HIGH-QUALITY FAST QPOs FROM MAGNETARS: AN ELECTRIC CIRCUIT MODEL

1
HIGH-QUALITY FAST QPOs FROM MAGNETARS AN
ELECTRIC CIRCUIT MODEL

• A.Stepanov (Pulkovo Observatory, St.Petersburg)
• V.Zaitsev (Institute of Applied Physics,
  N.Novgorod)
• E.Valtaoja (Tuorla Observatory, Turku)

Expanding the Universe Tartu 27-29 April 2011
2
Soft Gamma-ray Repeater - neutron star (D 10
km, M 1.5MSun) with magnetic field B 1014-15
G
3
Energy release in impulse phase (duration 1
s) up to 21046 ergs High-quality, Q 105,
high-frequency (18-2400 Hz) pulsations in
ringing tails of flares ( 1034-35
ergs). Background 0.1 Hz QPOs due to star
rotation (dipole emission).
4
Ringing tail (Strohmayer Watts ApJ 2006)
5
Starquakes electric current generationdriven
by crust cracking (Ruderman 1991)
Neutron star (D 10 km) with magnetic field B
1014-15 G
6
Flare scenario

• Fireball (1 MeV electron-positron plasma
  gamma-rays)
• the source of main pulse of flare.
• Trapped fireball ( 1 MeV e/p plasma ?) a
  source of ringing tail

dB ? SGR flux modulation
7
Existing models of magnetar fast QPOs

• Strohmayer Watts (2006), Sotani et al (2008)
  Torsion Alfven oscillations of relativistic star
  with global dipole magnetic field.
• Levin (2006, 2007) Torsion oscillations of
  crust. Interaction between normal modes of
  magnetars crust and MHD-modes in its fluid core.
  
• Israel et al (2005) Coupling of toroidal seismic
  modes with Alfven waves propagating along
  magnetospheric field lines.
• Vietri et al (2007) Estimation of magnetic field
  from Cavallo-Fabian-Rees luminosity variability
  limit of ringing tail, B 81014 G.
• Timokhin et al (2008) Variations of
  magnetospheric currents due to crust torsion
  oscillations.
• Glampedakis et al (2006) Interaction of global
  magneto-elastic vibrations of the star and fluid
  core.
• Bo Ma et al (2008) Standing slow magneto-sonic
  waves of flux tubes in magnetar coronae.
• These models do not explain
• - Excitation of oscillations in the ringing
  tail and before impulse phase
• - Very high Q-factor of fast QPOs, Q 104
  (Levin 2006 Q 30 )
• - Broad discrete spectrum of fast QPO
  frequencies (20 -2400 Hz).

8
The main task

• To estimate the physical parameters of trapped
• fireball plasma using oscillations of ringing
  tail
• 1-D physics because B is very high
• (no loss-cone, for example)

9
Helioseismology

• Inside the Sun check of standard model of
  the Sun
• ------------------------------------------------
  -----------------------------
• Asteroseismology Coronal seismology
• stellar evolution model waves
  oscillations in corona
• (flaring loops, coronal heating)

10
Solar-stellar analogyCoronal seismology

• Wave and oscillatory phenomena in solar and
  stellar coronae
• A new and rapidly developing branch of
  astrophysics.
• Two main approaches
• Coronal magnetic loops and flux tubes are
  resonators and wave guides
• for MHD oscillations and waves,
• Coronal loops as an equivalent electric (RLC)
  circuit.

11
Flare loop as an equivalent electric circuit

• Severny (1965) vertical currents I 3?1011 A
  near sunspot
• Electric circuit approach
• Alfven Carlquist (1967) electric circuit
  analog of a flare
• Stenflo (1969), Spicer (1977), Ionson (1982),
  Zaitsev Stepanov (1992), Melrose (1995),
• The last review
• Zaitsev Stepanov Coronal magnetic loops
  (Phys. Uspekhi 2008)

Alfven Carlquist (Sol.Phys.1967)
12
The Sun Loop formed by photosphere convection
Zaitsev, Stepanov, Urpo (AA 2001)
Magnetar corona Beloborodov Thompson (ApJ 2007)
Loop footpoints in nodes of supergranula
cells, ? 30000 km Convection velocity
Vr 0.1 -1.0 km/s
13
Our approach Coronal seismology (RLC-model)

• Based on Beloborodov Thompson model
• (2007) for magnetar corona and on the model
• of coronal loop as an equivalent electric
• circuit (Zaitsev Stepanov 2008).
• Current in a loop is closed in metallic crust
• Electric current appears due to crust
• cracking (Ruderman 1991)
• Trapped fireball consists of 5 -10 current-
• currying loops (RLC-circuits).
• Eigen-frequencies and Q-factors are

14
RLC-circuit model

• SGR 1806-20 flare on Dec. 27, 2004 . Total energy
  51039J
• Circuit energy E LI2/2, from loop geometry
• For loop length l 3104 m, loop radius r
  3103 m we obtain
• circuit inductance L 5104 m 510-3 H.
• From the energy of ringing tail E 0.5LI 2
  1037J we derive
• loop electric current I 31019 A.
• Using current magnitude we estimate the magnetic
  field minimum value
• Bf I/cr 1013 G lt Bq m2c3/he 4,41013
  G.
• Power released in ringing tail W R I 2
  1034 W ? R 2.310-6 Ohm
• For anomalous (turbulent) conductivity seff
  e2n/m?eff
• we get ?eff (Wp /nT)?p 0.1 ?p

