FERMI LARGE AREA TELESCOPE VIEW OF THE CORE OF THE RADIO GALAXY CENTAURUS A

The EGRET detection of Cen A (Sreekumar et al. 1999; Hartman et al. 1999) was confirmed early on by the Fermi-LAT. Based on three months of all-sky survey data, the initial LAT detection was reported in the LAT bright source list (BSL) paper (Abdo et al. 2009a) as 0FGL J1325.4–4303 with a 95% confidence localization, r₉₅ = 0304 = 183. In the companion LAT Bright AGN Sample paper (LBAS; Abdo et al. 2009c) to the BSL, a single power-law fit was reported, which gave F(>100 MeV) = 2.15 (±0.45) × 10⁻⁷ ph cm⁻² s⁻¹ with photon index, Γ = 2.91 ± 0.18, and a peak flux on a ∼1 week timescale of (3.23 ± 0.80) × 10⁻⁷ ph cm⁻² s⁻¹. Note that this only considered the γ-ray emission from Cen A as a single point source, i.e., it did not account for any lobe emission.

To these initial observations, seven additional months of all-sky survey data are added to the current analysis. Specifically, the observations span the time period from 2008 August 4 to 2009 May 31, corresponding to mission elapsed time 239557420–265507200. Diffuse event class (CTBCLASSLEVEL = 3) events were selected with a zenith angle cut of <105°and a rocking angle cut of 39°. The former are well calibrated and have minimal background while the latter greatly reduce Earth albedo γ-rays. For the analysis, LAT Science Tools⁷⁰ version v9r11 was utilized with the P6_V3_DIFFUSE instrument response function. The standard LAT Galactic emission model, GLL_IEM_V02.FIT⁷¹ was used, and the uniform background was represented by the isotropic diffuse γ-ray background and the instrumental residual background (isotropic_iem_v02.txt). We consider 11 point sources in the 1FGL catalog (Abdo et al. 2010a; see also Figure 1).

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Figure 1 shows the 0.2–30 GeV LAT image centered on Cen A, which is clearly detected. Also prominent are the Galactic emission toward the south and several faint sources in the field. We obtained a localization of the source at Cen A with gtfindsrc, which finds point-source locations based on an unbinned likelihood analysis. The resulting localization was reduced to r₉₅ = 0087 = 52 (5.7 kpc), centered at R.A. = 201399, decl. = −43033 (J2000.0 epoch) which is offset by 0029 = 17 (1.9 kpc) from the VLBI radio position of Cen A (Ma et al. 1998). Figure 2 shows the localization error circle of the LAT emission overlaid on the combined radio, optical, X-ray images. The new LAT position is consistent with that of 3EG J1324 − 4314 (Sreekumar et al. 1999; Hartman et al. 1999), but both are notably offset from EGR J1328 − 4337, the closest EGRET source in the Casandjian & Grenier (2008) catalog. The latter's derived position shifted in such a way that Cen A was outside of the r₉₅ localization circle, so that there was some ambiguity as to whether EGRET was actually detecting Cen A, but the new LAT position confirms the earlier 3EG result. The LAT significantly improves upon the previous EGRET γ-ray localization (r₉₅ = 053 = 32').

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The binned likelihood fitting was performed with the gtlike tool, first assuming that Cen A is a point source, i.e., that there is no γ-ray lobe emission (model A). The field point-source positions were fixed, and their spectra were assumed to be power laws, with the photon indices allowed to vary. The location of Cen A was fixed at its VLBI radio position (Ma et al. 1998). In addition to the 11 1FGL point sources used in the lobe paper, in order to treat the lobe emission as a background source, we include two 1FGL sources, 1FGL J1322.0 − 4515 and 1FGL J1333.4 − 4036, which are thought to be the local maxima of the lobe emission. A likelihood analysis with the energy information is binned logarithmically in 20 bins in the 0.2–30 GeV band, and the γ-ray directions binned into a 14° × 14° grid with a bin size of 01 × 01. For both the Galactic and isotropic emission models, one free parameter was introduced to adjust the normalization. Because the effective area of the LAT is rapidly changing below ∼200 MeV, we use events with energy above this value. Above 30 GeV the significance of detection is <3σ, so we make a cut as this energy as well.

