Cosmic rays and relativistic shock acceleration

Transcription

1 Cosmic rays and relativistic shock acceleration Thank you Athina Meli ECAP Erlangen Center for Astroparticle Physics Friedrich-Alexander Universität Erlangen-Nüremberg

2 Outline Cosmic ray spectrum (non) relativistic sources Shocks - Properties - Particle acceleration mechanism Simulations - Numerical Method - Studies Conclusions

3 E (dn/de) ~E -2.7 ~E - 3 knee 1 part m -2 yr -1 Auger LHC Ankle 1 part km -2 yr -1 ~E -2.7 Toe 1 part km -2 cent -1 [T. Gaisser 2005] 10 decades of energy 30 decades of flux

4 Ultra High Energy Cosmic Rays: At the toe

5 Maximum cosmic ray energies Magnetic field dimensions sufficient to contain the accelerating particles LHC Strong fields and large plasma speeds Hillas (1984)

6 Non-relativistic sources

7 Supernovae case SN 1987A

8 L ~ erg/s G ~ 1-2 E max ~ ev e.g. Berezinsky & Ginzburg 87, Giacobbe 05, Aharonian et al. (HESS) 06

9 Relativistic sources

10 Active Galactic Nuclei case L ~ erg/s G ~ E max ~ ev e.g. Lynden-Bell 69, Meier 03, Georganopoulos 05, Marcher et al. 08, etc

11 Gamma Ray Bursts case L ~ erg/s 100 < G <1000 E max ~ ev e.g. Cavallo & Rees 78, Goodman 86, Paczynski 86, Vietri 95, Waxmann 00, etc

12 The hidden power engine: Shocks in jets

13 Supersonic/superalfvenic strong compression waves change gas/plasma s v, d, p, T - Collisional shocks (ordinary fluid) - Colissionless astrophysical shocks: In diffuse regions of space, low densities, large bulk speeds Marcher et al. 08 Tregillis, Jones & Ryu 01

14 Shock-magnetic field inclinations y z -z y

15 Jump (Rankine-Hugoniot) conditions y u1 u2 For a stationary HD shock (1D) z Rankine (1870), Hugoniot (1887) Parker (1965), Hudson (1965), Parks (1984), etc

16 Lorentz frame transformations: The de Hoffmann-Teller frame in oblique shocks -x +x -z y1 V B -z -x +x = 0 Quasi-parallel Vs Quasi-perprendicular Sub- Vs Super-luminal shocks Physical causality: The Lorentz transformation is limited due to VHT V1 tany1 (de Hoffmann&Teller 54)

17 Particle shock acceleration mechanism No doubt collisionless astrophysical shocks accelerate particles Convincing evidence for efficient acceleration in heliospheric shocks and in young SNRs

18 The Fermi mechanism Transfer of the macroscopic kinetic energy of moving magnetized plasma to individual charged particles non-thermal distribution Second order Fermi acceleration (Fermi 49, magnetic clouds First order Fermi acceleration - diffusive acceleration (Krymskii 77, Bell 78, Blandford&Ostriker 78, Axford et al. plasma shocks

19 1 st order Fermi acceleration Non-relativistic shocks Test particle - diffusion - n acceleration shock cycles E n n x 1 E0 Energy gain: fraction of initial energy E E E0 x E 0 Average energy gain per collision: E / E (2V / c) Leading to a power-law energy behaviour i n n( E) 1 P N( E) E esc... = (r+2)/(r-1), r = V1/V2 = (g+1) / ( g-1) for mono-atomic gas: g =5/3 r = 4 E -2 (e.g. Krymskii 77, Bell 78a,b, Drury 83, etc) Upstream Downstream Note: For relativistic shocks V~c and particle distributions are not isotropic across reference frames difficult analytically

20 Acceleration time scale & diffusion The acceleration rate wins in competition with the time scale of the energy losses and the escape rate, defining the limit for the possible highest energies to be achieved. Acceleration rate: One cycle: (E)=(E cycle ) /DE= [3/(V 1 -V 2 ) ]( 1 /V /V 2 ) (Drury 83) Confinement distance cycle (E)= (4/c )( 1 /V /V 2 ) Diffusion coefficient: =(1/3) (Quenby & Meli 02) i.e. Proton 10GeV: about 10²² cm²/s cycle about 10 4 sec

21 Facts for non-relativistic shock acceleration: Particles are everywhere in isotropy and the diffusive approximation for solution of the transport equation can apply Spectral index independent of: inclination, scattering nature, strength of magnetic field Concepts are well understood and well studied - they work nicely as a comparison basis for relativistic studies

22 Modeling relativistic shock acceleration

23 Four techniques Semi-analytic (simplified) solutions to diffusion-convection equation (e.g. Eichler 84, Berezhko & Ellison 99, Blasi & Gabici 02-05, etc) Numerical solutions to diffusion-convection equation with flow hydrodynamics & momentum dependent diffusion (e.g. Berezhko, Voelk et al. 96, Kang & Jones 91-05, Malkov 97-01, etc) Monte Carlo simulations (!) (e.g. Ellison et al , Baring 03-05, Meli & Quenby etc) Particle-in-cell (PIC) plasma simulations (e.g. Nishikawa et al. 05, Dieckmann, Meli et al. 08, 09, Meli&Dieckmann 10)

