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Acceleration of highest energy cosmic rays in jets of powerful AGNs. Maxim Lyutikov (UBC, U. Rochester) in collaboration with Rashid Ouyed (UofC). UHECRs. CR spectrum, composition, confinement. second knee ?. toe ?. 1 particle per km 2 per century. knee, 4 10 15 eV.

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Acceleration of highest energy cosmic rays in jets of powerful agns

Acceleration of highest energy cosmic rays in jets of powerful AGNs

Maxim Lyutikov (UBC, U. Rochester)

in collaboration with

Rashid Ouyed (UofC)

Cr spectrum composition confinement

UHECRs powerful AGNs

CR spectrum, composition, confinement

second knee ?

toe ?

1 particle per km2

per century

knee, 4 1015 eV

ankle,3 1018 eV

heavy (Fe)

  • Isotropic to highest energies

  • Possible small-scale clustering

    at highest energies



  • UHECR composition: p-heavy-p

  • Propagation: B-field

  • rL~E21/B G pc, Galaxy ~ 10-6 G

  • only E < 1019 eV are confined

  • E > 1019 eV must be extragalactic

Proton fraction (green: HiRes stereo)

Gzk cut off greisen prl zatsepin kuzmin jetp lett 1966
GZK cut-off powerful AGNsGreisen PRL; Zatsepin & Kuzmin JETP Lett (1966)

  • Cosmic Microwave Background radiation (CMB) T=2.7 K

  • Photo-pion production

  • Attenuation length for ~ 1020 eV CR is

    ~ tens of Mpc. Very solid estimate;

    worse for Z> 1

  • UHECRs must be produced locally , < 100 Mpc

pair production energy loss

p + 2.7k +  p + 0

n + +

pion production energy loss

pion production rate

Is gzk cutoff seen
Is GZK cutoff seen? powerful AGNs

  • HiRes (fluorencence) and AGASA (ground array) disagree

Origin of cosmic rays powerful AGNs

Acceleration of cr

Low energy CRs (<10 powerful AGNs15 eV): in SNRs through Fermi shock acceleration

observed in interplanetary space

Spectrum is “right” dn/dE ~ E-2

But: not yet confirmed by γ-ray observations of π0 decay in SNR

SNs cannot accelerate beyond ~Z 1014

Acceleration of UHECRs

not clear if can be extended to UHECR regime

maximal efficiency (τacc ~ γ/ωB) is usually either assumed or put “by hand” by using

more than allowed (super-Bohm) cross-field diffusion

Hardening above the “ankle” ~ 1018 eV may indicate new acceleration mechanism

scattering off Alfven



v1 > v2


Acceleration of CR

We propose new, non-stochastic acceleration mechanism

that turns on above the ankle, E> 1018 eV

Alfven wave

General constraints on acceleration cite
General constraints powerful AGNson acceleration cite:

  • Constraints on UHECRs are so severe, “~“ estimates are useful

  • Maximal acceleration E-field < B-field: E=β0 B, β0 ≤ 1

  • Total potential Φ = E R= β0 B R

  • Maximal energy E~ Z e Φ = β0 Z e B R

  • Maximal Larmor radius rL ~ β0 R (Hillas condition)

  • Two possibilities:

    • E || B (or E>B) – DC field

    • E ┴ B – inductive E-field

} Two paradigms for UHECR acceleration

Dc linear acceleration for uhecr does not work

E powerful AGNs





DC (linear) acceleration for UHECR does not work


  • Full DC accelerations schemes (with E-field || to B-field or E>B) cannot work in principle for UHECRs

  • leptons will shut off E|| by making pairs (typically after ΔΦ << 1020 eV)

  • Double layer is very inefficient way of accelerating UHECRs: E-field will generate current, current will create B-field, there will be large amount of energy associated with B-field. One can relate potential drop with total energy:

    • Relativistic double layer:

    • Maximal energy

    • Total energy: E~ B2 R3~ I2 R c2


E b inductive potential

Lovelace 76 powerful AGNs

Blandford 99


E ┴ B : Inductive potential


E ┴ B: Poynting flux in the system: relate Φ to luminocity

Electric potential

Pictor A (FRII)

  • To reach Φ=3 1020 eV, L > 1046 erg/s (for protons)

  • This limits acceleration cites to high power AGNs (FRII, FSRQ,

    high power BL Lac, and GRBs)

  • There may be few systems with enough potential within GZK sphere

    (internal jet power higher than emitted), the problem is acceleration scheme

Potential energy of a charge in a sheared flow

For linear velocity profile powerful AGNs







Potential Φ~-x2

Potential Φ~x2

Potential energy of a charge in a sheared flow

E=-v x B

Depending on sign of (scalar) quantity (B *curl v) one sign of charge is at

potential maximum

Protons are at maximum for negative shear (B *curl v) < 0

This derivation is outside of applicability of non-relativisitc MHD

Astrophysical location agn jets

V powerful AGNs







Astrophysical location: AGN jets

  • There are large scale B-fields in AGN jets

  • Jet launching and collimation (Blandford-Znajek, Lovelace)

  • Observational evidence of helical fields (Lyutikov et al 2004; Zavala)

  • Jets may collimate to cylindrical surfaces (Heyvaerts & Norman)

  • Jets are sheared (fast spine, slow edge)

Protons are at maximum for negative shear (B *curl v) < 0.

