Barcelona, September 26, 2014,

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

NEUTRON STAR COOLING AS A PROBE

OF FUNDAMENTAL PHYSICS

NEUTRINO EMISSION IN NEUTRON STARS

Main features: • unobserved regulates cooling

• complete transparency

QdVL

Q

]c [erg luminosity neutrino and

]scm [erg emissivity neutrino :quantity acticalPr

1

13

e

ep

n

, e e e en p e p e n n n

27 6 3 1

9

46 6 1

9

~ 3 10

~ 10

Q T erg cm s

L T erg s

FeFpFn ppp 02 ~

Direct Urca Process

Lattimer, Pethick, Prakash, Haensel (1991)

Threshold: Can be open in

inner cores

of massive stars Similar processes with muons

In outer core – is forbidden 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

SLOW NEUTRINO EMISSION PROCESSES

EVERYWHERE IN NEUTRON STAR CORES

, e en N p N e p N e n N

8 8

SLOW 0S 9 SLOW 0S 9 Q Q T L L T

MODIFIED URCA [N=n or p = nucleon-spectator]

NUCLEON-NUCLEON BREMSSTRAHLUNG

N N N N

n n n n

n p n p

p p p p

{

Bahcall and Wolf (1965), Friman and Maxwell (1979), Maxwell (1987),

Yakovlev and Levenfish (1995)

Friman and Maxwell (1979)

Any neutrino

flavor

Enhanced emission in inner cores of massive neutron stars

Everywhere in neutron star cores

Neutrino Processes in Neutron Star Cores

6 6

FAST 0F 9 FAST 0F 9 Q Q T L L T

Model Process

Direct Urca

3 1

0 [erg cm s ]Q

e en p e p e n 26 2710 3 10

8 8

SLOW 0S 9 SLOW 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

Neutrino emission from cores of non-superfluid NSs

Outer core Inner core

Slow emission Fast emission

}

} }

e en p e p e n

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 6

FAST 0F FAST 0F Q Q T L L T

8 8

SLOW 0S SLOW 0S Q Q T L L T

STANDARD

Fast

erg

cm

-3 s

-1

NS with nucleon core:

N=n, p

n n

n p

p p

FAST AND SLOW NEUTRINO COOLING

FAST AND SLOW NEUTRINO COOLING

SUN

M 31

Effects of superfluidity on neutrino emission

Two effects:

1. Suppresses traditional neutrino processes

2. Creates specific neutrino emission due to Cooper pairing of nucleons

Neutrino emission due to Cooper pairing

Flowers, Ruderman and

Sutherland (1976)

Voskresensky and Senatorov

(1987)

Schaab et al. (1997)

n n

Temperature dependence of

neutrino emissivity due to

Cooper pairing

Features:

• Efficient only for

triplet-state pairing

of neutrons

•Non-monotonic

T-dependence

• Strong many-body

effects

Leinson (2001) Leinson and Perez (2006)

Sedrakian, Muether, Schuck

(2007)

Kolomeitsev, Voskresensky

(2008)

Steiner, Reddy (2009)

Leinson (2010)

Physics:

Jumping over cliff

from branch A to B

A

B

Neutrino emission due to Cooper pairing

Neutrino luminosity due to Cooper pairing

8)10010(~ TLL MurcaCooper

Gusakov et al. (2004)

Minimal and maximal cooling paradigms

Consider neutron stars with nucleon cores (simplest composition)

Minimal cooling paradigm: no direct Urca in all stars

Maximal cooling paradigm: direct Urca in heavy stars

Pradigm SF SF

Minimal cooling off on

Maximal cooling off on

Four cases

Minimal cooling theory:

Page, Lattimer, Prakash, Steiner (2004)

Gusakov, Kaminker, Yakovlev, Gnedin (2004)

Minimal and maximal cooling paradigms

Minimal

cooling

Maximal

cooling

SF off SF on

~ (10 100)Cooper MurcaL L

Minimal cooling. SF on

Non-superfluid star

with nucleon core

Standard Murca cooling

Add strong proton super-

fluidity

Very slow cooling

Add moderate neutron

superfluidity:

CP neutrino outburst

nn nn

np np

pp pp

nN pNe pNe nN

nN pNe pNe nN

np np

pp pp

nn nn

~ 0.01 MurcaL L MurcaL L

nN pNe pNe nN

nn nn

np np

pp pp

nn

MAXIMAL COOLING

EXAMPLE OF SUPERFLUID REDUCTION OF NEUTRINO EMISSION

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”)

MAXIMAL COOLING

STRONG PROTON AND MILD NEUTRON SUPERFLUIDITY

Summary of neutrino emission properties

Neutrino emission from neutron star cores is strongly regulated by

(1)Temperature

(2)Composition of the matter

(3)Superfluidity

These regulators may affect the emissivity in a non-trivial way

(enhance or suppress)

What is their effect? Next lecture

REFERENCES

U. Lombardo, H.-J. Schulze. Superfluidity in neutron star matter.

In: Physics of Neutron Star Interiors, edited by D. Blaschke,

N. Glendenning, A. Sedrakian, Berlin: Springer, 2001, p. 30.

D.G. Yakovlev, K.P. Levenfish, Yu.A. Shibanov. Cooling of neutron

stars and superfluidity in their cores. Physics – Uspekhi 42, 737, 1999.

