Magnetic energy dissipation and emission from magnetars
Andrei Beloborodov Columbia University Magnetars
• strong and evolving B • large variations in emission and spindown
• internal + external heating
• energy budget E ~ t L ~ 1047 −1048 erg Building up magnetic stresses
Hall drift
Goldreich Reisenegger (1992)
ambipolar diffusion
Observed quasi-thermal surface emission
Kaminker et al. (2009)
heating in the outer crust is required with E! ~ 1036 −1037 erg/s Crustal motions and internal heating
• No cracks
• No slippage except along magnetic flux surfaces
• Collapse of ideal crystal? (Chugunov, Horowitz 2010) • Plastic flow (motion of dislocations) heating q! = σ s!
heat is conducted toward the core and surface (Kaminker et al. 2009; Jose Pons) • QPOs (externally triggered) External (magnetospheric) dissipation Sun
Recorded in extreme ultraviolet from NASA’s Transition Region and Coronal Explorer satellite.
Sun: convective motions twist the magnetic field anchored to the surface
Dissipated/radiated power: L = I Φ vacuum: I = 0 force-free: Φ = 0
Voltage regulated by e+- discharge Φ ~ 109−10V
surface radiation: !ω ~ 3kT ~ 1 keV
B 2 Landau energy: !ωB = mec BQ
3 4 resonant scattering: γω ≈ ωB when γ ~ 10 −10 (σ res ≈ πreλ) 2 + − scattered photon: E ~ γωB ~ γ ω → e + e Magnetosphere
Twisted c j = ∇ × B ≠ 0, j || B force free 4π (cf. solar corona)
Filled with plasma
Dynamic -- Changing magnetic moment (spindown)
-- Changing pulse profiles
-- Bursts Flares δt ~ 0.1-0.3 s
Starquake?
Excitation of Alfven waves on field lines with length > cδt
Reconnection in the magnetosphere?
(Thomspon, Duncan 1996) Twisted magnetospheres and flares
Parfrey et al. 2013 Twist energy
W = W0 for untwisted dipole
Loss of magnetic equilibrium and reconnection
Parfrey et al. (2013)
SGR 1900+14 Observed “anti-glitch” in SGR ……
“anti-glitch”
Woods et al. (1999) Anti-glitch in 1E 2259+586
Archibald et al. (2013) Transient magnetars Crustal cooling? Lyubarsky et al. (2001)
Decay of magnetospheric activity? Beloborodov (2009)
Gotthelf, Halpern (2007) Untwisting magnetosphere XTE J1810-197
Untwisting magnetosphere
time units: µ t = 0 cRΦ
−1 tev ≈ 0.4 Φ10 B14 A12 yr ∂ψ ∂Φ = c ∂t ∂f
(hot spot area) Hard X-ray emission
AXP 4U 0142+61
Den Hartog et al. (2008) AXP 4U 0142+61
Den Hartog et al. (2008) Magnetospheric plasma
discharge: e+, e− injection, 36 −1 L± ~ IΦ ~ 10 erg s
the star emits thermal radiation, L ~ 1035 erg s−1
radiation controls the e± flow Relativistic e+- outflow
B γ ≈ 100 BQ
Beloborodov (2013) [mec] pair creation
B γ ≈ 100 BQ + h e− νsc
γ >> 10 keV γ ∼ 1 Lann ~ 0.1L keV
γ >> 10 e+ − hνsc
B B γ ≈ 100 , radiative zone: B < Q ≈ 1013 G BQ 4 Spectrum radiated by the decelerating outflow
Spectrum variation with inclination Observational test: phase resolved spectra Possible radio emission mechanism
Radiative drag tends to “lock” >> 1 particle velocity β
Electric current (two-fluid outflow model)
Dynamic equation
Two streams with different β => instability
Beloborodov (2013) Summary
Internal dissipation:
no cracks, plastic flow of the crust
(=> externally triggered QPOs)
External dissipation:
(a) Flares: reconnection (+ Alfven wave cascade)
(b) Persistent emission: e+- discharge => hard X-rays “radiative locking” => radio