24 Monte Carlo technique Random number generation simulation of the random nature of a physical process (Cashwell & Everett 59) Powerful tool large dynamic ranges in spatial and momentum scales Notion of test particles - very efficient & very fast in describing particle random walks - large number of particles Scattering can be treated via pitch angle diffusion approach (e.g. Kennel & Petscheck 66, Forman et al. 74, Jokipii 87, Quenby & Meli 05, Meli & Biermann 06) 2 cos y sin 2 y (!) Particles scatter as (Kennel&Petscheck 66): Fully relativistic Lorentzian transformations

25 Simulation studies on relativistic shocks: flow speed, inclination, scattering

26 θ Bn = 0 Ellison et al. 90 Spectrum flattens with velocity Spectrum depends on the scattering type magnetic field configurations Large angle scattering yields kinematically structured distributions Baring 04 Note: Universal power-law of -2.2 (e.g Achterberg et al 01, etc) only for fine scattering & parallel relativistic shocks! Niemec & Ostrowski 04

27 Oblique shock Scattering : q p 2.1 G 5 G 20 G 50 y 35 o Parallel shock Scattering : q p 1.8 G 5 G 20 G 50 y 0 o Oblique shock Scattering : q p/4 2.0 G 5 G 20 G 50 y 35 o Parallel shock Scattering : q < p/4 1.9 G 5 G 20 G 50 y 0 o Meli & Quenby 02

28 Angular distribution anisotropy G 100 q p y 0 o G 100 q 1/G y 0 o cosq cosq G 100 q p y 45 o G 100 q 1/G y 45 o cosq cosq Meli & Quenby 03a

29 Acceleration speed-up q p y 0 o q 1/G y 0 o The ratio of the simulation time exp to the theoretical acceleration time constant t th versus the log of shock speed. q p y 45 o q 1/G y 45 o t th (E)=(E cycle ) /DE= [3/(V 1 -V 2 ) ]( 1 /V /V 2 )] Meli & Quenby 03b

30 Applications to UHECR & extragalactic astronomy

31 Superluminal shocks Superluminal (highly oblique) shock Scattering : q p G 5 G 50 G 100 y 85 o Superluminal (highly oblique) shock Scattering : 1/G q 10/G G 50 G 10 G 100 Y 85 G 10 G 20 G 500 G 1000 y 85 o 2.7 < < 2.2 No power-law! Meli & Quenby 05 Meli, Becker, Quenby 08 Superluminal shocks not efficient accelerators

32 Subluminal shocks Subluminal (oblique) shocks Scattering : 1/G q 10/G Subluminal shocks Efficient (flat) accelerators Meli, Becker, Quenby 08 Meli, Becker & Quenby 08

33 Diffuse UHECR spectrum Gamma Ray Bursts or Active Galactic Nuclei? - We focus on hadronic nature: This source proton spectra can be translated into an expected diffuse proton flux from astrophysical sources by folding the spectra with the spatial distribution of the sources (Meli et al., 08, 09): - Adiabatic energy losses are taken into account - AGN & GRBs follow the star formation rate to determine the number density evolution with co-moving volume - Absorption of protons due to the interactions with the CMBR at Ep > ev (Auger) - Normalization of the overall spectrum as measured at Earth is achieved using observations

34 The total spectrum as observed at Earth Assumption: UHECRs come from AGN contribute a fraction 0 x 1 and for GRBs 1-x with 0.001<z<7 (main contribution: z~1-2 high no.of sources) The The diffuse diffuse energy energy spectrum spectrum of sources, of sources, compared multiplied to by the an total E 2.7, diffuse compared spectrum to the total diffuse spectrum. Dots and squares correspond to Hires and Auger data. (Meli, Becker, Quenby 08) Yet again, flat spectra, recent confirmation: GRB090816c E E -2.0 (Meli et al. 09)

35 Conclusions High energy cosmic ray acceleration in astrophysical shocks is a favourable and attractive theme of study (especially numerically) Relativistic shocks: Power-law spectrum and of -2.2 not universal! (observations confirm) Relativistic shocks can generate very high energy cosmic rays with a multitude of spectral forms, power-law incides dependent on shock parameters: flow speed, inclination and scattering properties : Faster shocks generate flatter primary distributions: - Subluminal shocks (quasi-parallel) efficient accelerators ~10 21 ev - Superluminal (quasi-perpendicular) shocks not efficient ~10 15 ev LAS q p : flatter distributions PAD q p : steeper distributions (but still flat) Important implications to gamma-ray and neutrino astronomy!

36 Thank you Thank you! With special thanks to collaborators: J. J. Quenby (London, UK), P. L. Biermann (Bonn, DE, Alabama, USA), J. K. Becker (Bochum, DE), A. Mastichiadis (Athens, GR) Selected references: [1] Meli & Quenby APh, 2003, 19, 637 [2] Meli & Quenby APh, 2003, 19, 649 [3] Meli & Biermann, 2006, A&A, 454, 687 [4] Meli, Becker, Quenby, 2008, A&A, 492, 323 [5] Meli & Mastichiadis, NIMPA, 2009, 588, 193