As a result, the test statistic (TS; Mattox et al. 1996) is found to be 378 for Cen A, which is smaller than the TS = 628 in the 1FGL catalog (Abdo et al. 2010a), since the lower energy limit is 200 MeV in our analysis instead of 100 MeV in the catalog. The relative normalizations of the Galactic and isotropic models become 1.02 ± 0.02 and 1.40 ± 0.06, respectively, and the fit is reasonable within the current background model uncertainty. This fit gives a power-law photon index of Cen A between 200 MeV and 30 GeV of Γ = 2.76 ± 0.07 and the flux extrapolated down to >100 MeV is (2.06 ± 0.20) × 10⁻⁷ ph cm⁻² s⁻¹(where errors are statistical only). As noted in Abdo et al. (2009c), the spectrum is very steep in comparison to the typical blazars of Γ = 1.5 − 2.5. The power-law photon index is consistent with the 3EG result of Γ = 2.58 ± 0.26 (Hartman et al. 1999). The 3EG flux was reported to be (1.36 ± 0.25) × 10⁻⁷ ph cm⁻² s⁻¹ with a peak value of (3.94 ± 1.45) × 10⁻⁷ ph cm⁻² s⁻¹ (Hartman et al. 1999), consistent with the average flux.

We next modeled the region with a radio image of the giant lobe (model B). This analysis is identical to that described in the lobe paper, and the reader is referred to it for details. We present a brief description below. We use the WMAP image at 20 GHz from Hardcastle et al. (2009) and eliminate the Cen A core region with a cut radius of 1°. In this analysis, we exclude two point sources (1FGL J1322.0 − 4515 and 1FGL J1333.4 − 4036), which are assumed to be emission from the lobes. The binned likelihood analysis was performed to extract the flux and spectral indices for the core and lobes. The relative normalizations of the Galactic and isotropic models become 1.00 ± 0.02 and 1.44 ± 0.06, respectively. The γ-ray detection in each energy range is significant at a 4σ level up to the 5.6–10 GeV energy bin for the core region, and the spectrum is consistent with the power-law model. This fit gives a photon index of the core between 200 MeV and 30 GeV of Γ = 2.67 ± 0.10_stat ± 0.08_sys and a flux extrapolated down to >100 MeV of (1.50 ± 0.25_stat ± 0.37_sys) × 10⁻⁷ ph cm⁻² s⁻¹, with statistical and systematic errors reported. Here, we consider the systematic errors from the effective area, the diffuse model, and WMAP inner cut radius, as described in the lobe paper. The photon index is almost identical to that of model A, but the flux is somewhat lower due to some of the core photons from model A being considered as being emitted by the lobes in model B. The results for model B can be seen in Figure 3.

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To quantify variability within the ∼10 months of LAT observation, we generated light curves in 30 and 15 day bins using the binned likelihood analysis with gtlike. We performed the analysis taking into account the lobe emission (i.e., model B in Section 3.2). The power-law normalizations of the core and background point sources are treated as free parameters, but the photon indices of all sources and the normalizations of the lobes and the diffuse background models are fixed to the values obtained in the 200 MeV–30.0 GeV range for the whole time region. Figure 4(a) shows the light curve of the flux (extrapolated down to >100 MeV) in 30 day bins. The χ² test results in χ²/dof = 0.98, and the light curve with 15 day bins gives χ²/dof = 0.89. These are consistent with no variability. The time behavior of Cen A is in contrast to large variability of typical blazars in the MeV/GeV range and similar to that of Perseus A (Abdo et al. 2009b) and M87 (Abdo et al. 2009d).

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Cen A was observed with VLBI on 2009 November 27/29, as part of the TANAMI program using the five antennas of the Australian Long Baseline Array (LBA), the 70 m DSS-43 antenna at NASA's Deep Space Network at Tidbinbilla, Australia, and two trans-oceanic telescopes TIGO (Chile) and O'Higgins (Antarctica) of the International VLBI Service (IVS) for Geodesy and Astrometry (the latter two participating at 8.4 GHz, only). The beam size achieved was (0.92 mas × 0.56 mas) at 8.4 GHz and (1.68 mas × 1.25 mas) at 22.3 GHz using natural weighting. These observations were part of the TANAMI monitoring of a radio and γ-ray selected sample of 65 blazars at 8.4 GHz and 22.3 GHz with observations approximately every two months.

