Kinetic modelling of pulsar magnetospheres
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1 Kinetic modelling of pulsar magnetospheres Benoît Cerutti IPAG, CNRS, Université Grenoble Alpes In collaboration with : Sasha Philippov (Princeton), Anatoly Spitkovsky (Princeton), Jérémy Mortier (U. Grenoble Alpes) Cosmic Ray Origin beyond the standard model, Sept , 2016, San Vito di Cadore. Casey Reed
2 Pulsars shine throughout the electromagnetic spectrum The Crab pulsar X MeV GeV Optical TeV Radio [Adapted from Bühler & Blandford 2014] A large fraction of the pulsar spindown is released in light, in particular in the gamma-ray band. => Efficient particle acceleration!
3 Most Galactic accelerators are pulsars Fermi-LAT ~ 100 gamma-ray pulsars Galactic coordinates [100 MeV 100 GeV] [2nd Fermi-LAT pulsar catalog] Pulsars emitting gamma rays young and ms, i.e., rotation-powered
4 Pulsars are efficient particle accelerators Lγ~1-10% Spin-down [2nd Fermi-LAT pulsar catalog] How does the star spin-down? How is this energy transferred to particles and radiation?
5 Typical gamma-ray pulsar signal Two peaks lightcurves Hard power-law + exponential cut-off «Bridge» [2nd Fermi-LAT pulsar catalog] How and where are particle accelerated and radiate?
6 Elements of a pulsar magnetosphere: vacuum Magnetosphere Rotation of the field lines induce electric field : RΩB E= c Ω E Potential difference pole/equator : 2 R ΩB 16 Δ Φ= 10 V c NS (for a Crab-like pulsar) E Rotation axis
7 Elements of a pulsar magnetosphere: plasma filled Dipole in vacuum is not a good model! Magnetosphere Copious pair creation in the polar caps Light-cylinder radius: RLCΩ=c Ω Here corotation is impossible! synchrotron γ-b absorption E.B 0 curvature NS Daugherty & Harding 1982 ; Timokhin & Arons 2013 ; Chen & Beloborodov 2014 ; Philippov et al., 2015 Potential polar cap (Crab): 3 2 R Ω B 14 Δ Φ pc = 10 V 2 c Wind region Rotation axis e+/e-
8 Elements of a pulsar magnetosphere: plasma filled Magnetosphere Open field lines Outflowing plasma and Poynting flux Wind region Light-cylinder radius: RLCΩ=c Ω Here corotation is impossible! e+/etoroidal field, Bφ NS e+/e- Jump in B => Current Sheet Inclined rotator Closed field lines Plasma confined, co-rotating Dead zone e+/e- Rotation axis Gralla & Jacobson 2014 Similar to the heliospheric current sheet.
9 Proposed sites for particle acceleration Acceleration in gaps, E.B 0 γ-ray : curvature radiation e.g. Arons 1983; Muslimov & Harding 2003; Cheng et al. 1986; Romani 1996 Polar-cap type model - Radio emission? - γ-rays? Unlikely because absorbed by B Wind region Magnetosphere e /e + - γ NS Outer/slot-gap type model Favored by γ-ray observations γ e+/e- e+/e- Rotation axis Light-cylinder radius Current Sheet
10 Proposed sites for particle acceleration Wind region Magnetosphere Particle acceleration via relativistic reconnection γ-ray: Synchrotron Coroniti 1990 ; Lyubarskii 1996 ; Kirk+2002 ; Bai & Spitkovsky 2010 ; Pétri 2012 ; Arka & Dubus 2013; Uzdensky & Spitkovsky 2014 Mochol & Pétri 2015 NS e+/eseparatrix e+/e- γ rays Current Sheet Y-point Analogy with Jupiter-Io magnetosphere e+/e- Models Rotation axis on dependent Light-cylinder radius the geometry of the magnetosphere LASP
11 Insight from the MHD approach (Force Free / Resistive Force Free / Full MHD) There is no analytical solution for the magnetosphere, need for numerical simulations! Numerical solution of the aligned rotator [Contopoulos et al. 1999] Numerical solution of the inclined rotator [Spitkovsky 2006] Tchekhovskoy et al Caveat: The fluid approach does not capture the microphysics (particle acceleration nor radiation)
12 Insight from the MHD approach (Force Free / Resistive Force Free / Full MHD) Ideal Force-Free field geometry with prescribed emitting field lines Bai & Spitkovsky 2010a,b Non-ideal Force-Free with prescribed resistivity Li et al. 2012; Kalapotharakos et al. 2012, 2014 Favor high-energy emission from the outer magnetosphere + current sheet Ad-hoc accelerating/radiating zones, large uncertainties Need for self-consistent approach PIC simulations!
