Ultra High Energy Cosmic Rays from Black Hole Jets of Radio Galaxies

The Auger Collaboration reports that the arrival directions of>60 EeV ultra-high energy cosmic rays (UHECRs) cluster along the supergalactic plane and correlate with active galactic nuclei (AGN) within ~100 Mpc. The association of several events with the nearby radio galaxy Centaurus A supports the paradigm that UHECRs are powered by supermassive black-hole engines and accelerated to ultra-high energies in the shocks formed by variable plasma winds in the inner jets of radio galaxies. The GZK horizon length of 75 EeV UHECR protons is ~100 Mpc, so that the Auger results are consistent with an assumed proton composition of the UHECRs. In this scenario, the sources of UHECRs are FR II radio galaxies and FR I galaxies like Cen A with scattered radiation fields that enhance UHECR neutral-beam production. Radio galaxies with jets pointed away from us can still be observed as UHECR sources due to deflection of UHECRs by magnetic fields in the radio lobes of these galaxies. A broadband ~1 MeV -- 10 EeV radiation component in the spectra of blazar AGN is formed by UHECR-induced cascade radiation in the extragalactic background light (EBL). This emission is too faint to be seen from Cen A, but could be detected from more luminous blazars.


Introduction
The Auger Observatory in the Mendoza Province of Argentina at ≈ 36 • S latitude determines the arrival directions and energies of UHECRs using four telescope arrays to measure Ni air fluorescence and 1600 surface detectors spaced 1.5 km apart to measure muons formed in cosmic-ray induced showers. Event reconstruction using the hybrid technique gives arrival directions better than 1 • , and energy uncertainties at 10 20 eV (100 EeV) of ∼ 11% for a 50% Fe and 50% p composition [3]. Analysis of the composition of the high energy showers in the early Auger analysis showed it becoming heavier, somewhere between p and Fe, at 10 19.4 eV [4,5]. By contrast, HiRes data are consistent with dominant proton composition at these energies [6], but uncertainties in the shower properties [7] and particle physics extrapolated to this extreme energy scale [8] preclude definite statements about composition.
In the Auger analysis [1,2], a probability statistic P corrected for exposure is constructed from the nearest-neighbor angular separation ψ between the arrival direction of an UHECR with energy E and the directions to AGN in the Veron-Cetty and Veron (VCV) catalog [9], containing 694 active galaxies with z < 0.024 or distance d < 100 Mpc. P was minimized for ψ = 3.1 • , threshold clustering energy E cl = 56 EeV, and clustering redshift z cl = 0.018 (d cl ∼ = 75 Mpc), containing 27 events (the two highest energy events were 90 and 148 EeV). Twelve events correlate within 3.1 • of the selected d < 75 Mpc AGN, and another three within the vicinity of one of these nearby AGN, ruling out an isotropic UHECR flux or a Galactic source population. Note that the VCV AGNs are not necessarily the sources of the UHECRs, but may only trace the same matter distribution as the actual UHECR sources.
This discovery opens the field of charged-particle astronomy. Only at the highest energies can arrival directions of charged particles be associated with their sources. This is because deflections by (i) the Galactic or (ii) intergalactic magnetic (IGM) field isotropizes the directions of lower energy cosmic rays.
Here we consider the Auger clustering results within the paradigm that extragalactic black-hole jet sources accelerate UHECRs. Estimates of deflection angle and delays are given in Section 2, specialized to an assumed proton composition of the UHECRs. The question of the GZK cutoff and the UHECR horizon is revisited in Section 3. In Section 4, we apply standard synchrotron theory to the lobes of Cen A in order to estimate the equipartition magnetic field and absolute jet power, using a new technique that uses the jet/counter-jet ratio to determine the speed of the outflow. From this, limits on UHECR acceleration in colliding shells of blazars are used to derive maximum particle energies. Also, an estimate is made of the flux of Compton-scattered cosmic microwave (blackbody) background radiation (CMBR), and compared with the flux of secondary nuclear production in Cen A's radio lobes. In Section 5, we present calculations of the broadband γ-ray νF ν flux from Cen A due to secondary cascading of protons on the EBL, for 1 nG (= 10 −9 G) IGM fields and show that Cen A is not detectable with current instrumentation. Concluding remarks are given in Section 6.

