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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
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