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

FAST AND SLOW NEUTRINO COOLING

SUN

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