TANAMI data are correlated on the DiFX software correlator (Deller et al. 2007) at Curtin University in Perth, Western Australia. Data inspection and fringe fitting was done with AIPS (National Radio Astronomy Observatory's Astronomical Image Processing System software). The images were produced by applying the program difmap (Shepherd 1997), using the CLEAN algorithm. More details about the data reduction can be found in Ojha et al. (2005).

Data from the first epoch (November 2009) of TANAMI observations are presented in Ojha et al. (2009). Figure 5 includes the fluxes at 22.3 GHz and 8.4 GHz measured on 2009 November 27 and 29, respectively. The total flux density, corresponding to the emission distributed over the inner ∼120 mas at 8.4 GHz, is S_total = 3.90 Jy. At 22.3 GHz, a total VLBI flux density of 3.2 Jy is distributed over the inner ∼ 40 mas of the jet, with very little emission on the counterjet side.

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Via model fitting, we found a component with an inverted spectrum, which is the brightest at both frequencies and which we identify with the jet core. The core flux density is 0.92 Jy at 8.4 GHz and 1.54 Jy at 22.3 GHz. The core size is consistently modeled at both frequencies to be (0.9–1.0) mas × (0.29–0.31) mas at the same position angle of 53°–55°(see Ojha et al. 2009).

Cen A was observed with Suzaku on 2009 July 20–21, August 5–6, and August 14–16 with a total exposure of 150 ks, during which time the flux approximately doubled. We utilized data processed with version 2.4 of the pipeline Suzaku software and performed the standard data reduction: a pointing difference of <15, an elevation angle of >5° from the Earth rim, and a geomagnetic cut-off rigidity (COR) of >6 GV. We did not use events from the time the spacecraft entered the South Atlantic Anomaly (SAA) to 256 s after it left the SAA. Further selection was applied: Earth elevation angle of >20° for the X-ray Imaging Spectrometer (XIS), COR > 8 GV, and the time elapsed from the SAA (T_SAA_HXD) of >500 s for the Hard X-ray Detector (HXD). The XIS response matrices are created with xisrmfgen and xissimarfgen (Ishisaki et al. 2007). The HXD responses used here are ae_hxd_pinhxnome5_20070914.rsp for the PIN and ae_hxd_gsohxnom_20060321.rsp and ae_hxd_gsohxnom_20070424.arf for the Gadolinium Silicate (GSO) crystal. The "tuned" (LCFIT) HXD background files (Fukazawa et al. 2009) are utilized. The detailed Suzaku analysis, including time variability, will be reported elsewhere (Y. Fukazawa et al. 2010, in preparation). The Suzaku data were fit with a single absorbed power law, which was found to have a spectral index Γ = 1.66 ± 0.01 with dust-absorbing column density N_H = (1.08 ±  0.01) × 10²³ cm⁻². The flux in the 12–76 keV band in 2009 July was (1.23 ±  0.01) × 10⁻⁹ ergs⁻¹ cm⁻² keV⁻¹, about twice the flux measured by Suzaku in 2005 (Markowitz et al. 2007).

Cen A was observed on six days between 2009 January 15 and 28 for a total exposure of 22 ks (see Table 1). The XRT (Burrows et al. 2005) data were processed with the XRTDAS software package (v. 2.5.1) developed at the ASI Science Data Center and distributed by the NASA High Energy Astrophysics Archive Research Center within the HEASoft package (v. 6.6). Event files were calibrated and cleaned with standard filtering criteria with the xrtpipeline task using the latest calibration files available in the Swift CALDB.

The XRT data set was taken entirely in Windowed Timing mode. For the spectral analysis, we selected events in the energy range 2–10 keV with grades 0–2. The source events were extracted within a box of 40 × 40 pixels (∼94 arcsec), centered on the source position and merged to obtain the average spectrum of Cen A during the XRT campaign. The background was estimated by selecting events in a region free of sources. Ancillary response files were generated with the xrtmkarf task applying corrections for the point-spread function losses and CCD defects.

