PARTICLE ACCELERATION AT PULSAR WIND TERMINATION SHOCKS

Transcription

1 PARTICLE ACCELERATION AT PULSAR WIND TERMINATION SHOCKS Gwenael Giacinti (MPIK Heidelberg) & John G. Kirk (MPIK Heidelberg) In Prep. (To be submitted soon)

2 Observations of the Crab nebula RADIO X RAYS X ray spectral index : d(ln N ) / d(ln ) = 2.1 Predicted particle spectrum at ultra relativistic shocks : d(ln Ne ) / d(ln ) = 2.2 Seems to be in perfect agreement BUT Perpendicular shock, so 1st order Fermi inoperative! Buehler & Blandford (2014) T=0: B t>0: ct/3 > Downstr. Rest Frame

3 Observations of the Crab nebula (1) Spectral index map Mori et al., ApJ (2004): Chandra Hard spectrum close to the shock, in the equatorial plane Photon index s ~ 1.9 => d(ln Ne ) / d(ln ) ~ 1.8! (2) How many X ray emitting electrons? N(e radio)/n(e X rays) ~ 104 e.g. Olmi et al., J. Plasma Phys. (2016).

4 Numerical simulations Model Simulations of Buehler & Giomi (2016) : OUR MODEL (PLANAR 1D) : z UPSTREAM z = 1016 cm DOWNSTREAM z=0 x s = 100 Equatorial plane c/3 z = 1016 cm

5 Numerical simulations Model Simulations of Porth et al. (2014, 2016) Crab nebula: OUR MODEL (PLANAR 1D) : z = 1016 cm z z=0 x s = 100 Equatorial plane c/3 z = 1016 cm B z uy for z < 1016 cm, At z = ±1016 cm, B = ±1mG

6 Numerical simulations Model Simulations of Porth et al. (2014, 2016) Crab nebula: OUR MODEL (PLANAR 1D) : z = 1016 cm z z=0 x s = 100 Equatorial plane c/3 z = 1016 cm B z uy for z < 1016 cm, At z = ±1016 cm, B = ±1mG, B/B = 0.1, cst. of z, Bohm.

7 Numerical simulations Model Simulations of Buehler & Giomi (2016) : OUR MODEL (PLANAR 1D) : B Striped wind z = 1016 cm z z=0 x s = 100 << rg B z uy for z < 1016 cm, Equatorial plane c/3 z = 1016 cm At z = ±1016 cm, B = ±1mG, B/B = 0.1, cst. of z, Bohm.

8 Numerical simulations Model OUR MODEL (PLANAR 1D) : z = 1016 cm Bu,RF = ( d/3 u )Bd,RF z z=0 x s = 100 Equatorial plane c/3 z = 1016 cm B z uy for z < 1016 cm, At z = ±1016 cm, B = ±1mG, B/B = 0.1, cst. of z, Bohm.

9 Numerical simulations Model OUR MODEL (PLANAR 1D) : Integrate trajectories of individual particles in 3D (test particle limit), Use 3D realizations of turbulent B fields, Integrate in Downstream or Upstream rest frame (E=0) ; If shock crossing: Do the Lorentz transfo. (Xd,td) (Xu,tu), 'Injected' electrons z = 0 positrons z x s = 100 Obs. Fr. ~ Shock Fr. (Xs,ts). z = 1016 cm Equatorial plane c/3 z = 1016 cm

10 Numerical simulations Model OUR MODEL (PLANAR 1D) : Wave period 33 ms, low density wind MHD invalid. z = 1016 cm 'Injected' Uniform injection Amano & Kirk (2013): z electrons over the central 5 %. Two fluid simulations of a shock z = 0 positrons front in a Poynting flux Equatorial plane dominated relativistic flow. x Giacchè & Kirk (2017): Propagate individual e±. s = 100 inj ~ => TeV electrons. c/3 z = 1016 cm

11 Numerical simulations In the equatorial current sheet : z [cm] z [cm] Ejected d(ln N) / d(ln ) 6 5 < 2.2 Trapped d(ln N) / d(ln ) 1.8 > 2.2! VERY SOFT HARD

12 Positrons ( or electrons depends on polarity) B Grad B drift can beat the advection at c/3 in small regions close to z=0 (on both sides).

13 ~E.dN/dE Positrons d(ln N) / d(ln ) 6 5

14 Electrons

15 Electrons

16 Electrons

17 Electrons ~E.dN/dE Turnover at high E : Lmax d(ln Ne ) / d(ln ) 1.8 Photon index s 1.9 (Chandra!) from turb. In practice: tsynch ~ tgyr at E ~ 1 10 PeV.

18 Electrons ~E.dN/dE Turnover at high E : Lmax d(ln Ne ) / d(ln ) 1.8 Photon index s 1.9 (Chandra!) from turb. In practice: tsynch ~ tgyr at E ~ 1 10 PeV. Outside this ± 5 % region : No/Very little acceleration. 7 % of injected particles => Enough for the X ray emitting electrons

19 Conclusions X ray emitting particles in the Crab Nebula can be accelerated at the termination shock by 1st order Fermi, Grad B drift does not help (particles advected after ~ 1 cycle), On the contrary, shock drift helps : Multiple shock crossings, hard electron (or positron) spectrum, Spectral hardening (photon index ~ 1.9) results from the drift of e (or e+) along the shock and into the current sheet, > Chandra observations Enough particles are accelerated to explain radio/x ray obs. ( Reconnection probably relevant only for radio electrons. )