Composition Results from Auger Markus Roth Karlsruhe Institute of - - PowerPoint PPT Presentation

composition results from auger
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Composition Results from Auger Markus Roth Karlsruhe Institute of - - PowerPoint PPT Presentation

OBSERVATORY Composition Results from Auger Markus Roth Karlsruhe Institute of Technology (KIT) The Pierre Auger Observatory Fluorescence detector 4 sites: E>10 18 eV HEAT: E>10 17 eV Surface detector array 1660 stations


slide-1
SLIDE 1

Composition Results from Auger

Markus Roth Karlsruhe Institute of Technology (KIT)

OBSERVATORY

slide-2
SLIDE 2

The Pierre Auger Observatory

Fluorescence detector

  • 4 sites: E>1018 eV
  • HEAT: E>1017 eV

Surface detector array

  • 1660 stations
  • Grid of 1.5 km: 3000 km2


E>1018.5 eV

slide-3
SLIDE 3

s l a n t d e p t h [ g / c m ]

1000 500 40 30

dE/dX [PeV/(g/cm )]

20 10

Shower observables 
 recorded at Auger

3

20 40 60 80 100 120 140 160 180 200 2 4 6 8 10 12 14 16 18 20

Time bins (25 ns) ) s t i n u . b r a ( l a n g i s r

  • t

c e t e D

r [m]

500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10 500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10

L

  • n

g i t u d i n a l p r

  • fi

l e Time structure Lateral distribution

E ∝ Z dE dX dX

S1000 ∝ E S1000

Xmax

slide-4
SLIDE 4

s l a n t d e p t h [ g / c m ]

1000 500 40 30

dE/dX [PeV/(g/cm )]

20 10

Shower observables 
 recorded at Auger

4

20 40 60 80 100 120 140 160 180 200 2 4 6 8 10 12 14 16 18 20

Time bins (25 ns) ) s t i n u . b r a ( l a n g i s r

  • t

c e t e D

r [m]

500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10 500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10

L

  • n

g i t u d i n a l p r

  • fi

l e Time structure Lateral distribution

E ∝ Z dE dX dX

S1000 ∝ E S1000

Xmax

slide-5
SLIDE 5

5

)

2

Slant depth (g/cm 200 300 400 500 600 700 800 900 1000 )

9

Number of charged particles (x10 1 2 3 4 5 6 7 8 Height a.s.l. (km) 2 4 6 8 10 12

eV

19

proton, E=10 Auger shower

)

2

Slant depth (g/cm 200 300 400 500 600 700 800 900 1000 )

9

Number of charged particles (x10 1 2 3 4 5 6 7 8 Height a.s.l. (m) 2000 4000 6000 8000 10000 12000

eV

19

iron, E=10 Auger shower

Primary mass and 
 longitudinal shower profiles

slant depth [g/cm ]

1000 500 40 30

dE/dX [PeV/(g/cm )]

20 10

L

  • n

g i t u d i n a l p r

  • fi

l e X

m a x

Mean depth of shower profiles and shower-to-shower fluctuations as measure of composition

slide-6
SLIDE 6

Average Shower Maximum

6

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

E [eV]

1018 1019 1020

σ(Xmax) [g/ cm2]

10 20 30 40 50 60 70 80

iron proton

E [eV]

1018 1019 1020

hXmaxi [g/

cm2]

650 700 750 800 850 data ± σstat

± σsys

EPOS-LHC Sibyll2.1 QGSJetII-04

iron proton

slide-7
SLIDE 7

HEAT+Coihueco telescopes: extended field of view

7

azimuth [deg] elevation [deg]

10 20 30 40 50 60 120 130 140 150 160 170 180 190

CO HEAT

]

2

slant depth [g/cm

400 500 600 700 800 900 1000 1100 1200

)]

2

dE/dX [PeV/(g/cm

0.1 0.2 0.3 0.4 0.5

/Ndf= 89.7/107

2

χ

CO HEAT

Coihueco: 2° - 30° FoV in elevation
 HEAT: 30° - 60° FoV in elevation

slide-8
SLIDE 8

End to end cross-checks with MC simulations

8

Proton, Iron and 50:50 mixture, 
 generated (lines) VS reconstructed (markers) Generated and reconstructed MC data are compatible, 
 with residual bias in the lowest energy bin: 
 correction using half of the 50:50 mixture,
 plus a symmetric systematic uncertainty accounted

slide-9
SLIDE 9

Xmax systematic uncertainties & resolutions

9

h i

  • ︎ Reconstruction bias (only left) and detector resolution (right)
  • Offset in time between SD-FD, calibration and telescopes alignment
  • Analysis
  • Atmospheric uncertainty in the geometry reconstruction and fluorescence light yield
slide-10
SLIDE 10

