EVIDENCE FOR GAMMA-RAY HALOS AROUND ACTIVE GALACTIC NUCLEI AND THE FIRST MEASUREMENT OF INTERGALACTIC MAGNETIC FIELDS

Intergalactic magnetic fields (IGMFs) had not been measured until now, despite their importance for gamma-ray and cosmic-ray astronomy and their likely connection to the primordial fields that could have seeded the stronger magnetic fields observed in galaxies, Sun, and Earth. This is because IGMFs are too small for conventional astronomical probes such as Zeeman splitting or Faraday rotation. Unlike the fields in galaxies, which are believed to have been amplified by the dynamo action of the large-scale convective motions of gas, the fields in voids remain low, close to their primordial values modified only by the relatively small contribution of the fields leaking out of galaxies (Kronberg 1994; Grasso & Rubinstein 2001; Widrow 2002; Kulsrud & Zweibel 2008). The observational and theoretical upper bounds on IGMFs constrain their magnitudes to be below 10⁻⁹ G (Barrow et al. 1997), whereas any value above ∼10⁻³⁰ G is sufficient to explain the ∼μG Galactic magnetic fields' generation by the dynamo mechanism (Davis et al. 1999).

One can detect such extremely weak fields using high-energy gamma rays (Aharonian et al. 1994; Plaga 1995). Very energetic photons emitted from active galactic nuclei (AGNs) or other strong sources produce pairs of electrons and positrons in their interactions with the extragalactic background light (EBL). These pairs upscatter the cosmic microwave background photons to high energies, giving rise to an electromagnetic cascade, and the photons from the cascade are detected by gamma-ray telescopes such as Fermi. Since the trajectories of electrons and positrons in the cascade are affected by magnetic fields, a gamma-ray image of AGNs is expected to exhibit a halo of secondary photons around a bright central point-like source (Aharonian et al. 1994; Dolag et al. 2009; Neronov & Semikoz 2009). The central image is expected to be composed of photons emitted directly from the source with energies below the pair production threshold. In addition, delays in arrival times of the secondary photons can be used to probe IGMFs (Plaga 1995; Ando 2004; Murase et al. 2008). Finally, at TeV energies, the secondary photons produced in interactions of cosmic rays with EBL may have already been observed by the air Cherenkov telescopes (Essey & Kusenko 2010; Essey et al. 2010).

Thus far, in TeV range, HEGRA (Aharonian et al. 2001) and MAGIC (Aleksic et al. 2010) did not detect any halo component of two bright blazars, Mrk 501 and Mrk 421, and they set upper limits on the flux. In particular, the analysis of MAGIC using gamma rays above 300 GeV excludes some range of IGMFs between 4 × 10⁻¹⁵ and 10⁻¹⁴ G. Very recently, IGMFs above 3 × 10⁻¹⁶ G were proposed as an explanation of non-observation by Fermi of several AGNs known to be bright TeV sources (Neronov & Vovk 2010; see also Tavecchio et al. 2010).

In this Letter, we present evidence of extended images and of IGMFs at 3.5σ level, based on gamma-ray data collected by the Large Area Telescope (LAT) on board Fermi, in the energy range between 1 GeV and 100 GeV. It is consistent with pair-halo scenario with IGMF, B_IGMF ≈ 10⁻¹⁵ G. The knowledge on IGMF will facilitate the future gamma-ray and cosmic-ray astronomy, and it will open a new window on the origin of cosmological magnetic fields (Cornwall 1997), inflation (Turner & Widrow 1988; Diaz-Gil et al. 2008), and the phase transitions in the early universe (Vachaspati 1991, 2001; Baym et al. 1996).

The individual photon data as well as the 11 month source catalog (Abdo et al. 2010a) are now publicly available.⁴ Among ∼700 AGNs in the Fermi AGN catalog (Abdo et al. 2010b), we select 170 AGNs that are detected at more than 4.1σ in the highest-energy band, 10–100 GeV, and located at high Galactic latitudes, |b|>10°. These sources are likely to have a hard spectrum and produce a large number of TeV primary photons, which is necessary for the appearance of the secondary halo. Although each individual AGN produces too few photon counts, especially in the highest-energy band, one can dramatically improve the statistics by stacking all of these 170 AGN maps. We perform the analysis in three separate energy bands: 1–3 GeV, 3–10 GeV, and 10–100 GeV, which allows us to study the energy dependence of the halos. To obtain source and model maps, we use official Science Tools made publicly available by the Fermi team. The photons that we use in the AGN analysis are collected between 239,557,417 s and 268,416,079 s in the mission elapsed time (MET), and they are of "Diffuse" class.

