Search for clustering of ultra high energy cosmic rays from the Pierre Auger Observatory

Abstract

We present the results of a search for clustering among the highest energy events detected by the surface detector of the Pierre Auger Observatory between 1 January 2004 and 31 August 2007. We analyse the autocorrelation function, in which the number of pairs with angular separation within a given angle is compared with the expectation from an isotropic distribution. Performing a scan in energy above 30 EeV and in angles smaller than 30 degrees, the most significant excess of pairs appears for E > 57 EeV and for a wide range of separation angles, between 9 and 22 degrees. An excess like this has a chance probability of about 2% to arise from an isotropic distribution and appears at the same energy threshold at which the Pierre Auger Observatory has reported a correlation of the arrival directions of cosmic rays with nearby astrophysical objects.

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arXiv:0901.4699v1 [astro-ph.HE] 29 Jan 2009
Search for clustering of ultra high energy cosmic rays from the Pierre
Auger Observatory
Silvia Mollerach, for the Pierre Auger Collaborationa∗
aPierre Auger Observatory, av. San Mart´ ın Norte 304, (5613) Malarg¨ ue, Argentina
CONICET, Centro At´ omico Bariloche, 8400 Bariloche, Rio Negro, Argentina
We present the results of a search for clustering among the highest energy events detected by the surface detector
of the Pierre Auger Observatory between 1 January 2004 and 31 August 2007. We analyse the autocorrelation
function, in which the number of pairs with angular separation within an angle α is compared with the expectation
from an isotropic distribution. Performing a scan in energy above 30EeV and in angles α < 30◦, the most
significant excess of pairs appears for E > 57EeV and for a wide range of separation angles, 9◦< α < 22◦. An
excess like this has a chance probability of ∼ 2% to arise from an isotropic distribution and appears at the same
energy threshold at which the Pierre Auger Observatory has reported a correlation of the arrival directions of
cosmic rays with nearby astrophysical objects.
1. Introduction
The identification of the sources of the ultra
high energy cosmic rays has been one of the main
open problems in astrophysics since their discov-
ery. The study of their arrival directions is likely
to provide significant insight into this question.
If cosmic rays are charged particles, protons or
heavier nuclei, their trajectories are expected to
be bent by the intervening galactic and extra-
galactic magnetic fields, and their arrival direc-
tions will not point back to their sources. The
intensity and orientation of these fields are not
well known, but as the deflections are inversely
proportional to the energy, the effect is smaller
at the largest energies. Thus, it is at the high-
est energies that cosmic ray arrival directions are
most likely to trace their sources.
On the other hand, the distance from which ul-
tra high energy protons can arrive to the Earth is
expected to be limited by the energy losses caused
by the photo-pion production processes in the in-
teraction with the cosmic microwave background
(Greisen Zatsepin Kuzmin, GZK effect [1]), and
similarly nuclei can undergo photo-disintegration
processes. Hence, at energies above ∼ 60 EeV,
cosmic rays should mostly come from nearby
∗mollerach@cab.cnea.gov.ar.
sources (closer than ∼ 200 Mpc).
These ideas have motivated an extensive search
for clustering signals at high energies looking for
excesses in the number of pairs at different an-
gular scales. Small angular scale searches essen-
tially look for cosmic rays coming from the same
source which would be the expected signal from
the strongest nearby sources. At intermediate an-
gular scales, a clustering signal would be an evi-
dence of the pattern characterising the distribu-
tion of the nearby sources, with pairs of events
resulting from cosmic rays coming from differ-
ent sources. The angular scale up to which we
can expect that pairs of events come from the
same source depends on the energy of the events,
on the (unknown) magnitude of intervening mag-
netic fields, and on the cosmic ray composition.
Although the data from a number of experi-
ments have shown a remarkably isotropic distri-
bution of arrival directions, there has been a claim
of small scale clustering at energies larger than
40 EeV by the AGASA experiment [2]. The most
recent published analysis [3] reports 8 pairs (five
doublets and a triplet) with separation smaller
than 2.5◦among the 59 events with energy above
40 EeV, while 1.7 were expected from an isotropic
flux. The probability for this excess to happen by
chance was estimated to be less than 10−4. The
1

