TeV Cosmic Ray Anisotropies at Various Angular Scales

TeV Cosmic Ray Anisotropies at Various Angular Scales Gwenael Giacinti University of Oxford, Clarendon Laboratory Based on : GG & G.Sigl GG, M.Kachelriess, D.Semikoz Phys. Rev. Lett. 109, 071101(2012) Phys. Rev. Lett. 108, 261101(2012) Phys. Rev. D 88, 023010 (2013) With thanks to Tony Bell, Brian Reville & Klara Schure for discussions

Outline I TeV PeV Cosmic Ray Propagation in the ISM Generic introduction ---> diffusion approximation (DA) II Observations of TeV PeV Cosmic Ray Anisotropies at Various Scales III Theoretical explanations for CR small & medium scale anisotropies

I TeV PeV cosmic ray propagation in the ISM

CR spectrum / Sources Cosmic Ray Flux : Mostly p+ + nuclei Influenced by the Sun Galactic Transition? Galactic SNRs (?) Extragalactic

Air shower structure and CR detection

Baloonborne det. : CR detection: On the ground : One can reconstruct energy + type + arrival direction of primary particle

CR detection: IceCube experiment PMTs

CR detection: IceCube experiment Detection of neutrinos

CR detection: IceCube experiment Detection of cosmic rays, too

Sources, acceleration mechanism Supernova remnants X rays shock Ejecta CISM R ISM Tycho - Composite Forward shock

Sources, acceleration mechanism Diffusive shock acceleration (Krymskii ; Axford et al. '77 ; Bell ; Blandford&Ostriker shock '78) CR R jcr ISM Tycho - Composite C in Rs t dr ab iv ili en ti es Ejecta CISM

CR trajectories in the Galaxy CR Interstellar MF Brms ~ few µ G ~ few 10-10 T Larmor radius at 1 PeV: ~ a fraction of a parsec (pc)

The Galactic (turbulent) magnetic field Satisfies : <B(x)> = 0, <B(x)2> = Brms2, and div B = 0 +ωt Fourier transform : with Power spectrum : for (α = 5/3, 3/2 plausible) with L min< 1 AU, Lmax~ 100 pc Coherence length : Lc ~ few 10s pc.

The Galactic (turbulent) magnetic field Satisfies : <B(x)> = 0, <B(x)2> = Brms2, and div B = 0 +ωt Fourier transform : with Power spectrum : for (α = 5/3, 3/2 plausible) with L min< 1 AU, Lmax~ 100 pc Coherence length : Lc ~ few 10s pc.

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 ~ rl/10? See part III 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? See part III rl,1pev~0.3pc ~ rl/10 mfp 10 PeV Lmax~100pc CR propagation in magnetic turbulence can be regarded as a Markovian process => diffusion approximation

II Observations of TeV PeV cosmic ray anisotropies at various scales

Experimental status

Experimental status

Experimental status

Experimental status

Experimental status

Experimental status

Experimental status

Experimental status / reference map :

Experimental status

Experimental status

Experimental status

Experimental status Northern and Southern skies: Tibet (arxiv :1001.2646) : ~ ''No'' variations during nearly a decade.

Experimental status Energy Dependence (IceCube Coll.) : 400 TeV 2 PeV

Observations (IceCube results, here) ~0.1% 'All right' ~0.01% «INCOMPATIBLE» WITH DIFFUSION!!! Shapes energy dependent but NOT time dependent Gwenael Giacinti TeV Cosmic Ray Anisotropies at Various Angular Scales Aniso U Amsterdam, Sept 25 (2013)

III Theoretical explanations for CR small and medium scale anisotropies Giacinti & Sigl Phys. Rev. Lett. 109, 071101 (2012)

CR diffusion in the Milky Way Halo Diffusion approximation Background from 'very old' sources Earth Rather isotropic

CR diffusion in the Milky Way Halo Background from 'very old' sources + Earth Flux from 'more recent' sources: More anisotropic > CR anisotropy at Earth due to 'most recent' sources

CR diffusion in the Milky Way (Erlykin & Wolfendale '06, Blasi & Amato '11) ~H Halo ~H 2H Earth CR anisotropy at Earth mostly due to 'most recent' and 'nearby' sources 2 α 1/3; 1/2 => DIPOLE δ ~ (E/Z) ~ (E/Z)

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

Small scale anisotropies : Suggestions Magnetic funnelling (Drury & Aharonian '08)

Small scale anisotropies : Suggestions Anisotropic turbulence (Malkov et al. '10)

Small scale anisotropies : Suggestions A local source in the heliotail (Lazarian & Desiati '10)

Small scale anisotropies : Suggestions Strangelets Molecular Clouds (Kotera et al. '13)

Small scale anisotropies : Suggestions Dark Matter (Harding '13)

Solution we propose: 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 Dipole grad n θ F = F0 (1+δ cos θ) Earth R=mfp

Diffusion approximation Dipole grad n Earth...or <=> several time dependent random scattering centers 'Globally' : Markovian process

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

In reality : Equivalence between forward and back tracking of individual cosmic rays the process is locally non Markovian 2) 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 Amplitude ~ 6 % here 20 smoothing Dipole Different E/Z add non constructively Smaller (~10x) (Giacinti, PPCF '13)

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 'domain' size 250 pc 100 pc

Dependence on the 'domain' size 250 pc 50 pc

Dependence on the 'domain' size 250 pc 25 pc

Dependence on the 'domain' size 250 pc 10 pc

Local trajectories grad n

Local trajectories grad n

Local trajectories grad n

Heliospheric B fields at ~ TeV energies? At PeV energies : probe ISMF up to ~10s of pc At 1 10 TeV energies : Same argument ; may start to probe fields in the heliosphere, see P. Desiati and A. Lazarian, Astrophys. J. 762, 44 (2013).

Heliospheric B fields at ~ TeV energies? Alternative possibility at 1 10 TeV : heliospheric electric fields, see L. Drury, arxiv:1305.6752 [astro ph.he].

Conclusions and perspectives Short review on TeV PeV CR propagation and confinement in our Galaxy. Observations : Dipolar anisotropy (~ 0.1%) + 'Mysterious' small scale anisotropies in the TeV PeV CR flux (higher order multipoles) Theory : higher order multipoles seem more 'mysterious' than the dipole, but actually should be present because of MF within a CR mean free path > May become the best way to probe the structure of local magnetic fields in the ISM in the future. > Once this question is solved : Potential for other interesting discoveries.

γ ray emission around sources pcr epism Inverse Compton γ γ γb γ pcr + pism -> π +... -> 2γ +... 0

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

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

Results of numerical simulations t = 2kyr

Results of numerical simulations t = 4kyr

Results of numerical simulations t = 6kyr

Results of numerical simulations... then starts to tend towards the r t 1/2 behaviour t = 10kyr ~ Lmax

CRs and local configuration of the magnetic field - t <~ t* /10 : - t ~ t* : - t >~ 10 t* : No visible difference Nearby field lines coherent over ~Lc : CRs in a flux tube Still high distance tail different from iso. diff. predictions

Observations : First hints at our findings? - Irregular images : (Tycho - VERITAS) -Offset from the source : (HESS) - Anisotropic diffusion around SNR W28? : Nava & Gabici MNRAS '12

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

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

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