acceleration of highest energy cosmic rays in jets of powerful agns maxim lyutikov (ubc, u....
TRANSCRIPT
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