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significance of the AGASA clustering result was,
however, subject of debate based on the concern
that the energy threshold and angular separation
were not fixed a priori. Tinyakov and Tkachev
[4] computed the penalisation arising from mak-
ing a scan in the energy threshold and obtained a
probability of 3×10−4. Finley and Westerhoff [5]
took also into account the penalisation for a scan
in the angular scale and obtained a probability of
3.5 × 10−3. The HiRes observatory has found no
significant clustering signal at any angular scale
up to 5◦for any energy threshold above 10 EeV
[6]. A hint of correlation at scales around 25◦
and energies above 40 EeV, combining data from
HiRes stereo, AGASA, Yakutsk and SUGAR ex-
periments has been pointed out in Refs. [7,8].
The Pierre Auger Observatory, whose construc-
tion has recently been completed in Argentina,
has been taking data since January 2004. Its in-
tegrated exposure, up to the end of August 2007,
is 9000 km2yr sr, representing the largest one
ever attained by an extensive air shower array at
ultra high energies. Thanks also to its angular
and energy resolutions it offers an excellent data
set for studies of anisotropies in the arrival direc-
tions.
We apply here the autocorrelation technique to
the events with energy above 30 EeV, scanning
over energy threshold and angular separation (up
to 30◦), with the aim of searching for possible
clustering in the arrival directions. A preliminary
analysis has been presented in Ref. [9].
The most clear anisotropy signal of the arrival
directions of high energy events (with E > 57
EeV) has been reported by the Auger collabo-
ration [10,11] through a completely independent
method by studying their correlation with the
nearby extragalactic matter distribution. The ob-
served correlation with nearby AGNs from the
V´ eron-Cetty and V´ eron catalog [12] was shown
to be incompatible with an isotropic distribution
at more than 99% CL. The autocorrelation anal-
ysis discussed here does not depend on an a pri-
ori selection of the possible sources location and,
therefore, gives complementary information with
respect to that analysis.
2. The observatory and the data set
The Pierre Auger Southern Observatory is lo-
cated in the Province of Mendoza, Argentina, at
35.1◦–35.5◦S, 69.0◦–69.6◦W and 1300–1400 m
a.s.l. The growing observatory has been in oper-
ation since 2004: the data presented here refer to
the period between 1 January 2004 and 31 August
2007, during which the number of surface stations
was increasing from 154 to 1388. The surface de-
tector consists of 10 m2× 1.2 m water Cherenkov
tanks spaced by 1500 m, covering an area that in
the period of interest ranged from about 200 km2
to around 3000 km2. While the experiment has
been described in detail elsewhere [13], the rele-
vant features with respect to the present analysis
will be outlined here.
The trigger requirement for the array is based
on a 3-fold coincidence, that is satisfied when
a triangle of neighbouring stations is triggered.
The 50% contamination from accidental events is
obviated by an appropriate event selection [14],
whose power for selecting real showers is larger
than 99%.
The arrival directions of the showers are ob-
tained through the time of flight differences
among the triggered stations. The angular res-
olution, defined as the angular radius around the
true cosmic ray direction that would contain 68%
of the reconstructed shower directions, is calcu-
lated on an event by event basis and checked
through the correlations with the fluorescence de-
tector. It depends on the number of triggered sta-
tions and is better than 2◦for 3-fold events (E <
4 EeV), better than 1.2◦for 4-folds and 5-folds
events (3 < E < 10 EeV) and better than 0.9◦
for higher multiplicity events (E > 10 EeV) [15].
The estimator for the primary energy is the re-
constructed signal at 1000 m from the shower core
[16]. The conversion from this estimator to en-
ergy is derived experimentally through the use of
a subset of showers detected by both the surface
and the fluorescence detectors [16]. The energy
resolution is 18% and the absolute energy scale
has a systematic uncertainty of 22% [17].
In the present analysis, we apply the following
cuts to the events:
• zenith angle θ < 60◦;

