Search for Correlations between HiRes Stereo Events and Active Galactic Nuclei
ABSTRACT We have searched for correlations between the pointing directions of ultrahigh energy cosmic rays observed by the High Resolution Fly's Eye experiment and Active Galactic Nuclei (AGN) visible from its northern hemisphere location. No correlations, other than random correlations, have been found. We report our results using search parameters prescribed by the Pierre Auger collaboration. Using these parameters, the Auger collaboration concludes that a positive correlation exists for sources visible to their southern hemisphere location. We also describe results using two methods for determining the chance probability of correlations: one in which a hypothesis is formed from scanning one half of the data and tested on the second half, and another which involves a scan over the entire data set. The most significant correlation found occurred with a chance probability of 24%.
arXiv:0804.0382v2 [astro-ph] 15 Aug 2008
Search for Correlations between HiRes Stereo
Events and Active Galactic Nuclei
R. U. Abbasia, T. Abu-Zayyada, M. Allena, J. F. Ammanb,
G. Archbolda, K. Belova, J. W. Belzc, S. Y. BenZvia,
D. R. Bergmane, S. A. Blakea, J. H. Boyerd, O. A. Brusovaa,
G. W. Burta, C. Cannona, Z. Caoa, W. Denga, Y. Fedorovaa,
J. Findlaya, C. B. Finleyd, R. C. Graya, W. F. Hanlona,
C. M. Hoffmanb, M. H. Holzscheiterb, G. Hughese,
P. H¨ untemeyerb, D. Ivanove, B. F Jonesa, C. C. H. Juia,
K. Kima, M. A. Kirnc, B. C. Knappd, E. C. Loha,
M. M. Maestasa, N. Managof, E. J. Manneld, L. J. Marekb,
K. Martensa, J. N. Matthewsa, S. A. Moorea, A. O’Neilld,
C. A. Painterb, L. Pererae, K. Reila, R. Riehlea,
M. D. Robertsg, D. RodriguezaN. Sasakif, S. R. Schnetzere,
L. M. Scotte,∗, M. Semand, G. Sinnisb, J. D. Smitha,
R. Snowa, P. Sokolskya, C. Songd, R. W. Springera,
B. T. Stokesa, S. R. Strattone, J. R. Thomasa, S. B. Thomasa,
G. B. Thomsone, D. Tupab, L. R. Wienckea, A. Zeche,
(The High Resolution Fly’s Eye Collaboration)
aUniversity of Utah, Department of Physics, Salt Lake City, UT 84112, USA
bLos Alamos National Laboratory, Los Alamos, NM 87545, USA
cMontana State University, Department of Physics, Bozeman, MT 59812, USA
dColumbia University, Department of Physics and Nevis Laboratory, New York,
NY 10027, USA
eRutgers — the State University of New Jersey, Piscataway, NJ 08854, USA
fUniversity of Tokyo, Institute for Cosmic Ray Research, Kashiwa City, Chiba
gUniversity of New Mexico, Department of Physics and Astronomy, Albuquerque,
NM 87131, USA
Preprint submitted to Elsevier 15 August 2008
We have searched for correlations between the pointing directions of ultrahigh
energy cosmic rays observed by the High Resolution Fly’s Eye experiment and
Active Galactic Nuclei (AGN) visible from its northern hemisphere location. No
correlations, other than random correlations, have been found. We report our results
using search parameters prescribed by the Pierre Auger collaboration. Using these
parameters, the Auger collaboration concludes that a positive correlation exists for
sources visible to their southern hemisphere location. We also describe results using
two methods for determining the chance probability of correlations: one in which a
hypothesis is formed from scanning one half of the data and tested on the second
half, and another which involves a scan over the entire data set. The most significant
correlation found occurred with a chance probability of 24%.
Key words: Active Galactic Nuclei, ultrahigh energy cosmic rays, anisotropy
The search for the sources of the highest energy cosmic rays is an important
topic in physics today. The energies of these cosmic rays exceed 100 EeV and
the acceleration mechanisms of the astrophysical objects responsible for these
events remain unknown. Anisotropy search methods such as those used in X-
or γ-ray astronomy are difficult to use due to deflections in the trajectories of
these charged cosmic rays from Galactic and extragalactic magnetic fields. For
a galactic magnetic field strength of ∼ 3µG and coherence length of ∼ 1 kpc, a
40 EeV cosmic ray should be deflected by two to three degrees over a distance
of only a few kpc .
