Ultra-High Energy Cosmic Rays in a Structured and

Magnetized Cosmic Environment

Günter SiglGReCO, Institut d’Astrophysique de Paris, CNRShttp://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

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!

The structure of the spectrum and scenarios of its origin

supernova remnants pulsars, galactic wind AGN, top-down ??

knee ankle toe ?

electrons

-rays

muons

Ground array measures lateral distributionPrimary energy proportional to density 600m from shower core

Fly’s Eye technique measuresfluorescence emissionThe shower maximum is given by

Xmax ~ X0 + X1 log Ep

where X0 depends on primary typefor given energy Ep

Atmospheric Showers and their Detection

ground arrays

fluorescence detector

ground array

Current data at the highest energies

A Tension between the Newest Fluorescence Data (HiRes)and Ground Array Results?

Or: Is there a Cut-Off after all?

but consistent with Haverah ParkDiscontinuity with AGASA, but betteragreement with Akeno

Lowering the AGASA energy scale by about 20% brings it in accordancewith HiRes up to the GZK cut-off, but not beyond.

HiRes collaboration, astro-ph/0208301

May need need an experiment combining ground array with fluorescencesuch as the Auger project to resolve this issue.

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

Experiments starting date

acceptancein km2sr

angularresolution

energyresolution

High – ResFly’s Eye

since 1999 350-1000 few degrees

~40% mono~10% stereo

Telescope Array

maybe with Auger North

1700-5000 ~1o ? ~20% ?

Auger ground

full size in about 2004

>7000 < 2o ~15%

Auger hybrid

~2004 >700 ~0.25o ~8%

EUSO/OWLspace-based

>2010 ~105 ? ~1o ? <30% ?

radio detection

??? >1000 ? few degrees ?

???

Next-Generation Ultra-High Energy Cosmic Ray Experiments

compare to AGASA acceptance ~ 230 km2sr

The southern Auger site is underconstruction.

The Ultra-High Energy Cosmic Ray Mystery consists of(at least) Three Interrelated Challenges

1.) electromagnetically or strongly interacting particles above 1020 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)

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 backyardOnly Lorentz symmetry breaking at Г>1011

could avoid this conclusion.

eV1044

2 192

th

mmm

E N

M.Boratav

First Order Fermi ShockAcceleration

This is the most widely acceptedscenario of cosmic ray acceleration

The fractional energy gain pershock crossing depends on thevelocity jump at the shock.Together with loss processes thisleads to a spectrum E-q withq > 2 typically.When the gyroradius becomescomparable to the shock size,the spectrum cuts off.

u1

u2

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

A possible acceleration site associated with shocks formed by colliding galaxies

Or Can Plasma Waves in Relativistic Shocks Occuring in -Ray Bursts accelerate up to 1024 eV?

Chen, Tajima, Takahashi,astro-ph/0205287

Arrival Directions of Cosmic Rays above 4x1019 eV

Akeno 20 km2, 17/02/1990 – 31/07/2001, zenith angle < 45o

Red squares : events above 1020 eV, green circles : events of (4 – 10)x1019 eV

Shaded circles = clustering within 2.5o.

Chance probability of clustering from isotropic distribution is < 1%.

galactic plane

supergalactic plane

HiRes sees no significant anisotropy above 1018 eV

Cosmic Magnetic Fields and their Role in Cosmic Ray Physics1.) Cosmic rays up to ~1018 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 LCR required to maintain its observed density uCR in the galactic volume Vgal for a confinement time tCR~107 y, LCR ~ uCR Vgal / tCR, is ~10% of the kinetic energy rate of galactic supernovae.

2.) Cosmic rays above ~1019 eV are probably extragalactic and may be deflected mostly by extragalactic fields BXG rather than by galactic fields. However, very little is known about about BXG: 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 strong deflection => few sources possible

Monoenergetic or « high before low » no time-energy correlation

burst sources continuous sources

clusters due to magnetic lensing or due to a neutral component

3.) Magnetic fields are main players in cosmic ray acceleration.

Example:Magnetic field of 10-10 Gauss, coherence scale 1 Mpcburst source at 50 Mpc distance

tim

e d

ela

ydiff

ere

nti

al sp

ect

rum

Lemoine, Sigl

cuts through the energy-time distribution:

To get an impression on the numbers involved:

Transition rectilinear-diffusive regime

Neglect energy losses for simplicity.

