Propagation of TeV PeV Cosmic Rays in the Galactic Magnetic Field

Propagation of TeV PeV Cosmic Rays in the Galactic Magnetic Field Gwenael Giacinti Clarendon Laboratory, University of Oxford In collaboration with : GG & G.Sigl / Based on : Phys. Rev. Lett. 109, 071101(2012) GG, M.Kachelriess, D.Semikoz Phys. Rev. Lett. 108, 261101(2012) With thanks to A.R. Bell, B. Reville, K. Schure for discussions

Outline I TeV PeV Cosmic Ray Propagation in the ISM Generic introduction / interstellar magnetic turbulence / diffusion approximation (DA) II TeV PeV Cosmic Ray Anisotropies at Small Scales 'Beyond' the DA : Explanation for CR small scale anisotropies III Filamentary/Anisotropic Diffusion of TeV PeV Cosmic Rays in the interstellar magnetic turbulence Anisotropic diffusion / implications for ray astronomy, etc.

I TeV PeV cosmic ray propagation in the ISM

Cosmic Rays in the ISM Cosmic Rays self confined below E < few GeV...1 TeV? (Wentzel '70s, Skilling Nature '75,...) > Spectrum inflection at 200 GeV? (Blasi et al. PRL '12) > See P. Blasi's talk. In this work : ECR > 1 TeV. Reacceleration on larger time scales.

Galactic magnetic field Galactic magnetic field made of : Large scale component (regular component) Small scale magnetic turbulence (turbulent component) > See talks of J L. Han and G. Farrar. Faraday rotation measurements: regular fields Large scale component ~ in the Galactic disk (Breg~ 2 G loc.) Synchrotron emission: both regular and turbulent fields Magnetic turbulence Brms~ 4 G locally > Breg

The Galactic turbulent magnetic field Satisfies : <B(x)> = 0, <B(x)2> = Brms2, and div B = 0 Fourier transform : with Power spectrum : ( = 5/3, 3/2 plausible) (see for ex. Strong, Moskalenko, Ptuskin '07) + t, in gen. (see, for example, O'Sullivan, Reville & Taylor, MNRAS '09)

The Galactic turbulent magnetic field Satisfies : <B(x)> = 0, <B(x)2> = Brms2, and div B = 0 Fourier transform : with Power spectrum : ( = 5/3, 3/2 plausible) for with Lmin< 1 AU, Lmax~ 100 pc Coherence length : => Lc ~ few 10s pc. Locally field 'coherent' over ~ 40 pc (see works of P. Frisch).

CR propagation in magnetic turbulence RL >> LTF CR B ~ LTF

CR propagation in magnetic turbulence RL ~ LTF CR B ~ LTF

Diffusion approximation «No» effect ~1 AU Resonant scattering of CRs? See part III ~ rl/10 rl,1pev~0.3pc mfp Lmax~100pc CR propagation in magnetic turbulence can be regarded as a Markovian process => diffusion approximation

Diffusion approximation «No» effect ~1 AU 200pc Resonant scattering of CRs ~ rl/10 rl,1pev~0.3pc mfp 10 PeV? See part III Lmax~100pc CR propagation in magnetic turbulence can be regarded as a Markovian process => diffusion approximation

II TeV PeV cosmic ray anisotropies at small scales GG & Sigl Phys. Rev. Lett. 109, 071101 (2012)

Observations IceCube results > See Talk of S. Benzvi ~0.1% ~0.01% Shapes energy dependent but NOT time dependent

Observations IceCube results > See Talk of S. Benzvi ~0.1% 'All right' ~0.01% «INCOMPATIBLE» WITH DIFFUSION!!!

