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The Interior Structure of Neutron Stars Evan Keane Jodrell Bank Centre for Astrophysics University of Manchester 08/04/2008 3rd Estrela Workshop Bonn, Deutschland. Neutron Star - Basics Bang! When stars, with initial masses in the range 11±1 -> ~25 M will, once they have evolved of the main sequence and burnt all their nuclear fuel (up to 56Fe), will end their main lives in a Type II Supernova and leave a neutron star (NS) remnant. Properties: From observations of binary pulsar systems most NSs are seen to have masses around M=1.35M which is taken as the canonical mass. Also must spin slower than break-up speed -> gives us Rmax=16.8km(P/ms). Requirining vsound<c implies Rmin=1.5RSchwarzschild=6.2km Take canonical radius of R=10km A Minimum Energy Argument The basic method for determining the composition of the internal structure is to minimise the energy density of the system as a whole with respect to A, Z and Yn Tricky bit: Determining a form for the energy density of the nucleus (i.e. need to chose a nuclear physics theory) Minimum energy configuration at a given ρ, gives (A,Z) the equilibrium composition at that density. At the crust the equilibrium configuration is 56Fe Equilibrium Nucleus down to ρdrip Measured in lab Theoretical Models Equilibrium Nuclei The Crust A NS is not a big ball of neutrons! We start with 56Fe ions in a degenerate electron gas and no free neutrons. P=Kρ5/3 (non-rel degenerate electron gas) but need corrections for Coulomb repulsion. “Coulomb lattice” of Wigner-Seitz cells. At ρ=1010kg/m3 electrons now relativistic enough to penetrate into nuclei and combine with protons to “neutronise” nuclei via unbalanced inverse beta decay. Towards Neutron Drip Above ρ=1010kg/m3 get more & more neutron-rich in an electron sea ->The equilibrium nucleus shifts to heavier configs. At a certain depth nuclei become saturated with neutrons ->More energetically favourable for neutrons to form outside the nucleus. This is because we have reached the ρ where the highest occupied neutron energy level is just at the neutron Fermi energy. As ρ increases further more neutrons “drip” free of nuclei & we get heavy nuclei in a neutron and electron sea Beyond Neutron Drip & Complications Neutron drip proceeds from ρdrip=(4.3)(1014)kg/m3 until all nuclei have dripped free of nuclei by ρnuclear=(2.7)(1017)kg/m3 At very slightly higher densities we reach the muon Fermi energy and these will be created & we have neutron fluid + proton fluid + electrons + muons There are other complications also: protons and neutrons form Cooper pairs just below nuclear density --> superfluids! --> p fluid is (Type II) superconductor More Complications I have also not mentioned magnetic fields!! Heavy nuclei are actually stretched out along direction of magnetic field lines. Also get quantum vortices in the superfluid interior. The core composition is unknown but decides whether or not he have a “hard” or “soft” eos. Pion/Kaon core -> higher ρcore, lower R, M, “soft” Quark core -> lower ρcore, higher R, M, “hard” --> binary pulsar observations can tell us which models are possible. The Core? Thank You