Magnetic Field Deflections of UHECRs
For case (i), the Galactic magnetic field can be approximated by a magnetic disk with characteristic height h md , giving a deflection angle θ df l ≈ h md csc b/r L . Here b is the Galactic latitude of the UHECR source, and the Larmor radius of a particle with energy E and charge Ze is Thus limited by the finite extent of the magnetic disk. Mean magnetic fields B in the ≈ 0.2 kpc thick gaseous disk of the Galaxy are ≈ 3 -5 µG, but could fall to ≪ 1µG in the kpc-scale halo [10]. Deflection angles < ∼ 3 • from Cen A (b = 19.4 • , galactic longitude ℓ = 309.5 • , declination −43 • , distance d ∼ = 3.5 Mpc) restrict UHECRs to protons or light-Z nuclei and a small ( < ∼ 0.1 µG) Galactic halo magnetic field. For case (ii), the deflection angle of an UHECR ion when propagating through the IGM field from a source at distance d is [11,12] is the number of reversals of the magnetic field (also expressed through the magnetic-field correlation length λ) and B −12 is the mean magnetic field of the IGM in pico-Gauss (1 pG = 10 −12 G). If UHECRs within 3 • of Cen A are accelerated by the radio jets of Centaurus A, then to avoid much larger deflections than those made by the Galactic magnetic field requires that B −12 < ∼ 2000 √ N inv E(60 EeV)/[Zd(3.5 Mpc)]. By this reasoning, the mean IGM field in the directions towards AGNs 75 Mpc distant in the supergalactic plane (SGP) is restricted to be < ∼ 100 √ N inv E(60 EeV)/Z pG [13]. Time delays between electromagnetic outbursts and UHECR arrival windows from Cen A due to propagation through the IGM are about ∆t ≈ d 3 where the final expression holds because N inv > ∼ 1. Variable γ-ray flaring activity from Cen A could be reflected in variable UHECR activity on sub-day timescales for IGM fields B −12 < ∼ 10 and λ < ∼ 0.1 Mpc or a large-scale (∼ Mpc) ordered field with mean strength B −12 < ∼ 1. The most intense magnetic fields between us and Cen A consistent with the deflection data for an assumed proton composition of the UHECRs are B ≈ 2 √ N inv nG. For the Auger data reaching to galaxies at distance d > ∼ 75 Mpc, B < ∼ 100 √ N inv pG. For N inv ∼ 100 (λ ∼ = 1 Mpc), B ≈ 1 nG. For the calculations in Section 5, we use B = 1 nG which is a more realistic value because UHECRs are correlated with more distant sources as well.

UHECR Proton Horizon
The clustering energy E cl ∼ = 60 EeV separates UHECRs formed mainly by sources along the SGP at d < ∼ d cl from lower-energy UHECRs formed nearby and on > ∼ 75 Mpc scales. A high-significance steepening in the UHECR spectrum at E ∼ = 10 19.6 eV ∼ = 4 × 10 19 eV and at E ∼ = 10 19.8 eV ∼ = 6 × 10 19 eV was reported, respectively, by the Auger [4] and HiRes [14] collaborations in 2007. These results confirm the prediction of Greisen, Zatsepin and Kuzmin [15,16] that interactions of UHECRs with CMBR photons cause a break in the UHECR spectral intensity near 10 20 eV.
The clustering and GZK energies coincide because > ∼ 60 EeV UHECR protons originating from sources at the > ∼ 100 Mpc scale have lost a significant fraction of their energy due to photopion losses with the CMBR, so that higher-energy particles from the more distant universe cannot reach us. The energy-loss mean free path r φπ = ct φπ = cγ|dγ/dt| −1 φπ of an UHECR proton with energy E = 10 20 E 20 eV to photopion losses with the CMBR at low redshifts is given, in good agreement with numerical calculations [17,18], by the expression [13]. The term r φπ gives the mean distance over which a particle with energy E loses ≈ 1 − e −1 ∼ = 63% of its energy. The MFPs for energy loss by photopair and photopion losses in different model EBLs, including an EBL consisting of the CMB alone, is shown in Fig. 1. UHECR p low z CMBR Figure 2. Heavy dotted curves give the horizon distance for UHECR protons as a function of total proton energy, using the local CMBR and the low and high EBL target radiation field shown in the inset to Fig. 1. Analytic approximation to photopion energy loss mean-free path, eq. (4), is given by dot-dashed curve, and the UHECR proton horizon, eq. (5), by dashed curve, for CMBR only. Auger clustering results are indicated by the shaded arrows. Distances to key radio galaxies are shown, and light dashed lines separate quasi-linear proton trajectories from trajectories with strong deflections in overall ordered magnetic fields with strength as labeled. Short-dashed lines give length for a proton to be deflected by 0.1θ −1 rad in magnetic fields ranging from 10 −8 -10 −11 G.