There are several reports on anisotropy by previous experiments. An excess
of events near the direction of the Galactic center has been reported by the
SUGAR and AGASA experiments [2,3]. The Pierre Auger collaboration, how-
ever, has recently reported that they have not seen any excess at that location
. In addition, the Auger collaboration reported no significant excesses in
any part of the southern hemisphere sky . Two reports of anisotropy have
been found in the northern hemisphere sky. A dip in the intensity of cosmic-
ray events near the direction of the Galactic anticenter has been reported by
Email address: firstname.lastname@example.org (L. M. Scott).
both the AGASA and High Resolution Fly’s Eye (HiRes) experiments, but the
significance is too low to claim an observation . Additionally the AGASA
“triplet” is correlated with a HiRes high-energy event . These reports of
anisotropy in the northern sky await confirmation or rejection by the Tele-
scope Array experiment .
Another method for searching for anisotropy is to search for correlations in
pointing directions of cosmic rays with known astrophysical objects that might
be sources. In these cases, a small event sample that shows no excess over the
expected background can, nevertheless, exhibit correlations with a priori can-
didate sources, adding up to a statistically significant signal. Past searches
have found correlations with BL Lacertae objects; BL Lacs are a class of AGN
with a jet pointing toward the Earth, and are plausible candidates for cosmic-
ray sources. Correlations have been found with data from the AGASA, HiRes
and Yakutsk experiments, all in the northern hemisphere . The Auger col-
laboration has searched for correlations with BL Lac objects in the southern
hemisphere but has found nothing significant . Again the northern hemi-
sphere correlations await confirmation by the Telescope Array experiment.
There have been speculations that Active Galactic Nuclei (AGN) may contain
acceleration regions of the appropriate size and magnetic field strength to
accelerate nuclei to the highest energies [11,12]. One should therefore expect
the brightest and closest AGN to produce the highest-energy cosmic ray events
at Earth. These events would also have suffered the smallest deflections due to
the intervening magnetic fields and would point back, most directly, to these
AGN. The large number of identified AGN make them interesting candidates
for studying possible correlations with ultrahigh energy cosmic rays. Three
ideal parameters for determining correlations between cosmic rays and AGN
are the maximum difference in angle between the cosmic-ray pointing direction
and the AGN θmax, the minimum cosmic-ray energy Emin, and the maximum
AGN redshift zmax.
The Pierre Auger Collaboration have reported a search of two independent
sets of their data for correlations with cosmic rays with AGN. They scanned
their first data set and found that the most significant correlation occurs for
cosmic rays with parameters (θmax, Emin, zmax) = (3.1◦, 56 EeV, 0.018). With
these selection criteria, they find 12 pairings with AGN from 15 events in the
first data set. In the second data set, they find 8 pairings from 13 events and
a corresponding chance probability of 0.0017 [13,14].
The HiRes experiment collected data from 1997 to 2006, operating two flu-
orescence detectors located atop desert mountains separated by 12.6 km in
west-central Utah. The HiRes data have been analyzed monocularly, using
the data from one detector at a time , and stereoscopically, using the data
from both detectors simultaneously . The angular resolution is about 0.8◦
Parameters for the functions in Equation 1 that give the coordinates (in celestial
right ascension and declination) of the lower boundaries of the 10 bins of equal
exposure for the HiRes detector shown as the 10 lightest shaded regions in Figures 3
A 67.9 55.345.536.928.8 20.712.3 3.3-12.1-32.0
2.0 3.03.84.75.56.6 7.99.4 17.60.0
-3.1-4.4 -5.6-7.0 -8.8 -11.5-15.7-26.2 -19.10.0
in stereo mode. The energy scales of the HiRes monocular and stereoscopic
reconstructions agree. Only stereo data were used in this analysis. The stereo
data, covering an energy range from 1017.4to 1020.1eV, consist of 6636 events.
The pointing directions of the stereo data extend from zenith to about −32◦in
declination (celestial coordinates). The corresponding exposure of is dependent
on right ascension due to seasonal variations in the duty cycle of the detector.
