COOLING OF MAGNETARS WITH INTERNAL LAYER HEATING

1. COOLING OF MAGNETARS WITH INTERNAL LAYER 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 Introduction Physics input Cooling calculations Nanjing 2006.07.25 Conclusions

2. Cooling theory with internal heating Thermal balance: Heat transport: - effectivethermal conductivity Photon luminosity: Heat blanketing envelope: Heat content: Main cooling regulators: 1. EOS 2. Neutrino emission 3. Reheating processes 4. Superfluidity 5. Magnetic fields 6. Light elements on the surface

3. Direct Urca (Durca) process Lattimer, Pethick, Prakash, Haensel (1991) in the inner cores of massive stars Threshold: ~ Similar processes with muons : produce Similar processes with hyperons, e.g.:

4. Everywhere in neutron star cores. Most important in low-mass stars. Modified Urca process Brems- strahlung Inner cores of massive neutron stars: Nucleons, hyperons Pion condensates Kaon condensates Quark matter

5. NONSUPERFLUID NEUTRON STARS: Modified URCA versus Direct URCA EOS:PAL-I-240 (Prakash, Ainsworth, Lattimer 1988)

6. Magnetars versus ordinary cooling neutron stars • Two assumptions: • The magnetar • data reflect • persistent • thermal surface • emission • Magnetars • are cooling • neutron stars There should be a REHEATING! Which we assume to be INTERNAL

7. EOS: APR III (n, p, e, µ)Gusakov et al. (2005) • Akmal-Pandharipande-Ravenhall (1998) -- neutron star models Parametrization: Heiselberg & Hiorth-Jensen (1999) Heat blanketing envelope: 2. -- relation; -- effective temperature; surface temperature, -- surface element

8. Model of heating: ergcm -3 s -1 at - characteristic time of the heating i H ii iii H0 iv erg s -1

9. 1- SGR 1900+14 2- SGR 0526-66 3-AXP 1E 1841-045 No isothermal stage 4- CXOU J010043.-721134 Core — crust decoupling 5-AXP 1RXS J170849-400910 Only outer layers of heating are appropriate for hottest NSs 6- AXP 4U 0142+61 7- AXP 1E2259+586

10. Modified Urca process : Duration of heating Direct Urcaprocess included :

11. Enhanced and weakened thermal conductivity =3 x 10 12 =10 14 g cm -3 to from Appearance of isothermal layers

12. Necessary energy input vrs. photon luminosity into the layer

13. THE NATURE OF INTERNAL HEATING THE 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

14. Neutrino emission mechanisms in the magnetar outer envelope

15. NEUTRINO EMISSION IN THE CRUST AT DIFFERENT TEMPERATURES

16. MAGNETARS WITH NEUTRINO SYNCHROTRON EMISSION

17. Conclusions 1. Our main assumption: the heating source is located inside the neutron star g cm -3 2. The heating source must be close to the surface: 3. The heat intensity should range: erg cm-3 s-1 4. Heating of deeper layersis extremely inefficient due to neutrino radiation 5. Pumping huge energy into the deeper layers would not increase 6. Strongly nonuniform temperature distribution: in the heating layer T> 109 K; the bottom of the crust and the stellar core remain much colderT<< 109 K 7. Thermal decoupling of the outer crust from the inner layers The total energyrelease(during 104 – 105 years) cannot be lower than1049—1050erg; only 1%of this energy can be spent to heat the surface 8.