1. Catania, October 2012, THERMAL EVOLUTION OF NEUTRON STARS: Theory and observations D.G. Yakovlev Ioffe Physical Technical Institute, St.-Petersburg, Russia 1. Formulation of the Cooling Problem 2. Superlfuidity and Heat Capacity 3. Neutrino Emission 4. Cooling Theory versus Observations

2. FERMI SYSTEMS Electrons, muons, neutrons, protons, hyperons, quarks = fermions = Fermi-Dirac statistics Fermi sea Thermal width of Fermi level 1

3. FERMI SEA AND FERMI SURFACE Bulk properties of matter: particle number density, energy density, pressure FERMI-SEA (Many fully occupied states; Many “dead” energetic particles) pXpX pZpZ pYpY pFpF

4. FERMI SEA AND FERMI SURFACE Second-order thermodynamic properties: entropy, heat capacity Kinetic properties: thermal and electric conductivity Neutrino processes Generally, any reactions Superfluid processes FERMI-SURFACE (Smaller amount of exchangable states and “reacting” particles ) IMPORTANT FOR:

5. Superfluidity – neutron stars Mechanism of superfluidity: Cooper pairing of degenerate neutrons and/or protons due to nuclear attraction Any superfluidity is defined by critical temperature T C, that depends on density Pairing type: singlet-state ( 1 S 0 ) or triplet state ( 3 P 2 ) Inner crust of neutron star: Singlet-state pairing of free neutrons Singlet-state pairing of nucleons in atomic nuclei Neutron star core (typically): Singlet-state pairing of protons Triplet-state pairing of neutrons SCHEME

6. Low densities Weak pairing Medium densities Strong pairing High densities Repulsion, no pairing Superfluidity – neutron stars

7. Superfluidity – microscopic manifestations Creates gap in energy spectrum near Fermi level Microscopic calculations of the gap are very model dependent (nuclear interaction; many-body effects) T=0 Free Fermi gas Superfluid Fermi gas Free Fermi gas T>T c Superfluid Fermi gas T~T c Superfluid Fermi gas T<<T c Temperature dependence

8. SUPERFLUIDITY IN NEUTRON STARS After Lombardo & Schulze (2001) A=Ainsworth, Wambach, Pines (1989) S=Schulze et al. (1996) W=Wambach, Ainsworth, Pines (1993) C86=Chen et al. (1986) C93=Chen et al. (1993) Density dependence of the gap Our task is to study in neutron star core

9. Effects of superfluidity Cooper pairing at T<T c : Modifies heat capacity Suppresses ordinary neutrino processes Creates a new process: neutrino emission due to Cooper pairing

10. HEAT CAPACITY OF NEUTRON STAR CORES Mixture of strongly degenerate fermions (the simplest version – n, p, e) Takes into account superfluidity In superfluid matter: (per cm 3 )

11. Heat Capacity in Nucleon Neutron Star Cores Non-superfluid core Superfluid core

12. Summary on superfluidity and heat capacity Neutrons, protons and other baryons in neutron star interiors can be in superfluid state Superfluidity is very model dependent (too many different microscopic models) Superfluidity is a Fermi surface phenomena which affects thermodynamics and kinetics of neutron star matter Superfluidity can strongly affect heat capacity of neutron stars What are the effects of superfluidity on neutrino emission and neutron star cooling?  Next lecture

13. U. Lombardo, H.-J. Schulze. Superfluidity in neutron star matter. In: Physics of Neutron Star Interiors, edited by D. Blaschke, N. Glendenning, A. Sedrakian, Berlin: Springer, 2001, p. 30. D.G. Yakovlev, K.P. Levenfish, Yu.A. Shibanov. Cooling of neutron stars and superfluidity in their cores. Physics – Uspekhi 42, 737, 1999. D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel. Neutrino emission from neutron stars. Phys. Rep. 354, Nums. 1,2, 2001. REFERENCES