COOLING OF MAGNETARS WITH INTERNAL COOLING OF MAGNETARS WITH INTERNAL LAYER HEATING 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 , Japan **Ohio State University, 760 1/2 Park Street, Columbus, OH 43215, USA Conclusions Introduction Physics input Cooling calculations Nanjing

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

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

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

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: -- relation; surface temperature, -- effective temperature; -- surface element

H H0H0 Model of heating: at i ii iii iv erg s -1 erg cm -3 s -1 - characteristic time of the heating

No isothermal stage Core — crust decoupling 1- SGR SGR AXP 1E AXP 1RXS J AXP 4U AXP 1E Only outer layers of heating are appropriate for hottest NSs 4- CXOU J

Direct Urca process included : Modified Urca process : Duration of heating

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

Necessary energy input vrs. photon luminosity into the layer

THETHE THE NATURE OF INTERNAL HEATING 1. The stored energy E TOT =10 49 —10 50 erg is released in t=10 4 —10 5 years. 2. It can still be the energy of internal magnetic field B=(1—3)x10 16 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 NoMechanismReaction 1Plasmon decay 2Electron-positron pair annihilation 3Electron-nucleus bremsstrahlung 4Photoneutrino 5Neutrino synchrotron

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: g cm -3 3.The heat intensity should range: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 increase5. 6.Strongly nonuniform temperature distribution: in the heating layer T > 10 9 K; the bottom of the crust and the stellar core remain much colder T << 10 9 K 7.Thermal decoupling of the outer crust from the inner layers 8. The total energy release (during 10 4 – 10 5 years) cannot be lower than —10 50 erg; only 1% of this energy can be spent to heat the surface