lessons 25 and 26 - istituto nazionale di fisica nucleare

A.A. 2021-2022 Prof. Antonio Capone - Particle and AstroParcle Physics 1

– Measurement of C.R. with E>1018 eV with hybrid detectors• The Telescope Array (TA) detector in the Northern

hemisphere• The "chemical composition" of UHE C.R. as measured by

hybrid detectors at ground with AUGER and Telescope Array detectors

• Search for U.H.E. neutrinos with Pierre Auger Observatory• Measurement of the CR anisotropy (AGASA, Pierre Auger,

ARGO, other experiments…)

Lessons 25 and 26


Detection of U.H.E. Cosmic Rays (E>> 100 PeV)

~ 10 particelle/s

GeV TeV PeV EeVJoule

The study of cosmic rays with E >> 100 PeVrequires:Þ large equipment (sampling, fluorescence

detection in the atmosphere, ...)Þ on the earth's surface or in space

1 particle/(Km2 • year)


Pierre Auger Observatory: the flux of UHE CR

ICRC-2015


Pierre Auger Observatory: UHE CR spectrum, "all particle", for different declination angles (1)All-particle spectrum in different declination bands

The large number of events and wide FOV allow for the study of the flux vs declination

9

No indication of a declination-dependent flux

(differences between sub-spectra and

all-sky flux < 5% below Esupp and <13% above)

[see talk by Ines Valiño tomorrow]

Valiño #271ICRC-2015


With the present spectrumAUGER reject the hypothesis thatthe cosmic ray spectrum continuesin the form of a power-law abovean energy of 4×1019 eV with morethan 20σ. This result isindependent of the systematicuncertainties in the energy scale,the suppression at high energiescan be due to the GZK cutoff[GZK] or just that sources arerunning out of power[Allard].

Pierre Auger Observatory: UHE CR spectrum (2)

[GZK] K. Greisen, Phys. Rev. Lett. 16, 748 (1966); G. T. Zatsepin and V. A. Kuzmin, Pis’ma Zh. Eksp. Teor. Fiz. 4, 114 (1966) JETP Lett. 4, 78 (1966).[Allard] D. Allard, Astropart. Phys., 39-40 (2012) 33.

E[eV]

1810 1910 2010

]�2

�eV

-1�s

r-1

�yr

-2�J

(E)�

[km

�3�E 3710

3810

(E�eV)10

log

18 18.5 19 19.5 20 20.5

Auger

power�laws

power�laws��smooth�function

Figure 5: The combined energy spectrum is fitted with two functions (see text).Only statistical uncertainties are shown. The systematic uncertainty in the en-ergy scale is 22%.

where Ec is the energy at which the flux is suppressed 50%186

compared to a pure power-law, and Wc determines the sharp-187

ness of the cut-off. The derived parameters are in Table 1 with188

statistical uncertainties.189

Table 1: Fitted parameters and their statistical uncertainties characterizing thecombined energy spectrum.

parameter broken power laws power laws

+smooth function

γ1(E < Eankle) 3.27 ± 0.02 3.27 ± 0.01

lg(Eankle/eV) 18.61 ± 0.01 18.62 ± 0.01

γ2(E > Eankle) 2.68 ± 0.01 2.63 ± 0.02

lg(Ebreak/eV) 19.41 ± 0.02

γ3(E > Ebreak) 4.2 ± 0.1

lg(Ec/eV) 19.63 ± 0.02

Wc 0.15 ± 0.02

χ2/ndof 37.8/16 = 2.4 33.7/16 = 2.1

See [4] for more details.190

4. Conclusion191

We have reported the measurement of the cosmic ray energy192

flux with the Pierre Auger Observatory. Two independent mea-193

surements have been performed, by exploiting surface detector194

and hybrid data, and then combined to derive the energy spec-195

trum above 1018 eV.196

The ground parameter S (1000) derived from the SD array is197

converted to S 38◦ using the constant intensity cut method, which198

is calculated from data assuming that the flux is isotropic. S 38◦199

may be regarded as the signal S (1000) the shower would have200

produced if it had arrived at θ = 38◦. Finally we use a high qual-201

ity sample of hybrid events to relate S 38◦ to EFD. The system-202

atic uncertainties in determining ES D coming from the FD sum203

up to 22%. Several activities are on-going to reduce the sys-204

tematic uncertainties of the energy estimate, e.g. the detector205

calibration uncertainty and the uncertainty of the fluorescence206

yield. Reducing these uncertainties will make it desirable to de-207

convolve the energy spectrum using the estimate of the energy208

resolution.209

The combination of the high statistics obtained with the sur-210

face detector and the extension to lower energies using hybrid211

observations enables the precise measurement of both the ankle212

and the flux suppression at highest energies. With the present213

spectrum we reject the hypothesis that the cosmic ray spectrum214

continues in the form of a power-law above an energy of 4×1019215

eV with more than 20σ. This result is independent of the sys-216

tematic uncertainties in the energy scale, the suppression at high217

energies can be due to the GZK cutoff[14] or just that sources218

are running out of power[15]. The astrophysical interpretation219

of the ankle depends on several factors like the primary com-220

position and the sources distribution, see [16] for more details.221

A precise measurement of the energy spectrum, together with222

anisotropy and mass composition studies in this energy range,223

will shed light on the origin of the highest energy particles ob-224

served in nature [17, 18].225

References226

[1] The Pierre Auger Collaboration, NIMA 523 (2004) 50.227



[4] F. Salamida, for The Pierre Auger Collaboration Proc. 32th ICRC, Beijing230

(2011), arXiv:1107.4809.231

[5] D. Barnhill, for The Pierre Auger Collaboration Proc. 29th ICRC, Pune232

(2005), 7, 291. astro-ph/0507590233

[6] D. Allard, for The Pierre Auger Collaboration Proc. 29th ICRC, Pune234

(2005), 7, 71. astro-ph/0511104235

[7] R. Pesce, for The Pierre Auger Collaboration Proc. 32th ICRC,236

arXiv:1107.4809 (2011).237

[8] M. Ave, for The Pierre Auger Collaboration Proc. 30th ICRC, Merida238

(2007), 4, 601, arXiv:0709.2125239

[9] H. Barbosa et al., Astropart. Phys., 22 (2004) 159.240

[10] M. Nagano, K. Kobayakawa, N. Sakaki, K. Ando, Astropart. Phys. 22241

(2004) 235.242

[11] The Pierre Auger Collaboration, JINST, in press (2013)243

[12] The Pierre Auger Collaboration, Astropart. Phys. 34 (2011) 368.244

[13] M. Settimo, for The Pierre Auger Collaboration, Eur. Phys. J. Plus. 127245

(2012) 87.246

[14] K. Greisen, Phys. Rev. Lett. 16, 748 (1966); G. T. Zatsepin and V. A.247

Kuzmin, Pis’ma Zh. Eksp. Teor. Fiz. 4, 114 (1966) JETP Lett. 4, 78248

(1966).249

[15] D. Allard, Astropart. Phys., 39-40 (2012) 33.250

[16] M. Unger, arXiv:0812.2763 (2008).251

[17] P. Facal, for The Pierre Auger Collaboration Proc. 32th ICRC,252

arXiv:1107.4804 (2011).253

[18] E. M. Santos, for The Pierre Auger Collaboration Proc. 32th ICRC,254

arXiv:1107.4805 (2011).255

4


Previous HiRes and AGASA measurements of UHE CR spectra

HiRes Group: astro-ph/0703099

- 5.1 +/- 0.7


Comparison HiRes-AUGER


Pierre Auger Observatory: the mass composition (1)


Fluorescence detectors field of view includes heights 1km- 5km above the sea-level: this is sufficient to observe the major part of the showers longitudinal development.


Pierre Auger Observatory: the mass composition (2)First measurement of the depth of shower maximum over 3 decades in energyDepth of shower maximum premiere observable for mass composition studies

HEAT data extends the FOV of the fluorescence detector up to 60˚ Extension of the depth of shower maximum measurements down to 1017 eV

Compared to expectations from proton and ironEPOS-LHC, QGSJETII-04, Sybill2.1 as hadronic interactions models

10

Porcelli #420

HEAT+FD

FDXmax resolution ~20 g cm-2

Syst uncertainty < 13 g g cm-2

<Xmax> became lower with ECR Xmax distribution became narrower with ECR

Increase of the mean mass with the energy ?? Inadequate interaction models for the simulation of the CR interaction and shower development in the atmosphere ?