The GZK horizon length giving the mean distance from which protons detected with energy 10 20 E 20 eV originate depends in general on injection spectra and source evolution [19] (see also [20,21]), but a model-independent definition that reduces to r φπ (E 20 ) for an energy-independent energy-loss rate considers the average distance from which a proton with measured energy E had energy eE. The horizon distance, defined this way, is given by where the last two expressions give the proton horizon on CMBR photons alone. Using the phenomenological fits to low and high EBLs at optical and IR frequencies, represented in the inset to Fig. 1 as a superposition of blackbodies [13], gives the corrected horizon distance shown in Fig. 2. The horizon distance for ≈ 57(75) EeV UHECR protons is ≈ 200(100) Mpc. A GZK horizon smaller than 40 Mpc applies to protons with E > ∼ 100 EeV. This explains the clustering observations observed by the Auger collaboration if UHECRs are predominantly protons, but would be inconsistent with the Auger results if the UHECRs are composed of high-Z material, as the mean free path for photodisintegration can be much larger than 100 Mpc for ≈ 10 20 eV ions like Fe [13]. If the Auger energy scale is underestimated by ≈ 20% due to systematic effects (which would also reconcile the discrepancy between the different HiRes and Auger GZK energies as determined from the spectral break), then GZK losses on UHECRs with a dominant proton composition would explain the clustering towards the SGP even more decisively. The higher energy scale for the Auger experiment might also explain the lack of clustering observed by HiRes at > 57 EeV [22], which would at this energy cut in the HiRes experiment include large numbers of lower-energy, more distant and less clustered cosmic rays.

UHECRs from AGN Jets
Discovery of UHECR arrival directions clustered towards the SGP was anticipated by analysis of UHECR data from Haverah Park, AGASA, Volcano Ranch, and Yakutsk observatories [23]; see also [17]. Compared to an isotropic source flux, the average and rms angular distances toward the SGP were enhanced at the 2.5 -2.8 σ level for events with E > 40 EeV. Stanev et al. [23] argued that their analysis favors radio galaxies as the sources of UHECRs. A radio-galaxy origin of UHECRs is consistent with harder radio sources [24] and clustering of sources in the two Jansky, 2.7 GHz Wall and Peacock catalog [25] towards the SGP.
The SGP runs through the Virgo Cluster at ≈ 20 Mpc, and contains an assortment of radio galaxies such as M87, Cen A and NGC 315, and the starburst galaxies M82 and NGC 253. Using infrared galaxy surveys to better define the SGP improves the significance of correlations of UHECRs with the SGP [26]. When weighted by hard X-ray flux, the UHECR arrival directions are strongly correlated with Swift Burst Alert Telescope galaxies within 100 Mpc, which trace the SGP [27]. Searches [28,29] for specific AGN in the VCV and NASA/IPAC NED catalogs finds Seyfert 2, low ionization, and other radio-quiet galaxies closest to the UHECR arrival directions, in addition to associations with Cen A, Cen B, an FR II radio galaxy and a BL Lac object within 140 Mpc. IGR J21247+5058, an FR II broad-lined radio galaxy at z = 0.02 or d ≈ 80 Mpc, recently discovered with INTEGRAL [30], is 2.1 degrees away from a HiRes Stereo event with E > 56 EeV [31]. At least 8 of the 27 UHECRs with E > 56 EeV are within 3.5 • of nearby radio galaxies [32].
We suppose that the evidence is compatible with an AGN origin of UHECRs in the black-hole jets of radio galaxies, with Centaurus A being the most prominent example. Cen A itself, though classified as an FR I radio galaxy, has a bolometric radio luminosity exceeding 4 × 10 41 ergs s −1 [33], near the dividing line between FR I and FR II galaxies in terms of radio power. The giant elliptical galaxy in Cen A is intercepted by a small spiral galaxy making the prominent dust lanes [34] which, including inner dust torus emission, could conceal the optical/UV line strengths and distribution of broad line region gas near the Cen A nucleus [35,36]. A strong scattered radiation field is important for photomeson losses and neutral beam production in AGN jets [37,38], and seems required in many BL Lac objects because of spectral fitting difficulties with synchrotron/SSC models [39,40,41].
The nucleus of the Cen A jet is visible at radio and X-ray energies, revealing subluminal (v ∼ c/2) relativistic outflows and jet/counterjet fluxes of X-ray knots consistent with mildly relativistic speeds on projected ∼ 10 pc scales [42,43]. Cen A was detected at hard X-ray and γ-ray energies with OSSE, COMPTEL and EGRET on the Compton Observatory [44,45], emitting ≈ 5 × 10 42 ergs s −1 in keV -MeV radiation with dayscale variability observed at ≈ 100 keV (see also [46]). Most of this emission is probably quasi-isotropic radiation from the hot accretion plasma. Variability of ∼ GeV radiation could be detected from Cen A with the Fermi Gamma ray Space Telescope if the jetted γ-ray emission is not too dim. Such a detection would also discriminate between an inner jet and extended origin of the γ-ray emission, for example, from Cen A's lobes [47].

