Abstract
A new analysis of the data set from the Pierre Auger Observatory provides evidence for anisotropy in the arrival directions of ultra-high-energy cosmic rays on an intermediate angular scale, which is indicative of excess arrivals from strong, nearby sources. The data consist of 5514 events above 
with zenith angles up to 80° recorded before 2017 April 30. Sky models have been created for two distinct populations of extragalactic gamma-ray emitters: active galactic nuclei from the second catalog of hard Fermi-LAT sources (2FHL) and starburst galaxies from a sample that was examined with Fermi-LAT. Flux-limited samples, which include all types of galaxies from the Swift-BAT and 2MASS surveys, have been investigated for comparison. The sky model of cosmic-ray density constructed using each catalog has two free parameters, the fraction of events correlating with astrophysical objects, and an angular scale characterizing the clustering of cosmic rays around extragalactic sources. A maximum-likelihood ratio test is used to evaluate the best values of these parameters and to quantify the strength of each model by contrast with isotropy. It is found that the starburst model fits the data better than the hypothesis of isotropy with a statistical significance of 4.0σ, the highest value of the test statistic being for energies above 
. The three alternative models are favored against isotropy with 2.7σ–3.2σ significance. The origin of the indicated deviation from isotropy is examined and prospects for more sensitive future studies are discussed.
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1. The Search for UHECR Anisotropies
Identifying the sources of ultra-high-energy cosmic rays (UHECRs) has been a prime goal of particle astrophysics for decades. The challenge is considerable because the flux falls rapidly with increasing energy, and because UHECRs have a mixed mass composition (Aab et al. 2014a, 2016a), so some or all of them experience substantial magnetic deflections. Many scenarios have been proposed involving different populations of host galaxies. In this Letter, we investigate whether intermediate-scale99 anisotropies in UHECR arrival directions are associated with either or both of two prominent classes of extragalactic sources detected by Fermi-LAT—active galactic nuclei (AGNs) and starburst galaxies (SBGs)—using the gamma-ray luminosity or its surrogate (radio emission for SBGs) as a proxy for the relative luminosity of each source in UHECRs.
The rate of energy production of UHECRs determined from observations above 
is close to 
(Unger et al. 2015). Based on the Fermi-LAT survey, Dermer & Razzaque (2010) argued that AGNs and SBGs match such rates in the gamma-ray band. Due to the low density of the detected SBGs and AGNs, and the attenuation of UHECR flux with increasing distance (GZK effect, Greisen 1966; Zatsepin & Kuz'min 1966), a few objects would be expected to dominate the local flux, naturally producing an intermediate-scale anisotropy if these sources contribute a sufficient fraction of the UHECR flux.
The AGN and SBG populations are well-motivated physically. AGNs are favored source candidates because their jets and radio lobes satisfy the Hillas criterion for shock acceleration (Hillas 1984). SBGs—being loci of intense star formation—potentially have increased rates of extreme events associated with the deaths of short-lived, massive stars, such as gamma-ray bursts, hypernovae, and magnetars (see, e.g., Biermann et al. 2016; Perley et al. 2016). Their winds have also been proposed as possible reacceleration sites (Anchordoqui et al. 1999).
The analysis presented here is an advance in several ways. First, Fermi-LAT observations of gamma-rays from two extragalactic populations provide us with possible ansatzes for the relative UHECR fluxes from source candidates. That information makes the present analyses potentially more sensitive than previous studies based solely on the source direction. Second, thanks to our improved knowledge of the energy-dependent composition, we can now account more accurately for the relative attenuation of fluxes from distant sources. Third, thanks to the significant increase in exposure of the Pierre Auger Observatory with respect to previous analyses, the data can reveal more subtle patterns.
2. UHECR Data Set
UHECRs are detected at the Pierre Auger Observatory (Argentina, latitude 
S, longitude 
W; Aab et al. 2015c) through the extensive air showers they induce in the atmosphere. Air showers are detected on the ground with an array of 1600 water-Cherenkov detectors with a duty cycle of nearly 100%. Twenty-four fluorescence telescopes map, during dark nights (duty cycle of ∼15%), the longitudinal profile of each shower via the nitrogen fluorescence produced dominantly by the electromagnetic cascade. The combination of both techniques provides the array with an energy scale insensitive to primary mass assumptions and air-shower simulation uncertainties. The systematic uncertainty in the energy scale is estimated to be 14% (Verzi 2013).