ICRC-2015



EPOS-LHC (Variance of lnA)

QGSJetII-04 (Variance of lnA)

From the depth of shower maximum to primary mass (lnA)

Epos-LHC

QGSJetII-04

Similar trend for both models:

heavier composition at low energies

(largest mass dispersion), lightest one at ≈ 2x1018

eV, getting heavier again towards higher energies

(smaller mass dispersion)[N.B: very few data above ≈ 40 EeV)

11

Porcelli #420

Not only inferences on mass but test of models tooThe conversion to σ2(lnA)

through QGSJETII-04 yields unphysical results

From the depth of shower maximum to primary mass (ln A)

ICRC-2015



(Simple) Model of UHECR to reproduce the Auger spectrum and Xmax distributions at the same timeHomogeneous distribution of identical sources accelerating p, He, N and Fe nuclei.

Fit parameters: injection flux normalization and spectral index γ, cutoff rigidity Rcut, p-He-N-Fe fractions

γ-1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

/V)

cut

(R10

log

18

18.5

19

19.5

20

20.5

0

2

4

6

8

10

12

γ

-1 0 1 2

200

250

300

350

Rcut and γ

(E/eV)10

log18 18.5 19 19.5 20

]-2

[g

cm

⟩m

axX⟨

650

700

750

800

850HHeNFe

EPOS-LHC

(E/eV)10

log18 18.5 19 19.5 20

]-2

) [g

cm

max

(Xσ

20

40

60 H

He

NFe

Energy spectrum and elements fractions<Xmax> and σ(Xmax)

What do spectrum and composition data tell us?

Best fit with very hard injection spectra (γ ≤ 1)Flux limited by maximum energy at the sources (Rcut ≤ 101..7 eV

Di Matteo #249

13

ICRC-2015


Pierre Auger Observatory: the muon content2.2 “Shower properties measurements might impose constraints on hadronic interaction models

at energies well beyond the reach of accelerator-based experiments...”

Longitudinal development of

the muonic component

Shower properties (mass-sensitive) measured with the surface detector

Muon content vs Energy in

inclined

showers

Rise-time asymmetry of shower signals vs zenith angle

14

Collica #336 Minaya #405

ICRC-2015

Testing hadronic models: the EAS muon content (FD and SD data)Horizontal showers (θ > 60˚) dominated by muons (em component largely absorbed)

Estimation of the number of muons vs energy from horizontal showers observed by FD and SD

Average n. of muons vs energy Average n. of muons vs <Xmax> at 10 EeV

High abundance of muons in dataSystematic uncertainty inherited from

energy scale

Fe

p

Collica #336

Predictions for n. of muons from Xmax-derived lnA

Tension between n. of muons and XmaxDeficit of muons in simulations between

30% and 80%15

174 evs

Testing hadronic models: the Muon Production Depth (SD data)

Horizontal showers (θ > 60˚) dominated by muons (em component largely absorbed)Muon production depth can be reconstructed from the time structure of SD signals in horizontal EAS

Max of the MPD distributions vs E Conversion of the max of the MPD distributions to lnA

481 evs

Evolution vs E for data flatter than pure p or Fe in both models

Data bracketed by QGSJetII-04

Comparison with lnA from Xmax data:values compatible within 1.5 σ for QGSJetII-04

incompatible at > 6 σ for Epos-LHC

Collica #336

16


A detector for UHECR in the Nord Hemisphere: the Telescope Array Hybrid Detector


The Telescope Array Fluorescence Detector


Telescope Array: an event in the Fluorescence Detector


Telescope Array: measurement of the UHECR spectrum - 1


Telescope Array: measurement of the UHECR spectrum - 2


Telescope Array: measurement of the UHECR composition (1)


Telescope Array: measurement of the UHECR composition (2)


Combined PAO and TA measurement of the UHECR spectra and composition – ICRC 2015 (1)

Data SamplesAuger:

I 8 yearsI hybrid (at least one surface

detector station)I 24 telescopesI 19,759 events above 1017.8 eV,

7365 events above 1018.2 eVI PRD 90 (2014) 12, 122005

TA:I 5 yearsI hybrid (at least three surface

detector station)I Middle Drum telescopes (MD)I 438 events above 1018.2 eVI APP 64 (2014) 49

18 18.5 19 19.5 20ev

ents

1

10

100

1000

Auger 2014 (8 yr)

TA MD 2014 (5 yr)

lg(E/eV)18 18.5 19 19.5 20

ratio

Aug

er/T

A

4

10

2030

3

Composition from Shower Maximum (Xmax)

Telescope Array Collaboration, APP 64 (2014) 49:

“[...] good agreement is evident between data and a light, largely protonic, composi-tion when comparing the measurements to predictions obtained with the QGSJetII-03 and QGSJet-01c models.”

Pierre Auger Collaboration, PRD 90 (2014) 12, 122005:

“[...] simulations have been performed using the three contemporary hadronic inter-action models (QGSJETII-04, EPOS-LHC, SIBYLL2.1). [...] there is an evolutionof the average composition of cosmic rays towards lighter nuclei up to energiesof 1018.27 eV. Above this energy, the trend reverses and the composition becomesheavier.”

4



Average Shower Maximum, hXmaxi

Energy log10(E/eV)

<Xmax

>[gm/cm

2 ]

Proton

Iron

18.5 19 19.5 20650

700

750

800

850DataQGSJETII(03QGSJET(01cSYBILL 2.1

Telescope Array Collaboration, APP 64 (2014) 49

E [eV]1018 1019 1020

hXm

axi[g

/cm

2 ]

650

700

750

800

850 data ± sstat± ssys

EPOS-LHCSibyll2.1QGSJetII-04

iron

proton

E [eV]1018 1019 1020

s(X

max)[g

/cm

2 ]

0

10

20

30

40

50

60

70

80

iron

proton

Pierre Auger Collaboration, PRD 90 (2014) 12, 122005

5



Different Analysis StrategiesSteven Saffi, University of Adelaide Ben Stokes, University of Utah

Auger:

I minimize measurement biasI result: “hXmaxi in atmosphere”I compare to: simulations at

generator level

TA:

I maximize statisticsI result: “hXmaxi in detector”I compare to: simulations including

detector effects6Result

lg(E/eV)18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20

]2 [g

/cm

⟩m

axX⟨

700

720

740

760

780

800

820

TA MD 2014

TA MD⊗Auger 2014

preliminary

average difference: h�i = (2.9 ± 2.7 (stat.) ± 18 (syst.)) g/cm211

Mean and Standard Deviation of Xmax Distribution

E [eV]1018 1019 1020

hXm

axi[g

/cm

2 ]

650

700

750

800

850 data ± sstat± ssys

EPOS-LHCSibyll2.1QGSJetII-04

iron

proton

E [eV]1018 1019 1020

s(X

max)[g

/cm

2 ]

0

10

20

30

40

50

60

70

80

iron

proton

14


Pierre Auger Observatory: other physics results Not only ultra-high energy cosmic rays

Ulrich #401

p-air cross-section measured at two energies

Data consistent with a rising cross-section with E

Particle Physics Fundamental Physics

Fujii #319 Masias-Meza #074

Solar Physics

Best upper limits on ultra-relativistic magnetic monopoles

for γ ≥ 109

Factor 10 improvement for γ ≥ 1010

8-yr period of the last solar

cycle observed at higher

rigidities than neutron monitors

21

ICRC-2015 ICRC-2015 ICRC-2015


The Pierre Auger Observatory can identify UHE neutrinos 5

FIG. 1. Pictorial representation of the different types of showers induced by protons, heavy nuclei and “down-going” (DG) aswell as “Earth-skimming” (ES) neutrinos. The search for down-going showers initiated deep in the atmosphere is the subjectof this work.

flat-Earth approximation D = (Xground − Xint)/ cos θ,where Xint is the interaction depth and θ the zenith an-gle. For very inclined showers the curvature of the atmo-sphere is taken into account.

The four fluorescence sites are located at the perime-ter of the surface array viewing the atmosphere aboveit [23]. In this work only data collected with the SDof the Pierre Auger Observatory are used to search fordown-going neutrinos.

A. The Surface Detector

Since the beginning of its operation for physics analy-sis, in January 2004, the SD array has grown steadily andit has been recording an increasing amount of data. Itconsists of ∼1660 detector units (water-Cherenkov sta-tions) regularly spaced in a triangular grid of side 1.5km. Each detector unit is a cylindrical polyethylene tankof 3.6 m diameter and 1.2 m height containing 12,000liters of purified water. The top surface has three pho-tomultiplier tubes (PMTs) in optical contact with thewater in the tank. The PMT signals are sampled byflash analog digital converters (FADC) with a frequencyof 40 MHz. Each surface detector is regularly moni-tored and calibrated in units of vertical equivalent muons(VEM) corresponding to the signal produced by a µtraversing the tank vertically and through its center [24].The surface stations transmit information by radio linksto the Central Data Acquisition System (CDAS) locatedin Malargue. The PMTs, local processor, GPS receiver,and the radio system are powered by batteries regulatedby solar panels. Once installed, the local stations workcontinuously without external intervention.

