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The structure and composition of the inner crust of neutron stars, as well as global stellar properties such as radius and moment of inertia, have been shown to correlate with parameters characterizing the symmetry energy of nuclear matter such as its magnitude J and density dependence L at saturation density. It is thus mutually beneficial to nuclear physicists and astrophysicists to examine the combined effects of such correlations on potential neutron star observables in the light of recent experimental and theoretical constraints on J, L, and relationships between them. We review some basic correlations between these nuclear and astrophysical observables, and illustrate the impact of recent progress in constraining the J-L parameter space on the composition of the inner crust, crust-core transition density and pressure, and extent of the hypothesized pasta region. We use a simple compressible liquid drop model in conjunction with a simple model of nuclear matter which allows for independent, smooth, variation of the J and L. We extend the model into the core using the same nuclear matter model to explore the effects on global crust and core properties, and on potential observables such as crust oscillation frequencies and mechanically supported crust deformation. Throughout we illustrate the importance of the relationship between J and L implicit in a particular model of nuclear matter to the predictions of neutron star properties.
The functional form of the nuclear symmetry energy in the whole range of densities relevant for the neutron stars is still unknown. Discrepancies concern both the low as well as the high density behaviour of this function. By use of Bezier curves thr
The form of the nuclear symmetry energy $E_s$ around saturation point density leads to a different crust-core transition point in the neutron star and affect the crust properties. We show that the knowledge about $E_s$ close to the saturation point i
X-ray observations of the neutron star in the Cas A supernova remnant over the past decade suggest the star is undergoing a rapid drop in surface temperature of $approx$ $2-5.5%$. One explanation suggests the rapid cooling is triggered by the onset o
In this book chapter we review plasma crystals in the laboratory, in the interior of white dwarf stars, and in the crust of neutron stars. We describe a molecular dynamics formalism and show results for many neutron star crust properties including ph
We demonstrate that observations of glitches in the Vela pulsar can be used to investigate the strength of the crust-core coupling in a neutron star, and suggest that recovery from the glitch is dominated by torque exerted by the re-coupling of super