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• core location within the array boundaries:
reconstructed core within a triangle of ac-
tive stations and station with the highest
signal surrounded by at least 5 active tanks;
• reconstructed energy E > 30 EeV.
After these cuts there are 203 events above 30
EeV and 81 events above 40 EeV. For these events
the surface detector trigger efficiency is 100%.
The acceptance is fully saturated and is deter-
mined by purely geometrical considerations [18],
thus allowing an accurate calculation of the ex-
posure even with a changing array configuration.
The exposure is flat as a function of sin2θ, where
θ is the zenith angle, and it is nearly uniform as a
function of the azimuth angle φ. There is a small
modulation of the flux in right ascension due to
the dead times and the growth of the array dur-
ing the data taking period, but this effect is small,
below 1%, and can be ignored in the present anal-
ysis.
3. The autocorrelation function analysis
3.1. The method
A standard tool for studying anisotropies is the
two-point angular correlation function. In the fol-
lowing we will use the correlation function given
by the number of pairs separated by less than an
angle α among the N events with energy larger
than a given threshold E,
np(α) =
N
?
i=2
i−1
?
j=1
Θ(α − αij),
(1)
where αij is the angular separation between
events i and j and Θ is the step function. The ex-
pected number of pairs and the 90% CL error bars
are obtained by generating a large number (106)
of Monte Carlo simulations with the same num-
ber of events as in the real data set, isotropically
distributed and modulated by the exposure of the
detector. The chance probability for any excess
of pairs at a fixed angle α and energy threshold
is found from the fraction of simulations with a
larger or equal number of pairs than what is found
in the data at the angular scale of interest.
The result of the autocorrelation function anal-
ysis depends on the chosen values of α and E.
The fact that the deflections expected from galac-
tic and extragalactic magnetic fields and the
distribution of the sources are largely unknown
prevents us from fixing these values a priori.
The significance of an autocorrelation signal at
a given angle and energy, when these values have
not been fixed a priori, is a delicate issue that
has made, for example, the significance of the
AGASA small scale clustering claim very con-
troversial. We adopt here the method proposed
by Finley and Westerhoff [5], in which a scan
over the energy threshold and the angular sep-
aration is performed. For each value of E and
α, we compute the fraction f of simulations hav-
ing an equal or larger number of pairs than the
data by generating 106simulated isotropic data
sets modulated by the exposure. The fraction f
takes here the role of the distance between the
experimental and expected distributions as used
in the Kolmogorov-Smirnov test. The most rel-
evant clustering signal corresponds to the values
of α and E that have the smallest value of f, re-
ferred here to as fmin. To establish the statistical
significance of this deviation, it is necessary to ac-
count for the fact that the angular bins, as well
as the energy ones, are not independent. To do
that, we perform 105isotropic simulations with
the same number of events as the data and calcu-
late for each realisation the most significant de-
viation fi
min. The statistical significance of the
deviation from isotropy is the integral of the nor-
malised fmin distribution above fdata
then estimate the probability that such cluster-
ing arises by chance from an isotropic distribu-
tion just from the fraction of simulations having
fi
min.
min. We can
min≤ fdata
3.2. Results
To study the autocorrelation function using the
scan technique we have to fix the range of the pa-
rameter space that we explore. We scan up to
30◦in the angular scale, what includes the range
where small scale signals from point sources and
intermediate angular scale signals from clustering
of the sources are expected to appear. We scan on
energies above 30 EeV: this range probes the high
energy region where anisotropies are expected in
the astrophysical sources scenario, and goes down