15

• The origin of turbulent resistance
• ?I
• 2.310-6 Ohm , Reff ?eff W I2
• Number density of e/p pair in trapped fireball
• I 2necS 31019 A ? n 21016 ??-3 ? ?p
  81012 s-1 (fp 1 THz )
• ?eff (Wp /nkBT)?p 10-1 ?p
• Possible origin of small-scale turbulence Beam
  instability in electron-positron
• plasma (Eichler et al 2002 Lyutikov 2002)

16

• Self-excitation of current oscillations
• Equation for oscillations of electric current
  in a loop
• Because Reff ?eff W I2, R aI2
• Current oscillations are excited if I lt Imax
  e.g. on the rising stage of a flare and on flare
  tail.
• dI ? dB ? SGR flux modulation

17

• From minimal (?1 18 Hz) and maximal (?2 2384
  Hz) frequencies of ringing tail we can estimate
  capacities of loops in trapped fireball
• C1 1,510-2 F, C2 810-7 F.
• From the other side, the loop capacity is
  (Zaitsev Stepanov 2008)
• C eAS/l, for S pr2 31011cm2,
• eA c2/VA2 1 ? l 3106cm, C 10-7 F.
• We can get various loop capacities C 10-2 -
  10-7 F for the loops with different lengths l and
  cross-sectional areas S.

18
Magnetar coronal loop a system with compact
parameters?

• Oscillations of electric current should be
  in-phase in all points of a loop. On the other
  hand, variations of the current propagate along
  the loop with the Alfven velocity. Therefore, for
  the condition of phase coincidence, the Alfven
  time should be substantially smaller than the
  period of oscillations .
• QPO-frequency ? ?RLC 20-2500 Hz lt ?Alfven
  c/l 104 Hz
• Because VA c (!) in magnetar coronae
• c for ? ? 0 or B ? 8

19
Why we choose the SGR 1806-20 flare on Dec. 27,
2004?Flare start 213026,35 UT
20
Polar Geophysical InstituteTumanny Ionospheric
Station
21
Flare start 213026,35 UT
22
Corona of SGR 1806-20 Diagnostics

• From loop geometry ? L 510-3 Henry
• From ringing tail energy LI2/2 ? I 31019 A.
• From current value I Bf cr ? Bmin 1013 G lt
  Bq 4.41013 G
• From energy release rate WRI2 ? R 2.310-6
  Ohm
• From current and loop cross-section area ? n
  2.51016 cm-3
• For R 2.310-6 Ohm collisional frequency ?eff
  (Wp /nT)?p 610-2 ?p
• For 625 Hz ? capacitance
  ? 1.310-5 F
• Circuit quality Q (RvC/L)-1 8105
• From observations Q p??t 4105 for train
  duration ?t 200 ?.
• Various high-quality QPOs detected in giant
  flare of SGR 1806-20
• (? 18, 30, 92, 150, 625, 1480 Hz) are due to
  persistence of loops
• with various geometry, plasma density, and
  magnetic field in a fireball.

23
Summary

• Phenomenological approach ringing tile - a
  trapped fireball - as a set of current-carrying
  coronal loops is quite effective diagnostic tool
  for magnetar corona.
• I 31019 A, Bmin 1013 G lt Bq 4.41013
  G, n 2.51016 cm-3
• Because B lt Bq 4.41013 G, the physical
  processes in trapped fireball can be studied in
  non-quantum plasma approach.
• Estimations from energetic reasons give us real
  physical parameters of magnetars. For impulse
  phase (fireball)
• I 1021 A, B 41014 G.

24
European Week of Astronomy and Space Science
(JENAM-2011)July 4 - 8 2011
Saint-Petersburgwww.jenam2011.org

• Important Dates - May 9 2011 Deadline of
  Abstracts submission/EAS Grant Applications -
  May 31 2011 Results of Grant applications/Final
  programme release - June 6 2011 End of early
  registration - June 27 2011 End of late
  registration - July 4-8 2011  EWASS-2011

25

• Symposia
• S1 Magnetic Universe
• S2 Planets of the Solar System and Beyond
• S3 The Sun New Challenges
• S4 Solar System Measurements of the Next Decade
• S5 Physics of Stars
• S6 Combined Radio/X-rays Approaches to
  Relativistic Astrophysics
• S7 Far-Infrared Spectroscopy comes of age the
  Herschel view
• S8 Status and prospects in high-energy
  particle astrophysics across the electromagnetic
  spectrum
• S9 Galaxy Evolution the key for Galaxy
  Formation theories
• Special Sessions
• SPS1 Close Binaries with Compact Components
• SPS2 Massive Stars Formation
• SPS3 Science with the Virtual Observatory
• SPS4 What powers AXPs and SGRs?
• SPS5 Minor merging as a driver of galaxy
  evolution,
• SPS6 Space Projects
• SPS7 The Missing Baryons and the Warm-Hot
  Intergalactic Medium Current State and Future
  Prospects,