The combined January X-ray spectrum is highly absorbed. Hence, it was fitted with an absorbed power-law model with a photon spectral index of 1.98 ± 0.05, an intrinsic absorption column of (9.73 ± 0.26) × 10²² cm⁻², in excess of the Galactic value of 8.1 × 10²⁰ cm⁻² in that direction (Kalberla et al. 2005). The average absorbed flux over the 2–10 keV energy range is (4.94 ± 0.05) × 10⁻¹⁰ erg cm⁻² s⁻¹, which corresponds to an unabsorbed flux of 9.15 × 10⁻¹⁰ erg cm⁻² s⁻¹.

The XRT spectrum included in the broadband SED was binned to ensure a minimum of 2500 counts per bin and was de-absorbed by forcing the absorption column density to zero in XSPEC and applying a correction factor to the original spectrum equal to the ratio of the de-absorbed spectral model over the absorbed model.

We used data from the Burst Alert Telescope (BAT) on board the Swift mission to derive a 14–195 keV spectrum of Cen-A contemporary to the LAT observations. The spectrum has been extracted following the recipes presented in Ajello et al. (2008, 2009b). This spectrum is constructed by calculating weighted averages of the source spectra extracted over short exposures (e.g., 300 s). These spectra are accurate to the mCrab level and the reader is referred to Ajello et al. (2009a) for more details.

The LAT spectrum of the core of Cen A is shown in Figure 3, extrapolated into the TeV regime, along with the HESS spectrum observed between 2004 and 2008 (Aharonian et al. 2009). Also shown is the HESS spectrum scaled down by its source flux normalization uncertainty. It seems that the LAT spectrum, with its statistical and systematic errors and extrapolated to higher energies, is just barely consistent with the HESS spectrum. However, one should keep in mind that the HESS and LAT spectra presented in this figure are not simultaneous, although the HESS data did not show any signs of variability. Additionally, γγ absorption makes it unlikely that the HESS and LAT emission originate from the same region, which is explored below (Section 5.2).

Since the cores of many blazars have been shown to be γ-ray loud, it is plausible to assume that the radio core is the source of the central γ-rays from Cen A. However, one should keep in mind that the error circles of the Fermi and HESS (Aharonian et al. 2009) observations are consistent with emission from the inner lobes, jet and radio core, so that these other regions could be sources of γ-rays as well. We construct the SED for the resolved sub-arcsec and arcsec-scale core as compiled in Meisenheimer et al. (2007), including their mm/IR/optical observations from 2003 to 2005. They have compiled additional points from the 1990s and have applied an extinction correction of A_V = 9 mag to the optical and IR data. We plot historical data in the X-ray (Evans et al. 2004), hard X-rays (Kinzer et al. 1995; Rothschild et al. 2006; Markowitz et al. 2007), COMPTEL (Steinle et al. 1998), and the HESS TeV γ-rays (Aharonian et al. 2009). The Swift XRT and BAT as well as Suzaku data, corrected for Galactic dust as well as dust in NGC 5128 and discussed in Section 4, were collected during time intervals which overlap with much of the Fermi-LAT data. Furthermore, we add the simultaneous radio data of the TANAMI VLBI jet components. All these are shown in Figure 5. The LAT data points in Figure 5 are from model B and include statistical errors only.

Single-zone synchrotron/synchrotron self-Compton (SSC) models have been very successful in explaining the multiwavelength (including γ-ray) emission from BL Lac objects (e.g., Bloom & Marscher 1996; Tavecchio et al. 1998). If FRIs are the misaligned counterpart to BL Lac objects, one would expect this model to apply to them as well. In the synchrotron/SSC scenario the low energy, radio through optical emission originates from nonthermal synchrotron radiation from a relativistically moving spherical homogeneous plasma blob, and the X-ray through VHE γ-rays from the Compton scattering of that synchrotron radiation by electrons in the same blob. The one-zone SSC model has successfully fit the emission from the other Fermi-LAT detected FRIs, Perseus A (NGC 1275; Abdo et al. 2009b) and M87 (Abdo et al. 2009d), and has been successfully applied to previous observations of Cen A (Chiaberge et al. 2001). Here, we apply the single-zone SSC model to fit the recent multiwavelength observations of Cen A, particularly the Fermi-LAT and HESS emission.

