1. Magneto-shear Oscillations of Magnetars Yasufumi Kojima Hiroshima Univ. 小嶌康史 ( 広島大学 ) 1 2014 年 1 月 13-15 日 新学術領域（重力波天体）研究会 東京工業大学 公募研究（ A05)

2. Magnetar Oscillation Observed in Giant Flares （ＱＰＯｓ） SGR1806-20(2004) 30Hz(2,0) 92Hz(6,0) 150Hz(10,0),… are observed in hard X-rays (<200kev) SGR1900+14 (1998) 28Hz(2,0) 53Hz(3,0) 84Hz(6,0),… SGR0526-66 (1979) … … … … -> Seismology /GW astrophysics 2 Upper limit of GW for SGR1806 (LIGO PRD07)

3. SGR1806-20 Israel+ 2005 Peaks at 20, 30, 95Hz during 200-300s 3

4. (Magneto-)Shear Oscillation Shear in Solid NS Crust Shear wave(transverse mode) -> Radius R -> Interior of NS (nuclear EOS) 4 fluid solid

5. Magneto-Shear Oscillation Effect of Magnetic Field on shear waves may be important for Magnetars Order-of-magnitude estimate Unknown factor for the magnetic field configuration 5 -->> Theoretical study is needed.

6. Puzzles Oscillations are NOT so simple. Broad peaks (Not sharp) ’QPO’ Damping time Observed time is too short (<1000s) Complicated by magnetic fields? 6

7. Theory of Damping Mechanism Review : McDermott et al. (1988)  Gravitational waves  Shear(Toroidal) Oscillation changes mass current moment. ( ‘ ’ in EM ) Damping time of l=2 is of order month-year. Cf. Poloidal f-mode (a few kHz) change of mass moment( ‘ ’ in EM ) 7

8. cont. (McDermott et al. (1988)  EM radiation approximated by Poynting flux loss. Oscillation E in Magnetar (Rot. E. in Pulsar )  Neutrino loss? Unkown, but expected to be small.  Viscosity? Unkown, but generally long Oscillating long, but dim in EM ？ →Or other mechanism? 8 No simple theoretical estimate of damping time

9. Magnetic Coupling is a key Ex. (Axial)Shear Oscillation Coupled to Core (Axial)Oscillation Coupled to Magnetosphere (Polar)Shear Oscillation Coupled to f-mode? -> GW during …. …(General complicated coupling by ) 9 Conjecture Gabler+ (2013) propagate oscillate propagate

10. Methods in detail 2D time-dependent linearized eqns. Spherical star in background Non-relativistic approx /fixed Newtonian gravity Barotropic (simple) EOS Magnetic field :equilibrium in background Poloidal field only connected to exterior dipole Oscillations Axial (or polar) perturbation only is given initially. Both are coupled if 10

11. (Axial)Oscillation Coupled to Magnetosphere 11 Ongoing Works 1 Magneto-shear Osc. in crust Magnetosphere( field line)

12. Result 12 Preliminary Coupling is not so big? Or improved ‘model’ is necessary BC: Cont. at surface 0 Small effect on exterior Zero in vacuum In magnetosphere Localized inside Enlarged thickness on display

13. Ongoing Works 2 (Polar)Shear Oscillation Coupled to f-mode? Shear motions solved without B Fluid motions solved without B + Coupling by B ->f-mode excited? How? 13 In Preparation

14. A giant flare in Magnetars is galactic, energetic event. Theory of magneto-shear oscillation in progress. In particular, f-mode oscillation relevant to GW excited by magnetic coupling is considering. 14 Summary