Damping of Magnetar
Oscillations induced byGiant Flares
Yasufumi Kojima
小嶌康史

2016年5月13-14日
Compact stars and gravitational wave astronomy
第4回DTAシンポジウム@国立天文台

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QPOs in Magnetar Giant Flare
Energetic events in our Galaxy○SGR1806-20(Galactic 6-15kpc) Event in 2004

P  7.5 sec, Bd  2.1 10 G
E EM  10 46 ergs
15[>>Bursts, Brightening AXP EEM  1041 42ergs ]EG  10 , E Rot  10 , E B  10 , ET  10 ,...ergs
53454843

 Magnetic Energy Source B  1015 G
 QPO observed in hard X-rays (<200kev)
30Hz(2,0) 92Hz(6,0) 150Hz(10,0),… Magneto-shear oscillation

Important timescale puzzle<-> GW emission 2

SGR1806-20 Israel+ 2005
P ( )

 [Hz ]
Peaks at 20, 30, 95Hz during 200-300s
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SGR1806-20 Israel+ 2005

100s

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Timescale Puzzle
QPO observed in a specific time ~1000 s• Long timescale >> dynamical one
3R / c  10 , R / cs  R / c A  0.1sec• Short compared with damping timescales
discussed later->Theoretical task to identify the mechanism
Numerical simulation < 10 sec(Gabler +, Sotani, Lasky, Zink, Kokkotas+ …..)->It is necessary to follow thousands ofoscillations

5Site of energy
depositE EM  10 46 ergs

Energy associated with mag. configuration change
Order-of-magnitude
estimate in magnetars

E EM  2 10 48 B152 .5 R63ergs

 mag  1( B15.5 ) 2 [kev / fm 3 ] g  200Mev / fm 3
• CoreStrong force allows ‘small’ deviations3
0.
1[kev/fm]str• CrustNS with mountain(Horowitz & Kadau 2009)  Estr / E gr  4 10 6• Magnetosphere
Change between twisted magnetic configurations
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1 Triggered in CoreIf (hypothetical) phase transition is a trigger,
E Flare ~ EOsc  E EM  10 46 ergs

magneto-shear oscillation in crust may be induced.
GW burst is expected before initial EM spike.
Otherwise, it is difficult to excite core vibration except
for extreme fieldB  1018 G
Observational upper bound in GW is important
Upper limit of GW(LIGOS5 PR07)4622
1/ 2hrms  4.5 10 Hz , E  7.7 10 erg
E  (c 5 / G)(hd / c) 2 t-> Hope for upper limit by aLIGO, KAGRA

2 Triggered in Crust
Strongly coupled with exteriorE  Ecr  Eex
Ecr  10 41 R62 R1 , Eex  10 47 B152 R63ergs

Dipole almost unchanged
Toroidal, higher multipoles
Reflection/transmission is important
Initial spike by Alfven wave collision at top of flux
tube (Takamoto+ 2014)

Transmission & Reflection ofAlfven waves at surface
Propagation from interior to exteriorat ( R / c A )rtr  1sec
In the evolution after 1sec., global structure
is important.
solidvcfluidv  10 2 c

rtr  0.1B152 37 cos @  kHz, B  1015 G

R / R  0.1
Melting crust by incoming Alfven wave
> 1sec (Li & Beloborodov 2015)

Damping of mechanisms for oscillations
EM radiation approximated by Poynting flux
No wave propagation with low freq.
Actual mechanism : pair creation, current,…
PEM  PPoyn
outward energy flows
By analogy with pulsars

  E / P  10 sec(l  2) ;7PPoyn  a(R / c) B
6Too long
Differences
Pulsar (stationary)E Rot  E EMMagnetar
EEM ?  or  EOsc ? strong B

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cont. 2
Joul loss
1 2
• Power P    1 j 2 dV  1033  22
B15 R6 [erg / s ]5• Damping timescale > 10 years2  e ne c / me
• Conductivity
core surface atmosphere(fully ionized gas)  10 ,10 ,10 [ s ]
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2218

1

• Or anomalous resistivity required  10 [ s ]141cont. 3
Damping by neutrino viscosity
Unkown, but expected to be small.
  0  T  L  0
Estimate by energyEmissivity by plasmon, brem, pair  10 20 erg / s / cm3@crust is small
Except for dir. Urca   1026 erg / s / cm3 @core

Cooling ~1 year

Summary
Giant flare is attractive to GW astronomy, butinvolves many uncertainties.

Timescale puzzle is briefly discussed, but therelevant mechanism is unknown.

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