cooling of n eutron st a r s
DESCRIPTION
COOLING OF N EUTRON ST A R S. D.G. Yakovlev. Ioffe Physical Technical Institute, St.-Petersburg, Russia. Introduction Neutrino emission Cooling theory Phenomenological concept Theory and observation Connections Conclusions. Main collaborators: A.D. Kaminker, Ioffe Institute - PowerPoint PPT PresentationTRANSCRIPT
COOLING OF NCOOLING OF NEUTRON STEUTRON STAARRS S
D.G. Yakovlev
Ioffe Physical Technical Institute, St.-Petersburg, Russia
Huntsville – May – 2009
• Introduction• Neutrino emission• Cooling theory• Phenomenological concept• Theory and observation• Connections• Conclusions
Main collaborators:• A.D. Kaminker, Ioffe Institute• A.Y. Potekhin, Ioffe Institute
Cooling Theory: Primitive and complicated at once
OVERALL STRUCTURE OF A NEUTRON STAR
Four main layers:1. Outer crust2. Inner crust3. Outer core4. Inner core
The main mystery:1. Composition of the core+2. The pressure of densematter=The problem ofequation of state (EOS)
Basic Ideas
48 29
Heat content:
~ 10TU T ergs
Main cooling regulators
Neutrino emission in neutron star cores
EOS, composition of matterSuperfluidity
Heat content and conduction in cores
Heat capacityThermal conductivity
Thermal conduction in heat blanketing envelopes
Thermal conductivityChemical compositionMagnetic field
Internal heat sources (for old stars and magnetars)
Viscous dissipation of rotational energyOhmic decay of magnetic fields, ect.
e
ep
n
, e e e en p e p e n n n
dfffwQ epnfi )1)(1(2
npeepn
A Tc
mmmgGQ
6
31022 )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
Strongest Neutrino Emission: Direct Urca Process
Lattimer, 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
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
Direct Urca, N/H
Neutrino Emission Processes in Neutron Star CoresOuter core Inner coreSlow emission Fast emission
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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
SUPERFLUIDITY IN NEUTRON STARS
After Lombardo & Schulze (2001)A=Ainsworth, Wambach, Pines (1989)S=Schulze et al. (1996)W=Wambach, Ainsworth, Pines (1993)C86=Chen et al. (1986)C93=Chen et al. (1993)
Density dependence of the gap10
0 ~ 1 MeV ~ 10 KcT
At high densities superfluidity disappears
Effects of superfluidity
Cooper pairing at T<Tc:
• Modifies heat capacity • Suppresses ordinary neutrino processes
• Creates a new process: neutrino emission due to Cooper pairing
• Possibly affects heat transport ?
SUPERFLUID SUPPRESSION OF NEUTRINO EMISSION
0( , ) ( , ) = neutrino emissivity
depends on / = superfluid reduction factorc
Q T Q T R
R T T
is exponentially suppressed
by strong superfluidity
(at )c
R
T T
A=1S0
B=3P2 (m=0)C=3P2 (m=2)
Cooper pairing neutrino emission
Flowers, Ruderman and Sutherland (1976) NN~~
s cm
erg )/( 1017.1
37
9F
*21
cNNN
N TTFaNTcm
p
m
mQ
Only the standard physics involved
Distribution over the stellar core
T=3x108 K
2x108
108
6x107
3x107
VQL d CPCP
Stage Duration Physics
Relaxation 10—100 yr Crust
Neutrino 10-100 kyr Core, surface
Photon infinite Surface, core,
reheating
THREE COOLING STAGES
HEAT( ) ( ) ( )sdT
C T L T L T Ldt
2 44 (1 / )
Heat blanketing envelope: ( )
( ) ( , ) exp( ( ))
s g
s s
L R T L L r R
T T T
T t T r t r
Analytical estimates
Thermal balance of cooling star with isothermal interior
Slow cooling viaModified Urca process
SLOW 69
1 year~tT
8 5~ 1.5 10 K in 10 yrsT t
Fast cooling viaDirect Urca process
FAST 49
1 min~tT
7~ 10 K in 200 yrsT t
OBSERVATIONS AND BASIC COOLING CURVENonsuperfluid starNucleon core EOS PAL (1988)Modified Urca neutrino emission:slow cooling
1=Crab2=PSR J0205+64493=PSR J1119-61274=RX J0822-435=1E 1207-526=PSR J1357-64297=RX J0007.0+73038=Vela9=PSR B1706-4410=PSR J0538+281711=PSR B2234+6112=PSR 0656+1413=Geminga14=RX J1856.4-375415=PSR 1055-5216=PSR J2043+274017=PSR J0720.4-3125
