MAGNETARS AS COOLING NEUTRON STARS MAGNETARS AS COOLING NEUTRON STARS

D.G. YakovlevIoffe Physical Technical Institute, Saint-Petersburg, Russia

Main coauthors:A.D. Kaminker, A.Y. Potekhin, D.A. Baiko

February 2009, Aspen

HISTORY

The first detection – SGR 0525—66 on March 5, 1979

The magnetar hypothesis on theoretical grounds:

TALK OUTLINE

• Matter in strong magnetic fields• Phenomenological internal heating• Physical model?• Conclusions

AIMS & ASSUMPTIONS

• To explain quasi-persistent thermal emission of magnetars• Assume that the emission is powered by internal heat sources• Heat sources: Where located? How strong? What is their nature?

ENERGY PROBLEM

The maximum stored energy ETOT=1049—1050 erg can be the energy

of internal magnetic field B=(1—3)x1016 G in the magnetar core.

MATTER IN STRONG MAGNETIC FIELDS

MATTER IN STRONG MAGNETIC FIELDS

MATTER IN STRONG MAGNETIC FIELDS

1/ 3

= / = ion plasma temperature

/ = magnetic field parameter

3 = ion sphere radius

4

pi pi B

Bi B

i

T k

b k T

an

ω

ω

π

=

=

�

�

)(TTT ss =

424 sTRL πσγ =

Heat diffusion with neutrino and photon losses

Photon luminosity:

Heat blanketingenvelope:

ergsTUT

2

9

4810~Heat content:

Cooling of ordinary neutron stars

Main cooling regulators:

1. EOS2. Neutrino emission3. Superfluidity

4. Magnetic fields5. Light elements on the surface

Testing: Internal structure of neutron stars

Surface, core,

reheating

InfinitePhoton

Core, surface10-100 kyrNeutrino

Crust10—100 yrRelaxation

PhysicsDurationStage

THREE COOLING STAGES

In a warm star:• Neutrino emission is much stronger

than the photon surface emission• The energy released in the isothermal

interior is mainly emitted via neutrinos,not through the surface photon emission!

35

4

For a star with ~ 10 erg/s

one has / ~ 10

S

S

L

L Lν−

46 50

INPUTExample: Supergiant flare of SGR 1806 20 on Dec. 27, 2004: ~ 10 erg ~ 10 ergX

W W− ⇒

TWO THERMAL REGIMES

div ( )T

C T Q Ht

νκ∂

= ∇ − +∂

Danger!Danger!Danger!

TWO THERMAL REGIMES

div ( )T

C T Q Ht

νκ∂

= ∇ − +∂

• Thermal conduction is strong

and makes NS interior isothermal• All places of NS interior are

thermally connected• Neutrino emission may dominate

cooling

• Typical for cooling of middle-agedisolated NSs

Regime I

TWO THERMAL REGIMES

div ( )T

C T Q Ht

νκ∂

= ∇ − +∂

• Neutrino emission is strong andmakes NS interior non-isothermal

• Different regions of NS interior are thermally decoupled

• Thermal state of the surface is

unaffected by thermal state ofinterior

• Highly specific regime; is notrealized in cooling middle-agedstars

• Typical for cooling of youngisolated NSs

• May be important for magnetars

Regime IIRegime II

Magnetars versus ordinary cooling neutron starsThe need for heating: Temperature representation

Magnetar box

Magnetars versus ordinary cooling neutron starsThe need for heating: Luminosity representation

Temperature profiles within magnetars:Expectation of thermal decoupling

Temperature profiles within magnetars in different parts

of the surface, with heating and without

Danger!

PHENOMENOLOGICAL HEATING IN A SPHERICAL LAYER

0021

0210

, , , :parametersFour

)/exp(),(),(

τρρ

τρρρ

H

tHtH −Θ=

yrs 1010~ ;s cm erg 10~ 54

0

-1-320

0 −τH

erg/s rate, heating integrated e d)( 2 == ∫Φ∞

HVtW

1.1x10399x10143x1013IV

1.1x103810143x1013III

1.9x10373x10121012II

4.0x103710113x1010I

No. (g/cc) 1ρ (g/cc) 2ρ (erg/s) ∞WNo. I No. II

No. III No. IV

years 105

,4.1 ,s cm erg 103For

4

0

SUN

-1-320

0

×=

=×=

τ

MMH

H0=3x1019 erg/cc/sLow intensity

H0=3x1020 erg/cc/s High intensity

Kaminker et al. (2007)

Neutron star models

• EOS: Akmal, Pandharipande, Ravenhall (APR III); neutrons,protons, electrons, and muons in NS cores

• Direct Urca: central density > 1.275x1015 g/cc, M>1.685 MSUN

• Maximum mass: MMAX=1.929 MSUN

• Example of slow cooling: M=1.4 MSUN, R=12.27 km,central density = 9.280x1014 g/cc

• Example of fast cooling: M=1.9 MSUN, R=10.95 km,central density = 2.050x1015 g/cc

• Effects of superfluidity are neglected

Location and intensity of internal heating

1. Quasi-stationary states supported by heating2. Non-uniform internal temperature distributions 3. Strong neutrino energy outflow yrs 105 4

0 ×=τ

10

b 10 g/ccρ =

Models with spherical layer

Slow and fast neutrino cooling

Models with spherical layer

ENERGY BUDGET AND HIGH THERMAL SURFACE LUMINOSITY

1. Heating rate should not be too high; Emax~1050 erg ���� Wmax~3x1037 erg/s2. The heating rate must exceed the surface emission, optimal: L/W~0.013. Photon surface luminosities should reach the magnetar level

I

Models with spherical layer

PHYSICAL MODEL?

Strong thermal insulation

Cold surface

Low electric conductivityTwisted B-linesStrongest Ohmic dissipationHeat source

Hot surface spots

PHYSICAL MODEL?

Ohmic dissipationheat rate

2 2 2

2 2~ ~

(4 )

j c BH

hσ σ π

14 21 1 20 3 1For ~ 3 10 G, ~ 10 s , ~ 30 m ~ 10 erg cm s B h Hσ − − −× ⇒

2 36 1 34 1

OHMICFor ( / ) ~0.1 ~ 10 erg s , ~ 3 10 erg sBB SR R W L− −⇒ ×

OHMICHEAT EFFICIENCY: / ~ 1/ 30S

L W

44 45

OHMIC

4

TOTAL ENERGY NEEDED: ~ 10 10 erg

( ~5 10 yr)

W τ

τ

−

×

Numerical example

HEATING THROUGH MAGNETIC SPOTS

SPOTS OR ENTIRE SURFACE?

CONCLUSIONSCONCLUSIONS

• Magnetars may be cooling neutron stars with internal heating. • It is economical to place heat sources in the outer crust.• The heat rate in the outer crust can be H~1020 erg s-1 cm-3,

the total heat rate exceeding the thermal surface luminosity withby a factor of >=30.

• The outer crust is thermally decoupled from deeper interior; the thermal radiation tests the physics of the outer crust.

• The heating may be supported by Ohmic decay under hot spots .

• One should never forget about neutrino physics