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