MODIFIED AND DIRECT URCA PROCESSES
1=Crab2=PSR J0205+64493=PSR J1119-61274=RX J0822-435=1E 1207-526=PSR J1357-64297=RX J0007.0+73038=Vela9=PSR B1706-4410=PSR J0538+281711=PSR B2234+6112=PSR 0656+1413=Geminga14=RX J1856.4-375415=PSR 1055-5216=PSR J2043+274017=PSR J0720.4-3125
15MAX c
14D c
1.977 2.578 10 g/cc
1.358 8.17 10 g/cc
From 1.1 to 1.98 with step 0.01
M M
M M
M M M M
BASIC PHENOMENOLOGICAL CONCEPT
SLOW FAST 1 2 SLOW FAST 1 2
BASIC PARAMETERS:
, , , , , , Q Q L L M M
Neutrino emissivity function Neutrino luminosity function
MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION
MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION
VELA 1.61 ?M M
1=Crab2=PSR J0205+64493=PSR J1119-61274=RX J0822-435=1E 1207-526=PSR J1357-64297=RX J0007.0+73038=Vela
9=PSR B1706-4410=PSR J0538+281711=PSR B2234+6112=PSR 0656+1413=Geminga14=RX J1856.4-375415=PSR 1055-5216=PSR J2043+274017=PSR J0720.4-3125
2p proton SF
MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION -- II
VELA 1.47 ?M M
Mass ordering is the same!
2p proton SF
Neutron stars with strongproton and mild neutron superfluidities in the cores
MAIN PHYSICAL MODELS
Problems:• To discriminate between neutrino mechanisms• To broaden transition from slow to fast neutrino emission
TESTING THE LEVELS OF SLOW AND FAST NEUTRINO EMISSION
Slow neutrino emission:
Fast neutrino emission:
(Mod Urca) / 30Q
(Mod Urca) 30Q
Two other parameters are totally not constrained
Direct Urca Pion condensate Kaon condensate
1 Aql X-12 4U 1608-5223 RX J1709-26394 KS 1731-2605 Cen X-46 SAX J1810.8-26097 XTE J2123-0588 1H 1905+0009 SAX 1808.4-3658
Data collected byKseniya Levenfish
CONNECTION: X-ray transients
Broadening of threshold for fast neutrino emission
Superfluidity:
Suppresses ordinary neutrino processesInitiates Cooper-pairing neutrino emissionShould be: Strong in outer core to suppress modified Urca Penetrate into inner core to broaden direct Urca thresholdCan be: proton or neutron
E.,g. pion polarizationVoskresensky &Senatorov (1984, 1986)Schaab et al. (1997)
Magnetic broadening Baiko & Yakovlev (1999)
Nuclear physics effects
Effects of accreted envelopes and surface magnetic fields
Different mass / of
accreted material on the surface
M M Dipole magnetic field
in heat blanketing layer
SUMMARY OF CONNECTIONS
Objects Physics which is tested
Middle-aged isolated NSa Neutrino luminosity function
Composition and B-field in heat-blanketing envelopes
Young isolated NSs Crust
Quasistationary XRTs Neutrino luminosity function
Composition and B-field in heat-blanketing envelopes
Deep crustal heating
Quasipersistent XRTsKS 1731—260; MXB 1659—29
Crust
Deep crustal heating
Superbursts Crust
Magnetars after outbursts Crust
Magnetars in quasistationary
states
??
CONCLUSIONS
TodayCooling neutron stars Soft X-ray transients
• Constraints on slow and fast neutrino emission levels• Mass ordering
CONCLUSIONSOrdinary cooling isolates neutron stars of age 1 kyr—1 Myr
• There is one basic phenomenological cooling concept (but many physical realizations)• Main cooling regulator: neutrino luminosity function • Warmest observed stars are low-massive; their neutrino luminosity seems to be <= 1/30 of modified Urca• Coldest observed stars are more massive; their neutrino luminosity should be > 30 of modified Urca (any enhanced neutrino emission would do)• Neutron star masses at which neutrino cooling is enhanced are not constrained• The real physical model of neutron star interior is not selected
Connections
• Directly related to neutron stars in soft X-ray transients (assuming deep crustal heating). From transient data the neutrino luminosity of massive stars is enhanced by direct Urca or pion condensation • Related to magnetars and superbusrts
Future
• New observations and accurate theories of dense matter• Individual sources and statistical analysis