1. Ultra-High Energy Cosmic Rays in a Structured and Magnetized Cosmic Environment Günter Sigl GReCO, Institut d’Astrophysique de Paris, CNRS http://www.iap.fr/users/sigl/homepage.html  General facts and the experimental situation  Acceleration (“bottom-up” scenario)  Cosmic magnetic fields and their role in cosmic ray physics

2. The cosmic ray spectrum stretches over some 12 orders of magnitude in energy and some 30 orders of magnitude in differential flux: many Joules in one particle!

3. The structure of the spectrum and scenarios of its origin supernova remnantspulsars, galactic windAGN, top-down ?? knee ankletoe ?

4. electrons  -rays muons Ground array measures lateral distribution Primary energy proportional to density 600m from shower core Fly’s Eye technique measures fluorescence emission The shower maximum is given by X max ~ X 0 + X 1 log E p where X 0 depends on primary type for given energy E p Atmospheric Showers and their Detection

5. ground arrays fluorescence detector ground array Current data at the highest energies

6. A Tension between the Newest Fluorescence Data (HiRes) and Ground Array Results? Or: Is there a Cut-Off after all? but consistent with Haverah Park Discontinuity with AGASA, but better agreement with Akeno

7. Lowering the AGASA energy scale by about 20% brings it in accordance with HiRes up to the GZK cut-off, but not beyond. HiRes collaboration, astro-ph/0208301 May need need an experiment combining ground array with fluorescence such as the Auger project to resolve this issue.

9. But HiRes has also seen a >200 EeV event in stereo mode with only ~20% exposure of the mono-mode

10. Experimentsstarting date acceptance in km 2 sr angular resolution energy resolution High – Res Fly’s Eye since 1999350-1000few degrees ~40% mono ~10% stereo Telescope Array maybe with Auger North 1700-5000~1 o ?~20% ? Auger ground full size in about 2004 >7000< 2 o ~15% Auger hybrid ~2004>700~0.25 o ~8% EUSO/OWL space-based >2010~10 5 ?~1 o ?<30% ? radio detection ???>1000 ?few degrees ? ??? Next-Generation Ultra-High Energy Cosmic Ray Experiments compare to AGASA acceptance ~ 230 km 2 sr

11. The southern Auger site is under construction.

12. The Ultra-High Energy Cosmic Ray Mystery consists of (at least) Three Interrelated Challenges 1.) electromagnetically or strongly interacting particles above 10 20 eV loose energy within less than about 50 Mpc. 2.) in most conventional scenarios exceptionally powerful acceleration sources within that distance are needed. 3.) The observed distribution seems to be very isotropic (except for a possible interesting small scale clustering)

13. The Greisen-Zatsepin-Kuzmin (GZK) effect Nucleons can produce pions on the cosmic microwave background nucleon   -resonance multi-pion production pair production energy loss pion production energy loss pion production rate  sources must be in cosmological backyard Only Lorentz symmetry breaking at Г>10 11 could avoid this conclusion.

14. M.Boratav First Order Fermi Shock Acceleration This is the most widely accepted scenario of cosmic ray acceleration The fractional energy gain per shock crossing depends on the velocity jump at the shock. Together with loss processes this leads to a spectrum E -q with q > 2 typically. When the gyroradius becomes comparable to the shock size, the spectrum cuts off. u1u1 u2u2

15. A possible acceleration site associated with shocks in hot spots of active galaxies

16. A possible acceleration site associated with shocks formed by colliding galaxies

17. Or Can Plasma Waves in Relativistic Shocks Occuring in  -Ray Bursts accelerate up to 10 24 eV? Chen, Tajima, Takahashi, astro-ph/0205287

18. Arrival Directions of Cosmic Rays above 4x10 19 eV Akeno 20 km 2, 17/02/1990 – 31/07/2001, zenith angle < 45 o Red squares : events above 10 20 eV, green circles : events of (4 – 10)x10 19 eV Shaded circles = clustering within 2.5 o. Chance probability of clustering from isotropic distribution is < 1%. galactic plane supergalactic plane