Events above 
recorded between 2004 January 1 and 2017 April 30 are used in this analysis. Above 
, both "vertical showers" (zenith angle 
; Abraham et al. 2010) and "inclined showers" (
; Aab et al. 2014b) trigger the array of detectors with 100% efficiency, the average angular resolution being below 1° and the statistical energy resolution being better than 12%.
Combining the vertical and inclined data sets, including unfolding correction factors as done in Aab et al. (2015a), enables sky coverage over the decl. range 
. Using the same selection criteria as in Aab et al. (2015b), the total exposure for the period considered here is 
.
3. Source Selection and UHECR Sky Models
3.1. Extragalactic Gamma-Ray Populations
We extract our list of gamma-ray AGNs (γAGNs hereafter) from the 2FHL catalog (Ackermann et al. 2016), which includes 360 sources detected by Fermi-LAT above 
. We study radio-loud objects within a 
radius, yielding 17 blazars and radio galaxies. Their 50 GeV–2 TeV integral flux is used as a proxy for the UHECR flux. Given the distance of these objects, the gamma-ray absorption by the extragalactic background light (e.g., Domínguez et al. 2011) is small.
The detections of seven SBGs have been reported using Fermi-LAT data: NGC 253, M82, NGC 4945, NGC 1068 (Ackermann et al. 2012), NGC 2146 (Tang et al. 2014), Arp 220 (Peng et al. 2016), and Circinus (Hayashida et al. 2013). Their gamma-ray luminosity has been shown to scale almost linearly with their continuum radio flux (Ackermann et al. 2012). We thus adopt as a proxy for the UHECR flux of SBGs their continuum emission at 
for which a larger census exists.
We select the 23 SBGs with a flux larger than 
among the 63 objects within 
searched for gamma-ray emission by Ackermann et al. (2012). Due to the possible incompleteness of that list near the Galactic plane (
) and in the southern sky (
), relevant SBGs could be missing from our selection. However, we checked that our conclusions remain unchanged:100
(a) using all 63 objects listed in Ackermann et al. (2012), (b) using the catalog from Becker et al. (2009) with 32 SBGs above 
, (c) adding the Circinus SBG absent from (a) and (b), (d) using only the six SBGs reported in the 3FGL (NGC 253, M82, NGC 4945, NGC 1068, Circinus, NGC 2146; Acero et al. 2015) and their 
integral flux as a UHECR proxy.
3.2. X-Ray and Infrared Samples
Following previous searches (Aab et al. 2015b), we additionally study two flux-limited samples: Swift-BAT sources up to 
, above a flux of 13.4 × 10−12 erg cm−2 s−1, and sources from the 2MASS redshift survey (2MRS catalog; Huchra et al. 2012) beyond 
, effectively taking out the Local Group as in Erdoǧdu et al. (2006). We use the 
flux and K-band flux corrected for Galactic extinction as UHECR proxies for each of these surveys.
The X-ray sky observed by Swift-BAT is dominated in flux by the nearby Centaurus A, often considered as a prime UHECR source candidate (e.g., Romero et al. 1996; Wykes et al. 2017), with additional diffuse structures arising from both radio-loud and radio-quiet AGNs. This constitutes a different selection of AGNs from that performed for the γ-ray sample (radio-loud only), dominated by the radio galaxies Centaurus A and M87 within 
and by the blazars Mrk 421 and Mrk 501 within 
.
The 2MRS infrared intensity traces the distribution of extragalactic matter, and includes both star-forming galaxies and AGNs. It is dominated by contributions from the nearby SBG NGC 253, close to the South Galactic pole, M82, only observable from the northern hemisphere, along with M83 and NGC 4945, belonging to the same group of galaxies as Centaurus A. Strong emission from Centaurus A, as well as cumulated emission from fainter objects, e.g., in the Virgo cluster, constitute distinctive features of the 2MRS sky model with respect to the SBG one.