B. The trigger

A local trigger selects signals, either with a high peakvalue, or with a long duration. The second condition

favours stations hit in the early stage of the shower devel-opment (moderately inclined or deeply induced showers).The global trigger requires either 4 stations satisfying oneof the conditions, or 3 stations satisfying the second one,in a compact configuration (see [25] for more details).

With the complete array, the global trigger rate isabout two events per minute, one half being actualshower events with median energy of 3 × 1017 eV.

III. SIMULATION OF NEUTRINOINTERACTIONS, INDUCED SHOWERS AND

THE RESPONSE OF THE SURFACEDETECTOR.

Monte Carlo simulations of neutrino-induced showersare used to establish identification criteria and to com-pute the acceptance of the SD to UHEνs. The wholesimulation chain is divided in three stages:

1. High energy processes:

• The ν-nucleon interaction is simulated withherwig [26].

• In the case of ντ CC interactions, the τ lep-ton propagation is simulated with a dedicatedcode and its decay (when necessary) withtauola [27].

2. The shower development in the atmosphere is pro-cessed by aires [28].

3. The Surface Detector simulation is performed withthe Offline software [29].

In the next subsections we discuss each stage in detail.

A. Neutrino interaction

herwig is a general-purpose event generator for high-energy processes, with particular emphasis on the de-tailed simulation of QCD parton showers. Here it is used

Let's remind: The SD is spread over a surface of ∼3000 km2 at an altitude of ∼1400 m above sea level. This corresponds to an average vertical atmospheric depth above ground of Xground = 880 g cm−2. The slant depth D is the total grammage traversed by a shower measured from ground in the direction of the incoming primary particle. In the flat-Earth approximation D = (Xground − Xint)/ cos θ, where Xint is the interaction depth and θ the zenith angle. For very inclined showers the curvature of the atmosphere is taken into account. 7

FIG. 2. Different types of atmospheric showers induced by neutrinos.

gated: L/W > 3, where L and W are the length andthe width (eigenvalues of the inertia tensor, as definedin [16]). These cuts reject only 10% of genuine inclinedshowers.

For events where all stations are aligned along one ofthe directions of the array, θrec cannot be computed andwe rely on the average speed of the event, 〈V 〉. These“in-line” events are of great importance since the MonteCarlo simulations show that low energy neutrinos (! 1018

eV) typically present this type of configuration in the SD.

There is an additional requirement for events consti-tuted by an in-line event plus a non-aligned station (anon-aligned event that would become in-line by remov-ing just one station). This kind of spatial configurationis particularly prone to bad reconstruction if the non-aligned station was triggered by accidental muons notbelonging to the shower front. To avoid this problemwe also reconstruct the in-line event obtained by the re-moval of the non-aligned station and require it to havemean ground speed compatible with a zenith angle largerthan 75◦.

V. IDENTIFICATION OF NEUTRINOCANDIDATES

For this analysis, the whole data period (1 Jan 04 -31 May 10), was divided into two separate samples. Se-lected events recorded between 1 Jan 04 and 31 Oct 07(equivalent to ∼ 1.4 years of a complete SD array work-ing continuosly) constitute the “training” sample, usedto develop and optimize the neutrino identification algo-rithms. Data collected between 1 Nov 07 and 31 May10 (equivalent to ∼ 2 yr of the full array), constitutethe “search” sample. These latter events were not pro-cessed before the final tuning of the algorithms definingthe neutrino identification criteria.

A. Discrimination of neutrinos from hadronicshowers

Neutrinos, unlike protons and heavier nuclei, can gen-erate showers initiated deeply into the atmosphere. Themain signature of these deep showers in the SD is a sig-nificant electromagnetic (EM) component spread in timeover hundreds of nanoseconds, especially in the regionon the ground at which the shower arrives earlier (seeFig. 5). On the other hand, hadron-induced showers starthigh in the atmosphere, their electromagnetic componentis fully absorbed and only high energy muons and theirradiative and decay products reach the surface, concen-trated within a few tens of nanoseconds.

We identify stations reached by wide EM-rich showerfronts via their Area-over-Peak ratio (AoP), defined asthe ratio of the integral of the FADC trace to its peakvalue, normalized to 1 for the average signal producedby a single muon. In background horizontal showers themuons and their electromagnetic products are concen-trated within a short time interval, so their AoP is closeto 1. In the first stations hit by a deep inclined shower,it is typically between 3 and 5 (see left panel of Fig. 6).

To quantify the distinctive features of hadronic anddeeply penetrating showers induced by neutrinos at largezenith angle, improve the separation between the samplesand enhance the efficiency, while keeping a simple physi-cal interpretation of the identification process, we choosea multivariate technique known as the Fisher discrimi-nant method [35]. To tune it we used as a “signal” sam-ple the Monte Carlo simulations – exclusively composedof neutrino-induced showers – and as “background” thetraining sample introduced above – overwhelmingly, ifnot totally, constituted of nucleonic showers. We use realdata to train the Fisher discrimination method, insteadof simulations of hadronic showers, for two main reasons:

• the composition of the primary flux is not known,and moreover the interaction models used to sim-ulate hadronic showers may bias some features ofthe tail of the distributions of the observables usedin this analysis.


The Pierre Auger Observatory can identify UHE neutrinos8

FIG. 3. Left panel: Event produced by a nearly horizontal shower (θrec = 80◦). The footprint (ellipse) is elongated along thereconstructed direction of arrival (arrow). Right panel: a non-inclined event with θrec = 79◦. The major axis of the footprintand the reconstructed direction of arrival do not point in the same direction. Close inspection of the event suggests that stations3 and 5 are accidental and corrupt the reconstruction. The numbers indicate the triggering order of the stations.

mean ground speed ⟨V⟩ [m ns

⟨V⟩ compat.with

]-1 0.29 0.3 0.31 0.32 0.33 0.34 0.350

100200300400500600700800900

1000

°>75recθ

arcsin(c/⟨V⟩) < 75°

Eve

nts

FIG. 4. Distribution of the mean ground speed of the signalfor events with θrec > 75◦ acquired between 1 January 2004and 31 October 2007.

• the detector simulation may not account for all pos-sible detector defects or fluctuations that may con-tribute to the background to ultra-high energy neu-trinos, while the real data contain all of them, in-cluding those which are not well known, or evennot yet diagnosed.

Note that, since we apply a statistical method for the dis-crimination, the use of real data as a background sampledoes not imply that we assume it contains no neutrinos,but just that, if any, they constitute a small fraction ofthe total recorded events.

After training the Fisher method, a good discrimi-

FIG. 5. Upper panel : sketch of an inclined shower inducedby a hadron interacting high in the atmosphere. The EMcomponent is absorbed and only the muons reach the detector.Lower panel : deep inclined shower. Its early region has asignificant EM component at the detector level.

nation is found when using the following ten variables[14]: the AoP of the four earliest triggered stations ineach event, their squares, their product, and a globalearly-late asymmetry parameter of the event. We in-clude the square of the AoP because when the distribu-tion of the input variables is not gaussian the additionof a non-linear combination of them improves the dis-crimination power [36]. The product of the AoP of theearliest four stations in the event aims at minimizing therelative weight of an accidentally large AoP produced,

Genuine inclined showers have a “footprint” (configuration of the stations) elongated in the direction of arrival (left panel of Fig. 3). The apparent speed of propagation of the signal, along the major axis of the footprint, is concentrated around the speed of light c


The Pierre Auger Observatory can identify UHE neutrinos

8



⟨V⟩ compat.with

]-1 0.29 0.3 0.31 0.32 0.33 0.34 0.350

100200300400500600700800900

1000

°>75recθ


Eve

nts







To select neutrinos event candidates: compute the apparent speed of propagation of the trigger between every pair of stations (Vij) and the average speed of the event (⟨V ⟩),


The Pierre Auger Observatory can identify UHE neutrinos

8



⟨V⟩ compat.with

]-1 0.29 0.3 0.31 0.32 0.33 0.34 0.350

100200300400500600700800900

1000

°>75recθ


Eve

nts







Stringent neutrino- and photon-flux limits at EeV energies

Bleve #1103

Observables to select neutrinos: shape of the footprint and time structure of signals in very inclined showers (θ>60˚)

EAS observables to select

photons: shape of the LDF and

time structure of signals in

showers with 30<θ<60˚

NEUTRINOS PHOTONS

Top-down models strongly disfavoredFirst limit from an EAS array below WB bound12

ICRC-2015

First limit from an EAS array below WB bound

Isotropy or anisotropy of the U.H.E. sky

• U.H.E. particles (>1018 eV) only slightly deflected by the galactic/intergalactic magnetic field

• The arrival direction of U.H.E. CR can identify the position in the sky of the accelerating sources

• Assuming that U.H.E. CR are extragalactic from the measurement of their incoming directions we can have hints about the isotropy/anisotropy of the U.H.E. universe.