One can show (see the Appendix) that, on the assumption that all of the emission in the multiwavelength SED of the Cen A core originates from the same region in a single-zone SSC model, γγ absorption gives the constraint on the Doppler factor

$$\begin{eqnarray} &&\delta _D \ge 5.3\, \end{eqnarray} \tag{ 1 }$$

where the Doppler factor is δ_D = [Γ_j(1 − β_jμ)]⁻¹, the bulk Lorentz factor of the jet is Γ_j = (1 − β²_j)^−1/2, β_jc is the speed of the jet, and θ = cos⁻¹μ is the angle of the jet with respect to our line of sight. Solving for Γ_j in terms of δ_D,

$$\begin{eqnarray} &&\Gamma _j = \frac{1 \pm \sqrt{1 - (1-\mu ^2)(1+\delta _D^2\mu ^2)} }{ \delta _D(1-\mu ^2) }. \end{eqnarray} \tag{ 2 }$$

In order for Γ_j to be real, the quantity under the radical must be positive, which implies

$$\begin{eqnarray} &&\delta _D \le \frac{1}{\sqrt{1-\mu ^2}}\ = \csc \theta \end{eqnarray} \tag{ 3 }$$

(e.g., Urry & Padovani 1995). For Cen A, estimates of θ vary from 15° to 80° (see Section 2). For the least constraining value, i.e., θ = 15°,

$$\begin{equation} \delta _D \le 3.8. \end{equation} \tag{ 4 }$$

Clearly, the constraints (1) and (4) are not compatible. Thus, if the radio through Fermi γ-ray data presented in Figure 5 is synchrotron and SSC emission originating from the same region of the jet, then the HESS emission cannot originate from the same part of the jet. Note also that the HESS emission cannot originate from the same region of the jet, yet be emitted from a different mechanism from SSC (say, Compton-scattered accretion disk or dust torus radiation) because even this radiation would be subject to the same γγ attenuation by synchrotron photons.

If the VLBI jet core is assumed to be the origin of the high-energy emission, the TANAMI core-size measurement can be used to calculate an upper limit on the size of the γ-ray emitting region of <0.017 pc = 5.3 × 10¹⁶ cm (Section 3.1). This is consistent with the VLBI observations of Kellermann et al. (1997) and Horiuchi et al. (2006) and with a variability timescale of t_v ∼ 1 day, given that the emitting region radius R_b is constrained by the variability time by R_b = δ_D c t_v. This variability timescale is consistent with the Suzaku observations, although it is not clear that the Suzaku X-rays come from the same region as the γ-rays. Using this variability timescale and Equations (A1) and (A2), one gets δ_D = 0.6 and B = 6 G. More precise modeling (Finke et al. 2008) gives the green curve in Figure 5 with the model parameters in Table 2. This curve demonstrates that the emission can be fit with a Doppler factor of unity. This is consistent with a Lorentz factor of unity or 7, a degeneracy which can be seen in Equation (2). A stationary, nonrelativistic jet can explain the entire SED, except the VHE emission. This fit is similar to the synchrotron/SSC fit by Meisenheimer et al. (2007) who fit similar data. We further note that a small change in δ_D leads to a large change in the Lorentz factor. This, combined with the uncertainty in the inclination angle leads to the fact that the Lorentz factor is not well constrained by modeling. We also note that VLBI observations show apparent motion with β_j,app ∼ 0.1 (Tingay et al. 1998), implying Γ_j ≳ 1.005, which is also not a particularly strong constraint.

What if the hard X-ray emission originates from thermal Comptonization near the disk, and not from jet emission? If we assume that the rest of the high-energy SED is from the jet, then ^SSC_pk = 1 and f^SSC_pk = 9 × 10⁻¹¹ erg s⁻¹ cm⁻², so that Equations (A1) and (A2) give δ_D = 2.4 and B = 0.6 G for a variability timescale of 1 day. More detailed modeling gives the violet curve seen in Figure 5 with the parameters in Table 2. The larger Doppler factor needed for this model requires a smaller angle to the line of sight. The Lorentz factor is again not strongly constrained and could plausibly be as high as Γ_j ∼ 8 and still provide a good fit, although this would push the parameters to their extremes. This model still underpredicts the HESS data.

