COOLING OF MAGNETARS WITH INTERNALCOOLING OF MAGNETARS WITH INTERNAL LAYER HEATINGLAYER HEATING

A.D. Kaminker, D.G. Yakovlev, A.Y. Potekhin, N. Shibazaki*, P. Sternin, and O.Y. Gnedin**

Ioffe Physical Technical Institute, St.-Petersburg, Russia*Rikkyo University, Tokyo 171-8501, Japan **Ohio State University, 760 1/2 Park Street, Columbus, OH 43215, USA

Conclusions

Introduction

Physics input

Cooling calculations

Nanjing 2006.07.25

)(TTT ss

Thermal balance:

Photon luminosity:

Heat blanketingenvelope:

ergsTUT2

94810~Heat content:

Cooling theory with internal heating

Main cooling regulators:

1. EOS2. Neutrino emission3. Reheating processes4. Superfluidity5. Magnetic fields6. Light elements on the surface

42L 4 sR T

Heat transport:

( )dT

C T W L Ldt

;dT

Fdr

- effective thermal conductivity

Direct Urca (Durca) process

e

ep

n

Lattimer, Pethick, Prakash, Haensel (1991)

ee nepepn ,

eenn

dfffwQ epnfi )1)(1(2

npeepn

A Tc

mmmgGQ

6

31022 )31(

10080457

169

4610~ sergTL

Threshold: FeFpFn ppp 02 ~in the inner coresof massive stars

Similar processes with muons : produce

Similar processes with hyperons, e.g.:

n

1369

27103~ scmergTQ

Inner cores of massive neutron stars:

Nucleons,hyperons

Pioncondensates

Kaoncondensates

Quarkmatter

e

e

nep

epn

e

e

nep

epn

~~

~~

e

e

qeq

eqq

~~

~~

e

e

deu

eud

scmerg

TQ 36

927103~

scmerg

TQ 36

9262410~

scmerg

TQ 36

9242310~

scmerg

TQ 36

9242310~

serg

TL 69

4610~

serg

TL 69

444210~

serg

TL 69

424110~

serg

TL 69

424110~

Everywhere in neutron star cores. Most important in low-mass stars.

ModifiedUrca process

Brems-strahlung

e

e

NnNep

NepNn

NNNN

scmerg

TQ 38

9222010~

scmerg

TQ 38

9201810~

serg

TL 89

403810~

serg

TL 89

383610~

,,e

NONSUPERFLUID NEUTRON STARS: Modified URCA versus Direct URCA

EOS: PAL-I-240 (Prakash, Ainsworth, Lattimer 1988)

Magnetars versus ordinary cooling neutron stars

Two assumptions:(1) The magnetar data reflect persistent thermal surface emission(2) Magnetars are cooling neutron stars

There should be a REHEATING!Which we assume to be INTERNAL

1. EOS: APR III (n, p, e, µ) Gusakov et al. (2005) Akmal-Pandharipande-Ravenhall (1998) -- neutron star models

Parametrization: Heiselberg & Hiorth-Jensen (1999)

2. Heat blanketing envelope: 310 /10 cmgb

sb TT -- relation;

)(sT surface temperature,

;4442 dTLTR seff

effT -- effective temperature;

d -- surface element

( )b bT T

21

H

H0

Model of heating:

at 21 10 11 3

1 23 10 ; 10 ;g cm i

12 12 31 210 ; 3 10 ;g cm ii

13 14 31 23 10 ; 10 ;g cm iii

14 32 ; =9 10 ;g cm iv

erg s -1

erg cm -3 s -1

- characteristic time of the heating

No isothermal stage

Core — crust decoupling

yrt 310 1- SGR 1900+142- SGR 0526-663- AXP 1E 1841-045

5- AXP 1RXS J170849-4009106- AXP 4U 0142+617- AXP 1E 2259+586

Only outer layers of heating are appropriate for hottest NSs

4- CXOU J010043.-721134

Direct Urca process included :

Modified Urca process :Duration of heating

Enhanced and weakened thermal conductivity

Appearance of isothermal layers

from tomin =3 x 10 12max =10 14 g cm -3

Necessary energy input vrs. photon luminosity

)(s

erg into the layer W 1 2

THE

THE NATURE OF INTERNAL HEATING

1. The stored energy ETOT=1049—1050 erg is released in t=104—105 years.

2. It can still be the energy of internal magnetic field B=(1—3)x1016 G in the magnetar core.

3. The energy can be stored in the entire star but relesed in the outer crust -- Ohmic dissipation? Generation of waves which dissipate in the outer crust?

}Energy release

Energy storage

Neutrino emission mechanisms in the magnetar outer envelope

No Mechanism Reaction

1 Plasmon decay

2 Electron-positron

pair annihilation

3 Electron-nucleus

bremsstrahlung

4 Photoneutrino

5 Neutrino synchrotron

e e

e Z e Z

e e

2 2 22 5 14 2 5F

SYN B 13 95 7 8 3

2 (5) erg ( ) 9.04 10

9 cm s

e G BQ C k T B T

c

e e

NEUTRINO EMISSION IN THE CRUST AT DIFFERENT TEMPERATURES

MAGNETARS WITH NEUTRINO SYNCHROTRON EMISSION

Conclusions

1. Our main assumption: the heating source is located inside the neutron star

2. The heating source must be close to the surface: 115 10 g cm -3

3. The heat intensity should range:19 20

03 10 3 10H erg cm-3 s-1

4. Heating of deeper layers is extremely inefficient due to neutrino radiation

Pumping huge energy into the deeper layers would not increase 5. sT

6. Strongly nonuniform temperature distribution:

in the heating layer T > 109 K;

the bottom of the crust and the stellar core remain much colder T << 109 K

7. Thermal decoupling of the outer crust from the inner layers

8. The total energy release (during 104 – 105 years)

cannot be lower than 1049—1050 erg;

only 1% of this energy can be spent to heat the surface