Thesis

Exploring the pasta phases in neutron stars

• Call:

  IDPASC Portugal - PHD Programme 2015

• Academic Year:

  2015 / 2016

• Domain:

  Astrophysics

• Supervisor:

  Constança Providência

• Co-Supervisor:

• Institution:

  Universidade de Coimbra

• Host Institution:

  CFisUC

• Abstract:

  Exploring the pasta phases in neutron stars Matter in the inner crust is formed by neutrons, protons and electrons. Protons and neutrons are bound in clusters that form a body-centered cubic lattice and coexist with a gas of neutrons that have dripped out of the clusters and electrons. In the Wigner-Seitz cell approximation the lattice is approximated by a single neutral cell, the Wigner Seitz cell, that has the geometric form of the cluster it lodges. The cell takes generally a spherical, cilindrical or flat shap. Due to electrical neutrality, the different cells do not interact and taking the symmetries of the cell into account it is possible to reduce the calculation to a single dimension, which reduces drastically the compational time. For the nuclear interaction we consider RMF models. Besides electrons and protons also interact through the Coulomb force. The free energy of the WS cell is calculated within the Thomas Fermi approximation. The numerical strategy followed is to expand the mesonic fields in a basis of the harmonic oscillator basis and the Poisson equation is calculated through the appropriate Green function. The most probable configurations are the ones that minimize the free energy. The present task includes the following subtasks: a) describe the pasta phase in the presence of a strong magnetic field including the anomalous magnetic field and study the effect of the field on the structue of the clusters, their magnetization and the polarization of the gas of free neutrons. b) include the contribution of light clusters (2^H, 3^H, 3^He and 4^He) at low densities close to the outer crust. They will be included as explicit degrees of freedom that behave as bosons (2^H and 4^He) or fermions (3^H, 3^He). It is expected that the inclusion of light clusters will affect the neutron skin of the clusters, Typel2014, and the density of dripped neutrons, and, consequently affect the transport properties of the inner crust. c) generalize the formalism and consider deformed clusters. These clusters are expected at densities between the appearance of spherical clusters and rod like clusters. Therefore taking them into account will shift the onset of rod to larger densities, and affecting the properties of the pasta, since rod-like and slab-like clusters will behave more like liquid crystals. In the presence of strong magnetic fields it is expectable that the deformed clusters will align along or against the field. With our approach we expect to be able to calculate deformed pasta phases using much less CPU time than more sophisticated calculations as in Pais2012. d) Various properties of a neutron star, e.g. the opacity with respect to neutrino propagation, are very sensitive to occurrence of pairing correlations. Therefore we included the possible effects of pairing in the pasta calculation. We will focus on isospin T =1 pairing for nucleon pairs with total momentum equal to zero. The standard BCS approach will be applied so that the the pairing gap for pair of nucleons with momenta k and − k is obtained by solving the gap equation. The formalism Kuckei2003 will followed. Kuckei2003 - J. Kuckei, F. Montani, H. Muther, and A. Sedrakian, Nucl. Phys. A723, 32 (2003) Gogelein2007 - Nuclear matter in the crust of neutron stars, P. Gögelein and H. Müther, Phys. Rev. C 76, 024312 (2007) Typel2014 - Neutron skin thickness of heavy nuclei with α-particle correlations and the slope of the nuclear symmetry energy, S. Typel, Phys. Rev. C 89, 064321 (2014)