The coordinates of the fixed equatorial system are:- the time angle (H) (right ascension), which is the angular distance between the

mid-point ♈ and the intersection of the celestial meridian passing through the star with the celestial equator; it is measured in hours, minutes and seconds (0h, 24h) starting from point ♈ clockwise (or in degrees 0o, 360o );

- the declination, i.e. the angular distance between the intersection of the celestial meridian for the star and the celestial equator and the star itself, measured along the celestial meridian; it is measured in degrees, first and second (0o, 90o) starting from the equator celestial to the celestial poles; we speak of positive declination in the northern hemisphere and negative declination in the austral one.

Horizontal coordinates system. Equatorial coordinates system.

Representing the arrival C.R. directions, the sky


In the last 2100 years, the precession of the equinoxes has rotated the Earth's axis by 30° to its right: at the spring equinox, while 2100 years ago the Sun was passing through the constellation of Aries, today, due to the precession, the same transits in that of Pisces.

The gamma point (from the symbol ♈ similar to γ that distinguishes the constellation of Aries), is one of the two equinoctial points in which the celestial equator intersects the ecliptic .When the Sun, in its apparent annual motion, passes through this point, the Earth finds itself in correspondence with the spring equinox: it is the point at which the Sun is positioned on March 21st calculated from the position of the Earth.

What's the ♈ point ?


In Equatorial coordinates:- the declination (δ) of a star is its angular

distance from the celestial equator (from -90o to the south pole, +90o to the north pole)

- the right ascension (α) of a star is the angular distance between the ♈ point and the intersection of his hour circle with the celestial equator; it is measured starting from the point of rotation counter-clockwise in degrees (0o, 360o) or equivalently in hours placing 1h = 15o.

… so, the sky coordinates


The density matter is supposed to be uniform into a narrow band, in "declination" (-90o,+90o) that spans on the full range in "right ascension" (-180o,+180o). If the C.R. sources are uniformly distributed in the sky the arrival directions of C.R. should be isotropic. In this case we can define the average of C.R. for an interval "i" in declination as

𝑛!"#$%"&$ =

∑!"#$ (%,!

'()*+,(-

)and in each "i,j" bin

(declination, right ascension) we expect to find

𝑛!,+$,-$./$0 = 𝑛!

"#$%"&$ ± 𝑛!"#$%"&$

Cosmic Rays isotropy/anisotropy


CR anisotropies ? The Compton-Getting effectThe CR flux on Earth is consistent with isotropy when the low-energy particles affected by the Sun are neglected. Small anisotropies are expected due to the global leakage of CRs from the Galaxy, to the possible contribution of individual sources, and due to the motion of the solar system in the Galaxy. In general, the presence of a cosmic ray anisotropy is strictly correlated with the streaming velocity V of the CR particles. This streaming velocity plays the same role as the drift velocity attained by electrons in the presence of an electric field. There isan anisotropy only if there is a net streaming velocity, which can expressed with a particular amplitude and phase. The amplitude of the CR anisotropy is defined as:

Imax , Imin represent the maximum and minimum intensity of cosmic rays from a given direction.

5.7 Anisotropies due to the Diffusion 153

is an anisotropy only if there is a net streaming velocity, which can expressed witha particular amplitude and phase. The amplitude of the CR anisotropy is defined as:

δ ≡ Imax − Imin

Imax + Imin(5.48)

where Imax, Imin represent the maximum andminimum intensity of cosmic rays froma given direction. Usually, the arrival direction of CRs is referred to the equatorialcoordinate system, see Extras # 2.

By simple dimensional arguments, the amplitude of the anisotropy depends on thestreaming velocity amplitude asV ∼ δc. It can be demonstrated using Lorentz invari-ance (Kachelriess 2008) that, for a flux of particles (such as the cosmic rays) withdifferential energy spectrum Φ(E) ∝ E−α , the streaming speed and the anisotropyamplitude are correlated through the spectral index α by:

V =[

δ

(α + 2)

]c (5.49)

Because the CR escape probability increases with energy, Eq. (5.40), the diffu-sion coefficient D is energy dependent as well. This corresponds to an increases ofthe streaming velocity V , according to Eq. (5.47). The expectation from our simpleconsiderations is that the amplitude δ of the anisotropy increases with energy. Thissimple prediction is confirmed by accurate calculations (Candia et al. 2003). Valuesas large as δ ∼ 10−1 can be obtained, depending on particle energy and on thestrength and structure of the galactic magnetic field.

Different predictions for an anisotropy amplitude of a dipole type (when the arrivalCR directions are expressed in the equatorial coordinate system) as a function of theCR energies are reported in Fig. 5.5. A dipole anisotropy is a form of anisotropy dueto the difference in the arrival intensity of particles from opposite directions, usuallyattributed to the motion of the observer relative to the source. As the CR diffusiondepends on the modeling of the galactic magnetic fields, two predictions (labeledwith “A” and “S” in the figure) refer to two different configurations of the galacticmagnetic fields. In the region of Ultra High Energy Cosmic Rays, above∼ 1018 eV, apossible galactic origin of these particles (model labeled with “Gal”) would producean anisotropy of large amplitude, δ ∼ 0.1. A much smaller anisotropy amplitude isexpected if the sources of CR is of extragalactic origin, as indicated by the modellabeled with “C-G Xgal.” The level of different anisotropy amplitudes can be testedwith experiments measuring the arrival direction of CRs in the region around andabove the knee.

From the experimental point of view, because of the small amplitude of theexpected anisotropy, a large data sample is necessary in order to have a statisticallysignificant measurement of (5.48). Many experimental studies on dipole anisotropies(also called large-scale anisotropies) are based on the fact that the exposure of thedetectors is uniform in the right ascension coordinate RA. The uniformity in theexposure guarantees that there is not bias from any particular sky region due toexperimental effects.


If the flux of Cosmic Rays is isotropic then the number of C.R. in each longitude bin should be compatible with a uniform distribution.If there is ONE source of C.R., or a reason for an excess of C.R., in one bin in "right ascension" the intensity of C.R. from the source direction will increase with respect to the average evaluated along the full declination band (and a deficit of C.R. will appear at 180o angular distance): the distribution of C.R. will show a "dipole".

100 times more events than the experimental one. These distributions were constructed in the

equatorial coordinate system. In our case, we consider a single coordinate only: a right ascension,

which varies from 0 to 360 degrees. All events distributed along a declination coordinate were

summarized.

Since the existence of the dipole anisotropy based on the ground-based observations is not

questioned, so far the task, as mentioned above, was to obtain its characteristics: the amplitude

and phase. We have approximately 600,000 coordinate values of right ascensions, reflecting the

direction of incidence of the particles in the experimental data.

The basis of the analysis is the hypothesis that there is the dipole in the experimental

distribution. For this reason the size of an integration bin equal to 180 degrees was chosen. In

our approach this bin reproduces an integration radius in HEALPIx method for the anisotropy

study in 3D map [16]. All events within this bin were integrated. The bin centre was shifting

through the entire range from 0 to 360 degrees with 5 degree step and the integration procedure

was repeated at each step. Then we took an average value for each 6 bins (we had 72 values in

total) and got 12 values which are shown in figure 1. The obtained dipole is demonstrated in

terms of relative intensities: Ir is the experimental one and Is is the reference one. The number

of events in the reference distribution was normalized to the experimental one.

Figure 1. The Ir/Is-1 depending on RA. Ir is the real intensity, Is is the simulated isotropic

intensity. The red line is a fit by the sine wave.

4. The results

The results were obtained by an approximation of the values in figure 1 by a sine function

with the Levenberg-Marquardt algorithm [17]. The amplitude A and phase � (a position of the

maximum) were obtained from this approximation: A=0.0013±0.0003, � =70±10 degree. For

the value of amplitude the factor k=2/⇡ (the di↵erence between amplitude of the real dipole and

the one obtained by the approximation) was taking into account. Uncertainties are the results

3

Several experiment have indicated that the C.R. arrival distribution is not isotropic and can be well represented with a "dipole". For example PAMELA reported the result shown in the figure on the side:Is is the expected intensity of C.R. in each bin in the hypothesis of isotropy, Ir is the measured intensity.In this analysis Is and Ir are intensities integrated over the full range in declination.In general anisotropies are energy and coordinates dependent.