Jet Power from Synchrotron Theory
The corrected Auger point source exposure is χω(δ s )/Ω 60 ∼ = (9000 × 0.64/π) km 2 yr, where χ is the exposure, ω(δ s ) ∼ = 0.64 is an exposure correction factor for the declination of Cen A, and Ω 60 ∼ = π is the Auger acceptance solid angle [48]. For a power law proton injection spectrum with number index α, the apparent isotropic UHECR luminosity from Cen A is It is interesting to note that the production of ≈ 10 40 ergs s −1 in UHECRs by Cen A, the dominant radio galaxy within ∼ 10 Mpc, represents an UHECR emissivity of ≃ 8 × 10 43 ergs yr −1 Mpc −3 (cf. [49]).

Equipartition Magnetic Field
The UHECR luminosity can be compared with the time-averaged jet power inferred from the magnetic field energy in the radio lobes, assumed to be inflated by the pressure of the black-hole jet. Knowing the power of a black-hole jet allows one to derive the maximum particle energy of UHECRs accelerated through Fermi processes.
Here we state some elementary results from synchrotron theory needed to derive the jet power [50]. We treat a standard blob model and assume that the measured radio emission is nonthermal synchrotron radiation from randomly oriented electrons in a randomly directed magnetic field. In this approximation, the equipartition magnetic field is defined by equating the magnetic-field energy density U B = B 2 /8π with the total particle energy density U par consisting of hadrons and electrons, assumed to be dominated by a large-scale, randomly oriented magnetic field of strength B.
The equipartition magnetic field B eq = B(k eq = 1) with U par = k eq U B , where Here B cr = m 2 e c 3 /eh = 4.414 × 10 13 G, U cr = B 2 cr /8π = 7.752 × 10 25 ergs cm −3 , and δ D is the Doppler factor. In this expression, a factor ζ pe more energy is assumed to be carried by protons and ions than leptons. This result applies to the F ν ∝ ν −1/2 portion of the synchrotron spectrum made by electrons with N ′ (γ ′ ) ∝ γ ′−2 that carry most of the energy.

Synchrotron Power
The total jet power of a one-sided jet, referred to the stationary black-hole reference frame, is then defining ε B = B/B cr From this, one can show [50,41] that and u ≡ B/B minL . The minimum power is The magnetic field giving the minimum jet power required to account for the synchrotron flux is This applies to either spherical or cubical volumes by writing the emitting volume in the fluid frame as The geometry factor is given by g = 1 for cubical and g = π/6 for spherical volumes.
To get the speed of the outflow, we use the jet/counterjet ratio ρ, which is a number taken directly from observations. If θ is the angle of the jet nearest to the line of sight, and we assume that all jets are two-sided with equal power ejected in the opposite direction, then it is easy to show [51,52] that the speed Thus we interpret the asymmetrical lobe flux in Cen A as a consequence of aberration of the mildly relativistic two-sided outflow, rather than as a difference of spectral properties due to distinct environmental effects. The jet power obtained from this interpretation can be compared with other methods to determine jet power [53]. Table 1 shows that the jet/counterjet ratio ρ ≈ 1.5 -2 for regions 1 and 5, and ρ ≈ 2 -4 for regions 2 and 4, each pair being at equal angular separation from Cen A's nucleus. The orientation θ of the jet of Cen A with respect to our line of sight is 54], implying that β ≈ 0.1 for regions 1 and 5, and β ≈ 0.2 for regions 2 and 3, which are the values used in the calculations of the jet power shown in Table  1. These speeds refer to the flow of plasma on the scale of hundreds of kpc from the nucleus of Cen A, so that the plasma from inner jet has to be ejected with much higher, probably relativistic speeds. The factor (Γ/δ D ) 2 , when included, reduces the power of the brighter lobe and increases the power of the dimmer lobe to reproduce the underlying assumption in the method that the powers of the two jets are equal. The minimum total jet power to produce the weakly boosted Cen A radio emission is therefore ≈ 2×4×10 43 ergs s −1 , or total jet power P tot * > ∼ 10 44 ergs s −1 , as follows from Table 1. With total mean absolute Cen A jet powers ≈ 10 44 ergs s −1 , apparent isotropic jet powers can reach 10 45 -10 46 ergs s −1 during flaring intervals. Indeed, apparent isotropic flaring luminosities in γ rays alone exceed 10 45 ergs s −1 in Mrk 501 and Mrk 421, and 10 46 ergs s −1 in PKS 2155-304 [55]. These AGN are nearby BL Lac objects that correspond to FR I radio galaxies like Cen A seen along the jet axis, though Cen A may have the added advantage, in terms of UHECR production, of an external radiation field to enhance photohadronic processes in the jet [37,38]. It will be interesting to apply this technique to a sample of radio galaxies, including Perseus A (3C 84, NGC 1275; z = 0.018 or d L ∼ = 76 Mpc) [56,57], Cyg A [31], etc.

