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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). 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

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  1. Acceleration of highest energy cosmic rays in jets of powerful AGNs Maxim Lyutikov (UBC, U. Rochester) in collaboration with Rashid Ouyed (UofC)

  2. UHECRs 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 protons protons • 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)

  3. 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 pair production energy loss p + 2.7k +  p + 0 n + + pion production energy loss pion production rate

  4. Is GZK cutoff seen? • HiRes (fluorencence) and AGASA (ground array) disagree

  5. Origin of cosmic rays

  6. 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 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 waves B-field v1 > v2 shock Acceleration of CR We propose new, non-stochastic acceleration mechanism that turns on above the ankle, E> 1018 eV Alfven wave

  7. 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

  8. E ji ie Φ,R B DC (linear) acceleration for UHECR does not work E • 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 B

  9. Lovelace 76 Blandford 99 B E ┴ B : Inductive potential E 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

  10. For linear velocity profile V V E~x E~-x B B 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

  11. V B v E x Bφ Er Er 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 Ω BH and disk can act as Faradey disk

  12. Acceleration by large scale inductive E-fields: E~∫ v•E ds V • 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 E B

  13. ∆ B ud F ∆ BφxBφ Er 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 B-field F Udrfit ~ F x B

  14. 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 Energy gain: For linear velocity profile, V=η x, E= η x B/c, x = ud t, →

  15. 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 δE B ∆ γmax/γ0 ud Alfven wave with shear Er Most of the energy gain is in sheared E-field (not E-field of the wave, c.f. wave surfing) Alfven wave without shear

  16. 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) η=V’

  17. ankle γ Mixed composition protons Spectrum • 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

  18. 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

  19. 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….

  20. 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

  21. 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

  22. 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

  23. 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 Detectors: two types When statistics is low, calibration problems begin

  24. Accelerators in Universe

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