Ladek Zdroj, February 2008,

• Neutrino emission in nonsuperfluid matter• The effects of superfluidity

COOLING OF NCOOLING OF NEUTRON STEUTRON STAARRSS 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

RICHNESS OF PHYSICAL CONDITIONS

MAIN NEUTRINO EMISSION MECHANISMS IN NEUTRON STARS

Main features:• unobserved (but governs the cooling)• complete transparency• neutrino energies ~ kT• massless but low-energy neutrinos

QdVL

Q

]c [erg luminosity neutrino and

]scm [erg emissivity neutrino :quantity acticalPr1

13

NEUTRINO PROCESSES IN NEUTRON STAR CRUST

TEMPERATURE AND DENSITY DEPENDENSE OF NEUTRINO EMISSION

93 10 KT 83 10 KT

e

ep

n

, e e e en p e p e n n n

dfffwQ epnfi )1)(1(2

npeepn

A Tcmmm

gGQ

6310

22 )31(10080457

27 6 3 19

46 6 19

~ 3 10

~ 10

Q T erg cm s

L T erg s

FeFpFn ppp 02 ~

n

Direct Urca ProcessLattimer, Pethick, Prakash, Haensel (1991)

Threshold:In inner cores of massive stars

Similar processes with muons

Similar processes with hyperons, e.g.

Is forbidden in outer core by momentum conservation:

0 9 330 MeV/c, 120 MeV/c, ~ / ~ 0.1 MeV/cFn Fe Fp Bp p p p k T c T

Gamow and Shoenberg: Casino da Urca in Rio de Janeiro

Neutrino theory of stellar collapse, Phys. Rev. 59, 539, 1941:

Unrecordable cooling agent

Photo andStory by R. Ruffini

Welcome to the Urca World - I

Welcome to the Urca World - II

ENCHANCED NEUTRINO EMISSION PROCESSES IN CORES OF MASSIVE NEUTRON STARS

, e e e en p e p e n n n

, n p p n

, e en e n e

0, =( , ), =( , , )e eB B e B e B B n B p

, =( , ) e eN N e N e N N n p

, e ed u e u e d

Prakash, Prakash, Lattimer, Pethick (1992)

Maxwell et al. (1977)

Brown et al. (1992)

Iwamoto (1980, 1982)

6 6FAST 0F 9 FAST 0F 9 Q Q T L L T

NUCLEON-HYPERON MATTER

PION CONDENSATE

KAON CONDENSATE

QUARK MATTER

SLOW NEUTRINO EMISSION PROCESSES EVERYWHERE IN NEUTRON STAR CORES

, e en N p N e p N e n N

8 8SLOW 0S 9 FAST 0S 9 Q Q T L L T

MODIFIED URCA [N=n or p = nucleon-spectator]

NUCLEON-NUCLEON BREMSSTRAHLUNG

N N N N

n n n n

n p n p

p p p p

{

LEPTON MODIFIED URCA, BREMS IN COULOMB COLLISIONS

, [ =any charged fermion]e eC e C e C C C

e C e C

Bahcall and Wolf (1965), Friman and Maxwell (1979), Maxwell (1987),Yakovlev and Levenfish (1995)

Friman and Maxwell (1979)

Any neutrino flavor

Enhanced emission in inner cores of massive neutron stars

Everywhere in neutron star cores

Neutrino Emission Processes in Neutron Star Cores

6 6FAST 0F 9 FAST 0F 9 Q Q T L L T

Model Process

N/H direct Urca

Pion condensate

Kaon condensate

Quark matter

3 10 [erg cm s ]Q

e eN N e N e N

e eB B e B e B

e ed u e u e d

e eB B e B e B 26 2710 3 10 23 2610 1023 2410 1023 2410 10

8 8SLOW 0S 9 FAST 0S 9 Q Q T L L T

Modified Urca

Bremsstrahlung

nN pNe pNe nN

N N N N

20 2110 3 10

19 2010 10

Nucleon Matter with Open Direct Urca Process

FAST AND SLOW NEUTRINO COOLING

SUN

Direct Urca, N/H

Neutrino Emission Processes in Neutron Star CoresOuter core Inner coreSlow emission Fast emission

}

}

}}

}

e en p e p e n

Pion condensate

Kaon condensation

Or quark matter

e eN N e N e N

e eB B e B e B

e ed u e u e d

Modified Urca nN pNe pNe nN

NN bremsstrahlung N N N N

Enhanced emission in inner cores of massive neutron stars:

Everywhere in neutron star cores:

6 6FAST 0F 9 FAST 0F 9 Q Q T L L T

8 8SLOW 0S 9 FAST 0S 9 Q Q T L L T

STANDARD

Fast erg

cm

-3 s

-1

MAIN PHYSICAL MODELS

Problems:To discriminate between neutrino mechanismsTo broaden transition from slow to fast neutrino emission

SUPERFLUID SUPPRESSION OF NEUTRINO EMISSION

0( , ) ( , ) = neutrino emissivity depends on / = superfluid reduction factorc

Q T Q T RR T T

is exponentially suppressed by strong superfluidity (at )c

R

T T

A=1S0

B=3P2 (m=0)C=3P2 (m=2)

AN EXAMPLE OF SUPERFLUID REDUCTION OF NEUTRINO EMISSION

Two models for proton superfluidity Neutrino emissivity profiles

Superfluidity:• Suppresses modified Urca process in the outer core• Suppresses direct Urca just after its threshold (“broadens the threshold”)

Cooper pairing neutrino emission

Flowers, Ruderman and Sutherland (1976) NN ~~

s cmerg )/( 1017.1 3

79

F*

21cN

NN

N TTFaNTcm

pmmQ

Only the standard physics involved

Distribution over the stellar core

T=3x108 K

2x108

108 6x107

3x107

VQL d CPCP

Neutrino luminosity due to Cooper pairing

8)10010(~ TLL MurcaCooper

Gusakov et al. (2004)

Summary of neutrino emission properties

Neutrino emission from neutron star cores is strongly regulated by(1)Temperature(2)Composition of the matter(3)Superfluidity

These regulators may affect the emissivity in a non-trivial way(enhance or suppress)

What is their effect? Next lecture

REFERENCES

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.