CR diffusion in the Milky Way Disk GC Earth Bulge «Leaky Box» model

CR diffusion in the Milky Way Disk Diffusion approximation Earth

CR diffusion in the Milky Way Disk Background from 'very old' sources Earth Rather isotropic

CR diffusion in the Milky Way Disk Background from 'very old' sources + Earth Flux from 'more recent' sources: More anisotropic

CR diffusion in the Milky Way Disk Earth CR anisotropy at Earth mostly due to 'more recent' sources

CR diffusion in the Milky Way Lost flux Disk Earth CR anisotropy at Earth mostly due to 'more recent' sources

CR diffusion in the Milky Way (Erlykin & Wolfendale '06, Blasi et al. '11) ~H ~H Disk 2H Earth CR anisotropy at Earth mostly due to 'more recent' and 'nearby' sources 2 => DIPOLE ~ (E/Z)

Remarks on the dipolar anisotropy D(E)

Remarks on the dipolar anisotropy A(20TeV) > A(400TeV) D(E) Blasi et al. '12

Small scale anisotropies : 'mysterious' In magnetic turbulence, only a dipolar anisotropy should be detected => Additional effects needed. Related to sources? CRs do not point back to their sources Magnetic funnelling (Drury & Aharonian '08) Anisotropic turbulence (Malkov et al. '10) A local source in the heliotail (Lazarian & Desiati '10) Etc...

Solution : In magnetic turbulence, only a dipolar anisotropy should be detected => Additional effects needed. Energy dependent smaller scales must automatically appear at multiple angular scales, provided a large scale anisotropy exists... even in pure isotropic turbulence No additional assumption

Diffusion approximation (1D) grad n Observer mfp mfp

Diffusion approximation Dipole grad n mfp Earth

Diffusion approximation Dipole grad n Earth F = F0 (1+ cos )

Diffusion approximation Dipole grad n Earth...or <=> several time dependent random scattering centers

Diffusion approximation Dipole grad n Earth 'Globally' : Markovian process

In reality : grad n Earth 1) The local field does not vary signif. within /c (10 km/s << c) Not diffusion > Need individual trajectories

In reality : Equivalence between forward and back tracking of individual cosmic rays 2) The process is locally non Markovian 3) The Earth is point like (/rl)

Numerical simulations R = 250 pc R < 250 pc (grad n)/n ~ (290 pc) 1 > (1kpc) 1 and E/Z = 1016 ev > 1013 ev Can be extrapolated to lower (grad n)/n and E/Z

Dipole / Smaller scales 90 smoothing 20 smoothing Dipole Amplitude ~ 6 % here

Dipole / Smaller scales 90 smoothing 20 smoothing Dipole

Dependence on the CR rigidity E/Z E/Z = 1016 ev E/Z = 5 x 1016 ev

Dependence on the «boundary» radius 250 pc 100 pc

Dependence on the «boundary» radius 250 pc 50 pc

Dependence on the «boundary» radius 250 pc 25 pc

Dependence on the «boundary» radius 250 pc 10 pc

Local trajectories grad n

III Filamentary / Anisotropic diffusion of cosmic rays around their sources GG, Kachelriess & Semikoz Phys. Rev. Lett. 108, 261101 (2012)

Perpendicular/Parallel diffusion coeffs. CR Regular only Breg Dparall Increasing turbulence Dperp Turbulent only

ray emission around sources > See talk of S. Gabici Molecular cloud pcr Synchrotron Here E > 100 GeV. e Inverse Compton pism b pcr + pism > +... > 2 +... 0

ray emission around sources Breg Molecular cloud Dperp In reviews : G.P. Gamma ray extended emission S Dparall Consider the most simple case : isotropic turbulence only n (...?) S

Large scale modes of the turbulence Lmax, Lc >> rl (TeV PeV) «No» effect ~1 AU Resonant scattering Act like local regular fields? ~ rl/10 rl,1pev Lmax~100pc ~0.3pc

Anisotropic diffusion in isotropic turbulence ~ Lmax ~ Lmax For t ~ 1 kyr, v10km/s t ~ 0.01 pc << (6D1PeV t)1/2 ~ few 10s pc

Generated magnetic turbulence B : 0 8 G 100 pc

Results of numerical simulations E/Z=1PeV, Kolmogorov spectrum, L max=150pc t = 100yr 200 pc ncr(x,y)