13 The Particle-In-Cell (PIC) approach Follow motion of millions of charged particles and evolved the electromagnetic fields y Computational domain Grid (E,B) fields known on the grid Cell Particles evolve in continuous space x
14 The numerical setup: an aligned rotator (2D) Philippov & Spitkovsky 2014 Chen & Beoborodov 2014 Cerutti et al Belyaev 2015 Ω Reflecting wall Bdipole Dipole in vacuum Injection of particles Star R* Reflecting wall Light cylinder radius Absorbing layer (no plasma, λe, λ*b terms)
15 Toroidal magnetic field Cerutti et al. 2015
16 Global PIC simulations with discharge Ref : Chen & Beloborodov 2014 ; Philippov et al., 2015 The stellar rotation impose a twist on the field lines, hence a current outside the light-cylinder. This current must be matched at the polar cap. Electrons alone carry enough current => No dicharge needed, no acceleration! J Positrons [Shibata 1997, Beloborodov 2008, Timokhin & Arons 2013] Electrons J<cρGJ Chen & Beloborodov 2014 => Low-multiplicity plasma (κ~1) are in contradictions with observations where κ>>1
17 General relativistic effects may be a way out! Ref : Beskin 1990 ; Muslimov &Tsygan 1992 ; Sakai & Shibata 2003 Lense-Thirring frequency : Frame-dragging effect reduces the stellar rotation Stanford University Significant only at the star surface, no changes at the light-cylinder! => Less particles are extracted from the polar cap => But the same current is needed Need a discharge => Particle acceleration!
18 2D GR PIC simulations Development of GRPIC code [Philippov et al. 2015b] : Zeltron 3+1 GR electrodynamics Courtesy of Sasha Philippov
19 2D GR PIC simulations Time-dependent discharge of the polar-cap : Origin of the radio emission? Power in stripes W~10 2 LO, enough to the observed radio emission Courtesy of Sasha Philippov
20 3D PIC with radiation reaction force Zeltron code : Assumption : Large plasma supply provided by the star surface = Efficient pair creation Initially in vacuum Radiation reaction force Emitted radiation spectra : Apply for synchrotron and curvature radiation (log(r) θ φ) :
21 Particle / radiation mean energy (χ=30 ) Cerutti, Philippov & Spitkovsky 2016 Photons Particle acceleration via relativistic reconnection in the current sheet High-energy radiation is synchrotron radiation Particle energy in the sheet given by : σ LC = B 2LC 4 π Γ n LC m e c 2 50 (here) See also in 2D axisymmetric Cerutti et al. 2015
22 Particle / radiation spectra Current sheet High-energy emission χ Particle acceleration and emission of energetic radiation decreases with pulsar inclination Cerutti, Philippov & Spitkovsky 2016
23 High-energy radiation flux (ν>ν0, χ=0 ) (from Local reconnection simulations) J J Kink Tearing Presence of spatial irregularities due to kinetic instabilities in the sheet (e.g., kink and tearing modes, see also Philippov et al. 2015a)
24 High-energy radiation flux (ν>ν0, χ=30 )
25 High-energy radiation flux (ν>ν0, χ=60 ) Small contribution from the wind regions : Could be due to reconnection induced inflow towards the sheet (Tchekhovskoy et al. 2013)
26 High-energy radiation flux (ν>ν0, χ=90 ) Even for the orthogonal rotator, high-energy photons are concentrated within the equatorial regions where most of the spin-down is dissipated.
27 Observed high-energy radiation flux (ν>ν0, χ=0 ) Gray : Total flux (all directions) Color : Observed flux HE flux concentrated close to the light-cylinder Observer Spatial extension of the observed emission in the sheet => Formation of a caustic
28 Observed high-energy radiation flux (ν>ν0, χ=30 ) Gray : Total flux (all directions) Light curve shaped by the geometry of the current sheet Color : Observed flux
29 Two-peaked lightcurves are very generic One peak per crossing of the current sheet Blue : Positronic emission Red : Electronic emission Viewing angle Fermi-LAT second pulsar catalog e+ e- Cerutti, Philippov & Spitkovsky 2016
30 Particle acceleration and origin of the e +/e- asymmetry 2D
31 Particle acceleration and origin of the e +/e- asymmetry 2D
32 Particle acceleration and origin of the e +/e- asymmetry 2D (aligned pulsar) Cerutti et al. 2015
33 Particle acceleration and origin of the e +/e- asymmetry In the co-rotating frame Cerutti, Philippov & Spitkovsky 2016
34 Particle acceleration and origin of the e +/e- asymmetry In the co-rotating frame Cerutti, Philippov & Spitkovsky 2016
35 Application to the Crab pulsar Fermi LAT [Abdo+2010] 3 ΔΦ 0.4 PIC model χ=60, α=130 Consistent with the nebula morphology in X rays [e.g. Weisskopf+2012] 3 ΔΦ 0.4
36 (Incoherent) Polarization signature : Observations Optical 2PA x Polarized flu [Słowikowska+2009]
37 (Incoherent) Polarization signature : PIC PIC model χ=60, α=130 Degree of polarization : % [Cerutti, Mortier & Philippov 2016]
38 The Crab pulsar as we may see it! Gray : Total flux (all directions) Color : Observed flux
39 Conclusions Global PIC simulations is the way to go to solve particle acceleration in pulsars General relativity helps at producing pairs in the polar cap, and hence at emitting radio waves. Simulations demonstrate the major role of relativistic reconnection in particle acceleration High-energy emission could be synchrotron radiation from the current sheet >~ RLC Pulse profile and polarization provide robust constraints on Crab pulsar inclination and viewing angles. More work needed to compare simulations to observations.
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