Jet powers for these models are given in Table 2. The proton and pair content of the jet are not well known, so the total jet power presented in Table 2 is for a pure pair jet and can be considered a lower limit. Even with 10–100 times more energy in ions than leptons, the absolute jet power is far below the Eddington luminosity for a 10⁸ M_☉ black hole (L_Edd = 1.3 × 10⁴⁶ erg s⁻¹). For the green curve, the parameters assume Γ = 7. The jet power needed to inflate the giant lobes of Cen A in their lifetime, as inferred from the radio spectral break, is 10⁴³ erg s⁻¹ (Hardcastle et al. 2009). This value is approximately consistent with the green curve model presented in Figure 5.

A possible explanation for the HESS observations is that the TeV emission is produced by another blob. We show in Figure 5 (brown curve) that another synchrotron/SSC-emitting blob can produce the HESS emission without overproducing any of the other multiwavelength data. The parameters for this blob are given in Table 2, although this fit is not unique and many parameter sets would fit the HESS data and not contribute at other wavelengths. Other possible origins for the VHE emission are discussed in Section 6.1.

Unification models for blazars suggest that FRII galaxies are FSRQs with the jet viewed away from our line of sight, and similarly FRIs are the parent population of BL Lac objects. In this case, one would expect nonthermal emission from the cores of radio galaxies de-beamed compared to blazars. However, the cores of FRIs seem brighter than what is expected from simply de-beamed emission from BL Lac objects, which implies that the radio galaxy core emission is from a slower region than that of BL Lac objects, since the beaming angle is related to the bulk Lorentz factor by θ_b ∼ 1/Γ_j. There are (at least) two possible explanations for this: (1) the jet consists of a faster "spine," which is responsible for the on-axis blazar emission, inside a slower outer "sheath," which would be responsible for the off-axis emission seen in the cores of radio galaxies (e.g., Chiaberge et al. 2000); and (2) a decelerating jet model where the on-axis blazar emission is produced by a faster flow closer to the black hole and the off-axis γ-rays seen in radio galaxies are produced by the slower flow farther out along the jet (Georganopoulos & Kazanas 2003).

As an example, we provide a fit to the Cen A SED using this decelerating flow, as the blue curve in Figure 5. In this model, the high-energy emission is due to upstream Compton scattering of synchrotron photons produced in the slower part of the flow being scattered by energetic electrons in the faster, upstream part of the flow. The jet starts with a bulk Lorentz factor Γ_j,max = 5 and decelerates down to Γ_j,min = 2 in a length of l = 3 × 10¹⁶ cm. The injected power-law electron distribution, n(γ) ∝ γ^−p, has an index p = 3.5 and extends from γ_min = 1600 to γ_max = 10⁷, and the magnetic field at the inlet is B = 0.3 G. Jet powers for this model are similar to the one-zone SSC model fits presented in Section 5.2, although this decelerating model fit is particle dominated rather than magnetic field-dominated. We also note that the parameters used in this fit are not unique.

Since the single blob model does not seem to be able to reproduce the broadband SED of Cen A, could something else be the origin of the VHE γ-rays? We have already shown that another blob emitting synchrotron and SSC radiation could explain the HESS emission without overproducing any of the other data (Figure 5, brown curve). Lenain et al. (2008) have presented a model with multiple blobs, moving at different angles to the line of sight from a large opening angle, to M87 and Cen A (among other objects). This model does seem to be able to explain this SED (Lenain et al. 2009). It has also been suggested that absorbed γ-rays create e⁺–e⁻ pairs, creating an isotropic halo of electrons in the interstellar medium which Compton-scatter the host galaxy's starlight, and lead to isotropically produced γ-rays (Stawarz et al. 2003, 2006). The HESS data do seem to match the Stawarz et al. (2006) predictions Cen A with a galactic magnetic field of 10 μG. Compton-scattering off of leptons accelerated by the supermassive black hole magnetosphere, similar to particle acceleration in pulsars, has been proposed to explain the VHE γ-ray radiation from M87 (Neronov & Aharonian 2007). This could also explain the HESS data from Cen A separate from the other multiwavelength emission. As we have noted earlier, what we designate in this paper as the γ-ray "core" actually encompasses the radio core, jet, and inner lobes of Cen A. This is also true for the HESS emission. Croston et al. (2009) have noted that a shock front observed in X-rays in the southwest inner lobe could be a source of TeV γ-rays, which seems consistent with these observations.