Time delay over distance d in a field Brms of coherence length λc for smalldeflection:

yr Mpc 1G 10Mpc 10eV10

105.14

),(),( c

2

9rms

22

2023

2

BdEZ

dEddE

This becomes comparable to distance d at energy Ec:

eV Mpc 1G 10Mpc 10

107.42/1

c7rms

2/1

19c

BdE

In the rectilinear regime for total differential power Q(E) injected insided, the differential flux reads

2)4(

)()(

d

EQEj

In the diffusive regime characterized by a diffusion constant D(E),particles are confined during a time scale

)(),(

2

ED

ddE

which leads to the flux

)()4(

)(

)4(

)()()(

232 EdD

EQ

d

EEQEj

For a given power spectrum B(k) of the magnetic field an often used(very approximate) estimate of the diffusion coefficient is

,

)(3

)()(

)(1/r

22

rmsg

g

E

kBdkk

BErED

where Brms2=∫0

∞dkk2<B2(k)>, and the gyroradius is

kpc G 10eV 10

110)(1

6-rms

201

rmsg

BEZ

ZeB

EEr

IF E<<Ec and IF energy losses can be approximated as continuous,dE/dt=-b(E) (this is not the case for pion production), the local cosmic raydensity n(E,r) obeys the diffusion equation

),(),(),(),()(),( rEqrEnrEDrEnEbrEn Et

Where now q(E,r) is the differential injection rate per volume,Q(E)=∫d3rq(E,r). Analytical solutions exist (Syrovatskii), but the necessaryassumptions are in general too restrictive for ultra-high energy cosmic rays.

Monte Carlo codes are therefore in general indispensable.

Strong fields in our Supergalactic Neighbourhood ?

Medina Tanco, Lect.Not.Phys 542, p.155

Principle of deflection code

A particle is registered every time a trajectory crosses the spherearound the observer. This version to be applied for individualsource/magnetic field realizations and inhomogeneous structures.

sourcesphere aroundobserver

source

sphere around source

A particle is registered every time a trajectorycrosses the sphere around the source. Thisversion to be applied for homogeneousstructures and if only interested in averagedistributions.

Effects of a single source: Numerical simulations

A source at 3.4 Mpc distance injecting protons with spectrum E-2.4 up to 1022 eVA uniform Kolmogorov magnetic field of strength 0.3 micro Gauss and largestturbulent 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.

105 trajectories,251 images between20 and 300 EeV,2.5o angular resolution

Same scenario, averaged over many magnetic field realisations

That the flux produced by CenA is too anisotropic can also be seen fromthe realization averaged spectra visible by detectors in different locations

AGASA, northernhemisphere solid angle

averaged

southern hemisphere

Isola, Lemoine, Sigl, Phys.Rev.D 65 (2002) 023004

Summary of spectral effects

Continuous source distributionfollowing the Gaussian profile.B=3x10-7 G, d=10 Mpc

)()( EQEj

)(

)()(

ED

EQEj

in rectilinear regime

in diffusive regime

)()(

2

ED

dE in diffusive regime

2)( EE in rectilinear regime

More detailed scenarios of large scale magnetic fields use largescale structure simulations with magnetic fields followed passivelyand 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 forstructured and unstructured distributions with and withoutmagnetization.

We analyze these scenarios and compare them with data based onlarge scale multi-poles, auto-correlations, and clustering.

Sigl, Miniati, Ensslin, astro-ph/0309695

Observer immersed infields of order 0.1 microGauss

Observer immersed infields of order 10-11

Gauss

Observer immersed infields of order 10-11

Gauss: Cut thru localmagnetic field strength

Filling factors of magneticfields from the large scalestructure simulation.

Result: Magnetized, structured sources are marginallyfavored if the observer is immersed in negligible fields.

Strong field observer:ruled out by isotropyaround 1019 eV.

Weak field observer:allowed.

However, even if fields around observer are negligible, deflection inmagnetized structures surrounding the sources lead to off-sets of arrival

direction from source direction up to >10 degrees up to 1020 eV in our simulations.This is contrast to Dolag et al., astro-ph/0310902.

=> Particle astronomy not necessarily possible !

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

Magnetized, Structured Sources

Deflection in magnetic fields makes autocorrelation and power spectrummuch 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.

The spectrum in the magnetizedsource scenario shows apronounced GZK cut-off.

Deflection can be substantial evenup to 1020 eV.

In the future, a suppressed auto-correlation function will be asignature 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.

Generalization to heavy nuclei

Example:If source injects heavy nuclei,diffusion can enhance the heavycomponent relative to theweak-field case.

All secondary nuclei are followedand registered upon crossing asphere around the source.

B=10-12 G, E>1019 eV

B=2x10-8 G, E>1019 eV

Bertone, Isola, Lemoine, Sigl, astro-ph/0209192

Here we assume E-2 iron injectionup to 1022 eV.

However, the injection spectrumnecessary to reproduce observedspectrum is ~E-1.6 and thus ratherhard.

B=2x10-8 G, d=7.1 Mpc

B=2x10-8 G, d=3.2 Mpc

Composition as function of energy.

2nd example: Helium primaries do not survive beyond ~20 Mpc at the highest energies

B=10-12 G, E>1020 eV

Bertone, Isola, Lemoine, Sigl, astro-ph/0209192

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.