Acceleration of highest energy cosmic rays in jets of powerful

AGNsMaxim Lyutikov (UBC, U. Rochester)

in collaboration withRashid Ouyed (UofC)

CR spectrum, composition, confinement

knee, 4 1015 eVankle,3 1018 eV

toe ?second knee ?

1 particle per km2

per century

UHECRs

Isotropic to highest energiesPossible small-scale clusteringat highest energies

UHECR composition: p-heavy-p

protons

heavy (Fe)protons

Proton fraction (green: HiRes stereo)

Propagation: B-fieldrL~E21/B G pc, Galaxy ~ 10-6 Gonly E < 1019 eV are confinedE > 1019 eV must be extragalactic

GZK cut-offGreisen 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

p + 2.7k + p + 0

n + +

pair production energy loss

pion production energy loss

pion production rate

Is GZK cutoff seen?

HiRes (fluorencence) and AGASA (ground array) disagree

Origin of cosmic rays

Acceleration of CR

Low energy CRs (<1015 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

shock

v1 > v2

B-field scattering off Alfvenwaves

Alfven wave

c

v

21~

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

We propose new, non-stochastic acceleration mechanism that turns on above the ankle, E> 1018 eV

General constraints on 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 Full DC accelerations schemes (with E-field || to B-

field or E>B) cannot work in principle for UHECRs1. leptons will shut off E|| by making pairs (typically

after ΔΦ << 1020 eV)2. 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

cZemI p maxE

4/14/1

6015 10

10eV10

R

kpc

erg

Etot

4/1~ RE ji

ie

Φ,R

4/12

max

R

EZecm tot

pE

BE

B

E ┴ B : Inductive potential

BR0ER~

,4

4 2 cBE

RLEM

cBRLB EM2

00 )(~ ,~E

I ~L ,377~4

~R EM Ec

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

cL0

2

~

,L 4 EM0

c

4

c L~I

2~

c

IRB

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

Lovelace 76Blandford 99

Electric potential

BE

Pictor A (FRII)

Potential energy of a charge in a sheared flow)(

4vB

c

B

VE~x

Potential Φ~-x2

B

VE~-x

Potential Φ~x2

Depending on sign of (scalar) quantity (B *curl v) one sign of charge is at potential maximumProtons are at maximum for negative shear (B *curl v) < 0 This derivation is outside of applicability of non-relativisitc MHD

2

4 : xv

2xB

c For linear velocity profile

,)( UFvB E=-v x B

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)

Er

v

x Bφ

Er

B

VE

Protons are at maximum for negative shear (B *curl v) < 0. Related to (Ω*B) on black hole

ΩBH and disk can act as Faradey disk

Acceleration by large scale inductive E-fields: E~∫ 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

EB

V

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

∆

BφxBφ ∆

ud

B

ErF

B-fieldF

Udrfit ~ F x B

Why this is all can be relevant? 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

EZeBc

ckAacc ||

1~

dt Eu)eZ eZ( vEEEnergy gain:

ZeB

tkAt 4

22EE

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

cZeB

ku Ad 2

E →

Wave surfing can help

Shear Alfven waves have δE~(VA/c) δB, Axial drift in δExB helps to keep particle in phase Particle also gains energy in δE

∆B

udAlfven wave with shear

Alfven wave without shear

γmax/γ0

Most of the energy gain is in sheared E-field (not E-field of the wave, c.f. wave surfing)

Er

δE

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)

2

11

/2

0000

B

critη=V’

1sin/1

, 1cos

tr

y

trx

BB

B

L

BBL

Spectrum

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

d

dn2

γ

2 p0

ankle

Particles below the ankle do notgain enough energy to get rL ~Rj

and do not leave the jet

Mixed composition protons This is what is seen

Radiative losses

Equate energy gain in E =B to radiative loss ~ UB γ2

As long as expansion is relativistic, total potential

remains nearly constant, one can wait yrs

– Myrs to accelerate

G 2-

EeV 100410 6~

2mceZcm

B

cm 3

EeV 100 1610~

3

2mcmceZ

r

3

2-

33

42

2-2-2

22

EE

EE

103

10

,L 4 0

c

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:

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 combinesSurface 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 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

2dFGalaxy Redshift Survey 2003

“Cosmic web”, Bond et al 1996

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)

electrons

-rays

muons

When statistics is low, calibration problems begin

Accelerators in Universe

Voltage Current

Sun 108 V 109 A

Pulsar 1016 V 3 1012 A

SGR 3 1014 V 1012 A

AGN 3 1020 V 1018 A

GRB 3 1022 V 1020 A

SLAC 1010 V 1 A