Trans-Debye Scale Plasma Simulations Jacob Trier Frederiksen Niels Bohr Institute

Dept. Astronomy & Physics, Århus Univ. Åke Nordlund Niels Bohr Institute Troels Haugbølle Dept. Astronomy & Physics, Århus Univ. Collaborators

Overview Trans-Debye Scale Modeling Example: GRB–CBM Interaction Particle-in-cell codes Random phase approximation, the hinge Continuous collisional transfer Challenges Example: GRB–CBM Interaction GRB-CBM model, setup First light, results ’bold statements’ On-line Radiation Spectral Synthesis Simple test, synchrotron, ω vs. log(ω) Demonstration (2 minutes) Challenges (if time leftover) Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Trans-Debye Scale Modeling

Trans-Debye Scale Modeling Particle-in-cell; reminder ... ALSO EXPLAINED YESTERDAY ... PIC codes solve self-consistently Maxwell’s equations (discretized space) Lorentz forces on particles (continuous phase space) Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Trans-Debye Scale Modeling Particle-in-cell codes PIC codes are ideally collisionless, interaction only through mean fields: Any collisionality must be explicitely implemented: PIC codes should: 1) approximately resolve Debye length 2) have ”many” particles in Debye sphere Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Trans-Debye Scale Modeling Random phase approximation (Pines & Bohm, ’52) RPA splits dynamics at Debye length Naturally achieve a split scheme for kinetic plasmas Frederiksen et al., 2004 Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Trans-Debye Scale Modeling Continuous collisional transfer Very detailed collision terms can be realized Continuous weighting of particles ~ 10+ magn. resolution in physical particle number density [P0,P1,P2,P3] 1 + [P0,P1,P2,P3] 2 conserved to ~10-6 Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Trans-Debye Scale Modeling Challenges, examples Refined particle merging Phase (search) space is multi-dimensional, Dtot ≈ Dr * Dp * Nsp * Ncollisions * Wpart * ... , at least Dtot ≈ 3*3*1*1*1... ~ 9+... ! Coupling grid photons with kinetic photons Quantum description needed? Delocalization of kinetic photons vs. localization of grid photons. Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Example: GRB-CBM Interaction ApJL, 680, L5-L8

Example: GRB–CBM Interaction Imagined scenery ? Rapid variation Slow variation ...as also explained yesterday... non-thermal Wijers & Galama 1999 Felix Ryde & Milan Battelino, 2005 quasi-thermal / hybrid Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Example: GRB–CBM Interaction Motivation and model Preconditioning of circumburst medium prior to shocked ejecta arrival Possible en-route burst lightcurve and spectral shaping Internal vs. external shocks (variable CE?) Model: Take a ’good’ case from BATSE catalogue (GRB951102) Make a quiescent cool CBM hydrogen plasma and inflict a burst of blackbody photons with Eγ ⊆ [50keV,1MeV] Compton interact photons and electrons Solve resulting plasma problem .... GRB 951102 Ryde & Battelino KTH, Stockholm Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Example: GRB–CBM Interaction First light, results ApJL, 680, L5-L8, http://lanl.arxiv.org/abs/0803.3618 PARTICLE ACCELERATION PHOTON BOOSTING QUASISTATIC MAGNETIC FIELD GENERATION Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Example: GRB–CBM Interaction Conclusions/Discussion and speculation Magnetic field generated in GRB front produces a solid back-scattering mechanism (propagating at ~light speed!) for UHECRs, i.e. naturally resolves Fermi-accel. escape problem. Counter-streaming γ-photons are prone to pair produce ⇒ sub-shocks Photon ‘spikes’ interesting; delayed HE emission? – waiting for GLAST results…! Movie? -- mailto:trier@astro.ku.dk arXiv:0809.1230v1 [astro-ph] Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Online Radiation Spectral Synthesis

Online Radiation Spectral Synthesis Motivation Radiation diagnostics strong tool in discerning physics ‘behind’ observations. Previous and very recent work; Hededal, & Nordlund (2005), Nishikawa et al. (2008) shows proofs of concept. – see for details. Need to collect spectra runtime rather than through passive tracing – to correctly capture electromagnetic effects (Hededal, thesis, 2005) PhotonPlasma code implements: On-line spectral synthesis Multiple observers Active windowing Sub-cycled tracing Tunable radiation ensemble Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Online Radiation Spectral Synthesis Simple test synchrotron, ω vs Online Radiation Spectral Synthesis Simple test synchrotron, ω vs. log(ω) Synchrotron, single particle, 3 obs, linear frequency scale, γ=25, θobs,max=1/γ Synchrotron, single particle, 3 obs, logarithmic frequency scale, γ=25, θobs,max=1/γ # bins = 100000 Runtime ~ 500 secs # bins = 100 Runtime ~ 0.8 sec Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

Synchrotron -- no distr. in pitch -- perfect p-decoherence Online Radiation Spectral Synthesis Slope 2/3 or 1/3 – flatter?? ... steeper?? ... Synchrotron -- no distr. in pitch -- perfect p-decoherence Mono-energetic electrons Perfectly de-phased Homogeneous B-field 10 radiating particles Gamma ~ 25 3 observers: perp – 1/Γ directions

Synchrotron -- distr. Pitch on [0 – ~ 2π/3] -- partial p-decoherence Online Radiation Spectral Synthesis Slope 2/3 or 1/3 – flatter?? ... steeper?? ... Synchrotron -- distr. Pitch on [0 – ~ 2π/3] -- partial p-decoherence Mono-energetic electrons Partially de-phased Homogeneous B-field 10 radiating particles Gamma ~ 25 3 observers: perp – 1/Γ directions OK – how expensive? (demo)

Online Radiation Spectral Synthesis Challenges Frequency interval for synthesis; howto, switch between intervals for high-res capture at varying gamma-factors (for individual particles)? Synchrotron self-absorption; howto, do kinetic radiative transfer?? Parseval’s theorem; howto, trust power binning of modes in log-space vs. binning in lin-space?? Wavelets; howto, capture temporal development more fully in future?? Cooling; howto, cool particles realistically when PIC sims are normalized to plasma parameters?? – is it necessary..? Several others...

Questions? NB: References next slide Thanks a bunch Questions? NB: References next slide Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute

References Pines D & Bohm D – Phys. Rev. 85, 338 (1952) Weibel E – PRL, 2, 83 (1959) Hurley et al., Nature, 372, 652 (1994) Medvedev M V & Loeb A – ApJ, 526, 697 (1999) Thompson C & Madau P – ApJ, 538, 105 (2000) Beloborodov A M -- ApJ, 565, 808 (2002) Ryde F & Svensson R – ApJ, 566, 210 (2002) Barbiellini, Celotti, Ghirlanda, Longo, Piro, Tavani -- MNRAS, 350, L5 (2004) Haugbølle T – PhD Thesis, NBI, ArΧiv Astrophysics e-prints, astro-ph/0510292 (2005) Hededal C – PhD Thesis, NBI, ArΧiv Astrophysics e-prints, astro-ph/0506559 (2005) Frederiksen J T – PhD Thesis, Stockholm Observatory, ISBN 978-91-7155-576-2 (2008) Hoshino M -- ApJ, 672, 940 (2008) Guiliani, ArXiv Astrophysics e-prints, astro-ph/0809.1230v1 (in press, A&A Letters). Kinetic Modeling of Astrophysical Plasmas, Krakow, Poland, October 5th – 9th, 2008 Jacob Trier Frederiksen, Niels Bohr Institute