Finally, we note that the SED presented here is constructed from non-simultaneous data. Although Fermi and HESS γ-rays do not show appreciable variability, they could still be variable on longer timescales. Perhaps for a good, simultaneous multiwavelength SED, a one-zone synchrotron/SSC model could provide a good fit to all of the data. Probably the best way to discriminate between the above models—simple SSC, Compton-scattering emission from a pair halo, multiple blobs, etc.—is correlated variability between LAT γ-rays and other bandpasses. This emphasizes the importance of simultaneous multiwavelength data.

The Auger Observatory results indicate that some UHECRs could be originating from Cen A (see Section 2). The UHECRs could interact with photons at the source and in the extragalactic background light leading to an observable signature in the HESS band. If the VHE γ-rays originate from cosmic rays, this could account for the discrepancy between HESS and Fermi γ-rays. Based on the green curve fit presented in Figure 5, we can analyze whether it is plausible for cosmic rays to originate from Cen A, keeping in mind that the parameters of that model are not well constrained (Section 5.2).

The maximum energy to which cosmic rays can be accelerated is limited by the size scale of the emitting region and the highest energy they can reach before they are cooled. The former constraint implies that the highest energy a cosmic ray can reach is

$$\begin{equation} E_Z = 4\times 10^{19}\ \frac{Z}{\phi }\ \left(\frac{B}{6.2\ G}\right)\ \left(\frac{t_{v}}{10^5\ \mathrm{s}}\right)\ \delta _D\ \left(\frac{\Gamma _j}{7.0}\right)\ \mathrm{eV}{,} \end{equation} \tag{ 5 }$$

and the latter implies

$$\begin{equation} E_Z = 5.7\times 10^{20}\ \sqrt{\frac{Z}{\phi }}\ \left(\frac{A}{Z} \right)^2\ \left(\frac{B}{6.2\ G}\right)^{-1/2}\ \left(\frac{\Gamma _j}{7.0}\right)\ \mathrm{eV}\ \end{equation} \tag{ 6 }$$

(e.g., Hillas 1984; Dermer & Razzaque 2010), where ϕ ≈ 1 is the acceleration efficiency factor, e is the elementary charge, Z is the atomic number, and A the atomic mass of the ion. Note that these timescales, and all quantities expressed above, are in the frame comoving with the blob, although for the particular model considered here δ_D = 1; so this is not important.

We assume that all parameters have values from the green curve model. Thus, it seems for this model that it is unlikely that protons will be accelerated to energies above ≈4 × 10¹⁹ eV, although it is possible for heavier ions to be accelerated this high before they are disintegrated by interacting with infrared photons from the Cen A core. The threshold energy for photomeson interaction with peak synchrotron photons is similar to E_Z. This process could create observational signatures from secondary emission (e.g., Kachelrieß et al. 2009), as well as convert protons to neutrons, which can escape as cosmic rays (Dermer et al. 2009). Again, we note that this result is strongly model-dependent, and the parameters of this model are not strongly constrained, so this limit should not be taken too seriously. For example, a small change in the Doppler factor would have little effect on the model fit but would require a large change in the bulk Lorentz factor, Γ_j. A large change in Γ_j would significantly affect the highest energy to which particles could be accelerated, as seen in Equations (5) and (6). Furthermore, if we are viewing a slower sheath, UHE cosmic rays could be accelerated in the faster spine beamed away from our line of sight, which could have significantly different parameters. Acceleration of protons up to 10²⁰ eV requires jet powers of P_j ≳ 10⁴⁶ erg s⁻¹, which may take place in occasional flaring activities in Cen A (Dermer et al. 2009).