The boundaries of regions of equal exposure are best described by
A + B sin
(if α ≤ 200◦)
A + C sin
8(α − 200◦)
(if α > 200◦)
where δ and α are celestial declination and right ascension measured in degrees
and A, B and C are fit parameters. Table 1 gives values of A, B and C for
plotting the boundaries of the 10 bins of equal exposure shown in Figures 3
Figure 1 shows the monocular spectra for the two HiRes sites  and that
of the Pierre Auger Observatory . At the highest energies where Auger
observes an anisotropy signal, the energy scales of HiRes and Auger differ by
about 10%. To account for this difference, the energy scale of the HiRes stereo
data set used in this analysis has been decreased by 10% to agree with the
Auger energy scale. All energies quoted for the HiRes data from this point
on will include this 10% shift. There are 13 events with energies greater than
56 EeV in the full HiRes stereo data set, the same number as in the Auger
test data set.
Flux*E3/1024 (eV2 m-2 s-1 sr-1)
1717.5 1818.5 19 19.520 20.521
Fig. 1. Energy spectrum [E3J] for HiRes-1 and HiRes-2 monocular data  and
for the surface detector data from the Pierre Auger Observatory .
2The V´ eron-Cetty and V´ eron catalog
In this paper, we report on searches for correlations between the pointing
directions of ultrahigh energy cosmic rays observed stereoscopically by the
HiRes experiment and AGN from the V´ eron-Cetty and V´ eron (VCV) catalog,
12thedition . The VCV catalog includes ∼ 22000 AGN, ∼ 550 BL-Lacs
and ∼ 85000 quasars compiled from observations made by other scientists, and
does not evenly cover the sky. Not only does the Galaxy and its associated
dust cover large parts of the sky, particularly in the southern hemisphere,
making the identification of AGN extremely difficult in those areas, but some
of the sky surveys included in the catalog have covered only small bands of
the sky. This makes the total density of AGN in the VCV catalog very uneven
across the sky in a way that is neither totally random nor systematic. The
locations of a closer subset of sources, with redshift z < 0.1, are more evenly
One property of the search method in (θmax, Emin, zmax) is that the large size
of the catalog and the size of the correlation angle circles determine that one
can scan over only a narrow range of θmaxand zmax. To illustrate this using
simulated events with isotropically distributed pointing directions, Figure 2
shows that the number of random pairings with AGN is determined by the
Fig. 2. The average fraction of correlated events found in 5000 simulated sets of
isotropic events with identical statistics to the HiRes data for E > 56 EeV as a
function of θmaxand zmax. The fraction of correlated pairs of simulated events with
AGN is 0.02 at (1.0◦, 0.010); 96% of events are correlated at (10.0◦, 0.100).
choice of θmaxand zmax. As θmaxand zmaxare increased, the number of random
pairings increases, rapidly overcoming any real correlations between cosmic
rays and AGN.
We perform three searches for correlations between cosmic rays and AGN. In
the first search we look for correlations in the HiRes stereo data using the
(θmax, Emin, zmax) parameters prescribed by the Auger collaboration . In
the second, we divide our stereo data into two equal parts in a random manner,
determine the optimum search parameters in the first half of the data by
scanning in a three-dimensional grid in (θmax, Emin, zmax), and then examine
the second half of the data using these “optimum” parameters. By choosing
the best parameters from the first half of the data and using them to form a
hypothesis to be tested using a statistically independent sample, no statistical
penalties are incurred in the application to the second half of the data. In the
third and last search, we analyzed the complete data set using the statistical
prescription described by Finley and Westerhoff  (see also Tinyakov and
Tkachev ) to arrive at a chance probability that includes the statistical
penalty from scanning over the entire data set. Finally, in addition to searching
for correlations with AGN, we analyzed the degree of auto-correlation in the
stereo data over all possible angles and values of Emin.
To arrive at the appropriate chance probabilities for the numbers of correla-
tions seen in each method, we generated 5001 random samples of events using
the hour angle - declination method [21,6]. In this method the hour angle and
declination of one event and the sidereal time of another are randomly paired
to generate a sky plot with the same number of events as the data. Such a
sample reproduces the overall observed distribution of events very well.