3.3. Impact of Attenuation
We account for attenuation of UHECRs from distant objects (GZK effect) using a data-driven scenario that reproduces the composition and spectral constraints obta-ined by the Observatory (Aab et al. 2017b). Assuming a homogeneous distribution of sources in the local universe, it was shown that an interpretation of the air-shower data using the EPOS-LHC interaction model together with a hard injection index 
at the sources (scenario A) best matches the data, accounting for propagation effects (Aloisio et al. 2012; Alves Batista et al. 2016). We also consider two other scenarios matching the data reasonably well: EPOS-LHC with 
(B) and Sibyll 2.1 with 
(C). These scenarios differ in the composition and maximum rigidities attainable at the sources. For each scenario and a chosen energy threshold, we evaluate the flux attenuation factor due to propagation for each source and correct its expected UHECR flux accordingly.
The two extragalactic gamma-ray populations under study and the relative weight of each source are provided in Table 1. The relative contributions accounting for the directional exposure of the Observatory are shown in the last column. Because SBGs are mostly nearby, attenuation from them is much less important than that from the more distant blazars in the γAGN sample. Taking into account attenuation, 
of the accumulated flux from SBGs emerges from a 
radius region, while the radius goes up to 
for γAGNs. For both the 2MRS and Swift-BAT flux-limited samples, the 
radius is 
.
4. Analysis and Results
4.1. Maximum-likelihood Analysis
We build the UHECR sky model as the sum of an isotropic component plus the anisotropic contribution from the sources. For the anisotropic component, each source is modeled as a Fisher distribution (Fisher 1953), the equivalent of a Gaussian on the sphere. Its distribution is centered on the coordinates of the source, the integral being set by its flux attenuated above the chosen energy threshold, and the angular width—or search radius101 —being a free parameter common to all sources. No shift of the centroid position is considered, avoiding dependence on any particular model of the Galactic magnetic field in this exploratory study. After mixing the anisotropic map with a variable fraction of isotropy, as in Abreu et al. (2010), the model map is multiplied by the directional exposure of the array and its integral is normalized to the number of events. The model map thus depends on two variables aimed at maximizing the degree of correlation with UHECR events: the fraction of all events due to the sources (anisotropic fraction) and the rms angular separation between an event and its source (search radius) in the anisotropic fraction.
We perform an unbinned maximum-likelihood analysis, where the likelihood (L) is the product over the UHECR events of the model density in the UHECR direction. The test statistic (TS) for deviation from isotropy is the likelihood ratio test between two nested hypotheses: the UHECR sky model and an isotropic model (null hypothesis). The TS is maximized as a function of two parameters: the search radius and the anisotropic fraction. We repeat the analysis for a sequence of energy thresholds.
For a given energy threshold, we confirmed with simulations that the TS for isotropy follows a 
distribution with two degrees of freedom, as expected (Wilks 1938), directly accounting for the fit of two parameters of the model. As in Aab et al. (2015b), we penalize the minimum p-value for a scan in threshold energy, by steps of 
up to 
, estimating the penalty factor with Monte-Carlo simulations. The p-values are converted into significances assuming 1-sided Gaussian distributions.
4.2. Single Population against Isotropy
Previous anisotropy studies (e.g., Aab et al. 2015b) have considered a scan in energy threshold starting at 
, where the observed flux reaches half the value expected from lower-energy extrapolations, but as shown in Figure 1, there is a maximum in the significance close to this starting point. Therefore we have evaluated the TS down to 
.
Figure 1. TS scan over the threshold energy for SBGs and AGNs (left) and Swift-BAT and 2MRS sources (right), including attenuation (lighter dashed lines) or not (darker solid lines).
Download figure:
Standard image High-resolution imageThe TS is maximum for SBGs above 
(894 events), with or without attenuation. For γAGNs, the TS is maximum above 
(177 events) after accounting for attenuation. As shown in Figure 1, left, attenuation mildly impacts SBGs that are nearby: we obtain TS = 24.9/25.5/25.7 for scenarios A/B/C, respectively. The impact is more pronounced for γAGNs, a larger attenuation reducing contributions from distant blazars: we obtain a maximum TS of 15.2/9.4/11.9 for scenarios A/B/C. Shifting the energy scale within systematic uncertainties (
) affects the maximum TS by ±1 unit for γAGNs, ±0.3 for SBGs.