UHECR Acceleration
The particle energy density of a cold relativistic wind with apparent isotropic luminosity L and Lorentz factor Γ = 1/ √ 1 − β 2 at radius R from the source is u p = L/(4πR 2 βΓ 2 c). If a fraction ǫ B is channeled into magnetic field B ′ in the fluid frame, then RB ′ Γ = 2ǫ B L/βc, implying maximum particle energies E ′ max ∼ = QB ′ (R/βΓ), so This simple, optimistic estimate begs the question how to transform directed particle kinetic energy into magnetic field energy in a cold wind. In other words, it is simply a dimensional analysis that contains no physical basis, whether for the source that emits a wind with such large apparent powers, or for the particle acceleration mechanism. Within the picture of particle acceleration through Fermi processes, a maximum particle energy in colliding shells can be derived in a straightforward manner. The underlying limitation of Fermi acceleration, whether first-or second-order, is that a particle cannot gain a significant fraction of its energy on a timescale shorter than the Larmor timescale. A colliding shell picture due to inhomogeneities in the relativistic wind realistically applies to the inner jets of radio galaxies and blazars, and to GRBs.
Consider the ejection of two shells, with shell a ejected at stationary frame times 0 ≤ t * < ∆t * a , and shell b at times t * d ≤ t * < t * d + ∆t * b . The coasting Lorentz factor, wind luminosity (assumed constant during the duration of shell ejection), and energy are Γ a(b) , L * ,a(b) and E * ,a(b) , respectively, with stars referring to the stationary jet frame. For a collision, ρ Γ ≡ Γ a /Γ b < 1. For relativistic winds, i.e., Γ a ≫ 1, the collision radius is r coll ∼ = 2Γ 2 a c(t * d − ∆t * a ) when ρ Γ ≪ 1. When Γ b > Γ a ≫ 1, the shocked fluid Lorentz factor Γ ≫ 1.
Collisions between relativistic shells divide into a number of cases depending on whether the forward shock (FS) and reverse shock (RS) are relativistic or nonrelativistic [58]. We consider the case of a nonrelativistic reverse shock (NRS) and relativistic forward shock (RRS), which is probably most favorable for particle acceleration. Thus the FS Lorentz factor Γ f ≫ 1. The magnetic field of the forward-shocked fluid in the shocked fluid (primed) frame is and ǫ B,f , the ǫ B parameter for the FS, is familiar from blast wave studies (e.g., [59]). The maximum particle energy in the comoving frame is E ′ max ∼ = ZeB ′ f c∆t ′ a , where ∆t ′ a is the comoving duration when particles are undergoing acceleration. If this is equated with the time that it takes for the FS to pass through shell a, then From this, we obtain The factor Γ/Γ 2 a is at best of order unity, so this expression shows that for protons to reach > ∼ 10 20 eV cosmic ray energies through Fermi processes, it is essential to consider sources with apparent isotropic luminosities > ∼ 10 46 ergs s −1 . Acceleration of UHECRs in Cen A is therefore in principle possible during powerful episodes of jet activity. Acceleration of UHECRs can also take place in colliding winds of moderately powerful blazars with L > ∼ 10 46 ergs s −1 where strong Doppler collimation takes place.

Deflection of UHECRs
The milliarcsec-scale radio jets in Cen A show moderate asymmetry, consistent with Cen A's radio jet being mildly relativistic and misaligned by ∼ 60 • [60]. Off-axis radiation beaming factors would conceal on-axis Cen A blazar-type flares with apparent powers L > ∼ 10 46 ergs s −1 . These events would eject cosmic rays to > ∼ 10 20 eV energies into the ∼ 100 kpc × 500 kpc radio lobe structure. If the equipartition field characterizes the large-scale magnetic field of the lobes (i.e., N inv ∼ 1), then 60 EeV UHECR protons with r L ∼ = 65 kpc (see eq. [1]), could be deflected by the magnetic field of Cen A's lobe, or in the lobes of other radio galaxies or BL Lac objects, as suggested in arrival direction maps [28].
If UHECRs are formed through a neutron beam, then they will travel on average ≈ 500[E/(60 EeV)] kpc before decaying. Thus UHECRs will be deposited throughout the radio lobe, with some not decaying until outside the radio lobe structure. Thus both radio galaxies and blazars can be sources of UHECRs. For distant sources, though, energy losses will reduce the arrival energies of UHECRs, so that searches for enhancements of UHECRs towards specific sources should also take into account the EBL-dependent horizon energy, as illustrated in Fig. 2.
The proton Larmor radius is formally r L ∼ = 110E 20 /B pG Gpc (eq. [1]), and photomeson interactions with the CMBR and EBL take place on a horizon distance scale ≈ r hor (E 20 ), where the received proton has lost ≈ 63% of its energy. If the proton is hardly deflected out of the beam, so d ≪ r L , then we should expect a pulse pile-up at a specific energy r hor (E 20 ) ∼ = d L . For PKS 2155-304 at z = 0.116 or a propagation distance d ∼ = 400 Mpc (Fig. 2), searches should be made for enhancements of UHECRs with E CR < ∼ 40 EeV, which is insensitive to the level of the EBL. If BL Lac objects accelerate UHECRs, then enhancements at E CR ∼ 40 -60 EeV can be searched for from Mrk 421 and Mrk 501. Failure to detect a signal would constrain the minimum IGM field and number of inversions, or call into question a radio/γ-ray galaxy origin of UHECRs.
