are further supported by the compression modulus. Lastly, to show its physical validity we have fitted six well known compact stars in M − R curve within their observational error bars.
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We analyze here whether polytropic equations of state can be a good approximation for neutron stars. Dividing the matter in the star interior in different regions that can be well-reproduced by different polytropics and imposing the continuity of the pressure among the regions, we obtain the corresponding neutron star mass–radius diagram. A comparison with the results obtained with the polytropic approximation and the exact relativistic mean-field equation of state (EoS) is shown for two compositions of the hadronic matter. We conclude that with more than one polytropic EoS, it is possible to obtain a good fit to neutron stars only if the pressure is written as a power-law in the energy density (or mass density) and not in the baryonic density (the usual polytropic). We also found a correlation between the sound velocity at the star center and its mass. The sound velocity at the interface between the polytropic regions shows a small discontinuity that is greater for the hadronic matter including hyperons.
Polytrope
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We present solution of the equations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG) using the polytropic equation of state. A polytropic equation of state, which has a good fitting with a more realistic one, is used. Results are obtained for all variables of a single neutron star in the model of MDG. The maximum mass about two solar masses is in accordance with the latest observations of pulsars. Several new effects are observed for the variables related with the dilaton $\Phi$ and the cosmological constant $\Lambda$. The mass-radius relation is also obtained. Special attention is paid to the behavior of the quantities which describe the effects analogous to those of dark energy and dark matter in MDG. The results of the present paper confirm the conclusion that the dilaton $\Phi$ is able to play simultaneously the role of dark energy and dark matter.
Dilaton
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We present solution of the equations for relativistic static spherically symmetric stars (SSSS) in the model of minimal dilatonic gravity (MDG) using the polytropic equation of state. A polytropic equation of state, which has a good fitting with a more realistic one, is used. Results are obtained for all variables of a single neutron star in the model of MDG. The maximum mass about two solar masses is in accordance with the latest observations of pulsars. Several new effects are observed for the variables related with the dilaton $\Phi$ and the cosmological constant $\Lambda$. The mass-radius relation is also obtained. Special attention is paid to the behavior of the quantities which describe the effects analogous to those of dark energy and dark matter in MDG. The results of the present paper confirm the conclusion that the dilaton $\Phi$ is able to play simultaneously the role of dark energy and dark matter.
Dilaton
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The role of the crust on the tidal deformability of a cold nonaccreted neutron star is studied using the recent unified equation of state BSk24. This equation of state, which is based on the nuclear energy-density-functional theory, provides a thermodynamically consistent description of all stellar regions. Results obtained with this equation of state are compared to those calculated for a putative neutron star made entirely of homogeneous matter. The presence of the crustal layers is thus found to significantly reduce the Love number ${k}_{2}$, especially for low-mass stars. However, this reduction mainly arises from the increase in the stellar radius almost independently of the equation of state. This allows for a simple analytic estimate of ${k}_{2}$ for realistic neutron stars using the equation of state of homogeneous matter only.
Dense matter
Star (game theory)
r-process
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r-process
Dense matter
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Equation-of-state parameter plays a significant role for guessing the real nature of dark energy. Here polytropic equation-of-state p = ωρ n is chosen for some of the kinematical Λ-models viz., [Formula: see text], [Formula: see text] and Λ ~ ρ. Although in dust cases (ω = 0) closed form solutions show no dependency on the polytropic index n, but in non-dust situations some new possibilities are opened up including phantom energy with supernegative (ω < -1) equation-of-state parameter.
Polytrope
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