Penalizing for the energy scan, the maximum TS obtained for SBGs and γAGNs within scenario A corresponds to 
and 
deviations from isotropy, respectively. As shown in Figure 2 (left), the maximum deviation for γAGNs is found at an angular scale of 
and a 
fraction of anisotropic events. For SBGs, a stronger deviation from isotropy is uncovered at an intermediate angular scale of 
and an anisotropic fraction of 
. The systematic uncertainty induced by the energy scale and attenuation scenario is at the level of 
for the anisotropic fraction and 0
5 for the search radius obtained with SBGs.
Figure 2. TS profile above 
(top) and 
(bottom) over the fit parameters for SBG-only and γAGN-only models (left) and for composite models including both SBGs and γAGNs with the same free search radius (right). The lines indicate the 
regions.
Download figure:
Standard image High-resolution imageFor Swift-BAT and 2MRS sources attenuated within scenario A, we obtain maximum TSs of 18.2 (
) above 
and 15.1 (
) above 
, respectively (see Figure 1, right). These correspond to values of the best-fit parameters of 
and 
for Swift-BAT, 
and 
for 2MRS.
The different degrees of anisotropy obtained from each catalog can be understood from Figure 3 (top) showing a UHECR hotspot in the direction of the Centaurus A/M83/NGC 4945 group. The γAGN model (
) and Swift-BAT model (
) are dominated by Centaurus A, which is 
and 
away from NGC 4945 and M83, respectively. The starburst model additionally captures the UHECR excess close to the Galactic South Pole, interpreted as contributions from NGC 1068 and NGC 253, yielding an increase in the anisotropy signal from 
to 
. Additional diffuse contributions from clustered sources in the 2MRS catalog are not favored by the data, resulting in the smaller deviation from isotropy.
Figure 3. Top to bottom: observed excess map; model excess map; residual map; model flux map, for the best-fit parameters obtained with SBGs above 
(left) and γAGNs above 
(right). The excess maps (best-fit isotropic component subtracted) and residual maps (observed minus model) are smeared at the best-fit angular scale. The color scale indicates the number of events per smearing beam (see inset). The model flux map corresponds to a uniform full-sky exposure. The supergalactic plane is shown as a solid gray line. An orange dashed line delimits the field of view of the array.(FITS files for this figures are available.)
Download figure:
Standard image High-resolution image4.3. Composite Models against Single Populations
To compare the two distinct gamma-ray populations above their respective preferred thresholds, we investigate a composite model combining contributions from γAGNs and SBGs, adopting a single search radius and leaving the fraction of events from each population free. The TS in this case is the difference between the maximum likelihood of the combined model and that of the null hypothesis of a single population at the selected energy threshold. The parameter added to the more complex model results in a 
distribution with one degree of freedom.
The best-fit anisotropic fractions obtained for the composite model (free search radius) are shown in Figure 2 (right). Above 
, the γAGN-only model is disfavored by 
relative to a combined model with a 
contribution from SBGs and 
contribution from γAGNs. Above 
, the TS obtained with the composite model is not significantly higher than what is obtained by either model. This is illustrated in Figure 2 (right) by the agreement at the 
level of a model including 
SBGs/
γAGNs with a model including 
SBGs/
γAGNs above 
.
As summarized in Table 2, composite models including SBGs and either 2MRS or Swift-BAT sources best match the data above 
for 9%–7% fractions of events associated to SBGs and 1%–3% to the flux-limited samples. A 
advantage is found for the composite models including SBGs with respect to the 2MRS-only and Swift-BAT-only models.