In Fig. 3 we plot the arrival directions of 27 cosmic rays from Auger (blue circles) and 13 cosmic rays from HiRes (red circles), all with > 56 EeV energy and with 1 • angular uncertainty in their arrival directions (reflected in the radii of the circles; cf. Ref. [61]). We also plot the arrival directions of 58 AGASA UHECRs, consisting of 24 with E > 56 EeV (magenta circles) and 34 with 40 EeV < E < 56 EeV (orange circles). Their arrival directions are displayed with an average angular resolution of 1.8 • , as previously reported by the AGASA experiment [62]. The number of AGASA UHECRs may suggest, given AGASA's exposure relative to HiRes and Auger, an energy calibration discrepancy between these experiments, which should be considered in more detailed studies but is ignored here. Note that the arrival directions of the cosmic rays from the prominent nearby AGNs (labelled) are deflected by the galactic (pink and purple circles) and inter-galactic (green circles) magnetic field. We used two energies, 40 EeV (pink circles) and 20 EeV (purple circles), to calculate deflections in the µG galactic magnetic field according to eq. (2). The deflections from the AGN near the galactic plane (horizontal line) are larger because of the larger magnetic field. If Cyg A, BL Lac, 1959+65 or Mrk 501 are the possible sources of UHECR, then we should expect a large scattering, due to the galactic magnetic field, in the arrival directions of UHECRs below the GZK energy. For distant sources, e.g., 0152+17, the deflection in the intergalactic magnetic field, plotted here for 0.1 nG field using green circles, may be larger. However, reversals of the field orientation over ∼ Mpc scale may reduce the deflection in the intergalactic magnetic field from the values plotted in Fig. 3. These deflections in magnetic fields and related uncertainties can prevent positive identification of the UHECR sources below the GZK energy, although one should expect a clustering effect as evident from the lower energy AGASA data in the northern hemisphere.

Nuclear γ rays from Cen A's Radio Lobes
Typical ∼ 1 µG magnetic fields in Cen A's lobes carry an amount of energy ∼ = V lobes B 2 /8π ∼ = 4 × 10 57 V 71 B 2 µG ergs cm −3 , denoting the Cen A lobe volume V lobes = 10 71 V 71 cm −3 . For magnetic fields near equipartition, only ≈ few Myr are required for a jet power of ≈ 10 44 ergs s −1 and total energy of ≈ 10 58 ergs. Thus the Cen A jet activity is likely to operate intermittently.
Assuming at least equal energy in nonthermal protons and ions as nonthermal electrons, and using the equipartition assumption to normalize particle number and energy, we write the total cosmic ray spectrum over the Cen A lobes as with γ max ∼ 10 11 and total cosmic-ray energy W CR = 10 58 W 58 ergs. A δ-function approximation for the inelastic nuclear cross section, dσ pH→γ /dE γ ∼ = 2σ π 0 X (γ)δ(E γ − ξE p ), where σ π 0 X (γ) ∼ = 27 ln γ + 58/ √ γ − 41 mb is the π 0 inclusive cross section [63] and γ-ray secondary fractional energy ξ ∼ 5 -10%, gives a lobe-integrated > ∼ 1 GeV νF ν spectrum For ξ = 0.05 and p ∼ = 2.3, the nuclear γ-ray flux from the lobes of Cen A is with E γ now in GeV. Based on lack of observed internal depolarization and measured soft X-ray flux, Ref. [47] argue that thermal particle target densities n ℓ ∼ 10 −4 cm −3 . The number of source counts with E γ (GeV) ≥ E 1 detected with the Fermi Telescope for ξ = 0.05 and p ∼ = 2.3 is where the effective area of the Fermi Telescope is A G (E γ ) ∼ = 8500/ E γ cm 2 below 1 GeV and A G (E γ ) ∼ = 8500 cm 2 at higher energies, and X ≈ 1/5 in the scanning mode. The number of background counts from the angular extent, ∆Ω ∼ = 12/57.3 2 , of the lobes of Cen A, using as background the diffuse extragalactic γ-ray background of Galactic background [64], is B(> E γ ) ∼ = 280(X/0.2)∆t(yr)E −1.1 γ § . Unless n ℓ ≫ 10 −4 cm −3 , this emission signature would be too faint to be detected with the Fermi Gamma ray Space Telescope. Thus the cosmic-ray induced nuclear emission in the lobes of Cen A is probably entirely negligible. The much more optimistic estimates in Ref. [65] are due to the assumption of a very soft injection index p ∼ = 2.7 extending from GeV to ZeV energies, which requires a much larger cosmic-ray power.

