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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
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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
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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
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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
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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
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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
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Nucleon Matter with Open Direct Urca Process
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FAST AND SLOW NEUTRINO COOLING
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FAST AND SLOW NEUTRINO COOLING
SUN
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Effects of superfluidity on neutrino emission
Two effects:1.Suppresses traditional neutrino processes2.Creates specific neutrino emission due to Cooper pairing of nucleons
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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
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Distribution over the stellar core
T=3x108 K
2x108
108
6x107
3x107
VQL d CPCP
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Neutrino luminosity due to Cooper pairing
8)10010(~ TLL MurcaCooper
Gusakov et al. (2004)
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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)
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Minimal and maximal cooling paradigms
Minimal cooling
Maximal cooling
SF off SF on
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~ (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
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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”)
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MAXIMAL COOLINGSTRONG PROTON AND MILD NEUTRON SUPERFLUIDITY
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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
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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.