Table 1. Populations Investigated
| SBGs | l  ) |
b  ) |
Distancea (Mpc) | Flux Weight (%) | Attenuated Weight: A/B/C (%) | % Contributionb: A/B/C (%) |
|---|---|---|---|---|---|---|
| NGC 253 | 97.4 | −88 | 2.7 | 13.6 | 20.7/18.0/16.6 | 35.9/32.2/30.2 |
| M82 | 141.4 | 40.6 | 3.6 | 18.6 | 24.0/22.3/21.4 | 0.2/0.1/0.1 |
| NGC 4945 | 305.3 | 13.3 | 4 | 16 | 19.2/18.3/17.9 | 39.0/38.4/38.3 |
| M83 | 314.6 | 32 | 4 | 6.3 | 7.6/7.2/7.1 | 13.1/12.9/12.9 |
| IC 342 | 138.2 | 10.6 | 4 | 5.5 | 6.6/6.3/6.1 | 0.1/0.0/0.0 |
| NGC 6946 | 95.7 | 11.7 | 5.9 | 3.4 | 3.2/3.3/3.5 | 0.1/0.1/0.1 |
| NGC 2903 | 208.7 | 44.5 | 6.6 | 1.1 | 0.9/1.0/1.1 | 0.6/0.7/0.7 |
| NGC 5055 | 106 | 74.3 | 7.8 | 0.9 | 0.7/0.8/0.9 | 0.2/0.2/0.2 |
| NGC 3628 | 240.9 | 64.8 | 8.1 | 1.3 | 1.0/1.1/1.2 | 0.8/0.9/1.1 |
| NGC 3627 | 242 | 64.4 | 8.1 | 1.1 | 0.8/0.9/1.1 | 0.7/0.8/0.9 |
| NGC 4631 | 142.8 | 84.2 | 8.7 | 2.9 | 2.1/2.4/2.7 | 0.8/0.9/1.1 |
| M51 | 104.9 | 68.6 | 10.3 | 3.6 | 2.3/2.8/3.3 | 0.3/0.4/0.5 |
| NGC 891 | 140.4 | −17.4 | 11 | 1.7 | 1.1/1.3/1.5 | 0.2/0.3/0.3 |
| NGC 3556 | 148.3 | 56.3 | 11.4 | 0.7 | 0.4/0.6/0.6 | 0.0/0.0/0.0 |
| NGC 660 | 141.6 | −47.4 | 15 | 0.9 | 0.5/0.6/0.8 | 0.4/0.5/0.6 |
| NGC 2146 | 135.7 | 24.9 | 16.3 | 2.6 | 1.3/1.7/2.0 | 0.0/0.0/0.0 |
| NGC 3079 | 157.8 | 48.4 | 17.4 | 2.1 | 1.0/1.4/1.5 | 0.1/0.1/0.1 |
| NGC 1068 | 172.1 | −51.9 | 17.9 | 12.1 | 5.6/7.9/9.0 | 6.4/9.4/10.9 |
| NGC 1365 | 238 | −54.6 | 22.3 | 1.3 | 0.5/0.8/0.8 | 0.9/1.5/1.6 |
| Arp 299 | 141.9 | 55.4 | 46 | 1.6 | 0.4/0.7/0.6 | 0.0/0.0/0.0 |
| Arp 220 | 36.6 | 53 | 80 | 0.8 | 0.1/0.3/0.2 | 0.0/0.2/0.1 |
| NGC 6240 | 20.7 | 27.3 | 105 | 1 | 0.1/0.3/0.1 | 0.1/0.3/0.1 |
| Mkn 231 | 121.6 | 60.2 | 183 | 0.8 | 0.0/0.1/0.0 | 0.0/0.0/0.0 |
| γAGNs | ||||||
| Cen A Core | 309.6 | 19.4 | 3.7 | 0.8 | 60.5/14.6/40.4 | 86.8/56.3/71.5 |
| M87 | 283.7 | 74.5 | 18.5 | 1 | 15.3/7.1/29.5 | 9.7/12.1/23.1 |
| NGC 1275 | 150.6 | −13.3 | 76 | 2.2 | 6.6/6.1/7.5 | 0.7/1.6/1.0 |
| IC 310 | 150.2 | −13.7 | 83 | 1 | 2.3/2.4/2.6 | 0.3/0.6/0.3 |
| 3C 264 | 235.8 | 73 | 95 | 0.5 | 0.8/1.0/0.8 | 0.4/1.3/0.5 |
| TXS 0149 + 710 | 127.9 | 9 | 96 | 0.5 | 0.7/0.9/0.7 | 0.0/0.0/0.0 |
| Mkn 421 | 179.8 | 65 | 136 | 54 | 11.4/48.3/14.7 | 1.8/19.1/2.8 |
| PKS 0229-581 | 280.2 | −54.6 | 140 | 0.5 | 0.1/0.5/0.1 | 0.2/2.0/0.3 |
| Mkn 501 | 63.6 | 38.9 | 148 | 20.8 | 2.3/15.0/3.6 | 0.3/5.2/0.6 |
| 1ES 2344 + 514 | 112.9 | −9.9 | 195 | 3.3 | 0.0/1.0/0.1 | 0.0/0.0/0.0 |
| Mkn 180 | 131.9 | 45.6 | 199 | 1.9 | 0.0/0.5/0.0 | 0.0/0.0/0.0 |