We use locations of AGNs from the 11 month source catalog, i.e., those obtained solely by the gamma-ray data. This does not introduce any significant uncertainty of the stacked images, because the localization accuracy using gamma rays is typically much better than the size of point-spread function (PSF), especially for hard AGN (Abdo et al. 2010b).

Figure 1 shows the gamma-ray count maps of stacked 170 AGNs and the "best-fit" point-source model generated with the Fermi Science Tools as well as point-source catalog, smeared only by the PSF of LAT (we use the latest "Pass6 version 3" instrument response function of LAT). It is evident that the counts map and the model map are not consistent with each other, especially in the 10–100 GeV range.

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We have performed maximum likelihood analysis assuming that, in addition to the central point sources and diffuse backgrounds (Strong et al. 2004; Abdo et al. 2009, 2010d), there is a third component, namely, the halo component, whose spatial extent is given by the Gaussian distribution:

$$\begin{equation} P_{\rm halo}\big(\theta ^2|\theta _{\rm halo}^2\big) = \frac{2}{\pi \theta _{\rm halo}^2} \exp \left({-\frac{\theta ^4}{\pi \theta _{\rm halo}^4}}\right), \end{equation} \tag{ 1 }$$

where θ is the angle from the map center and θ²_halo is the mean of θ² over this distribution function, θ²_halo ≡ 〈θ²〉. We fit the histogram of photon counts as a function of θ² read from the maps by minimizing

$$\begin{equation} \chi ^2 \,{=}\, \sum _i \!\frac{1}{N_i}\! \left[ N_{\rm psf} P_{\rm psf}\big(\theta _i^2\big) \,{+}\, N_{\rm halo} P_{\rm halo}\big(\theta _i^2 | \theta _{\rm halo}^2\big) \,{+}\, N_{{\rm bg},i} \,{-}\, N_i\right]^2\!, \end{equation} \tag{ 2 }$$

where N_psf, N_halo, and θ_halo are treated as free parameters. The index i refers to the ith bin, N_i is the total number of events in this bin, P_psf is the normalized PSF, and N_bg,i is the events due to diffuse backgrounds. We fix the backgrounds to the values at θ² = 2.025–2.25 deg² and 0.233–0.25 deg² for 3–10 GeV and 10–100 GeV, respectively, in the simulated maps, assuming that they are homogeneous. Thus, N_psf and N_halo are the total numbers of photons in the map attributed to the point source and the halo, respectively, and θ_halo is the apparent angular extent of the halo component.

The inclusion of the halo component improves the fit significantly at high energies. The minimum χ² over degree of freedom (ν) is χ²_min/ν = 18.8/19 and 13.3/12 for 3–10 GeV and 10–100 GeV, respectively. In contrast, the "best-fit" point-source model, where N_psf and the background amplitude are treated as free parameters, gives χ²_min/ν ≃ 66/20 and 62/13 for 3–10 GeV and 10–100 GeV, respectively. This clearly shows that, even though we stack many AGNs, this simple Gaussian halo model gives a very good fit to the data. The surface brightness profiles dN/dθ² of the best-fit halo model are juxtaposed with the data points in Figure 2.

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In Figure 3(a), we show the allowed regions of θ_halo and f_halo at 68% and 95% confidence levels. Here, f_halo is the fraction of the halo photons, i.e., f_halo ≡ N_halo/(N_psf + N_halo). The best-fit values and 1σ statistical errors for these parameters are θ_halo = 049 ± 003 and f_halo = 0.097 ± 0.014 for 3–10 GeV, and θ_halo = 026 ± 001 and f_halo = 0.20 ± 0.02 for 10–100 GeV. For the lowest energy band, 1–3 GeV, only an upper limit on f_halo is obtained, which is f_halo < 0.046 at 95% confidence level.