3.1 Search for Correlations using the Auger criteria
The Auger collaboration has reported the results of searches in (θmax, Emin,
zmax) over two independent data sets. In a scan over the first data set, 12 of
the 15 events with Emin = 56.0 EeV were found to lie within θmax = 3.1◦
of AGN with zmax
= 0.018 with 3.2 chance pairings expected. Using the
parameters (3.1◦, 56.0 EeV, 0.018), 8 of 13 events in an independent test data
set were found to be paired with AGN with 2.7 chance pairings expected. The
chance probability for this occurrence was found to be 0.0017 [13,14].
A scan of the entire HiRes data set at (3.1◦, 56.0 EeV, 0.018) found 2 AGN
pairings for a total of 13 events. Figure 3 shows the locations of the 2 correlated
events and the 11 uncorrelated events. We looked for correlations in the 5000
simulated data sets at (3.1◦, 56.0 EeV, 0.018) and found the average number of
correlated pairs to be 3.2. In addition, 4121 sets had 2 or more correlated events
for a chance probability of 82%. We thus find no evidence for correlations of
cosmic-ray events with AGN in our field of view at (3.1◦, 56.0 EeV, 0.018).
The HiRes data are therefore consistent with random correlations.
3.2Search in two independent data sets
Next, we randomly divide the HiRes stereo data into two equal sets, first
examining only one half and setting the other aside. We scan the first half
simultaneously in θmaxfrom 0.1 to 4.0◦in bins of 0.1◦, in Eminfrom 1019.05to
1019.80eV in bins of 0.05 decade, and with an AGN zmaxfrom 0.010 to 0.030
in bins of 0.001. For each grid point in the scan, the total number of cosmic
rays correlated with at least one AGN is accumulated. We then conduct the
same scan in each of 5000 simulated sets with identical statistics to the first
half, adding up the total number of correlations in each set for each grid point.
Fig. 3. Sky map in Galactic coordinates. The black dots are the locations of the
457 AGN and 14 QSOs with redshift z < 0.018. The green circle and triangle mark
the locations of Centaurus A and M87, respectively. The red circles (with radii
of 3.1◦) mark the 2 correlated events. The blue squares mark the locations of the
11 uncorrelated events. Of the eleven blue shaded regions, the 10 lightest shades
delineate regions of constant exposure in HiRes as given in Table 1. The darkest
shade indicates the region with no exposure.
At each point, the number of correlated events in each of the 5000 simulated
sets is compared with the result in the first half of the data. The criteria for
the most significant correlation were found to be (1.7◦, 15.8 EeV, 0.020) with
20 correlated events from a total of 97. Only 25 of 5000 simulated sets had 20
or more correlations.
Using these criteria as our hypothesis, we then examine the second half of the
data at (1.7◦, 15.8 EeV, 0.020) and find 14 correlated pairs from 101 events.
In a set of 5000 simulated events with identical statistics to the second half,
741 sets contained 14 or more correlated events for a chance probability of
15%. For comparison, the point with the most significant correlation in the
second half occurs at (2.0◦, 20.0 EeV, 0.016) with 14 correlated events of a
total 69 and a chance probability of 1.5%. These results are again consistent
with random correlations.
3.3Scanning the entire data set
We follow the prescription of Finley and Westerhoff  for determining the
most significant correlation in the entire data set while also calculating an ap-
propriate statistical penalty for scanning over the entire data set. We scan the
data simultaneously in θmax, Eminand zmaxcounting the number of correlated
events, ncorrat each point. This process is repeated for each of the 5001 sim-
ulated sets with Pdata, the probability for observing ncorror more correlations
at (θmax, Emin, zmax) calculated from
where Pmc(θmax,zmax,Emin,n) is the fraction of the first 5000 simulated sets
with exactly n events at (θmax, Emin, zmax). The value of Pminis then taken
to be the values of (θc, Ec, zc) which minimize Pdata. This is found to occur at
the critical values (2.0◦, 15.8 EeV, 0.016) where there are 36 correlated events
out of 198 in the data and 9 of 5000 simulated sets with 36 or more correlated
events, for a chance probability of 0.18%.
To find the true significance of this signal, we apply the same process to each
of the first 5000 simulated sets, finding the value Pi
of simulated sets n∗
min = Pi(θi
corrwith ncorrfor the other 5000 sets. We then count the number
mcfor which Pi
min≤ Pmin. The chance probability is then
In this, our most robust method, there were 1210 simulated sets with Pi
values of 0.0018 or less for a chance probability, Pchance= 24%. Figure 4 shows
a sky map of the most significant correlation in the HiRes data. From this final
analysis, we draw the same conclusion: HiRes data are consistent with random
correlations with AGN.
