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