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—
Figure 1. Autocorrelation scan for events with
energy above 30 EeV and angles up to 30◦. The
fraction of simulations with more pairs than that
observed in the data is plotted for each angular
scale and number of events (or energy).
enough to cover the energy range where past
anisotropy claims with data from previous exper-
iments using a similar technique were made, al-
lowing for a possible energy calibration difference
of up to 30% between the experiments. We there-
fore compute the number of pairs as a function of
the separation angle from 1◦to 30◦in steps of 1◦,
and as a function of the number of events start-
ing from the 10 highest energy events and adding
events one by one in decreasing energy order up
to 100 events, and in groups of ten up to 200
events, corresponding to a threshold energy of 30
EeV, and then compare them with isotropic dis-
tributed simulations.
In figure 1 we present the fraction of simula-
tions with more pairs than the data as a function
of the angular scale α and the number of events
N (or equivalently the energy threshold).
A broad region with an excess of pairs appears
for energies above around 50 EeV, at angular
scales between about 9◦to 22◦. In particular, the
minimum value of f (fmin≃ 1.5×10−4) is found
0
10
20
30
40
50
60
0 5 10 15 20 25 30
np
α
1e-04
0.001
0.01
0.1
1
0 5 10 15
α
20 25 30
f
Figure 2. Upper panel: Autocorrelation function
for the 27 events with energy larger than 57 EeV
as a function of the angle (dots) and autocorre-
lation function for an isotropic distribution with
90% confidence level band. Lower panel: Frac-
tion of isotropic simulations with larger or equal
number of pairs than the data.
for the 27 highest energy events (corresponding
to E > 57 EeV), for α = 11◦(18 observed pairs
against 5.2 expected).
In Figure 2 the autocorrelation function (upper
panel) and the fraction of isotropic simulations
with equal or larger number of pairs than the data
(lower panel) is shown for these 27 events as a
function of the angular scale. The broad region
of low values of f (< 10−3) is visible between 9◦
and 22◦, with the minimum at 11◦.
The chance probability of a fmin≤ 1.5 × 10−4
to arise from an isotropic distribution was esti-
mated by performing the same scan to 105simu-

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Figure 3.
with energy larger than 57 EeV in equatorial co-
ordinates centered in the south pole. The circles
around each event have a 5.5◦radius. The dashed
line represents the galactic plane (with the galac-
tic center identified by a cross) and the solid line
represents the supergalactic plane.
Arrival directions of the 27 events
lations, and it is P ≃ 1.6 × 10−2.
Figure 3 shows the arrival directions of the 27
events with E > 57 EeV in equatorial coordi-
nates centered in the south pole. The galactic and
supergalactic planes are displayed by the dashed
and solid lines respectively. Circles of 5.5◦around
each event guide the eye to identify pairs sepa-
rated by less than 11◦. The arrival directions and
energies of the 27 events are listed in the Ap-
pendix of [11].
The analysis of the autocorrelation function
shows in particular no significant clustering sig-
nal at the small angular scales corresponding to
the AGASA claim. At energies above 40 EeV,
with 81 detected events, we observe 4 pairs within
2.5◦, while 2.5 were expected from an isotropic
flux (with a fraction f = 0.24 of isotropic simula-
tions showing a larger or equal number of pairs).
Due to a possible difference in the energy calibra-
tion between AGASA and Auger, the clustering
signal reported by AGASA could appear in Auger
data at a lower energy scale. For energies above
30 EeV the observed number of pairs is 23, while
the isotropic expectation is 16 (f = 0.05). This
excess is much smaller than the one reported by
AGASA.
4. Conclusions
Using the events recorded by the surface de-
tector of the Pierre Auger Observatory between
January 2004 and Augist 2007 we have performed
a scan to search for possible clustering using the
autocorrelation technique.
performed in energy (above 30 EeV, 203 events
detected) and angular separation (between 1◦
and 30◦). The most significant excess of pairs
is found for E > 57 EeV (corresponding to 27
events) and α = 11◦, with a chance probabil-
ity of P = 1.6 × 10−2to arise from an isotropic
distribution. Above this energy we observe, in
fact, a broad region of low probabilities, for an-
gular scales between 9◦and 22◦. At higher energy
thresholds the chance probabilities become larger,
however the number of events becomes rather lim-
ited. At lower energies the autocorrelation func-
tion becomes progressivelycloser to that expected
from an isotropic flux.
It should be noted that the energy threshold
that maximises the significance is the same one
as the energy at which the Pierre Auger collab-
oration has observed a departure from isotropy
using the correlation of the arrival directions of
events with nearby AGNs. It is also the energy
at which the cosmic ray flux at ultra high ener-
gies reported by the Pierre Auger collaboration
[16] is suppressed by 50% compared to a power
law extrapolation of the flux measured at lower
energies. This suppression, if interpreted as due
to the GZK horizon [1], would imply that nearby
sources dominate the flux at these energies. As
the matter distribution in the nearby Universe
becomes increasingly anisotropic for smaller dis-
tances, it is to be expected that the ultra high
energy cosmic ray sky should become anisotropic
The scan has been