D.G. Yakovlev, A.D. Kaminker, O.Y. Gnedin, P. Haensel.

Neutrino emission from neutron stars. Phys. Rep. 354, Nums. 1,2, 2001.

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 via

Modified Urca

process SLOW 6

9

1 year~

i

tT

8 5~ 1.5 10 K in 10 yrsiT t

Fast cooling via

Direct Urca

process FAST 4

9

1 min~

i

tT

7~ 10 K in 200 yrsiT t

Roberto Turolla

Roberto explained how to detect thermal emission of neutron stars

THERMAL RADIATION FROM ISOLATED NEUTRON STARS

These data are now incomplete, a few more sources can be added

OBSERVATIONS AND BASIC COOLING CURVE

Nonsuperfluid star

Nucleon core

Modified Urca

neutrino emission:

slow cooling

Minimal cooling; SF off – does not explain all data

MAXIMAL COOLING; SF OFF MODIFIED AND DIRECT URCA PROCESSES

1=Crab

2=PSR J0205+6449

3=PSR J1119-6127

4=RX J0822-43

5=1E 1207-52

6=PSR J1357-6429

7=RX J0007.0+7303

8=Vela

9=PSR B1706-44

10=PSR J0538+2817

11=PSR B2234+61

12=PSR 0656+14

13=Geminga

14=RX J1856.4-3754

15=PSR 1055-52

16=PSR J2043+2740

17=PSR J0720.4-3125

15

MAX c

14

D 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

SUN

SUN

SUN SUN SUN

M M

M M

M M M M

Does not explain

the data

MAXIMAL COOLING: STRONG 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”)

MAXIMAL COOLING: STRONG PROTON SF

This model explains the

data but such explanation is not

unique

MINIMUM AND MAXIMUM COOLING

SF on

Gusakov et al. (2004, 2005)

Minimum cooling

Gusakov et al. (2004)

Minimum-maximum cooling

Gusakov et al. (2005)

MYSTERIOUS COMPACT CENTRAL OBJECT IN Cas A SNR

Very bright radio source

Discovery: Tananbaum (1999)

first-light Chandra X-ray observations

Later 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 pulsations

2. 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

Distance: 3.4 kpc (Reed et al. 1995)

Age: 330 yrs => 1680

COOLING NEUTRON STAR IN Cas A SNR

Ho and Heinke (2009) Nature 462, 671 Fitting the observed spectrum

with carbon atmosphere model

gives the emission from the entire

neutron star surface

Conclusion:

Cas A SNR contains cooling neutron

star with carbon surface

It is the youngest cooling NS whose

thermal radiation is observed

Main features:

1. Rather warm neutron star

2. Consistent with standard

cooling

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 NS:

1. Warm as for standard cooling

2. Cools much faster

ln0.1

ln

sd Ts

d t

ln1.35 0.15 (2 )

ln

sd Ts

d t

Standard

cooling

curve slope

Superfluid cooling neutron star?

APR EOS

Neutrino emission peak: ~80 yrs ago

Superfluid Cas A NS:

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

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

L108 (2011)

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

Is there rapid cooling of Cas A NS real (2013)?

K. G. Elshamouty,

C. Heinke et al.

B. Posselt,

G. Pavlov,

V. Suleimanov,

O. Korgaltsev

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 heating Cooling of initially

hot star

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 XRTs

KS 1731—260; MXB 1659—29

Crust

Deep crustal heating

Superbursts Crust

Magnetar outbursts Crust

Magnetars in quasistationary

states

Crustal heating

Main Cooling Objects

Vela pulsar, M=1.4 MSUN, APR I EOS

Greatest headache: heat blankets

Chemical composition of heat

blanketing envelope is basically

unknown =>

extracting neutrino cooling rate

from observations is basically uncertain =>

internal neutrino cooling is disguised by

by unknown thermal insulation

Important issue: to study composition of

envelopes (Bildsten et al.)

56.8 10 KsT

CONCLUSIONS

THEORY

• Main cooling regulator: neutrino luminosity function

• Warmest observed stars INSs are low-massive; their neutrino luminosity

<= 0.01 of modified Urca

• Coldest observed stars INSs are massive; their neutrino luminosity

>= 100 of modified Urca

OBSERVATIONS

•Include sources of different types

• Observations seem more important that theory

•Are still insufficient to solve NS problem

Evidence for SF from NS cooling •Warmest observed isolated INSs and NSs in quasi-stationary XRTs

require very slow cooling => consistent with strong proton

superfluidity which suppresses many neutrino processes

•Unusual cooling behavior of Cas A NS

CONCLUSIONS

Future

•New observations => good practical theories of dense matter

• Proper inclusion of B-field, rotation, superfluidity

• Independent measurements of masses, radii, etc.

• Good luck

Warning

• Do not expect from cooling theory more than it can give

• Cooling theory by itself will hardy allow accurate mass and radius

measurements – it has to be calibrated by independent measurements

and/or reliable theory of nuclear matter

• Info on internal neutrino emission is disguised by unknown

composition of heat blanket

Start. 1960s. To discover NSs

as cooling X-ray objects

Now. INSs

XRTs

Magnetars

Magneto-rotational evolution

Rotational-chemical evolution

Bursts and outbursts

Glitches

Internal and magnetospheric activity

etc.

FROM CINDERELLA TO REAL BEAUTY