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4.1. Dependence on Redshifts and Spectra

4.2. Quantitative Estimate of Instrumental Effects

The two independent tests described above give one confidence that instrumental effects cannot account for all the observed halos. Neronov et al. (2010) repeated our stacking analysis and found the same anomalous excess in the 10–100 GeV band. However, they argue, "most, if not all, of this excess is due to the imperfect knowledge of the PSF for the back-converted gamma rays." This argument is based on the observation that the extent of the Crab pulsar is the same as that of the AGN, and the excess is different between front and back-converted photons. While we agree with Neronov et al. (2010) that it is good to perform other independent tests, we shall show that their arguments fail to exclude the physical halos and overturn the statistical significance of redshift and spectrum tests discussed above. To this end, we have performed an alternative analysis, using the observed Crab profile as a calibrated PSF template. This confirms our initial conclusion and demonstrates that the halos are indeed physical, at 3.5σ level. For the analysis, we mainly focus on the 3–10 GeV band, because the data have more statistical power than in 10–100 GeV as well as the pre-launch PSF is better calibrated at lower energies (Burnett et al. 2009).

In Figure 4, we show surface brightness profiles of our nearby and distant samples of AGNs, where one can see clear difference between the two populations of AGNs. In the same figure, we also plot the profile of Crab,⁵ which appears to be more consistent with the distant AGN than the nearby set. The backgrounds have been subtracted from the sources; they were estimated based on the large angular regions, where the contributions from both the point sources and halos are expected to be small. We note that the excess of AGN over Crab seen in Figure 4 was not found by Neronov et al. (2010), who analyzed the data in the 10–100 GeV band, which, as mentioned above, lacks statistical power in comparison with the 3–10 GeV band used here.

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To proceed with a quantitative analysis, we use this Crab profile as a PSF model in this energy range and regard Crab statistical errors as systematic uncertainties of PSF. For example, in angular bin θ² = 0.225–0.27 deg², Fermi-LAT received 22 photons from Crab, and the background is estimated to be 1.9. This is interpreted as 24% systematic uncertainty of PSF in this particular bin. This method is independent of our previous analysis and is free of any uncertainties related to pre-launch PSF calibration.

A possible source of additional systematic uncertainties is an energy dependence of PSF. In general, gamma-ray spectra are different between AGNs and pulsars, and so are expected PSF sizes. However, the detected spectra of both stacked AGN and Crab are well approximated by a power law with similar indices; dN/dE_γ ∝ E^−2.2_γ for nearby AGN (z < 0.5) and ∝E^−2.4_γ for Crab, where E_γ is the gamma-ray energy. To probe the spectrum dependence of PSF even further, we compare the brightness profiles of simulated maps of nearby/hard and distant/soft AGNs. Both profiles look very similar, while the profile of hard AGNs is slightly less extended. In angular bin θ² = 0.225–0.27 deg², these AGN profiles differ only by 4.4%, which is negligible compared with 24% uncertainty of the Crab-based PSF due to Crab statistics. Finally, we note that the width of the PSF decreases with energy. We verified this by comparing Crab images in 3–5 GeV and 5–10 GeV bands and confirming that the former is broader than the latter. Since the spectrum of the nearby AGN is harder than that of Crab, the instrumental systematics can only make the AGN image sharper, not broader, but the opposite is inferred from Figure 4. Therefore, it is conservative to ignore the small systematic uncertainties due to spectrum dependence of PSF.

Adopting the Crab profile as a calibrated PSF, we quantitatively investigate the excess of nearby/hard AGN profiles identified at θ² ≳ 0.2 deg² in Figure 4. The PSF and AGN profiles are normalized to each other such that they give the same brightness in the innermost angular bin, θ² < 0.045 deg². The excess photon counts are N^(z<0.5)_excess(θ²>0.225 deg²) = 125 ± 30(stat) ± 21(sys). By taking square root of quadratic sum of the statistical and systematic errors as a total error, we find that this excess is of 3.5σ significance. For the distant/soft AGN population, on the other hand, the excess is N^(z>0.5)_excess(θ²>0.225 deg²) = −5 ± 27(stat) ± 29(sys), consistent with null hypothesis. Dividing N_excess by the total number of PSF counts, we obtain the values of f_halo for both AGN populations:

$$\begin{equation} f_{\rm halo} = \left\lbrace \begin{array}{@{}ll} 0.073 \pm 0.017({\rm stat}) \pm 0.012({\rm sys}), & \mbox{for } \ z<0.5,\\ -0.002 \pm 0.011({\rm stat}) \pm 0.012({\rm sys}), & \mbox{for } \ z>0.5.\\ \end{array} \right. \end{equation} \tag{ 3 }$$

Clearly, this conclusion using the Crab-calibrated PSF agrees with that based on the pre-launch calibration.