Thomson-Scattered CMBR
The same electrons that make the radio synchrotron radiation also upscatter photons of the surrounding radiation fields. Using a δ-function approximation for Thomson scattering of quasi-monochromatic photons with mean energy m e c 2 ǫ o and energy density U o gives the Thomson-scattered νF ν flux For the CMBR, the mean dimensionless energy of a photon that is scattered by an electron radiating most of its synchrotron emission at ǫ pk is implying emission at MeV .
The WMAP observations at 22.5, 32.7, 40.4, 60.1, and 92.9 GHz used by Hardcastle et al. [47] allowed these authors to predict the Thomson-scattered flux. As can be seen from this approximation, this flux extends only to the low-energy end ( < ∼ 100 MeV) of the Large Area Telescope frequency range on the Fermi Gamma ray Space Telescope [66].

Cascade γ rays from UHE Neutral Beams
For flares in BL Lacs exceeding > ∼ 10 46 ergs s −1 , and the much more energetic flares in FR II galaxies and flat-spectrum radio quasars reaching apparent γ-ray powers § The Galactic diffuse γ-ray background has a softer spectrum than the extragalactic background, so is probably not significant at E γ ≫ 1 GeV at the ≈ +20 • galactic latitude of Cen A. > ∼ 10 48 ergs s −1 , we describe the sequence of events starting to produce cascade radation following the acceleration of particles in black-hole jets [38]. A neutral beam is formed as a consequence of photomeson interactions of the accelearted UHECR protons with the synchrotron and scattered radiation field in the inner jet. Some > ∼ 10% of the hadronic energy can be transformed into an escaping neutron beam, with a few percent in a UHE γ-ray beam and a few percent into neutrinos [37,38]. Escaping neutrons with energy E n travel E n /10 20 eV Mpc before decaying into protons and low-energy β-decay leptons and neutrinos. The γ rays formed by p, n + γ → π 0 → 2γ processes in the inner jet and particle beam are attenuated by CMBR photons through γγ → e ± on length scales λ bb γγ (kpc) ∼ = 2E P eV / ln(0.4E P eV ) kpc for E P eV ≫ 1 and λ bb γγ (kpc) ∼ = 4 √ E P eV exp(1/E P eV ) kpc for E P eV ≪ 1, valid until E P eV < 0.1, when absorption on the extragalactic background light from stars and dust dominates. Leptons with γ ≡ 10 9 γ 9 Comptonscatter the CMBR photons, losing energy on length scales λ T ∼ = 0.75/γ 9 kpc when γ 9 ≪ 1, and λ KN ∼ = 2.1γ 9 /[ln(1.8γ 9 ) − 2] kpc when γ 9 ≫ 10.
If the distance d to the source is smaller than the particle Larmor radius and the correlation length (formally, N inv = 1), the cascade pairs are deflected out of a beam with opening angle θ = 0.1θ −1 radian when θr L < λ T , implying that the collimation of the electromagnetic cascade is preserved until γ 9 ∼ = 0.4 B −11 /θ −1 . Before the beam disperses, CMBR photons are scattered to energies ǫ ∼ 10 −9 γ 2 , or E γ ∼ = 100B −11 /θ −1 TeV. Fig. 4 shows that the ratio B −11 /θ −1 < ∼ 0.1 is unique in that Compton-scattered CMBR from the cascade emerges from behind the EBL absorbing screen to form a hard γ-ray component at 10 GeV -10 TeV energies. If B IGM < ∼ 10 −12 G, then the cascade emission from sources like 1ES 1101-232, if UHECR sources, could make an anomalous One-year Fermi Gamma ray Space Telescope/GLAST and 50 hr VERITAS sensitivities are shown for comparison.
The high-energy cascade flux induced by rectilinear motions of UHECRs from Cen A towards us is shown in Fig. 5. This calculation is a one-zone model, because it assumes that the properties of the IGM remain unchanged between Cen A and the Galaxy. Cosmic ray propagation through the extended magnetized environment in the cocoon and radio lobes of Cyg A [31] can also produce a γ-ray signature, but Cyg A is beyond the GZK horizon, so only lower energy UHECRs can reach us from this source. (For UHECRs accelerated in galaxy clusters [67] or other accelerators see, e.g., [68].) This calculation is normalized to 2 protons from Cen A with E > 60 EeV for the exposure and area of the Auger observatory (eq. [6]).