| 1ES 1959 + 650 | 98 | 17.7 | 209 | 6.8 | 0.0/1.7/0.1 | 0.0/0.0/0.0 |
| AP Librae | 340.7 | 27.6 | 213 | 1.7 | 0.0/0.4/0.0 | 0.0/1.3/0.0 |
| TXS 0210 + 515 | 135.8 | −9 | 218 | 0.9 | 0.0/0.2/0.0 | 0.0/0.0/0.0 |
| GB6 J0601 + 5315 | 160 | 14.6 | 232 | 0.4 | 0.0/0.1/0.0 | 0.0/0.0/0.0 |
| PKS 0625-35 | 243.4 | −20 | 245 | 1.3 | 0.0/0.1/0.0 | 0.0/0.5/0.0 |
| I Zw 187 | 77.1 | 33.5 | 247 | 2.3 | 0.0/0.2/0.0 | 0.0/0.0/0.0 |
Notes.
aA standard, flat ΛCDM model (h0 = 0.7,
) is assumed. The distances of the SBGs are based on Ackermann et al. (2012), accounting for a small difference in h0. The distances of the γAGNs are based on their redshifts, except for the nearby Cen A (Tully et al. 2013).
b% contributions account for the directional exposure of the array.
Download table as: ASCIITypeset image
Table 2. Results—Scenario A
| Test | Null | Threshold | TS | Local p-value | Post-trial | 1-sided | AGN/Other | SBG | Search |
|---|---|---|---|---|---|---|---|---|---|
| Hypothesis | Hypothesis | Energya |
|
p-value | Significance | Fraction | Fraction | Radius | |
| SBG + ISO | ISO |
|
24.9 |
|
|
4.0σ | N/A |
|
129 |
| γAGN + SBG + ISO | γAGN + ISO |
|
14.7 | N/A |
|
3.7σ |
|
|
125 |
| γAGN + ISO | ISO |
|
15.2 |
|
|
2.7σ |
|
N/A | 69 |
| γAGN + SBG + ISO | SBG + ISO |
|
3.0 | N/A | 0.08 | 1.4σ |
|
b
|
70 |
| Swift-BAT + ISO | ISO |
|
18.2 |
|
|
3.2σ |
|
N/A | 123 |
| Swift-BAT + SBG + ISO | Swift-BAT + ISO |
|
7.8 | N/A |
|
2.6σ |
|
|
126 |
| 2MRS + ISO | ISO |
|
15.1 |
|
|
2.7σ |
|
N/A | 132 |
| 2MRS + SBG + ISO | 2MRS + ISO |
|
10.4 | N/A |
|
3.0σ |
|
|
126 |
Notes. ISO: isotropic model.
aFor composite model studies, no scan over the threshold energy is performed. bMaximum TS reached at the boundary of the parameter space.Download table as: ASCIITypeset image
5. Discussion
We have compared the arrival directions of UHECRs detected at the Pierre Auger Observatory with two distinct gamma-ray samples and two flux-limited samples of extragalactic sources. Our comparison with SBGs shows that isotropy of UHECRs is disfavored with 
confidence, accounting for the two free parameters and including the penalty for scanning over energy thresholds. This is the most significant evidence found in this study for anisotropy of UHECRs on an intermediate angular scale. It should be noted, however, that numerous anisotropy studies have been conducted with data from the Observatory, not only those that have been published by the Collaboration. There is no rigorous way to evaluate a statistical penalty for other searches.
