MAGNETARS AS COOLING NEUTRON STARS WITH MAGNETARS AS COOLING NEUTRON STARS WITH INTERNAL HEATING INTERNAL HEATING A.D. Kaminker, D.G. Yakovlev, A.Y. Potekhin,

MAGNETARS AS COOLING NEUTRON STARS WITHMAGNETARS AS COOLING NEUTRON STARS WITH INTERNAL HEATINGINTERNAL 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

Games with cooling code

)(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

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

1- SGR 1900+14

2- SGR 0526-66

3- AXP 1E 1841-045

4- AXP 1RXS J170849-400910

5- AXP 4U 0142+61

6- AXP 1E 2259+586

21

H

H0

3. Model of heating:

)exp(1

1)(

2

22

f;)exp(1

1)(

1

11

f at

)exp(),( 210 t

ffHtH

21

10 11 31 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

No isothermal stage

Core — crust decoupling

yrt 310 1- SGR 1900+14

2- SGR 0526-66

3- AXP 1E 1841-045

4- AXP 1RXS J170849-400910

5- AXP 4U 0142+61

6- AXP 1E 2259+586Only outer layers of heating are appropriate for hottest NSs

Necessary energy input vrs. photon luminosity

)(s

erg into the layer W 1 2

Direct Urca process included

Enchanced thermal conductivity

Appearance of isothermal layers

from min to max

Conclusions

1. High thermal state of magnetars demand a powerful reheating

2. The heating should be located in a thin layer at :11 35 10 g cm

in the outer crust. The heat intensity 0H should range

from 19 3 10 to 20 3 13 10 erg cm s Deeper heating would be extremely inefficient due to neutrino radiation

4. Pumping huge energy into deeper layers can not increase -- effT

5.

.

Temperature distributions within NS are strongly nonuniform due to

thermal decoupling of the outer crust from the inner parts of the star

3. Only ~ 1% of the total energy released in the heat layer can be spent to heat the NS surface