The parameters of this calculation are d = 3.5 Mpc, B = 10 −9 G, and particle injection index α = 2.2. The proton injection spectrum is exponentially cutoff at energy E max = 2×10 20 eV. The EBL used is from Ref. [69]. Twelve cascade cycles are sufficient to reach convergence, and this is the number used to calculate the total Cen A spectral energy distribution induced by UHECRs interacting with intervening radiation fields. The synchrotron cascade radiation is colored blue. For the assumed magnetic field, the synchrotron flux is produced by γ > ∼ 10 12 electrons and remains collimated. However, the Compton flux between ≈ 1 -100 TeV does not take into account the deflection of electrons. It should therefore be considered as an upper limit that could be reached if B < ∼ 10 −12 G. The solid curve in Fig. 5 shows the multiwavelength νF ν flux, but is clearly far too faint to be seen with present technology. In this case, the proximity of Cen A works against it being a bright hadronic source: there is not enough pathlength to extract a significant fraction of the UHECR proton's energy. In future work (Atoyan et al. 2009, in preparation), details of cascades formed by UHE leptons and γ-rays formed by photohadronic processes will be presented. The prospects of detecting more distant, aligned blazar jets, if they are sources of UHECRs, could be more favorable if B < ∼ 10 −12 G. UHECR production in luminous flat spectrum radio quasars could make anomalous hard components at multi-GeV energies to be detected with the Fermi Gamma ray Space Telescope. Such emission signatures could also be seen in GRBs [70,71].

Summary and Conclusions
We have considered the implications of the discovery [1,2] by the Pierre Auger collaboration of clustering of UHECR arrival directions towards Cen A and AGN in the SGP. To guide out thinking, we have introduced a model-independent definition of the GZK horizon distance, shown in Fig. 2 (cf. [19,20]). Assuming that black-hole jets energize and inflate the radio lobes of radio galaxies, a new method to calculate jet power based on the radio spectrum, size, and jet/counterjet ratio is applied to Cen A data. The average absolute jet power of Cen A is found from this technique to be ≈ 10 44 ergs s −1 . The apparent isotropic power in a small beaming cone could easily, therefore, exceed 10 46 ergs s −1 during flaring intervals.
An apparent jet power at least this great is needed to accelerate UHECRs through Fermi processes. The collimated UHECRs, consisting mainly of neutron-decay protons, can be deflected by the ≈ µG fields in the lobes of radio galaxies (for acceleration in the lobes of radio galaxies see, e.g., [72]). This can give the appearance that UHECRs are emitted from Cen A's radio lobes [28], or allow UHECRs to originate from more distant, misaligned radio galaxies like Cyg A, which itself has a highly magnetized, ≈ 20 µG cavity within several hundred kpc of the central engine [31]. The enhancement of UHECRs in the directions to specific radio jet sources at different redshifts would give valuable information about the IGM magnetic fields and intensity of the EBL.
The inner jets of radio galaxies, including Cen A, can make an escaping neutral beam of UHECRs. Because Cen A is a nearby radio galaxy with its closer jet misaligned by ∼ 35 • -70 • to the line of sight, the UHECR flux received from it is small, and the cascade radiation flux is not detectable with current instrumentation. Neither is the secondary nuclear γ-ray emission from cosmic ray interactions with the lobe's thermal gas if its density is ≈ 10 −4 cm −3 [47], though the pair halo flux could be detectable [73,74]. The most prominent multi-MeV radiation signature is due to the CMB photons Compton-scattered by the radio-emitting electrons to soft γ-ray energies [66,47]. Use of the transient event class in analysis of Cen A data [75] could help pull out the lowenergy, ≈ 10 -100 MeV signal, which would be important for normalizing its magnetic field and total jet power.
For UHECR blazar sources pointed towards us, anomalous hard cascade γ radiation spectra is potentially detectable with the Fermi Gamma ray Space Telescope or groundbased γ-ray telescopes, as we show in detail in future work. Detection of anomalous γ-ray signatures in blazars (or GRBs) could reveal emissions from UHECR acceleration in these sources. Lack of association of UHECR arrival directions with radio galaxies could require that various other classes of extragalactic bursting sources be admitted, including long duration GRBs [76,77], low luminosity GRBs [78], or magnetars. For instance, Ghisellini et al. [79] argue that the Auger UHECRs are not actually associated with Cen A, but with the background Centaurus cluster at ≈ 40 -50 Mpc. They argue that the rapid discharge of young, highly magnetized pulsars, which are the progenitors of magnetars, might have sufficient power to explain UHECR origin. Here the future pattern of UHECR arrival directions found with the Pierre Auger Observatory is of great interest, and whether a concentration builds toward the direction to Cen A.
Spectral signatures associated with UHECR hadron acceleration in studies of radio galaxies and blazars with the Fermi Gamma ray Space Telescope and ground-based γ-ray observatories can provide evidence for cosmic-ray particle acceleration in blackhole plasma jets. Together with IceCube or a northern hemisphere neutrino telescope, observations of PeV neutrino and MeV -GeV -TeV γ rays can confirm whether blackhole jets in radio galaxies accelerate the UHECRs.