MAGNETARS AS COOLING NEUTRON STARS

Transcription

1 MAGNETARS AS COOLING NEUTRON STARS D.G. Yakovlev Ioffe Physical Technical Institute, Saint-Petersburg, Russia Main coauthors: A.D. Kaminker, A.Y. Potekhin, D.A. Baiko February 2009, Aspen

2 HISTORY The first detection SGR on March 5, 1979 The magnetar hypothesis on theoretical grounds:

3 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 E TOT = erg can be the energy of internal magnetic field B=(1 3)x10 16 G in the magnetar core.

4 MATTER IN STRONG MAGNETIC FIELDS

5 MATTER IN STRONG MAGNETIC FIELDS

6 MATTER IN STRONG MAGNETIC FIELDS T = ħω / k = ion plasma temperature pi pi B b = ħωbi / kbt = magnetic field parameter 1/ 3 3 a = = ion sphere radius 4π ni

7 Cooling of ordinary neutron stars Heat diffusion with neutrino and photon losses Photon luminosity: Heat blanketing envelope: Heat content: L πσr = 2 4 γ 4 Ts T s = T s (T ) 48 2 U T ~ 10 T 9 ergs Main cooling regulators: 1. EOS 2. Neutrino emission 3. Superfluidity 4. Magnetic fields 5. Light elements on the surface Testing: Internal structure of neutron stars

8 THREE COOLING STAGES Stage Relaxation Neutrino Photon Duration yr kyr Infinite Physics Crust Core, surface Surface, core, reheating 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! For a star with one has L / L ν ~ 10 S L S 35 ~ 10 erg/s 4 Example: Supergiant flare of SGR on Dec. 27, 2004: W ~ 10 erg W ~ 10 erg X INPUT

9 TWO THERMAL REGIMES T C = div ( κ T ) Qν + H t Danger!

10 TWO THERMAL REGIMES T C = div (κ T ) Qν + H t Regime I 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-aged isolated NSs

11 TWO THERMAL REGIMES T C = div (κ T ) Qν + H t Regime II Regime II Neutrino emission is strong and makes NS interior non-isothermal Different regions of NS interior are thermally decoupled Thermal state of the surface is unaffected by thermal state of interior Highly specific regime; is not realized in cooling middle-aged stars Typical for cooling of young isolated NSs May be important for magnetars

12 Magnetars versus ordinary cooling neutron stars The need for heating: Temperature representation Magnetar box

13 Magnetars versus ordinary cooling neutron stars The need for heating: Luminosity representation

14 Temperature profiles within magnetars: Expectation of thermal decoupling Danger! Temperature profiles within magnetars in different parts of the surface, with heating and without

15 PHENOMENOLOGICAL HEATING IN A SPHERICAL LAYER Kaminker et al. (2007) H ( ρ, t) = H Four parameters : 0 Θ( ρ, ρ ) 1 2 ρ, 1 exp( t / τ ) ρ, H 0 ~ 10 erg cm s ; τ 0 ~ W ( t) = dv e 2Φ 2 H 0, τ yrs H = integrated heating rate, erg/s No. I No. II No. ρ (g/cc) 1 ρ 2 (g/cc) W (erg/s) I 3x x10 37 II x x10 37 III 3x x10 38 IV 3x x x10 39 For H 0 0 = 3 10 τ = erg years cm -3 s -1, M = 1.4 M SUN, High intensity H 0 =3x10 20 erg/cc/s No. III No. IV Low intensity H 0 =3x10 19 erg/cc/s

16 Neutron star models EOS: Akmal, Pandharipande, Ravenhall (APR III); neutrons, protons, electrons, and muons in NS cores Direct Urca: central density > 1.275x10 15 g/cc, M>1.685 M SUN Maximum mass: M MAX =1.929 M SUN Example of slow cooling: M=1.4 M SUN, R=12.27 km, central density = 9.280x10 14 g/cc Example of fast cooling: M=1.9 M SUN, R=10.95 km, central density = 2.050x10 15 g/cc Effects of superfluidity are neglected

17 Location and intensity of internal heating Models with spherical layer ρ = 1. Quasi-stationary states supported by heating b 2. Non-uniform internal temperature distributions 3. Strong neutrino energy outflow 4 = 5 10 yrs τ g/cc

18 Slow and fast neutrino cooling Models with spherical layer

19 ENERGY BUDGET AND HIGH THERMAL SURFACE LUMINOSITY Models with spherical layer 1. Heating rate should not be too high; E max ~10 50 erg W max ~3x10 37 erg/s 2. The heating rate must exceed the surface emission, optimal: L/W~ Photon surface luminosities should reach the magnetar level I

20 PHYSICAL MODEL? Strong thermal insulation Cold surface Low electric conductivity Twisted B-lines Strongest Ohmic dissipation Heat source Hot surface spots

21 PHYSICAL MODEL? Numerical example Ohmic dissipation heat rate H j c B ~ ~ σ σ h (4 π ) 2 2 For B ~ 3 10 G, σ ~ 10 s, h ~ 30 m H ~ 10 erg cm s For ( R / R) ~0.1 W ~ 10 erg s, L ~ 3 10 erg s BB OHMIC S HEAT EFFICIENCY: L / W ~ 1/ 30 S OHMIC TOTAL ENERGY NEEDED: WOHMICτ ~ erg τ 4 ( ~5 10 yr)

22 HEATING THROUGH MAGNETIC SPOTS

23 SPOTS OR ENTIRE SURFACE?

24 CONCLUSIONS 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~10 20 erg s -1 cm -3, the total heat rate exceeding the thermal surface luminosity with by 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