Neutron Stars Aree Witoelar

What is a neutron star? A collapsed core of a massive star Composed entirely from neutron Incredibly high density

Creation of a neutron star Fusion from H to Fe in the core of stars No more fuel -> core reaches tremendous density and explodes (Supernova) Inverse ß–decay takes place:

Properties Mass = 1.3-1.5 Msun (3.1030 kg) Radius = 10 km Density = 1014g/cc Magnetic field = 1012 Gauss

Interior Increasing pressure inwards creates ‘Pasta’ layers

Nuclear Physics of Neutron Stars Neutron stars are like giant neutron supernuclei Testing models of Nuclei-Nuclei Interaction on neutron stars Estimating Neutron Star radius: Binding Energy Fermi Gas model Nuclei-Nuclei Interaction (first principles)

Binding Energy Binding energy for a nucleus Assumptions for a huge ‘neutron nucleus’: No Coulomb energy Neglect pairing energy Neglect surface term with respect to volume term

Binding Energy (2) Simplified Binding energy Bound state exist if binding energy is positive Filling the constants, the result is A = 5 x 1055 R = 4.3 km M = 0.045 solar mass Same order of magnitude as observations

Fermi Gas model Treat neutron stars as degenerate Fermi gases (of neutrons) held by gravity Assume Constant density: average pressure No nucleon-nucleon interaction Number of possible states Integrate to Fermi momentum pF

Fermi Gas model (2) Calculate <Ekin/N> from Fermi momentum and <Epot /N> from gravitational energy Minimize total of kinetic and potential energy The results are R = 12 km  = 0.25 nucleons/fm3 (nucleus = 0.17 nucleons/fm3 ) Close to experimental values: gravitational pressure compensated by Fermi pressure and nucleon-nucleon repulsion

Nucleon-Nucleon Interaction Nuclear force is an interaction between colourless nucleons with range of the same order of magnitude as the nucleon diameter It is not possible to extract n-n potential directly from structure of nucleus Different models with different parameterization

General form of n-n potential Quantities to determine interaction Separation of nucleons x Relative momenta p Total orbital angular momentum L Relative orientation of spins s1 and s2 Potential is scalar Symmetric under exchange of the two nuclei central spin-spin Tensor spin-orbit

-meson theory Nucleons are surrounded by field of massive (virtual) particles called -mesons (pions) Pion could be absorbed by another nucleon in its lifetime Momentum transfer -> akin to force (but attractive) Direct analogy of EM force but photons have no mass, pion have mass of 140 MeV/c2 -> finite range Heisenberg uncertainty principle

Covalent and Meson exchange Covalent bonds (direct q-exchange) are suppressed by color restriction Meson exchange: color-neutral Yukawa potential:

Equation of State The relations between the density and temperature to its pressure and internal energy, specific heats, etc. Pure neutron matter is unbound

Many-Body Theory Hamiltonian: Four-body and higher order interaction are neglected

Neutron Star Radius Different models have different parameterizations of vijR

Summary Neutron stars are interesting! Nuclear Physics: Approximate Neutron Star radius with Binding Energy, Fermi Gas model, or Nucleon-Nucleon interaction Nucleon-Nucleon interaction is caused by meson exchange (virtual particles) Different n-n models predict different radii of neutron stars