1. Two talks for the price of one: Cooling by angulon annihilation and Asymmetrical fermion superfluids P. Bedaque (Berkeley Lab) G. Rupak, M. Savage, H. Caldas

2. Cooling of neutron stars by "angulon" annihilation Light element envelope Heavy element envelope Geminga Vela Neutron stars start their lives hot and cool down by neutrino and photon emission After a minute, degenerate Cooling curves depend on emissivity, specific heat, thermal conduction, etc … Determined by low-lying excitations Unique laboratory to learn about dense matter Page et al.

3. Neutron pairing in the 3 P 2 channel for densities higher than nuclear saturation most attractive channel traceless symmetric matrix

4. D ij real (favored close to T c ) D determined by an orthonormal frame + 2 eigenvalues D eigenvalues are roots of 1

5. Symmetry (breaking) pattern tensor/spin-orbit discrete tensor/spin-orbit approximate exact 4 exactly massless Goldstone bosons

6. angulons Ripples in the sea of frames = angulons Contrary to other excitations, not exponentially suppressed by Boltzman factors, dominate low energy/temperature properties Couples to neutrino through neutral currents Dimensional analysis:

7. Effective theory For E << D 0 : phase spin rotation orbital rotation Matching to a simple "microscopic" theory

8. Rate for angulon+angulon No rotation symmetry: big complicated mess w = v k enhancement on the number of angulons ~ (T/v) 3 suppression due to E ~ v suppression due to kinematical constraint (no decay with v=0) suppression on the coupling ~ v

9. Does it matter for cooling ? Above T c no: (modified) Urca N+N N+N+l+      Below T c maybe: e+e e+e+        But pair formation around T c on a shell ~ 10 20 T 9 7 A more detailed study is probably necessary

11. Pairing in asymmetrical superfluids Two fermion species: A and B up and down quarks, two different atoms or hyperfine states in a trap, … different Fermi surfaces, pairing ?

12. Relevance for neutron (quark) stars, atomic traps renewed the interest on the problem: some new, interesting suggestions for the ground state Variational arguments can rigorously show what is NOT a ground state

13. To make it concrete: mean-field, low density, D / m <<1 Bogoliubov transformation:

14. slightly different problem: m A and m B fixed: minimize H- m N Fill states with negative E k b BCS filled with B

15. mA=mBmA=mB 1 st order transition m B - m A =2 D

16. In the real problem n A and n B are fixed: local maximum (Sarma state) suggested as the ground state (Liu &Wilczek, gapless superconductor)

17. Mixed state: minimize Which is smaller: E MIXED or E SARMA ? normal fraction

18. Sarma=BCS=Mixed Sarma mixed Sarma=normal E MIXED < E SARMA

19. In atomic traps, bubbles can be imaged. Long sought evidence for superfluidity in fermionic atomic traps ? Different dispersion relations (relativity) don’t change anything Three flavors is (may be) different !