Related to (Ω*B) on black hole


BH and disk can act as Faradey disk

Acceleration by large scale inductive e fields e v e ds
Acceleration by large scale inductive E-fields: powerful AGNsE~∫ v•E ds


  • Potential difference is between different flux surface (pole-equator)

  • In MHD plasma is moving along V=ExB/B2 – cannot cross field lines

  • Particle has to cross flux surfaces

  • Kinetic motion across B-fields- particle drift



Drift due to sheared alfven wave

powerful AGNs






Drift due to sheared Alfven wave

  • Electric field Er ~- vz x Bφ : particle need to move radially, but cannot do it freely (Bφ).

  • Kinetic drift

  • Inertial Alfven wave propagating

    along jet axis ω=VA kz

  • Bφ(z) → Ud ~ ~er



Udrfit ~ F x B

Why this is all can be relevant very fast energy gain
Why this is all can be relevant? powerful AGNs Very fast energy gain :

  • highest energy particles are accelerated most efficiently!!!

  • low Z particles are accelerated most efficiently!!! (highest rigidity are accelerated most efficiently)

  • Acceleration efficiency does reach absolute theoretical maximum 1/ωB

  • Jet needs to be ~ cylindrically collimated; for spherical expansion adiabatic losses dominate

Energy gain:

For linear velocity profile, V=η x, E= η x B/c, x = ud t,

Wave surfing can help
Wave surfing can help powerful AGNs

  • Shear Alfven waves have δE~(VA/c) δB,

  • Axial drift in δExB helps to keep particle in phase

  • Particle also gains energy in δE





Alfven wave

with shear


Most of the energy gain is in

sheared E-field (not E-field of

the wave, c.f. wave surfing)

Alfven wave

without shear

Acceleration rate does reach absolute theoretical maximum b
Acceleration rate DOES reach absolute theoretical maximum ~ γ/ωB

  • Final orbits (strong shear), rL ~ Rj, drift approximation is no longer valid

  • New acceleration mechanism

  • For η < ηcrit < 0, ηcrit = - ½ ωB/γ, particle motion is unstable

  • non-relativistic:

  • Acceleration DOES reach theoretical

    maximum ~ γ/ωB

  • Note: becoming unconfined is GOOD

    for acceleration (contrary to shock acceleration)



ankle ~






  • From injection dn/dγ~γ-p →dn/dγ ~ γ-2

Particles below the ankle do not

gain enough energy to get rL ~Rj

and do not leave the jet

This is what is seen

Radiative losses
Radiative losses ~

  • Equate energy gain in E =B to radiative loss ~ UBγ2

  • As long as expansion is relativistic, total potential remains nearly constant, one can wait yrs – Myrs to accelerate

Astrophysical viability
Astrophysical viability ~

  • Need powerful AGN FR I/II (weak FR I , starbursts are excluded)

    • UHECRs (if protons) are not accelerated by our Galaxy, Cen A or M87

  • Several powerful AGN within 100 Mpc, far way → clear GZK cut-off should be observed

  • For far-away sources hard acceleration spectrum, p~ 2 , is needed

  • Only every other AGN accelerates UHECRs

  • Clustering is expected but IGM B-field is not well known

    • μGauss field of 1Mpc creates extra image of a source (Sigl)

    • Isotropy & clustering: need ~ 10 sources (Blasi & Di Marco)

  • Fluxes: LUHECR ~ 1043 erg/sec/(100 Mpc)3 – 1 AGN is enough

  • Matching fluxes of GCR and EGCR….

Main properties of the mechanism
Main properties of the mechanism: ~

  • Protons are at maximum of electric potential for negative shear (B *curl v) < 0 (related to (B*ΩBH))

  • Acceleration rate increases with energy and does reach absolute theoretical maximum τacc ~ γ/ωB

  • At a given energy, particles with smallest Z (smallest rigidity) are accelerated most efficiently (UHECRs above the ankle are protons)

  • produces flat spectrum

  • Acceleration @ 1 pc < r< Mpc: no radiative losses, lots of time

  • Pierre Auger: powerful AGNs?

    • GZK cut-off

    • few sources

  • May see ν & γ fluxes toward source (HESS, IceCube)

Let’s wait and see

The auger observatory argentina hybrid detector
The Auger Observatory (Argentina): hybrid detector ~

  • The Auger Observatory combines

  • Surface Detector Array and Air Fluorescence Detectors

  • Advanced control of position, performance, weather (e.g. T, humidity)

  • Independent measurement techniques allow control of systematics

  • Energy: ΔE/E ~ .5 @ 1020 eV

  • Angle: 0.6 o

  • Primary mass measured in complementary ways

  • First result:

    • no extra flux from Galactic center (contrary to AGASA and SUGER)

    • < 25% of photons @ > 1019 eV

    • (bad for top-down and Z-model)

  • Coverage ~ AGASA

Intergalactic propagation of uhecr
Intergalactic propagation of UHECR ~

  • Structure of intergalactic B-field, not very known

  • Average B-field < 10-9 G , rL ~ 100 Mpc for 1019 eV

  • Layers of high B-field with voids. Levi flights???

  • Structures of ~ 10Mpc, 10-7 G are seen in synchrotron emission (Kronberg), enough to deflect ~ radian

“Cosmic web”, Bond et al 1996

2dFGalaxy Redshift Survey 2003

Detectors two types

Earth atmosphere is a telescope ~

Ground monitors of charged particles (e.g. AGASA)

Neutron Monitors and Supermonitors

Ionization Chambers

Muon Telescope

Observation of fluorencence and Cherenkov light (Fly’s eye & HiRes, Haverah Park)


  • -rays


Detectors: two types

When statistics is low, calibration problems begin