Journal of Physics: Conference Series 675 (2016)doi:10.1088/1742-6596/675/3/032005

PAMELA

𝑓 𝛼 = 𝐴 ' cos 𝛼 − 𝜙

A=0.0013±0.0003, φ =70±10 degrees

One example of "Large Scale Anisotropy"

In this analysis the "reference flux" Is has been obtained "scrambling" the observed data (attributing to the events a "wrong time"). The same events has been used ~100 times, with different "sidereal time" in order to reduce the fluctuations on Is.


CR flux anisotropy vs detector position and energy


R. Iuppa RICAP 2013. Roma - May 23rd, 2013

A data compilation

From ARGO-YBJ 32° ICRC contribution

Usually, data are projected along the R.A. projection (e.g. IC22):

Then a 2-harmonics fit is performed and amplitude and phase of the first harmonics are discussed (see the compilation for reference). They are generally interpreted as important signature, as the dipole is a trace of the source distribution. BUT…

A data compilation on CR anisotropy

A


Other examples of measured C.R. anisotropy


Representation of anisotropies with spherical harmonicsGiven a spherical coordinate system, a point on a sphere of unit radius isidentified by the versor

where we indicated with θ and φ, respectively, the angle of zenith and azimuth. Spatial distribution on this unit sphere of a series of objects can be described through the use of a series of functions, called spherical harmonics, that depend on the two angles θ and φ. Spherical harmonics are an orthogonal set of functions solution of the Legendre equation. The solutions of the Legendre equation are polynomial (having fixed ℓ positive and integer) and are a generalization of the Legendre polynomials which are obtainable for m = 0. These solutions have the expression:

where Pl (x) are the Legendre polynomials. The spherical harmonics are therefore defined as:

with 𝑚 ≤ ℓ.


Representation of anisotropies with spherical harmonicsSpherical harmonics are a set of orthonormal functions, satisfying the following orthogonality rule:

explicit form of the spherical harmonics up to the third degree (ℓ = 3)


Representation of anisotropies with spherical harmonicsAny distribution Φ(θ,φ) on the unit sphere can therefore be describedthrough the development in multipoles, that is through a combination of spherical harmonics 𝑌ℓ2, each multiplied by the respective coefficient 𝑎ℓ2, through the expression:

where n is the maximum degree of approximation and Φ34 is a constant.

For n=0 we obtain the isotropic component of the distribution Φ(θ,φ):

For n=1 the relative dipolar component of the distribution Φ(θ,φ) is also obtained

where:

is the versor of the generic direction (θ,φ) while 𝐷(𝜃0!-, 𝜙0!-) is the dipole vector,relative to the direction (θdip, φdip)


Representation of anisotropies with spherical harmonics

𝐷(𝜃0!-, 𝜙0!-) is the dipole vector, relative to the direction (θdip, φdip), defined as

For n=2 the sum is extended to the second order, which returns the term ofquadrupole. By increasing the value of n, the terms of the expansion of ever higher order are then introduced, obtaining an always better approximation of the distribution that one wants to describe.


Another example on real data (ANTARES)The figure shows the "deviations" from the mean value of the number of "down-going" muons measured by ANTARES, as a function of the right ascension angle (incorrect data for all possible systematic effects).We try to represent such data with a "constant", with a harmonic function of the first order and with a function in which the first and second order appear


ARGO: Large scale Anisotropy (LSA)


ARGO: Medium Scale Anisotropy (MSA)


C.R. observed anisotropyR. Iuppa RICAP 2013. Roma - May 23rd, 2013

Cosmic ray anisotropy 5

Abbasi R. et al. (IceCube Collaboration), ApJ 746, 33 (2012)


Recent observations of CR anisotropy


Recent observations of the CR anisotropy

6

Tibet AS-γ - Science 20 October 2006: Vol. 314 no. 5798 pp. 439-443

MILAGRO - 2009 ApJ 698 2121

Super-Kamiokande – ICRC 2007 Proceedings

ICE-CUBE - 2010 ApJ 718 L194

ARGO-YBJ– ICRC 2011 Proceedings

10 TeV 5 TeV

2 TeV

4 TeV

20 TeV


IceCube: study of TeV-PeV Cosmic-Ray anisotropy


Anisotropy as a function of CR Energy


LSA as a function of the primary energy 7

0.9 TeV

1.5 TeV

2.4 TeV

3.6 TeV

7.2 TeV

12.5 TeV

23.6 TeV

Tibet ASγ

Anisotropy seems to disappear. From the absence of the CG effect they infer the corotation of GCR with the GMF environment

ARGO-YBJ


The observed CR anisotropy power spectrum


4-pole, 6-pole and 8-pole (the old 2° harmonics…)

ICECUBE has been the first experiment showing a CL spectrum of the arrival direction distribution. Strong L=2-3-4 components are visible.

When a “traditional” 1D R.A. projection is presented, a 2 harmonics function is fot to the experimental distribution (ARGO-YBJ example).

There are strong L=2-3-4 components in the CR anisotropy, even below 1015 eV. If dipole means

sources, what is this power related to?



What is behind the intermediate scale anisotropies? Stochastic MHD approach

Giacinti& Sigl Phys. Rev. Lett. 109, 071101 (2012)

Energy-dependent small scale anisotropies naturally arise from the local concrete realization of the turbulent magnetic field within the cosmic ray scattering length.

The CR arrival distribution at Earth contains multipoles:

a

Dipole amplitude

Dipole direction

Direction after the propagation of the particle with initial direction n. It depends

on the magnetic field turbulence spectrum!

There is a connection between the observed angular power spectrum and the magnetic field turbulence spectrum.

What can we learn from the observed anisotropies ?



Outlook to the future: towards a complete TeV CR sky-map

19

ARGO-YBJ + IceCube-59

ARGO-YBJ 1 TeV

3 hr = 45°

Smoothing radius 10°

PSF-Smoothed map

Outlook to the future: towards a complete TeV CR sky-map


154 5 Diffusion of Cosmic Rays in the Galaxy

As an example, let us consider the n events that a particular experimental apparatushas classified as CRs in the energy range between E and E + ∆E. The n events arethen analyzed in terms of the so-called Rayleigh formalism of harmonic analysis.The Rayleigh formalism gives the amplitudeA (that can be identified with the δ givenin Eq.5.48) and phase φ of the first harmonic, and additionally the probability P fordetecting a spurious amplitude due to fluctuations from a sample of n events whichare drawn from a uniform distribution (Mardia and Jupp 1999). Two quantities canbe obtained from the dataset, with the sum includes n right ascension values RAi:

S = 2n

n∑

i=1

sin(RAi), C = 2n

n∑

i=1

cos(RAi). (5.50)

If the CR arrival directions are completely random, clearly S = C = 0. In thepresence of anisotropy, the amplitude A and the phase Φ of the first harmonic aregiven by:

A =√C2 + S2; φ = arctan

SC. (5.51)

The results of some experiments measuring CRs at different energies are reportedin Fig. 5.5. Few evidences on large-scale anisotropies were reported from extensive

Fig. 5.5 The anisotropy amplitude as a function of energy. In red are the limits obtained by theAuger Observatory over the full energy range as reported at the ICRC in 2013 [see Abreu et al.(2011) for the reference to the experiments]. The lines denoted as A and S up to 1018 eV refer topredictions for two different galactic magnetic field models. The predictions for a purely galacticorigin of ultra-high energy cosmic rays (UHECRs) is denoted as (Gal), and the expectations fromthe Compton-Getting effect for an extragalactic component of CRs (C-GXgal). In this case, theCRs are assumed to be isotropic in the cosmic microwave background rest frame. Courtesy of thePierre Auger Observatory

C.R. isotropy/anisotropyM. Spurio – Particle and Astrophysics - Springer


Pierre Auger Observatory: the CR arrival direction (1)2.3 “...a systematic study of the arrival directions, that will indicate if there is anisotropy in the distribution and/or clusters which would indicate the existence of point sources...”

17

ICRC-2015

“...a systematic study of the arrival directions, that will indicate if there is anisotropy in the distribution and/or clusters which would indicate the existence of point sources...”

No room for anisotropy from these data !


Pierre Auger Observatory, the CR arrival direction (2)Sept. 2017: new result !!COSMIC RAYS

Observation of a large-scale anisotropyin the arrival directions of cosmicrays above 8 × 1018 eVThe Pierre Auger Collaboration*†

Cosmic rays are atomic nuclei arriving from outer space that reach the highest energiesobserved in nature. Clues to their origin come from studying the distribution of theirarrival directions. Using 3 × 104 cosmic rays with energies above 8 × 1018 electronvolts, recorded with the Pierre Auger Observatory from a total exposure of 76,800 km2

sr year, we determined the existence of anisotropy in arrival directions. The anisotropy,detected at more than a 5.2s level of significance, can be described by a dipole with anamplitude of 6:5þ1:3

"0:9 percent toward right ascension ad = 100 ± 10 degrees and declinationdd = "24þ12

"13 degrees. That direction indicates an extragalactic origin for these ultrahigh-energy particles.