19. HiRes sees no significant anisotropy above 10 18 eV

20. Cosmic Magnetic Fields and their Role in Cosmic Ray Physics 1.) Cosmic rays up to ~10 18 eV are confined in the Galaxy Energy densities in cosmic rays, in the galactic magnetic field, in the turbulent flow, and gravitational energy are of comparable magnitude. The galactic cosmic ray luminosity L CR required to maintain its observed density u CR in the galactic volume V gal for a confinement time t CR ~10 7 y, L CR ~ u CR V gal / t CR, is ~10% of the kinetic energy rate of galactic supernovae. 2.) Cosmic rays above ~10 19 eV are probably extragalactic and may be deflected mostly by extragalactic fields B XG rather than by galactic fields. However, very little is known about about B XG : It could be as small as 10 -20 G (primordial seeds, Biermann battery) or up to fractions of micro Gauss if concentrated in the local Supercluster (equipartition with plasma). strength of BXG small deflection => many sources Monoenergetic or « high before low » burst sources no time-energy correlation continuous sources strong deflection => few sources possible clusters due to magnetic lensing or due to a neutral component 3.) Magnetic fields are main players in cosmic ray acceleration.

21. Example: Magnetic field of 10 -10 Gauss, coherence scale 1 Mpc burst source at 50 Mpc distance time delay differential spectrum Lemoine, Sigl cuts through the energy-time distribution: To get an impression on the numbers involved:

22. Transition rectilinear-diffusive regime Neglect energy losses for simplicity. Time delay over distance d in a field B rms of coherence length λ c for small deflection: This becomes comparable to distance d at energy E c : In the rectilinear regime for total differential power Q(E) injected inside d, the differential flux reads

23. In the diffusive regime characterized by a diffusion constant D(E), particles are confined during a time scale which leads to the flux For a given power spectrum B(k) of the magnetic field an often used (very approximate) estimate of the diffusion coefficient is where B rms 2 =∫ 0 ∞ dkk 2, and the gyroradius is

24. IF E<<E c and IF energy losses can be approximated as continuous, dE/dt=-b(E) (this is not the case for pion production), the local cosmic ray density n(E,r) obeys the diffusion equation Where now q(E,r) is the differential injection rate per volume, Q(E)=∫d 3 rq(E,r). Analytical solutions exist (Syrovatskii), but the necessary assumptions are in general too restrictive for ultra-high energy cosmic rays. Monte Carlo codes are therefore in general indispensable.

25. Strong fields in our Supergalactic Neighbourhood ? Medina Tanco, Lect.Not.Phys 542, p.155

26. Principle of deflection code A particle is registered every time a trajectory crosses the sphere around the observer. This version to be applied for individual source/magnetic field realizations and inhomogeneous structures. source sphere around observer source sphere around source A particle is registered every time a trajectory crosses the sphere around the source. This version to be applied for homogeneous structures and if only interested in average distributions.

27. Effects of a single source: Numerical simulations A source at 3.4 Mpc distance injecting protons with spectrum E -2.4 up to 10 22 eV A uniform Kolmogorov magnetic field of strength 0.3 micro Gauss and largest turbulent eddy size of 1 Mpc. Isola, Lemoine, Sigl Conclusions: 1.) Isotropy is inconsistent with only one source. 2.) Strong fields produce interesting lensing (clustering) effects. 10 5 trajectories, 251 images between 20 and 300 EeV, 2.5 o angular resolution

28. Same scenario, averaged over many magnetic field realisations

29. That the flux produced by CenA is too anisotropic can also be seen from the realization averaged spectra visible by detectors in different locations AGASA, northern hemisphere solid angle averaged southern hemisphere Isola, Lemoine, Sigl, Phys.Rev.D 65 (2002) 023004

30. Summary of spectral effects Continuous source distribution following the Gaussian profile. B=3x10 -7 G, d=10 Mpc in rectilinear regime in diffusive regime in rectilinear regime