The pattern of UHECR arrival directions is best matched by a model in which about 
of those cosmic rays arrive from directions that are clustered around the directions of bright, nearby SBGs. We evaluated the possibility of additional contributions from nearby γAGNs, such as Centaurus A, and from more distant sources through a comparison with samples tracing the distribution of extragalactic matter. We find that the contribution from SBGs to the indication of anisotropy is larger than that of the alternative catalogs tested. Nonetheless, caution is required in identifying SBGs as the preferred sources prior to understanding the impact of bulk magnetic deflections.
The sky maps used in this analysis are derived without incorporating any effects of the extragalactic or Galactic magnetic fields and winds (e.g., Pshirkov et al. 2011; Jansson & Farrar 2012; Biermann et al. 2015). In particular, the arrival directions of UHECRs from a given source are modeled by a symmetric Fisher distribution centered on the source position. We checked the plausibility of the best-fit search radius obtained above 
by simulating sky maps passed through the Galactic magnetic field from Jansson & Farrar (2012), including a random component with a coherence length of 
as in Erdmann et al. (2016). For large deflections, UHECRs from a given SBG can leak in the direction of a neighboring source. The three composition scenarios discussed in Section 3.3 yield reconstructed search radii of 5°–25°, bracketing the observed radius of 13°. The agreement is considered satisfactory given the uncertainties in our knowledge of the composition above 
and of the deflections by the Galactic magnetic field (Unger & Farrar 2017). Further studies aiming at possibly improving the model maps including deflections are underway.
It can be seen in Figure 3 (bottom) that M82 is expected to be one of the dominant sources in the full-sky starburst model presented here. Its declination of 
N is outside the exposure of the Observatory but is covered in the northern Hemisphere by the Telescope Array (Abu-Zayyad et al. 2012). As noted, e.g., by Fang et al. (2014) and He et al. (2016), the excess of events observed at the Telescope Array (Abbasi et al. 2014) has some overlap with the position of M82, as well as with the position of the blazar Mkn 421 that would be a bright northern source in a low-attenuation scenario.
An analysis of full-sky data from the Pierre Auger Observatory and the Telescope Array may provide a more powerful test of the starburst and AGN models by probing all production regions of UHECRs. Combining the data is complicated, however, due to the spurious anisotropies that may be induced by possible mismatches in the relative exposures and/or systematic differences in the nominal energy scales used at each observatory. The first attempts at conducting such surveys are being made (Di Matteo et al. 2017).
Additional exposure will bring better constraints on the brightest sources. At the same time, an instrumentation upgrade of the Observatory is being deployed on the water-Cherenkov detectors, adding a planar plastic scintillator of 4 m2 area to each of them (Aab et al. 2016b). The upgrade will provide mass-sensitive observables for each shower, enabling charge-discriminated studies with a duty cycle of nearly 
. Excluding highly charged nuclei from the analysis could eliminate a quasi-isotropic background that may mask the signature of individual sources imprinted by protons and other low-charge nuclei.
Finally, a large-scale dipolar anisotropy has been discovered above 
(Aab et al. 2017a). While a direct connection between the large and intermediate angular-scale patterns has not yet been identified, the emergence of anisotropies at ultra-high energy will certainly trigger further investigations of the scenarios underlying the production of UHECRs.
The successful installation, commissioning, and operation of the Pierre Auger Observatory would not have been possible without the strong commitment from the technical and administrative staff in Malargüe, and the financial support from a number of funding agencies in the participating countries, listed at https://www.auger.org/index.php/about-us/funding-agencies.
Footnotes
- *
Any correspondence should be addressed to auger_spokespersons@fnal.gov.
- 99
"Intermediate" hereafter denotes angular scales larger than the experimental resolution,
, and smaller than large-scale patterns, . - 100
Test statistic for anisotropy within ±1 unit.
- 101
Inverse square root of Fisher's concentration parameter.