Particles with energies ranging from below109 eV up to beyond 1020 eV, known as cos-mic rays, constantly hit Earth’s atmosphere.The flux of these particles steeply decreasesas their energy increases; for energies above

10 EeV (1 EeV ≡ 1018 eV), the flux is about oneparticle per km2 per year. The existence of cosmicrayswith suchultrahigh energies has been knownfor more than 50 years (1, 2), but the sites andmechanisms of their production remain a mys-tery. Information about their origin can be ob-tained from the study of the energy spectrumand the mass composition of cosmic rays. How-ever, the most direct evidence of the location ofthe progenitors is expected to come from studiesof the distribution of their arrival directions. In-dications of possible hot spots in arrival direc-tions for cosmic rays with energies above 50 EeVhave been reported by the Pierre Auger and Tel-escope Array Collaborations (3, 4), but the statis-tical significance of these results is low.We reportthe observation, significant at a level ofmore than5.2s, of a large-scale anisotropy in arrival direc-tions of cosmic rays above 8 EeV.Above 1014 eV, cosmic rays entering the atmo-

sphere create cascades of particles (called exten-sive air-showers) that are sufficiently large to reachthe ground. At 10 EeV, an extensive air-shower(hereafter shower) contains ~1010 particles spreadover an area of ~20 km2 in a thin disc movingclose to the speed of light. The showers contain anelectromagnetic component (electrons, positrons,and photons) and a muonic component that canbe sampled using arrays of particle detectors.Charged particles in the shower also excite ni-trogen molecules in the air, producing fluores-cence light that can be observed with telescopesduring clear nights.The Pierre AugerObservatory, located near the

city of Malargüe, Argentina, at latitude 35.2°S, isdesigned to detect showers produced by primary

cosmic rays above 0.1 EeV. It is a hybrid system, acombination of an array of particle detectors anda set of telescopes used to detect the fluorescencelight. Our analysis is based on data gathered from1600 water-Cherenkov detectors deployed overan area of 3000 km2 on a hexagonal grid with1500-m spacing. Each detector contains 12metrictons of ultrapure water in a cylindrical container,1.2mdeepand 10m2 inarea, viewedby three9-inchphotomultipliers. A full description of the obser-vatory, together with details of the methods usedto reconstruct the arrival directions and energiesof events, has been published (5).It is difficult to locate the sources of cosmic

rays, as they are charged particles and thus in-teract with themagnetic fields in our Galaxy andthe intergalactic medium that lies between thesources and Earth. They undergo angular deflec-tionswith amplitude proportional to their atomicnumber Z, to the integral along the trajectory ofthemagnetic field (orthogonal to the direction ofpropagation), and to the inverse of their energyE. At E ≈ 10 EeV, the best estimates for the massof the particles (6) lead to a mean value for Z be-tween 1.7 and 5. The exact number derived isdependent on extrapolations of hadronic physics,which are poorly understood because they liewell beyond the observations made at the LargeHadron Collider. Magnetic fields are not wellconstrained bydata, but if we adopt recentmodelsof the galactic magnetic field (7, 8), typical valuesof the deflections of particles crossing the galaxyare a few tens of degrees forE/Z= 10 EeV, depend-ing on the direction considered (9). Extragalacticmagnetic fields may also be relevant for cosmicrays propagating through intergalactic space (10).However, even if particles from individual sourcesare strongly deflected, it remains possible that an-isotropies in the distribution of their arrival di-rectionswill be detectable on large angular scales,provided the sources have a nonuniform spatialdistribution or, in the case of a single dominantsource, if the cosmic-ray propagation is diffusive(11–14).

Searches for large-scale anisotropies are con-ventionally made by looking for nonuniformitiesin the distribution of events in right ascension(15, 16) because, for arrays of detectors that op-erate with close to 100% efficiency, the total expo-sure as a function of this angle is almost constant.The nonuniformity of the detected cosmic-ray fluxin declination (fig. S1) imprints a characteristicnonuniformity in the distribution of azimuthangles in the local coordinate systemof the array.From this distribution it becomes possible to ob-tain information on the three components of adipolar model.

Event observations, selection,and calibration

We analyzed data recorded at the Pierre AugerObservatory between 1 January 2004 and 31August 2016, from a total exposure of about76,800 km2 sr year. The 1.2-m depth of the water-Cherenkov detectors enabled us to record eventsat a useful rate out to large values of the zenithangle, q.We selected eventswith q <80° enablingthe declination range −90° < d < 45° to be ex-plored, thus covering 85% of the sky.We adopted4 EeV as the threshold for selection; above thatenergy, showers falling anywhere on the arrayare detectedwith 100% efficiency (17). The arrivaldirections of cosmic rays were determined fromthe relative arrival times of the shower front ateach of the triggered detectors; the angular res-olution was better than 1° at the energies con-sidered here (5).Twomethods of reconstruction have beenused

for showers with zenith angles above and below60° (17, 18). These have to account for the effectsof the geomagnetic field (17, 19) and, in the caseof showers with q < 60°, also for atmospheric ef-fects (20) because systematic modulations to therates could otherwise be induced (see supple-mentary materials). The energy estimators forboth data sets were calibrated using events de-tected simultaneously by the water-Cherenkovdetectors and the fluorescence telescopes, witha quasi-calorimetric determination of the energycoming from the fluorescencemeasurements. Thestatistical uncertainty in the energy determina-tion is <16% above 4EeV and <12%above 10 EeV,whereas the systematic uncertainty on the abso-lute energy scale, common to both data sets, is14% (21). Evidence that the analyses of the eventswith q < 60° and of those with 60° < q < 80° areconsistentwith each other comes from the energyspectra determined for the two angular bands.The spectra agree within the statistical uncer-tainties over the energy range of interest (22).We consider events in twoenergy ranges, 4EeV<

E < 8 EeV and E ≥ 8 EeV, as adopted in previousanalyses [e.g., (23–25)]. The bin limits follow thosechosenpreviously in (26, 27). Themedian energiesfor these bins are 5.0EeVand 11.5EeV, respectively.In earlier work (23–25), the event selection re-quired that the station with the highest signalbe surrounded by six operational detectors—ademanding condition. The number of triggeredstations is greater than four for 99.2%of all eventsabove 4 EeV and for 99.9% of events above 8 EeV,

RESEARCH

The Pierre Auger Collaboration, Science 357, 1266–1270 (2017) 22 September 2017 1 of 5

*Author names and affiliations appear at the end of this paper.†Email: [email protected]

on October 31, 2017

http://science.sciencem

ag.org/Downloaded from

making it possible to use events with only fiveactive detectors around the one with the largestsignal. With this more relaxed condition, the ef-fective exposure is increased by 18.5%, and thetotal number of events increases correspond-ingly from 95,917 to 113,888. The reconstructionaccuracy for the additional events is sufficientfor our analysis (see supplementary materialsand fig. S4).

Rayleigh analysis in right ascension

A standard approach for studying the large-scaleanisotropies in the arrival directions of cosmicrays is to perform a harmonic analysis in rightascension, a. The first-harmonic Fourier compo-nents are given by

aa ¼ 2N

XN

i¼1

wi cos ai

ba ¼ 2N

XN

i¼1

wi sin ai ð1Þ

The sums run over all N detected events, eachwith right ascension ai, with the normalizationfactor N ¼

XN

i¼1wi. The weights, wi , are intro-

duced to account for small nonuniformities inthe exposure of the array in right ascension andfor the effects of a tilt of the array toward thesoutheast (see supplementarymaterials). Theaver-age tilt between the vertical and the normal tothe plane onwhich the detectors are deployed is0.2°, so that the effective area of the array is slight-ly larger for showers arriving from the downhilldirection. This introduces aharmonic dependencein azimuth of amplitude 0.3% × tan q to the ex-posure. The effective aperture of the array is de-termined everyminute. Because the exposure hasbeen accumulated over more than 12 years, thetotal aperture is modulated by less than ~0.6%as the zenith of the observatory moves in rightascension. Events are weighted by the inverse

of the relative exposure to correct these effects(fig. S2).The amplitude ra and phase ϕa of the first

harmonic of the modulation are obtained from

ra ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2a þ b2a

q

tanϕa ¼ baaa

ð2Þ

Table 1 shows theharmonic amplitudes andphasesfor both energy ranges. The statistical uncertain-ties in the Fourier amplitudes are

ffiffiffiffiffiffiffiffiffiffi2=N

p; the un-

certainties in the amplitude andphase correspondto the 68% confidence level of the marginalizedprobability distribution functions. The rightmostcolumn shows the probabilities that amplitudes

larger than those observed could arise by chancefrom fluctuations in an isotropic distribution.These probabilities are calculated as PðraÞ ¼expð–N r2a=4Þ (28). For the lower-energy bin (4EeV < E < 8 EeV), the result is consistent withisotropy, with a bound on the harmonic ampli-tude of <1.2% at the 95% confidence level. For theevents with E ≥ 8 EeV, the amplitude of the firstharmonic is 4:7þ0:8