One can go even further and design two separate Crab-calibrated PSFs for two classes of photons, namely, those that convert in the front layer and those in the back layer of the detector. While all of these photons must be used in an analysis, allowing for the differences in PSF offers yet another opportunity to find and eliminate some unexpected instrumental effects. To this end, we introduce another statistical quantity δ_excess ≡ N^front_excess/N^front_psf + N^back_excess/N^back_psf, where all the N's with self-explanatory superscripts and subscripts refer to photon counts at θ²>0.225 deg² after the homogeneous backgrounds were subtracted. This way, we explicitly include any PSF differences between front and back-converted photons. The meaning of δ_excess is clear: a value consistent with zero corresponds to the absence of physical halos. We obtain δ^(z<0.5)_excess = 1.4 ± 0.5(stat) ± 0.2(sys), 2.7σ away from the null hypothesis. We also find that the individual values of δ_excess for the front and back photons are consistent with each other, within errors.

We have also performed the same analysis for 10–100 GeV. Here, we renormalized the Crab and AGN profiles using θ² < 0.025 deg² bin and counted the excess photons over Crab-calibrated PSF in θ² = 0.075–0.25 deg². We obtain N^(z<0.5)_excess = 19 ±  13(stat) ±  15(sys) and N^(z>0.5)_excess = −3.6 ±  9.1(stat) ±  8.2(sys). The excess for nearby/hard AGNs is found significant at 1σ level.

We interpret the size of the halo θ_halo of a few tenths of degree, in terms of the secondary photon model, especially parameters of IGMF. A simple analytic model gives the following relation between these quantities (Neronov & Semikoz 2009):

$$\begin{equation} \theta _{\rm halo} = \left\lbrace \begin{array}{@{}l} 5\mbox{$^\circ $}(1+z)^{-2} \tau ^{-1} \left(\frac{E_\gamma }{10\, {\rm GeV}}\right)^{-1} \left(\frac{B_{\rm IGMF}}{10^{-15}\,{\rm G}}\right), \\ \qquad \mbox{for }\lambda _B \gg D_e, \\ 0\mbox{.\!\!^\circ $}4 (1+z)^{-1/2} \tau ^{-1} \left(\frac{E_\gamma }{10\, {\rm GeV}}\right)^{-3/4} \left(\frac{B_{\rm IGMF}}{10^{-15}\,{\rm G}}\right) \left(\frac{\lambda _B}{1\,{\rm kpc}}\right)^{1/2}, \\ \qquad \mbox{for }\lambda _B \ll D_e, \end{array} \right. \end{equation} \tag{ 4 }$$

where τ is the optical depth for the TeV photons that produce halo gamma rays, λ_B are the correlation length of IGMFs, and D_e is the energy-loss length of the electrons and positrons produced by primary TeV photons. Because the lower-energy secondary photons originate from the less energetic electrons and positrons that are deflected by larger angles in IGMF, one expects a larger halo size θ_halo at lower energy. As for the dependence on λ_B, if it is much longer than D_e, then the charged particles can be regarded as propagating in homogeneous magnetic fields (equivalent to infinite λ_B), and therefore, the deflection angle is given by the ratio of D_e and the Larmor radius. If λ_B is much smaller than D_e, on the other hand, then the electrons and positrons propagate by random walk, with deflections proportional to λ^1/2_B.

The halo size for the nearby AGN sample is θ_halo ≈ 05–08 (Figure 4). Assuming τ ∼ 1–10 and using an average redshift of the nearby AGN sample, 〈z〉 = 0.2, the measured extent of the halos is consistent with B_IGMF ≈ 10⁻¹⁵ G. This is the first measurement of the strength of IGMFs based on a positive detection. With the halo detection also in the 10–100 GeV band, we would be able to constrain the correlation length by investigating the energy dependence of θ_halo.

At the mean redshift of the nearby AGN sample, the observed halo size of ∼05–08 corresponds to 6–10 Mpc. There are no known astrophysical sources capable of producing images of such a large size. Therefore, we conclude that the halos of the secondary photons provide the only realistic explanation of the data.

S.A. was supported by Japan Society for Promotion of Science and partially by NASA through the Fermi GI Program grant NNX09AT74G. A.K. was supported by DOE grant DE-FG03-91ER40662 and NASA ATP grant NNX08AL48G. A.K. thanks Aspen Center for Physics for hospitality.