1. Neutrino Processes in Neutron Stars
Evgeni E. Kolomeitsev
(Matej Bel University, Banska Bystrica, Slovakia)

2. What can we learn from neutron stars about processes in dense matter?
Data: star temperatures and ages
Interpretation: star cooling
Theory: ns cooling in a nutshell
luminosity of basic reactions
Problems: one scenario for all data points
How to calculate nuclear reactions in dense medium?
Green’s function method
Fermi liquid approach
quasiparticles and effective charges
Fermi liquid approach for superfluid medium
anomalous Green’s functions
conservation laws and Ward Identity

3. Northern hemisphere

5. fastly rotating magnetized body
..a little beacon
Nuclei and electrons
Neutron-rich nuclei and electrons
Nuclei, electrons and neutrons
neutrons, protons,
electrons, muons
density increase
Exotics:
hyperons,
meson-condensates,
quark matter
fastly rotating magnetized body
~10 km

6. mass, size, dynamics of SN explosion
integral quantity
equation of state of dense matter
phase transitions
changed in degrees of freedom
We want to learn about properties of microscopic excitations in dense matter
How to study response function of the NS?
How to look inside the NS?

7. important for supernova
At temperatures smaller than the opacity temperature (Topac~1-few MeV)
mean free path of neutrinos and antineutrinos is larger than the neutron star radius
white body radiation problem
After >105 yr –black body radiation of photons
At temperatures T>Topac
neutrino transport problem
important for supernova

8. debris of supernova explosion; accreted “nuclear trash”
[Yakovlev et al., A&A 417, 169]
M=1.4 Msol
R=10 km
internal T
external T
Text depends on
envelop composition
debris of supernova explosion; accreted “nuclear trash”

9. rotation frequency
period
for non-accreting systems, period increases with time
power-law spin-down
braking index
for magnetic dipole spin-down n=3
“spin-down age"
2) pulsar speed and position w.r. to the
geometric center of the associated SNR
1) age of the associated SNR
3) historical events
Crab : 1054 AD
Cassiopeia A: 1680 AD
Tycho’s SN: 1572 AD

10. Cooling scenario [neutrino production]
Given:
EoS
Cooling scenario [neutrino production]
Mass of NS
Cooling curve

11. slow cooling intermediate cooling rapid cooling 3 groups:
How to describe all groups within one cooling scenario?

12. neutron star is transparent for neutrino
CV – heat capacity, L - luminosity
emissivity
each leg on a Fermi surface / T
neutrino phase space ´ neutrino energy

13. ~T6 ~T8 Cooling: role of crust and interior?
most important are reactions in the interior
(The baryon density is
where n0 is the nuclear saturation density)
one-nucleon reactions:
direct URCA (DU)
~T6
modified URCA (MU)
two-nucleon reactions:
~T8
nucleon bremsstrahlung (NB)
URCA=Gamow’s acronym for “Un-Recordable Coolant Agent”

14. black body radiation
star is too hot;
crust is not formed
external temperature
heat transport
thru envelop
“memory” loss
crust is formed
1 yr ' 3 ¢107s

15. volume neutrino radiation
DU:
neutrino cooling
MU:
DATA Tn
photon cooling

16. Cabibbo angle Low-energy weak interaction of nucleons
effective weak coupling constant
Cabibbo angle
nucleon current
lepton current

17. Weinberg’s Lagrangian:
lepton current
nucleon current
Note 1/2 in neutral channel,
since Z boson is neutral and W is charged!

18. ONE-NUCLEON PROCESS
DIRECT URCA

19. emissivity:
matrix element
traces over lepton (l) and nucleon (n) spins

20. phase space integration
simplifications for
on Fermi surfaces
angle integration
triangle inequality
critical condition

21. energy integration
since the integration over energy goes from -¥ to +¥ and
under integral we can replace

22. proton concentration > 11-14%

23. energy-momentum conservation
requires
processes on neutral currents are forbidden!

24. Bose condensate of pions
assume e reaches m
Bose condensate of pions
k=(m ,0)
neutrons in both initial and final states
energy-momentum conservation is easily fulfilled

25. condensate amplitude
Migdal’s pion condensate k=(,kc): <m, kc» pF,e p-wave condensate
Kaon condensate processes yield a smaller contribution
All “exotic” processes start only when the density exceeds some critical density

26. TWO-NUCLEON PROCESSES
MODIFIED URCA

28. Friman & Maxwell AJ (1979)
(1)
(3) k
(2)
(4)
Additionally one should take into account exchange reactions (identical nucleons)

29. Emissivity:
s=2 is symmetry factor. Reactions with the electron in an initial state yield extra factor 2.
Finally
due to exchange reactions
Coherence: only axial-vector term contributes (!)
whereas for PU processes both vector and axial-vector terms contribute

30. are not close to each others
[Blaschke, Grigorian, Voskresensky A&A 424 (2004) 979]
But masses of NS
are not close to each others

31. Klähn et al. PRC 74, (2006)

32. SUPERFLUID MATTER

33. A
2-n separation energy

34. attraction
repulsion
Hebeler, Schwenk, and Friman,
PLB 648 (2007) 176

35. U. Lombardo and H.-J. Schulze, astro-ph/0012209

36. 1ns for neutrons 1p for protons HSF [Kaminker, Yakovlev, Gnedin,
A&A 383 (2002) 1076]
1ns for neutrons
1p for protons
HSF

37. For the s-wave paring for HDD EoS from
[Blaschke, Grigorian, Voskresnesky PRC 88, (2013)]
For the s-wave paring

38. Ground state Excited state unpaired fermions paired fermions pair
breaking
“exciton” D
pairing gap
excitation spectrum
emission spectrum

39. In superfluid (T<Tc<0
In superfluid (T<Tc<0.1-1 MeV) all two-nucleon processes are suppressed by factor exp(-2/T)
new “quasi”-one-nucleon-like processes (one-nucleon phase space volume) become permitted
[Flowers, Ruderman, Sutherland, AJ 205 (1976), Voskresensky& Senatorov, Sov. J. Nucl. Phys. 45 (1987) ]
un-paired nucleon
paired nucleon
[ Voskresensky, Senatorov, Sov. J. Nucl. Phys. 45 (1987); Senatorov, Voskresensky, Phys. Lett. B184 (1987); Voskresensky astro-ph/ ]
nn is neutron gap
not
as in Flowers et al. (1976)
Naively one expect the emissivity of p p to be suppressed by extra cV2~0.006 factor.

40. pair breaking and formation (PBF) processes are important!
[Page, Geppert, Weber , NPA 777, 497 (2006)]

41. standard
exotic

42. How to calculate nuclear reactions in dense medium?
Green’s function method
Fermi liquid approach
quasiparticles and effective charges