%0:7%, which has a probability ofarising by chance of 2.6 × 10−8, equivalent to atwo-sided Gaussian significance of 5.6s. The evo-lution of the significance of this signal with timeis shown in fig. S3; the dipole became more sig-nificant as the exposure increased. Allowing for apenalization factor of 2 to account for the factthat two energy bins were explored, the signifi-cance is reduced to 5.4s. Further penalization forthe four additional lower-energy bins examinedin (23) has a similarly mild impact on the signif-icance, which falls to 5.2s. The maximum of the


0.9 0.92 0.94 0.96 0.98

1 1.02 1.04 1.06 1.08

1.1

0 60 120 180 240 300 360

Nor

mal

ized

rat

es

Right Ascension [deg]

data E>8 EeVfirst harmonic

Fig. 1. Normalized rate of events as a func-tion of right ascension. Normalized rate for32,187 events with E ≥ 8 EeV, as a function ofright ascension (integrated in declination). Errorbars are 1s uncertainties. The solid line showsthe first-harmonic modulation from Table 1,which displays good agreement with the data(c2/n = 10.5/10); the dashed line shows aconstant function.

0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

360 0

Fig. 2. Map showing the fluxes of particles in equatorial coordinates. Sky map in equatorialcoordinates, using a Hammer projection, showing the cosmic-ray flux above 8 EeV smoothed with a45° top-hat function. The galactic center is marked with an asterisk; the galactic plane is shownby a dashed line.

0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

180 -180

2MRS

5 EeV

2 EeV

Fig. 3. Map showing the fluxes of particles in galactic coordinates. Sky map in galacticcoordinates showing the cosmic-ray flux for E ≥ 8 EeV smoothed with a 45° top-hat function. Thegalactic center is at the origin. The cross indicates the measured dipole direction; the contoursdenote the 68% and 95% confidence level regions. The dipole in the 2MRS galaxy distribution isindicated. Arrows show the deflections expected for a particular model of the galactic magneticfield (8) on particles with E/Z = 5 or 2 EeV.

RESEARCH | RESEARCH ARTICLE

on October 31, 2017






aa ¼ 2N

XN

i¼1

wi cos ai

ba ¼ 2N

XN

i¼1

wi sin ai ð1Þ


XN






q

tanϕa ¼ baaa

ð2Þ



p; the un-





0.9 0.92 0.94 0.96 0.98

1 1.02 1.04 1.06 1.08

1.1

0 60 120 180 240 300 360

Nor

mal

ized

rate

sRight Ascension [deg]



0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

360 0


0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

180 -180

2MRS

5 EeV

2 EeV



on October 31, 2017



The Pierre Auger Collaboration, Science 357, 1266–1270 (2017) 22 September 2017


0.38

0.42

0.46

km

-2 sr

-1 y

r-1

-90

90

360 0

OBSERVATION OF A LARGE SCALE ANISOTROPY Auger, Science 57 (2017) 1266-1270

0.9 0.92 0.94 0.96 0.98

1 1.02 1.04 1.06 1.08 1.1

0 60 120 180 240 300 360

Nor

mal

ized

rat

es



harmonic analysis in right ascension

modulation is at right ascension of 100° ± 10°.Themaximum of the modulation for the 4 EeV <E < 8 EeV bin, at 80° ± 60°, is compatible withthe one determined in the higher-energy bin,although it has high uncertainty and the ampli-tude is not statistically significant. Table S1 showsthat results obtained under the stricter triggercondition and for the additional events gainedafter relaxing the trigger are entirely consistentwith each other.Figure 1 shows the distribution of the normal-

ized rate of events above 8 EeV as a function ofright ascension. The sinusoidal function corre-sponds to the first harmonic; the distribution iscompatible with a dipolar modulation: c2/n =10.5/10 for the first-harmonic curve and c2/n =45/12 for a constant function (where n is thenumber of degrees of freedom, equal to the num-ber of points in the plot minus the number ofparameters of the fit).The distribution of events in equatorial coor-

dinates, smoothedwith a 45° radius top-hat func-tion to better display the large-scale features, isshown in Fig. 2.

Reconstruction of thethree-dimensional dipole

In the presence of a three-dimensional dipole,the Rayleigh analysis in right ascension is sen-sitive only to its component orthogonal to therotation axis of Earth, d⊥. A dipole component inthe direction of the rotation axis of Earth, dz,induces no modulation of the flux in right ascen-sion, but does so in the azimuthal distribution ofthe directions of arrival at the array. A non-vanishing value of dz leads to a sinusoidal modu-lation in azimuth with a maximum toward thenorthern or the southern direction.To recover the three-dimensional dipole, we

combine the first-harmonic analysis in right as-cension with a similar one in the azimuthal angleϕ, measured counterclockwise from the east.The relevant component, bϕ, is given by an ex-pression analogous to that in Eq. 1, but in terms

of the azimuth of the arrival direction of theshower rather than in terms of the right as-cension. The results are bϕ = −0.013 ± 0.005 inthe 4 EeV < E < 8 EeV bin and bϕ = −0.014 ±0.008 in the E ≥ 8 EeV bin. The probabilitiesthat larger or equal absolute values for bϕ arisefrom an isotropic distribution are 0.8% and8%, respectively.Under the assumption that the dominant

cosmic-ray anisotropy is dipolar, basedonpreviousstudies that found that the effects of higher-ordermultipoles are not significant in this energy range(25, 29, 30), the dipole components and its direc-tion in equatorial coordinates (ad, dd) can beestimated from

d⊥ ≈ rahcos di

dz ≈ bϕcos ‘obshsin qi

ad ¼ ϕa

tan dd ¼ dz

d⊥ð3Þ

(25), where hcos di is the mean cosine of the dec-linations of the events, hsin qi is the mean sineof the zenith angles of the events, and ‘obs ≈−35.2° is the average latitude of the observa-tory. For our data set, we find hcos di = 0.78 andhsin qi = 0.65.The parameters describing the direction of

the three-dimensional dipole are summarizedin Table 2. For 4 EeV < E < 8 EeV, the dipoleamplitude is d = 2:5þ1:0

%0:7%, pointing close to thecelestial south pole, at (ad, dd) = (80°, −75°),although the amplitude is not statistically sig-nificant. For energies above 8 EeV, the total di-pole amplitude is d = 6:5þ1:3

%0:9%, pointing toward

(ad, dd) = (100°, −24°). In galactic coordinates,the direction of this dipole is (‘, b) = (233°,−13°). This dipolar pattern is clearly seen inthe flux map in Fig. 2. To establish whether thedepartures from a perfect dipole are merelystatistical fluctuations or indicate the pres-ence of additional structures at smaller angularscales would require at least twice as manyevents.

Implications for the origin ofhigh-energy cosmic rays

The anisotropy we have found should be seen inthe context of related results at lower energies.Above a fewPeV, the steepening of the cosmic-rayenergy spectrum has been interpreted as beingdue to efficient escape of particles from the gal-axy and/or because of the inability of the sourcesto accelerate cosmic rays beyond a maximumvalue of E/Z. The origin of the particles remainsunknown.Although supernova remnants are oftendiscussed as sources, evidence has been reportedfor a source in the galactic center capable ofaccelerating particles to PeV energies (31). Diffu-sive escape from the galaxy is expected to lead toa dipolar component with a maximum near thegalactic center direction (32). This is compatiblewith results obtained in the 1015 to 1018 eV range(15, 16, 23, 24, 33), which provide values for thephase in right ascension close to that of thegalactic center, aGC = 266°.Models proposing a galactic origin up to the

highest observed energies (34,35) are in increasingtension with observations. If the galactic sourcespostulated to accelerate cosmic rays above EeVenergies, such as short gamma-ray bursts orhypernovae, were distributed in the disk of thegalaxy, a dipolar component of anisotropy ispredicted with an amplitude that exceeds existingbounds at EeV energies (24, 33). In this sense, theconstraint obtained here on the dipole amplitude(Table 2) for 4 EeV < E < 8 EeV further disfavors apredominantly galactic origin. This tension couldbe alleviated if cosmic rays at a few EeV weredominated by heavy nuclei such as iron, butthis would be in disagreement with the lightercomposition inferred observationally at theseenergies (6). Themaximum of the flux might beexpected to lie close to the galactic center region,whereas the direction of the three-dimensionaldipole determined above 8 EeV lies ~125° fromthe galactic center. This suggests that the an-isotropy observed above 8 EeV is better explainedin terms of an extragalactic origin. Above 40 EeV,where the propagation should become less dif-fusive, there are no indications of anisotropiesassociated with either the galactic center or thegalactic plane (36).There have been many efforts to interpret the

properties of ultrahigh-energy cosmic rays in termsof extragalactic sources. Because of Liouville’stheorem, the distribution of cosmic rays mustbe anisotropic outside of the galaxy for an an-isotropy to be observed at Earth. An anisotropycannot arise through deflections of an originallyisotropic flux by a magnetic field. One predictionof anisotropy comes from the Compton-Getting


Table 2. Three-dimensional dipole reconstruction. Directions of dipole components are shown inequatorial coordinates.