Results of numerical simulations t = 500yr

Results of numerical simulations t = 1kyr

Results of numerical simulations t = 2kyr

Results of numerical simulations t = 3kyr

Results of numerical simulations t = 4kyr

Results of numerical simulations t = 6kyr

Results of numerical simulations t = 8kyr

Results of numerical simulations t = 10kyr... then starts to tend towards the r t1/2 behaviour ~ Lmax

Eigenvalues of the diffusion tensor Inject N particles at x = 0 in one single B field realization 'b' (i, j = X,Y, Z) Calculate Compute its eigenvalues :

Eigenvalues of the diffusion tensor Inject N particles at x = 0 in one single B field realization 'b' (i, j = X,Y, Z) Calculate Compute its eigenvalues : Average di(b) over M field realizations : (i = 1, 2, 3) Other authors computed Dii and averaged over different realizations/initial injection points => No anisotropic diffo

Eigenvalues of the diffusion tensor Inject N particles at x = 0 in one single B field realization 'b' (i,j = X,Y, Z) Calculate d3/d1~ few 10s Compute its eigenvalues : Average over M field realizations : (i = 1, 2, 3)

Eigenvalues of the diffusion tensor Inject N particles at x = 0 in one single B field realization 'b' (i,j = X,Y, Z) Calculate d3/d1~ few 10s Compute its eigenvalues : For Bohm spectrum ( = 1) : d3/d1 ~ 3 : 4 Average over M field realizations (i = 1, 2, 3)

Dependence on parameters t* >> 4D/c2 Interestingly, (6Dt*)1/2 ~ Lmax => t* Lmax2? ~ yes.

Dependence on parameters 2 0.5 7 t(kyr) 0.1 1 10 E(PeV) t* 1/D E 1/3 (Kolmogorov)? ~ 'yes'.

Anisotropic diffusion and ray astro. p p 0 CR column density Very forward beamed ray emissivity

Anisotropic diff. and observations HESS? Nava & Gabici '12 Tycho? : (Tycho VERITAS) Hints of an irregular 'halo' or other effects?

Conclusions and perspectives 'Mysterious' small scale anisotropies in the TeV PeV CR flux due to the local magnetic turbulence configuration within ~ CR m.f.p. > May become the best way to probe local magnetic fields in the future. Suggested that gamma ray 'halos' around sources should be expected to be (highly?) anisotropic. > Probe fields around sources; the interstellar turbulence...

(1) Superposition of a finite nb. of modes Write B(r) as a sum of Nm plane waves : Main drawback : computing time. (2) Precompute field on a 3 D grid Faster : Precompute the field on a 3 D grid with N3 vertices. (typically N~256 512 grids can be stored on 2 GB RAM) Problem : limited by grid size : rl/10 rl,1pev~0.3pc Lmax/Lmin Lmax~150pc

(2)... With nested grids Solution : Nested grids. (Giacinti et al. JCAP 07, 031 (2012)) Lmin=L0 L1...... Li With ( Lmax=LN ) Put the right power on each grid : => => Plot

(2)... With nested grids 2 nested grids (3D in reality)

Cosmic Rays in the ISM CR propagation eqn for given species (see for ex. Strong, Moskalenko, Ptuskin '07) : source DIFFUSION convection reacceleration adiab. p gain/loss fragm. decay With CR density per unit of total momentum p Phase space density

Observations IceCube results (arxiv:1105.2326) : ~0.1% ~0.01% Shapes energy dependent but NOT time dependent

Cosmic Rays in the ISM Backreaction on the ISM. Cosmic Rays Interstellar Medium (Magnetized fluid) Deflection through B. (+ Reacceleration). Cosmic Rays self confined below E <?

Cosmic Rays in the ISM In this work : ECR > 1 TeV. Cosmic Rays Interstellar Medium (Magnetized fluid) Deflection through B. (+ Reacceleration). Cosmic Rays self confined below E < few GeV... 1 TeV (Wentzel '70s, Skilling Nature '75,...) > Spectrum inflection at 200 GeV? (Blasi et al. PRL '12) > See P. Blasi's talk.