31. More detailed scenarios of large scale magnetic fields use large scale structure simulations with magnetic fields followed passively and normalized to a few micro Gauss in galaxy clusters. We use a (75 Mpc) 3 box, repeated by periodic boundary conditions, to take into account sources at cosmological distances. We then consider different observer and source positions for structured and unstructured distributions with and without magnetization. We analyze these scenarios and compare them with data based on large scale multi-poles, auto-correlations, and clustering. Sigl, Miniati, Ensslin, astro-ph/0309695

32. Observer immersed in fields of order 0.1 micro Gauss Observer immersed in fields of order 10 -11 Gauss

33. Observer immersed in fields of order 10 -11 Gauss: Cut thru local magnetic field strength Filling factors of magnetic fields from the large scale structure simulation.

34. Result: Magnetized, structured sources are marginally favored if the observer is immersed in negligible fields. Strong field observer: ruled out by isotropy around 10 19 eV. Weak field observer: allowed. However, even if fields around observer are negligible, deflection in magnetized structures surrounding the sources lead to off-sets of arrival direction from source direction up to >10 degrees up to 10 20 eV in our simulations. This is contrast to Dolag et al., astro-ph/0310902. => Particle astronomy not necessarily possible !

35. Comparison with AGASA data => The required source density is ~ 10 -5 Mpc -3. Similar numbers were found in several independent studies, e.g. Yoshiguchi et al. ApJ. 586 (2003) 1211, Blasi and de Marco, astro-ph/0307067 Unmagnetized, Unstructured Sources Source density=2.4x10 -6 Mpc -3 Source density=2.4x10 -4 Mpc -3 Autocorrelation function sensitive to source density in this case

36. Magnetized, Structured Sources Deflection in magnetic fields makes autocorrelation and power spectrum much less dependent on source density and distribution ! Comparing predicted autocorrelations for source density = 2.4x10 -4 Mpc -3 (upper set) and 2.4x10 -5 Mpc -3 (lower set) for an Auger-type exposure.

37. The spectrum in the magnetized source scenario shows a pronounced GZK cut-off. Deflection can be substantial even up to 10 20 eV.

38. In the future, a suppressed auto-correlation function will be a signature of magnetized sources. Comparing predicted autocorrelations for source density = 2.4x10 -5 Mpc -3 with (lower set) and without (upper set) magnetization for an Auger-type exposure.

39. Generalization to heavy nuclei Example: If source injects heavy nuclei, diffusion can enhance the heavy component relative to the weak-field case. All secondary nuclei are followed and registered upon crossing a sphere around the source. B=10 -12 G, E>10 19 eV B=2x10 -8 G, E>10 19 eV Bertone, Isola, Lemoine, Sigl, astro-ph/0209192 Here we assume E -2 iron injection up to 10 22 eV.

40. However, the injection spectrum necessary to reproduce observed spectrum is ~E -1.6 and thus rather hard. B=2x10 -8 G, d=7.1 Mpc B=2x10 -8 G, d=3.2 Mpc Composition as function of energy.

41. 2 nd example: Helium primaries do not survive beyond ~20 Mpc at the highest energies B=10 -12 G, E>10 20 eV Bertone, Isola, Lemoine, Sigl, astro-ph/0209192

42. Conclusions 1.) The origin of very high energy cosmic rays is one of the fundamental unsolved questions of astroparticle physics. This is especially true at the highest energies, but even the origin of Galactic cosmic rays is not resolved beyond doubt. 2.) Acceleration and sky distribution of cosmic rays are strongly linked to the in part poorly known strength and distribution of cosmic magnetic fields. 4.) The coming 3-5 years promise an about 100-fold increase of ultra-high energy cosmic ray data due to experiments that are under either construction or in the proposal stage. 3.) Already current cosmic ray data (isotropy) favor an observer immersed in fields < 10 -11 G. Future data (auto-correlation) will test source magnetization.