Benoît Cerutti CNRS & Université Grenoble Alpes (France)

Transcription

1 Gamma-ray Gamma-ray pulsars: pulsars: What What have have we we learned learned from from ab-initio ab-initio kinetic kinetic simulations? simulations? Benoît Cerutti CNRS & Université Grenoble Alpes (France) Collaborators: S. Philippov (Berkeley), A. Spitkovsky (Princeton), K. Parfrey (Berkeley), J. Mortier (Grenoble), A. de Valon (Grenoble), G. Dubus (Grenoble) Agile Symposium, Rome, Dec , 2017

2 Some of the big questions How does the star spin down? How is this energy channeled to particles and radiation? How is the plasma generated? How are particle accelerated and radiate? Where is the emission coming from? To address these questions, we need a model of the magnetosphere! Casey Reed

3 Elements of a pulsar magnetosphere: vaccum (See review, e.g., Kirk+2009, Cerutti & Beloborodov 2016) Magnetosphere Rotation of the field lines induce electric field : Ω RΩB E= c E Potential difference pole/equator : 2 R ΩB 18 Δ Φ= 10 V c NS (for a Crab like pulsar) E Rotation axis

4 Elements of a pulsar magnetosphere: plasma filled Dipole in vacuum is not a good model! Magnetosphere Copious pair creation in the polar caps Ω synchrotron γ B absorption E.B 0 curvature NS Daugherty & Harding 1982 ; Timokhin & Arons 2013 ; Chen & Beloborodov 2014 ; Philippov et al., 2015 Rotation axis

5 Elements of a pulsar magnetosphere: plasma filled Magnetosphere Open field lines Outflowing plasma and Poynting flux Ω Wind region Light cylinder radius: RLCΩ=c e+/e Here corotation is impossible! Toroidal field, Bφ NS Closed field lines Plasma confined, co rotating Dead zone e+/e e+/e Rotation axis Jump in B => Current Sheet

6 Ballerina skirt: oblique rotator current sheet Relativistic analog to the heliospheric current sheet

7 Proposed sites for particle acceleration Acceleration where E.B 0 γ ray : curvature or synchrotron radiation e.g. Arons 1983; Muslimov & Harding 2003; Cheng et al. 1986; Romani 1996; Coroniti 1990 ; Lyubarskii 1996 Polar cap type model Wind region Magnetosphere e+/e γ NS Outer/slot gap type model γ e+/e γ Current Sheet (Magnetic reconnection) e+/e Pb Rotation Light cylinder radius unsolved analytically=> Need for axis simulations!

8 Insights from the MHD approach and why we need PIC (Force Free / Resistive Force Free / Full MHD) There is no analytical solution for the magnetosphere, need for numerical simulations! First numerical solution of the aligned rotator [Contopoulos et al. 1999] First numerical solution of the inclined rotator [Spitkovsky 2006] Tchekhovskoy et al Caveat: The fluid approach does not capture the microphysics (particle acceleration nor radiation)

9 Insights from the MHD approach and why we need PIC (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

10 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

11 Computing cycle per timestep Solve Newton's equation Δt Solve Maxwell s equations (E,B) Deposit Charge and current densities (ρ,j) Capture self-consistently the electrodynamics, non-thermal particle acceleration and radiation

12 PIC simulations of pulsar magnetosphere: An overview References Aligned/ Oblique Particle injection Philippov & Spitkovsky (2014) Aligned Volume injection Chen & Beloborodov (2014) Aligned Pair creation Cerutti et al. (2015) Aligned Stellar surface Belyaev (2015) Aligned Injection E.B 0 Philippov et al. (2015a) Oblique Pair creation Philippov et al. (2015b) Aligned Pair creation GR corrections Cerutti et al. (2016a,b) Oblique Stellar surface Radiation & Polarization Philippov & Spitkovsky (2017) Oblique Pair creation GR corrections & radiation Kalapotharakos et al. (2017) Oblique Volume/surface injection Radiation (curvature) Brambilla et al. (2017) Oblique Volume/surface injection Extra physics

13 The numerical setup: an aligned rotator (2D) Philippov & Spitkovsky 2014 Chen & Beloborodov 2014 Cerutti et al Belyaev 2015 Ω Reflecting wall Initially in vacuum Bdipole Dipole in vacuum Injection of particles (Most delicate and discussed issue) Star R* Reflecting wall Light cylinder radius Absorbing layer (no plasma, λe, λ*b terms)

14 Toroidal magnetic field Cerutti et al. 2015

15 Pulsar spin down and dissipation Force free L0=cB*2R*6/4RLC ~30% drop Significant dissipation within a few RLC! => Energy transferred to energetic particles and radiation!

16 Particle / radiation mean energy (χ=30 ) Cerutti et al Relativistic reconnection Photons Mostly synchrotron radiation

17 Positron orbits in oblique pulsar (30 ) In the co rotating frame From Cerutti et al See also Philippov & Spitkovsky 2017 and Brambilla et al. 2017

18 High energy radiation flux (ν>ν0, χ=0 ) Cerutti et al. 2016

19 High energy radiation flux (ν>ν0, χ=30 ) (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) Cerutti et al. 2016

20 The tearing mode in action (mid plane)

21 Observed high energy radiation flux (ν>ν0, χ=0 ) Relativistic beaming 1/γ<<1 Particle photons β 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

22 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 One pulse per crossing of the current sheet Cerutti et al. 2016

23 Skymaps High energy photons are concentrated within the equatorial regions where most of the spin down is dissipated.

24 A few typical lightcurves Bridge Cerutti et al See also Philippov & Spitkovsky 2017 Kalapotharakos+2017

25 Fitting Fermi LAT pulsar lightcurves PRELIMINARY Second catalog (Abdo+2013) : 117 pulsars Observations PIC model χ² method Courtesy of Aloïs de Valon (Univ. Grenoble Alpes), Master thesis project

26 Fitting Fermi LAT pulsar lightcurves PRELIMINARY Key findings : Pulsar viewing angles are consistent with a random distribution (>90 % chance) Millisecond pulsars are closer to alignment (χ<~45 ) than young isolated pulsars. Evidence for alignment with age, alignment timescale years. Magnetic axis of very young pulsars nearly randomly distributed => Random distribution at birth? Age < yrs do ran yrs < Age < 105 yrs m Age > 105 yrs 0 Obliquity 90 Courtesy of Aloïs de Valon

27 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] e- pulse ΔΦ e+ pulse

28 (Incoherent) Polarization signature : Observations Optical 2PA x Polarized flu [Słowikowska+2009]

29 (Incoherent) Polarization signature : PIC PIC model χ=60, α=130 Degree of polarization :? % [Cerutti, Mortier & Philippov 2016]

30 The Crab pulsar as we may see it! Gray : Total flux (all directions) Color : Observed flux Obs

31 Conclusions Global PIC simulations is the way to go to solve particle acceleration in pulsars 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. Open questions : - How to scale simulations up to realistic pulsars? - How to refine pair creation modeling? - What is origin of the radio emission? -...