Superluminal waves in pulsar winds The striped wind and its - PowerPoint PPT Presentation

Superluminal waves in pulsar winds Ioanna Arka Superluminal waves in pulsar winds The striped wind and its termination shock Brief review Poynting flux reflection and Ioanna Arka propagation in the upstream Superluminal waves Model and calculations in collaboration with John Kirk Results Max Planck Institut f¨ ur Kernphysik Conclusions Heidelberg, Germany HEPRO III, Barcelona, 28/6/2011

Superluminal Outline waves in pulsar winds Ioanna Arka The striped wind and its termination shock The striped wind and its termination shock Brief review Poynting flux Brief review reflection and propagation in the Poynting flux reflection and propagation in the upstream upstream Superluminal waves Model and calculations Superluminal waves Results Conclusions Model and calculations Results Conclusions

Superluminal The striped wind waves in pulsar winds Ioanna Arka ◮ Rotating neutron star, frequency Ω, magnetic moment µ The striped wind ◮ Misaligned rotator, B φ ∝ r − 1 dominant at r ≫ r LC = c and its termination Ω shock ◮ Striped wind: entropy wave with Γ ≫ 1 Brief review Poynting flux reflection and propagation in the upstream Magnetization Strength parameter Superluminal waves B 2 eB σ = 4 π Γ nmc 2 ≫ 1 a = mc Ω ≫ 1 Model and calculations Results Conclusions

Superluminal Magnetic flux dissipation waves in pulsar winds Ioanna Arka ◮ In the nebula σ < 1 (Kennel & Coroniti 1984) The striped wind and its termination shock Need for field dissipation in the wind or at the shock Brief review Poynting flux ◮ reconnection at the current sheets (Coroniti 1990) reflection and propagation in the upstream ◮ however, reconnection slows down as flow accelerates Superluminal waves (Lyubarsky & Kirk 2001) Model and calculations ◮ reconnection at the termination shock (Lyubarsky Results Conclusions 2003, P´ etri & Lyubarsky 2007, Lyubarsky & Liverts 2008) σ ≫ 1 a ≫ 1 δ l ≪ λ Michel 1982: square wave

Superluminal Interaction of wind with termination shock waves in pulsar winds Ioanna Arka ◮ ”instantaneous” current reversal at shock The striped wind ◮ alternating current emits electromagnetic waves and its termination shock ◮ in vacuum this wave would have an amplitude Brief review Poynting flux reflection and B ref = ρ − 1 propagation in the upstream B 0 4 Superluminal waves Model and ρ : shock compression ratio, B 0 : wind field amplitude at shock calculations Results ◮ However perpendicular shock with σ ≫ 1 → Conclusions ρ ≃ 1 + 1 2 σ (Kennel & Coroniti 1984) ◮ only a small fraction of the flux is reflected ◮ reconnection at shock: reflection of strong wave: B ref = B 0 4 → possibility of a precursor to the shock

Superluminal Wave propagation in plasma waves in pulsar winds Ioanna Arka Assume that there is a reflected wave that propagates in the The striped wind and its termination upstream cold plasma. shock Brief review Wave propagation condition in plasma: Poynting flux reflection and propagation in the upstream ◮ linear waves ω > ω p , ω p : plasma frequency Superluminal waves ⇒ Γ 4 > a ◮ strong waves ω > ω p √ a ⇐ Model and σ calculations Results (e.g. Max 1973) Conclusions Reconnection at shock (P´ etri & Lyubarsky 2007) : a ◮ no dissipation: Γ < 4 σ 3 / 2 ◮ partial dissipation: 4 σ 3 / 2 ≤ Γ ≤ a a σ ◮ full dissipation: Γ > a σ for full dissipation the reflected wave always propagates

Superluminal Strong waves in magnetized plasma waves in pulsar winds Ioanna Arka Self-consistent approach needed: The striped wind and its termination ◮ two-fluid approach, cold e + − e − plasma shock Brief review ◮ wave propagating transversely to the magnetic field: Poynting flux reflection and propagation in the X-mode upstream ◮ linear X-mode in e + − e − plasma is purely transverse Superluminal waves Model and (Iwamoto 1993) calculations Results Conclusions Non-linear X-mode already studied in the past analytically in some limiting cases (Kennel & Pellat 1976, Clemmow 1974, Asseo et al. 1978 and others) ◮ waves with β φ > 1 can have arbitrarily large amplitudes and can propagate in thin plasmas ◮ full treatment is possible numerically

Superluminal Wind conversion waves in pulsar winds Ioanna Arka The striped wind Assumptions: and its termination shock ◮ conversion happens in δ R ≪ R → plane wave Brief review Poynting flux approximation reflection and propagation in the upstream ◮ wave’s frequency imposed by central rotator (pulsar) Superluminal waves Conditions: conservation of phase-averaged Model and calculations 1. particle flux Results Conclusions 2. energy flux 3. momentum flux 4. magnetic flux at conversion → ”jump conditions” for the transition (see also Kirk 2010)

Superluminal Computation waves in pulsar winds Ioanna Arka 1. Choose pulsar parameters: The striped wind ◮ Luminosity L and its termination shock ◮ Magnetization σ Brief review Poynting flux reflection and ◮ Lorentz factor of outflow Γ propagation in the upstream 2. Solve equations for cold e − − e + plasma: Superluminal waves ◮ Maxwell’s equations Model and calculations Results ◮ Equations of motion + continuity equations Conclusions 3. Apply ”jump conditions” to choose from above solutions. Solutions dependend on radius and the parameter χ where � B � χ = � � B 2 �

Superluminal Superluminal waves in the upstream waves in pulsar winds Ioanna Arka χ =0.65 χ =0.95 The striped wind 1 1 and its termination shock 0.8 0.8 Brief review Poynting flux 0.6 0.6 reflection and 1/ β φ 1/ β φ propagation in the 0.4 0.4 upstream Superluminal 0.2 0.2 waves Model and 0 0 calculations Results 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(R) log(R) Conclusions (plots for σ = 100 , Γ = 100 ) ◮ χ ranges from 0 to 1 from equator to end of striped wind zone ◮ minimum radius for conversion ◮ upstream propagating modes possible (propagating inwards from the shock)

Superluminal New ”magnetization parameter” waves in pulsar winds Ioanna Arka ◮ Energy transferred from fields to particles The striped wind Field energy flux and its termination ◮ introduce wave parameter σ w : shock Particle energy flux Brief review Poynting flux ◮ σ w /σ plotted, where σ : magnetization in striped wind reflection and propagation in the upstream Superluminal (plots for σ = 100 , Γ = 100 ) waves Model and calculations Results χ =0.65 χ =0.95 Conclusions 0 0 -0.5 -0.5 -1 -1 log( σ w / σ ) log( σ w / σ ) -1.5 -1.5 -2 -2 -2.5 -3 -2.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 log(R) log(R)

Superluminal Conclusions waves in pulsar winds Ioanna Arka The striped wind and its termination ◮ Striped wind can be converted to a strong, superluminal shock Brief review wave through interaction with the termination shock Poynting flux reflection and propagation in the upstream ◮ During conversion, energy gets transferred from fields to Superluminal waves particles: Model and calculations → efficient particle acceleration Results → magnetic field dissipation Conclusions ◮ Implication for particle acceleration at the shock : σ < 1 shocks are efficient particle accelerators ◮ Possibility for recovery of Fermi I at shock front