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. 1. Formulation of the Cooling Problem 2. Superlfuidity and Heat Capacity 3. Neutrino Emission 4. Cooling Theory versus Observations. History Cooling stages - PowerPoint PPT PresentationTRANSCRIPT
COOLING OF NCOOLING OF NEUTRON STEUTRON STAARRSS
D.G. Yakovlev
Ioffe Physical Technical Institute, St.-Petersburg, Russia
Ladek Zdroj, February 2008,
1. Formulation of the Cooling Problem
2. Superlfuidity and Heat Capacity 3. Neutrino Emission
4. Cooling Theory versus Observations• History• Cooling stages• Observations• Tuning theory to explain observations• Conclusions
PRE-PULSAR HISTORY
Stabler (1960) – PhD, First estimates of X-ray surface thermal emission
Chiu (1964) – Estimates that neutron stars can be discovered from observations of thermal X-rays
Morton (1964) , Chiu & Salpeter (1964), Bahcall & Wolf (1965) – First simplified cooling calculations
Tsuruta & Cameron (1966) – Basic formulation of all elements of the cooling theory
NEW HISTORY
Lattimer, Pethick, Prakash & Haensel (1991) The possibility of direct Urca process in nucleon matter
Page & Applegate (1992) Crucial importance of superfluidity for cooling
Schaab, Voskresensky, Sedrakian, Weber & Weigel (1997); Page (1998) The importance of Cooper pairing neutrino emission
Stage Duration Physics
Relaxation 10—100 yr Crust
Neutrino 10-100 kyr Core, surface
Photon infinite Surface, core,
reheating
THREE COOLING STAGES
After 1 minute of proto-neutron star stage of Sanjay Reddy
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: MAIN PRINCIPLES
Sp
in a
xis B-
axis
Isolated (cooling) neutron stars – no additional heat sources:Age tSurface temperature Ts
MEASURING DISTANCES: parallax; electron column density from radio data; association with clusters and supernova remnants; fitting observed spectra
MEASURING AGES: pulsar spin-down age (from P and dP/dt); association with stellar clusters and supernova remnants
MEASURING SURFACE TEMPERATURES: fitting observed spectra
See lectures by Roberto Turolla
OBSERVATIONS
Chandraimage of the Velapulsarwind nebulaNASA/PSUPavlov et al
Chandra XMM-Newton
MULTIWAVELENGTH SPECTRUM OF THE VELA PULSAR
4(1.1 2.5) 10 yr
0.65 0.71 MKS
t
T
THERMAL RADIATION FROM ISOLATED NEUTRON STARS
OBSERVATIONS AND BASIC COOLING CURVENonsuperfluid starNucleon coreModified 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
MAIN PHYSICAL MODELS
Problems:To discriminate between neutrino mechanismsTo broaden transition from slow to fast neutrino emission
AN EXAMPLE OF SUPERFLUID BROADENING OF DIRECT URCA THRESHOLD
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”)
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
VELA 1.61 ?M M
MODIFIED AND DIRECT URCA PROCESSES: SMOOTH TRANSITION -- II
VELA 1.47 ?M M
Mass ordering is the same!
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
Summary of cooling regulators
Regulators of 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.
Levenfish, Haensel (2007)
CONNECTION: Soft X-ray transients
Deep crustal heating: Brown, Bildsten, Rutledge (1998)Energy release: Haensel & Zdunik (1990,2003), Gupta et al. (2007)
SAX J1808.4-3658, talk by Craig HeinkeMore in the next talk by Peter Jonker
CONNECTION: Magnetars
Kaminker et al. (2006)
SUMMARY OF CONNECTIONS
Sources: X-ray transients; magnetars; superburstsProcesses: quasistationary and transient
CONCLUSIONS
Future
Today
• New observations and good practical theories of dense matter• Individual sources and statistical analysis
Cooling 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 should 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
C.J. Pethick. Cooling of neutron stars. Rev. Mod. Phys. 64, 1133, 1992.
D.G. Yakovlev, C.J. Pethick. Neutron Star Cooling. Annu. Rev. Astron. Astrophys. 42, 169, 2004.
D. Page, U. Geppert, F. Weber. The cooling of compact stars. Nucl. Phys. A 777, 497, 2006.
REFERENCES