(15, 16, 23, 24, 33), which provide values for the
phase in right ascension close to that of the
galactic center, aGC = 266°.
Models proposing a galactic origin up to the
highest observed energies (34, 35) are in increasing
tension with observations. If the galactic sources
postulated to accelerate cosmic rays above EeV
energies, such as short gamma-ray bursts or
hypernovae, were distributed in the disk of the
galaxy, a dipolar component of anisotropy is
predicted with an amplitude that exceeds existing
bounds at EeV energies (24, 33). In this sense, the
constraint obtained here on the dipole amplitude
(Table 2) for 4 EeV < E < 8 EeV further disfavors a
predominantly galactic origin. This tension could
be alleviated if cosmic rays at a few EeV were
dominated by heavy nuclei such as iron, but
this would be in disagreement with the lighter
composition inferred observationally at these
energies (6). The maximum of the flux might be
expected to lie close to the galactic center region,
whereas the direction of the three-dimensional
dipole determined above 8 EeV lies ~125° from
the galactic center. This suggests that the anisotropy observed above 8 EeV is better explained
in terms of an extragalactic origin. Above 40 EeV,
where the propagation should become less diffusive, there are no indications of anisotropies
associated with either the galactic center or the
galactic plane (36).
There have been many efforts to interpret the
properties of ultrahigh-energy cosmic rays in terms
of extragalactic sources. Because of Liouville’s
theorem, the distribution of cosmic rays must
be anisotropic outside of the galaxy for an an-
isotropy to be observed at Earth. An anisotropy
cannot arise through deflections of an originally
isotropic flux by a magnetic field. One prediction
of anisotropy comes from the Compton-Getting
effect (37), which results from the proper motion
of Earth in the rest frame of cosmic-ray sources,
but the amplitude is expected to be only 0.6%
(38), well below what has been observed. Other
studies have predicted larger anisotropies. These
assume that ultrahigh-energy cosmic rays originate
from an inhomogeneous distribution of sources
(13, 14, 39), or that they arise from a dominant
source and then diffuse through intergalactic
magnetic fields (11–14). The resulting dipole ampli-
tudes are predicted to grow with energy, reaching
5 to 20% at 10 EeV. These amplitudes depend on
the cosmic-ray composition as well as the details of
the source distribution. On average, the predic-
tions are smaller for larger source densities or for
more isotropically distributed sources. If the
sources were distributed like galaxies, the distri-
bution of which has a significant dipolar compo-
nent (40), a dipolar cosmic-ray anisotropy would
be expected in a direction similar to that of the
dipole associated with the galaxies. This effect
would be due to the excess of cosmic-ray sources
in this direction and is different from the Compton-
Getting effect due to the motion of Earth with
respect to the rest frame of cosmic rays. For the
infrared-detected galaxies in the 2MRS catalog
(40), the flux-weighted dipole points in galactic
coordinates in the direction (‘, b) = (251°, 38°).
In this coordinate system, the dipole we detect
for cosmic rays above 8 EeV is in the direction
(233°, −13°), about 55° away from that of the
For an extragalactic origin, the galactic magnetic fields modify the direction of the dipole
observed at Earth relative to its direction outside the galaxy. For illustration, Fig. 3 shows a
map of the flux above 8 EeV in which the direction of the cosmic-ray dipole is shown along
with the direction toward the 2MRS dipole. The
arrows in the plot indicate how a dipolar distribution of cosmic rays, in the same direction
as the 2MRS dipole outside the galaxy, would
be affected by the galactic magnetic field (8).
The tips of the arrows indicate the direction of
the dipole of the flux arriving at Earth, assuming
common values of E/Z = 5 EeV or 2 EeV. Given
the inferred average values for Z 1.7 to 5 at
10 EeV, these represent typical values of E/Z for
the cosmic rays contributing to the observed dipole. The agreement between the directions of
the dipoles is improved by adopting these assumptions about the charge composition and
the deflections in the galactic magnetic field.
For these directions, the deflections within the
galaxy will also lead to a lowering of the amplitude of the dipole to about 90% and 70% of the
original value, for E/Z = 5 EeV and 2 EeV, respectively. The lower amplitude in the 4 EeV < E < 8
EeV bin might also be the result of stronger
magnetic deflections at lower energies.
Our findings constitute the observation of an
anisotropy in the arrival direction of cosmic
rays with energies above 8 EeV. The anisotropy
can be well represented by a dipole with an
amplitude of 6:5þ1:3 ;0:9 in the direction of right
ascension ad = 100° ± 10° and declination dd =
–24þ12 ;13°. By comparing our results with phenom-
enological predictions, we find that the magni-
tude and direction of the anisotropy support
the hypothesis of an extragalactic origin for
the highest-energy cosmic rays, rather than
sources within the galaxy.
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SCIENCE sciencemag.org 22 SEPTEMBER 2017 • VOL 357 ISSUE 6357 1269
Table 2. Three-dimensional dipole reconstruction. Directions of dipole components are shown in
declination dd (°)
ascension ad (°)
4 to 8 −0.024 ± 0.009 0.006;0.003 þ0.007 0.025;0.007 þ0.010 −75;8 þ17 80 ± 60 .....................................................................................................................................................................................................................
≥8 −0.026 ± 0.015 0.060;0.010 þ0.011 0.065;0.009 þ0.013 −24;13 þ12 100 ± 10