Energy(EeV)

Dipolecomponent dz

Dipolecomponent d⊥

Dipoleamplitude d

Dipoledeclination dd (°)

Dipole rightascension ad (°)

4 to 8 −0.024 ± 0.009 0.006%0.003þ0.007 0.025%0.007

þ0.010 −75%8þ17 80 ± 60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 −0.026 ± 0.015 0.060%0.010þ0.011 0.065%0.009

þ0.013 −24%13þ12 100 ± 10

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

Table 1. First harmonic in right ascension. Data are from the Rayleigh analysis of the firstharmonic in right ascension for the two energy bins.

Energy(EeV)

Numberof events

Fouriercoefficient aa

Fouriercoefficient ba

Amplitudera

Phaseϕa (°)

ProbabilityP (≥ ra)

4 to 8 81,701 0.001 ± 0.005 0.005 ± 0.005 0.005 %0.002þ0.006 80 ± 60 0.60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 32,187 −0.008 ± 0.008 0.046 ± 0.008 0.047 %0.007þ0.008 100 ± 10 2.6 × 10−8

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


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d⊥ ≈ rahcos di


ad ¼ ϕa

tan dd ¼ dz

d⊥ð3Þ












Energy(EeV)

Dipolecomponent dz


Dipoleamplitude d



4 to 8 −0.024 ± 0.009 0.006%0.003þ0.007 0.025%0.007

þ0.010 −75%8þ17 80 ± 60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 −0.026 ± 0.015 0.060%0.010þ0.011 0.065%0.009

þ0.013 −24%13þ12 100 ± 10

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


Energy(EeV)

Numberof events



Amplitudera

Phaseϕa (°)


4 to 8 81,701 0.001 ± 0.005 0.005 ± 0.005 0.005 %0.002þ0.006 80 ± 60 0.60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 32,187 −0.008 ± 0.008 0.046 ± 0.008 0.047 %0.007þ0.008 100 ± 10 2.6 × 10−8

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


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equatorial coordinates

GC

modulation > 8 EeV at 5.2 σ

d = 6.5−0.9+1.3% αd,δd( ) = 1000,−240( )3d dipole > 8 EeV

0.38

0.42

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km

-2 sr

-1 y

r-1

-90

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180 -180

2MRS

5 EeV

2 EeV

with a similar analysis on azimuth angle:

first time!

25

Auger Observation of a Large scale anisotropy


Pierre Auger Observatory: the arrival direction (3)




aa ¼ 2N

XN

i¼1

wi cos ai

ba ¼ 2N

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wi sin ai ð1Þ


XN






q

tanϕa ¼ baaa

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0.9 0.92 0.94 0.96 0.98

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5 EeV

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on October 31, 2017






aa ¼ 2N

XN

i¼1

wi cos ai

ba ¼ 2N

XN

i¼1

wi sin ai ð1Þ


XN






q

tanϕa ¼ baaa

ð2Þ



p; the un-





0.9 0.92 0.94 0.96 0.98

1 1.02 1.04 1.06 1.08

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5 EeV

2 EeV



on October 31, 2017



The Pierre Auger Collaboration, Science 357, 1266–1270 (2017) 22 September 2017

Large scale anisotropies in the arrival directions of CRs arecharacterized by harmonic analysis in right ascension, a.The first-harmonic Fourier components are given by

where N = detected events= weight introduced to account for small

non-uniformities in the exposure of the array in right ascension.

The amplitude ra and phase φa of the first harmonic of the modulation are:

The dominant cosmic-ray anisotropy is dipolar, the dipole components and its direction in equatorial coordinates (ad, dd) can be estimated from


Pierre Auger Observatory: the arrival direction (4)The Pierre Auger Collaboration, Science 357, 1266–1270 (2017) 22 September 2017









d⊥ ≈ rahcos di


ad ¼ ϕa

tan dd ¼ dz

d⊥ð3Þ












Energy(EeV)

Dipolecomponent dz


Dipoleamplitude d



4 to 8 −0.024 ± 0.009 0.006%0.003þ0.007 0.025%0.007

þ0.010 −75%8þ17 80 ± 60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 −0.026 ± 0.015 0.060%0.010þ0.011 0.065%0.009

þ0.013 −24%13þ12 100 ± 10

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


Energy(EeV)

Numberof events



Amplitudera

Phaseϕa (°)


4 to 8 81,701 0.001 ± 0.005 0.005 ± 0.005 0.005 %0.002þ0.006 80 ± 60 0.60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 32,187 −0.008 ± 0.008 0.046 ± 0.008 0.047 %0.007þ0.008 100 ± 10 2.6 × 10−8

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


on October 31, 2017






aa ¼ 2N

XN

i¼1

wi cos ai

ba ¼ 2N

XN

i¼1

wi sin ai ð1Þ


XN






q

tanϕa ¼ baaa

ð2Þ



p; the un-





0.9 0.92 0.94 0.96 0.98

1 1.02 1.04 1.06 1.08

1.1

0 60 120 180 240 300 360

Nor

mal

ized

rat

es




0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

360 0


0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

180 -180

2MRS

5 EeV

2 EeV



on October 31, 2017



aα =2N

ωi cos(αi ) i=1

N

∑ bα =2N

ωi sin(αi ) i=1

N

∑ ωi

rα = aα2 + bα

2 tan(ϕα ) =bαaα

d⊥ =rα

< cosδ > ; dz = bϕ

cos(ℓobs )< sinθ > ; αd =ϕα ; tan(δd ) = dzd⊥

The dominant cosmic-ray anisotropy is dipolar, the dipole components and its direction in equatorial coordinates (ad, dd) can be estimated from

where z= the Earth axis<cos d> is the mean cosine of the declinations of the events <sin q> is the mean sine of the zenith angles of the events, lobs ≈ −35.2° is the average latitude of the observatory


Pierre Auger Observatory: the arrival direction (5)The Pierre Auger Collaboration, Science 357, 1266–1270 (2017) 22 September 2017

d⊥ =rα

< cosδ > ; dz = bϕ

cos(ℓobs )< sinθ > ; αd =ϕα ; tan(δd ) = dzd⊥




aa ¼ 2N

XN

i¼1

wi cos ai

ba ¼ 2N

XN

i¼1

wi sin ai ð1Þ


XN






q

tanϕa ¼ baaa

ð2Þ



p; the un-





0.9 0.92 0.94 0.96 0.98

1 1.02 1.04 1.06 1.08

1.1

0 60 120 180 240 300 360

Nor

mal

ized

rat

es




0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

360 0


0.38

0.42

0.46

km-2 sr

-1 yr-1

-90

90

180 -180

2MRS

5 EeV

2 EeV



on October 31, 2017











d⊥ ≈ rahcos di


ad ¼ ϕa

tan dd ¼ dz

d⊥ð3Þ












Energy(EeV)

Dipolecomponent dz


Dipoleamplitude d



4 to 8 −0.024 ± 0.009 0.006%0.003þ0.007 0.025%0.007

þ0.010 −75%8þ17 80 ± 60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 −0.026 ± 0.015 0.060%0.010þ0.011 0.065%0.009

þ0.013 −24%13þ12 100 ± 10

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


Energy(EeV)

Numberof events



Amplitudera

Phaseϕa (°)


4 to 8 81,701 0.001 ± 0.005 0.005 ± 0.005 0.005 %0.002þ0.006 80 ± 60 0.60

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .

≥8 32,187 −0.008 ± 0.008 0.046 ± 0.008 0.047 %0.007þ0.008 100 ± 10 2.6 × 10−8

.. .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... .. ... ... .. ... ... .. ... ... .. .


on October 31, 2017



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 centre or the galactic plane.

lessons 25 and 26 - istituto nazionale di fisica nucleare

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