In addition to searching for correlations with AGN, studies of auto-correlation
can be useful for searching for anisotropy in the data. We have analyzed the
degree of auto-correlation in the data over all possible angles and made com-
parisons with the average number of pairs of events for 2000 isotropic simulated
Fig. 4. Sky map in Galactic coordinates. The black dots are the locations of the 389
AGN and 14 QSOs with redshift z < 0.016. The green circle and triangle mark the
locations of Centaurus A and M87, respectively. The red circles (with radii of 2.0◦)
mark the 36 correlated events at (2.0◦, 15.8 EeV, 0.016). The blue squares mark the
locations of the 162 uncorrelated events. Of the eleven blue shaded regions, the 10
lightest shades delineate regions of constant exposure in HiRes as given in Table 1.
The darkest shade indicates the region with no exposure.
data sets. We find no evidence of auto-correlation for any values of Emin. Fig-
ure 5 shows a comparison of the normalized number of pairs of events with
energies above 56 EeV in the stereo data to the average normalized number
of pairs for 2000 isotropic simulated data sets. The 1σ uncertainty is found
by ordering the simulated sets by their maximum deviation from the average
and plotting only the first 68% of those simulated sets.
As a further check, we scan the data in θmaxand Eminand determine a sta-
tistical penalty using the same method presented in Section 3.3. We scan the
data in θmax from 0.5◦to 30.0◦in bins of 0.5◦and in Emin from 1019.05to
1019.80eV in bins of 0.05 decade. The critical values which minimize Pdataare
found to occur at (2.0◦, 44.7 EeV) where there is one pair of events out of a
possible 406 in the data and 227 of 1000 simulated sets with one or more pairs
for a chance probability of 23%. Applying the same process to the 1000 sim-
ulated sets, we find 971 sets for which the critical point occurs with a chance
probability less than 23%. The probability of measuring the observed degree
of correlation in an isotropic data set is 97%.
Number of pairs (normalized)
0 20 406080100 120140160180
Fig. 5. Normalized number of pairs as a function of θmax. The 13 events above 56
EeV in the HiRes data are shown in closed circles. The open circles are the average
of 2000 simulated sets. The gray shaded region represents the 1σ uncertainty in the
distribution of simulated sets.
We have searched for correlations between the pointing directions of HiRes
stereo events with AGN from the the V´ eron-Cetty V´ eron catalog using three
different methods. As search parameters for our analysis, we used the max-
imum difference in angle between the cosmic-ray pointing direction and an
AGN θmax, the minimum cosmic-ray energy Emin, and the maximum AGN
Our first analysis, using the criteria prescribed by the Pierre Auger Obser-
vatory for their most significant correlation, (3.1◦, 56.0 EeV, 0.018), finds 2
correlated of 13 total events with an expectation of 3.2 chance correlations.
The corresponding chance probability was found to be 82%.
In our second search the total HiRes stereo data were then divided into two
equal but random parts and we performed a scan in θmax, Eminand zmaxover
one half of the data to determine which parameters optimized the correla-
tion signal. We then examined the other half of the data using these search
parameters and found a smaller signal with a chance probability of 15%.
Finally, we examined the entire HiRes stereo data using a more robust method
to calculate the chance probability with appropriate statistical penalties. The
most significant correlation was found to occur at (2.0◦, 15.8 EeV, 0.016) with
36 correlated of 198 total events. This corresponds to a chance probability of
We conclude that there are no significant correlations between the HiRes stereo
data and the AGN in the V´ eron-Cetty V´ eron catalog. We also examined the
degree of auto-correlation at all angles and energies. The probability that the
data are consistent with isotropy is 97%.
This work was supported by US NSF grants PHY-9100221, PHY-9321949,
PHY-9322298, PHY-9904048, PHY-9974537, PHY-0073057, PHY-0098826, PHY-
0140688, PHY-0245428, PHY-0305516, PHY-0307098, PHY-0649681, and PHY-
0703893, and by the DOE grant FG03-92ER40732. We gratefully acknowledge
the contributions from the technical staffs of our home institutions. The co-
operation of Colonels E. Fischer, G. Harter and G. Olsen, the US Army, and
the Dugway Proving Ground staff is greatly appreciated.
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