Catania, October 2012,

THERMAL EVOLUTION OF NTHERMAL EVOLUTION OF NEUTRON STEUTRON STAARRS:S:Theory and observationsTheory 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

MAIN NEUTRINO EMISSION MECHANISMS IN NEUTRON STARS

Main features:• unobserved (but governs the cooling)• complete transparency

QdVL

Q

]c [erg luminosity neutrino and

]scm [erg emissivity neutrino :quantity acticalPr1

13

e

ep

n

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

27 6 3 19

46 6 19

~ 3 10

~ 10

Q T erg cm s

L T erg s

FeFpFn ppp 02 ~

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

Threshold:In inner cores of massive stars

Similar processes with muons

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

SLOW NEUTRINO EMISSION PROCESSES EVERYWHERE IN NEUTRON STAR CORES

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

8 6SLOW 0S 9 FAST 0F 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

{

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

Direct Urca

3 10 [erg cm s ]Q

e en p e p e n 26 2710 3 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

Direct Urca

Neutrino emission from cores of non-superfluid NSs

Outer core Inner core Slow emission Fast emission

}

}}

e en p e p e n

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 FAST 0F Q Q T L L T

8 8SLOW 0S SLOW 0S Q Q T L L T

STANDARD

Fast

erg

cm

-3 s

-1

NS with nucleon core: N=n, p

n n

n p

p p

Nucleon Matter with Open Direct Urca Process

FAST AND SLOW NEUTRINO COOLING

FAST AND SLOW NEUTRINO COOLING

SUN

Effects of superfluidity on neutrino emission

Two effects:1.Suppresses traditional neutrino processes2.Creates specific neutrino emission due to Cooper pairing of nucleons

Neutrino emission due to Cooper pairing

Flowers, Ruderman and Sutherland (1976)Voskresensky and Senatorov (1987)Schaab et al. (1997)

n n

Temperature dependence of neutrino emissivity due to Cooper pairing

Features:• Efficient only for triplet-state pairing of neutrons •Non-monotonic T-dependence• Strong many-body effects

Leinson (2001)Leinson and Perez (2006)Sedrakian, Muether, Schuck (2007)Kolomeitsev, Voskresensky (2008)Steiner, Reddy (2009)Leinson (2010)

Physics:Jumping over cliff from branch A to B

A

B

Neutrino emission due to Cooper pairing

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)

Minimal and maximal cooling paradigms

Consider neutron stars with nucleon cores (simplest composition)

Minimal cooling paradigm: no direct Urca in all stars

Maximal cooling paradigm: direct Urca in heavy stars

Pradigm SF SF

Minimal cooling off on

Maximal cooling off on

Four cases

Minimal cooling theory:

Page, Lattimer, Prakash, Steiner (2004)

Gusakov, Kaminker, Yakovlev, Gnedin (2004)

Minimal and maximal cooling paradigms

Minimal cooling

Maximal cooling

SF off SF on

~ (10 100)Cooper MurcaL L

Minimal cooling. SF on

Non-superfluid star with nucleon core Standard Murca cooling

Add strong proton super- fluidityVery slow cooling

Add moderate neutron superfluidity: CP neutrino outburst

nn nn

np np

pp pp

nN pNe pNe nN

nN pNe pNe nN

np np

pp pp

nn nn

~ 0.01 MurcaL L MurcaL L

nN pNe pNe nN

nn nn

np np

pp pp

nn

MAXIMAL COOLING 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”)

MAXIMAL COOLINGSTRONG PROTON AND MILD NEUTRON SUPERFLUIDITY

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.