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 .