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

Catania, October 2012,

1. Formulation of the Cooling Problem

2. Superlfuidity and Heat Capacity 3. Neutrino Emission

4. Cooling Theory versus Observations

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

( ) ( ) ( )ii i s

dTC T L T L T

dt

2 44 (1 / )

Heat blanketing envelope: ( )

( ) ( , )exp( ( ))

s g

s s

i

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~

i

tT

8 5~ 1.5 10 K in 10 yrsiT t

Fast cooling viaDirect Urca process

FAST 49

1 min~

i

tT

7~ 10 K in 200 yrsiT 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

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

Minimal cooling; SF off – does not explain all data

MAXIMAL COOLING; SF OFFMODIFIED 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

Does not explain the data

MAXIMAL COOLING: SRTONG PROTON SF

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”)

VELA 1.61 ?M M

MAXIMAL COOLING: SRTONG PROTON SF

MAXIMAL COOLING: STRONG PROTON SF – II

VELA 1.47 ?M M

Mass ordering is the same!

MINIMUM AND MAXIMUM COOLING SF on

Gusakov et al. (2004, 2005)

Minimum coolingGusakov et al. (2004)

Minimum-maximum coolingGusakov et al. (2005)

Cassiopeia A supernova remnant

Cassiopeia A observed by the Hubble Space Telescope

Very bright radio sourceWeak in optics due to interstellar absoprtion

Distance: kpc (Reed et al. 1995)

Diameter: 3.1 pc

No historical data on progenitor

Asymmetric envelope expansionAge yrs => 1680 from observations of expanding envelope (Fesen et al. 2006)

MYSTERIOUS COMPACT CENTRAL OBJECT IN Cas A SNR

Various theoretical predictions: e.g., a black hole (Shklovsky 1979)

Discovery: Tananbaum (1999) first-light Chandra X-ray observationsLater found in ROSAT and Einstein archives

Later studies (2000-2009):

Pavlov et al. (2000)Chakrabarty et al. (2001)Pavlov and Luna (2009)

Main features:1.No evidence of pulsations2.Spectral fits using black-body model or He, H, Fe atmosphere models give too small radius R<5 km

Conclusion: MYSTERY – Not a thermal X-ray radiation emitted from the entire surface of neutron star

A Chandra X-ray Observatory image of the supernova remnant Cassiopeia A.Credit: Chandra image: NASA/CXC/Southampton/W.Ho; illustration: NASA/CXC/M.Weiss

COOLING NEUTRON STAR IN Cas A SNR

Ho and Heinke (2009) Nature 462, 671Fitting the observed spectrum with carbon atmosphere model gives the emission from the entire neutron star surface

Neutron star parameters

OBSERVATIONS available for Ho and Heinke (2009)Heinke and Ho (2010):16 sets of Chandra observations in 2000, 2002, 2004, 2006, 2007, 2009 totaling 1 megasecond (two weeks)

Conclusion:Cas A SNR contains cooling neutron star with carbon surfaceIt is the youngest cooling NS whose thermal radiation is observed

Main features:1. Rather warm neutron star2. Consistent with standard cooling3. Not interesting for cooling theory!!! (Yakovlev et al. 2011)

Heinke & Ho, ApJL (2010): Surface temperature decline by 4% over 10 years

Ho & Heinke 2010

New observation

Standard cooling

“Standard cooling” cannot explain these observations

M, R, d, NH are fixed

Observed cooling curve slope

REVOLUTION: Cooling Dynamics of Cas A NS!

Cas A neutron star:1.Is warm as for standard cooling2.Cools much faster than for standard cooling

ln0.1

lnsd T

sd t

ln1.35 0.15 (2 )

lnsd T

sd t

Standard cooling curve slope

Neutron superfluidity:

Proton superfluidity:

Together:

Faster cooling because of CP neutrino emission

Slower cooling because of suppression of neutrino emission

Sharp acceleration of cooling

Effects of Superfluidity on Cooling

Superfluidity naturally explains observations!Both, neutron and proton, superfluids are needed

Superfluidity Strong proton Moderate neutron

Tc – profile >3x109 K, profile unimportant maximum: TCn(max)~(5-9)x108 K and wide Tc –profile over NS core

Appears Early a few decays ago

What for? suppresses neutrino emission before the appearance of neutron superfluidity

produces neutrino outburst

Example: Cooling of 1.65 Msun Star

APR EOSNeutrino emission peak: ~80 yrs ago

Neutron stars of different masses

Only Tcn superfluidity I explains all the sources

One model of superfluidity for all neutron stars

Alternatively: wider profile, but the efficiency of CP neutrino emission at low densities is weak

Gusakov et al. (2004)

Cas A neutron star among other isolated neutron stars

Slope of cooling curve

logMeasure ( )~ infer

logs s

s

d TT t t s

d t

1 /12

1 / 8

s

s

s

= standard cooling (Murca)

= slope of cooling curve

= enhanced cooling (Durca)

>> 0.1 => something extraordinary! {

Theoretical model for Cas A NS Shternin et al. (2011)Now: s = 1.35 = very big number => unique phenomenon!Happens very rarely!

Measurements of s in the next decade confirm or reject this interpretation

Cooling objects – connections

• Isolated (cooling) neutron stars• Accreting neutron stars in X-ray transients (heated inside)• Sources of superbursts• Magnetars (heated inside)

Deep crustal heating:Theory: Haensel & Zdunik (1990) Applications to XRTs:

Brown, Bildsten & Rutledge (1998)

INSs XRTs Magnetars

Magnetic heatingCooling of initially hot star

CONCLUSIONS (without Cas A)

THEORY

•Too many successful explanations

• Main cooling regulator: neutrino luminosity • Warmest observed stars are low-massive; their neutrino luminosity <= 0.01 of modified Urca

• Coldest observed stars are more massive; their neutrino luminosity >= 100 of modified Urca

OBSERVATIONS

•Include sources of different types

•Seem more important than theory

•Are still insufficient to solve NS problem

CONCLUSIONS about Cas A • Observations of cooling Cas A NS in real time – matter of good luck! • Natural explanation: onset of neutron superfluidity in NS core about 80 years ago; maximum Tcn in the core >~7 x 108 K

• Profile of critical temperature of neutrons over NS core should be wide

• Neutrino emission prior to onset of neutron superfluidity should be 20-100 times smaller than standard level strong proton superfluidity in NS core?

• To explain all observations of cooling NSs by one model of superfluidity, Tcn profile has to be shifted to higher densities

• Prediction: fast cooling will last for a few decades

• Cooling of Cas A NS direct evidence for superfluidity?

Two Cas A teams

Minimal cooling theory:

Page, Lattimer, Prakash, Steiner (2004)

Gusakov, Kaminker, Yakovlev, Gnedin (2004)

Superfluid Cas A neutron star:

D. Page, M. Prakash, J.M. Lattimer, A.W. Steiner, PRL, vol. 106, Issue 8, id. 081101 (2011)

P.S. Shternin, D.G. Yakovlev, C.O. Heinke, W.C.G. Ho, D.J. Patnaude, MNRAS Lett., 412, L108 (2011)

Doubts

Carbon atmosphere: why?

Theory: probability to observe is small (too good to be true)

Theory: to explain observations of all cooling neutron stars one needs unusual Tcn – profile over neutron star core

Observations: data processing???