Standard FD vs HEAT+Coihueco

10

Standard VS HeCo dataset

2

Compatible within expected uncorrelated systematic uncertainties (∼ 7 g/cm2)

slide-11
SLIDE 11

Average shower maximum and RMS

11

Dip model (ankle due to pure proton flux)
 seems to be ruled out

Pierre Auger Collaboration, to be presented at ICRC15

slide-12
SLIDE 12

Statistical moments of ⟨ln A⟩

12

EPOS-LHC QGSJetII-04 Mean Variance

slide-13
SLIDE 13

Average shower maximum

13

Energy log10(E/eV)

<Xmax > [gm/cm2] Proton Iron

18.5 19 19.5 20 650 700 750 800 850 Data QGSJETII−03 QGSJET−01c SYBILL 2.1

E [eV]

1018 1019 1020

hXmaxi [g/

cm2]

650 700 750 800 850 data ± σstat

± σsys

EPOS-LHC Sibyll2.1 QGSJetII-04

iron proton Telescope Array Collaboration, APP 64 (2014) 49 Pierre Auger Collaboration, PRD 90 (2014) 12, 122005

Telescope array Auger

  • Unbiased estimate of Xmax and 


higher moments

  • Reduced statistics
  • EAS simulations are folded with detector


response (det. resolution and bias introduced)

  • Maximized statistics
slide-14
SLIDE 14

Average shower maximum

14

Energy log10(E/eV)

<Xmax > [gm/cm2] Proton Iron

18.5 19 19.5 20 650 700 750 800 850 Data SYBILL 2.1

E [eV]

1018 1019 1020

hXmaxi [g/

cm2]

650 700 750 800 850 data ± σstat

± σsys

Sibyll2.1

iron proton

Telescope array Auger

Telescope Array Collaboration, APP 64 (2014) 49 Pierre Auger Collaboration, PRD 90 (2014) 12, 122005

  • Unbiased estimate of Xmax and 


higher moments

  • Reduced statistics
  • EAS simulations are folded with detector


response (det. resolution and bias introduced)

  • Maximized statistics
slide-15
SLIDE 15

Average shower maximum

15

Pierre Auger and TA Collaborations, Proc. UHECR 2014, arXiv:1503.07540

lg(E/eV)

18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20

]

2

[g/cm 〉

max

X 〈

700 720 740 760 780 800 820

TA MD 2014 TA MD ⊗ Auger 2014

preliminary

⟨∆⟩ = (2.9 ± 2.7 (stat.) ± 18 (syst.)) g/cm2

TA data from 
 MD telescopes
 
 Parameterized 
 Auger data 
 folded with the 
 MD acceptance

MD = Middle Drum
 (site of one telescope station)

slide-16
SLIDE 16

Composition fit of the whole distribution

16

Pierre Auger Collaboration, PRD 90 (2014) 12, 122006

E [eV]

1018 1019 1020

hXmaxi [g/

cm2]

650 700 750 800 850 data ± σstat

± σsys

Sibyll2.1

iron proton

100 200 300 400 500 600 500 600 700 800 900 1000

Xmax [g/cm2]

EPOS-LHC log(E/eV) = 17.8-17.9 p = 0.769 p.d.f. [arb. units]

slide-17
SLIDE 17

0.2 0.4 0.6 0.8 1

p fraction

0.2 0.4 0.6 0.8 1

He fraction

0.2 0.4 0.6 0.8 1

N fraction

0.2 0.4 0.6 0.8 1

Fe fraction

Sibyll 2.1 QGSJET II-4 EPOS-LHC 10-4 10-3 10-2 10-1 100 1018 1019

p-value E [eV]

Composition Fit (Xmax distribution)

17

Pierre Auger Collaboration, PRD 90 (2014) 12, 122006

Data available


  • nly up to


< 5x1019 eV

H i c s u n t 
 d r a c

  • n

e s

slide-18
SLIDE 18

s l a n t d e p t h [ g / c m ]

1000 500 40 30

dE/dX [PeV/(g/cm )]

20 10

Shower observables 
 recorded at Auger

18

20 40 60 80 100 120 140 160 180 200 2 4 6 8 10 12 14 16 18 20

Time bins (25 ns) ) s t i n u . b r a ( l a n g i s r

  • t

c e t e D

r [m]

500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10 500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10

L

  • n

g i t u d i n a l p r

  • fi

l e Time structure Lateral distribution

E ∝ Z dE dX dX

S1000 ∝ E S1000

Xmax

slide-19
SLIDE 19

Shower observables 
 recorded at Auger

19

20 40 60 80 100 120 140 160 180 200 2 4 6 8 10 12 14 16 18 20

Time bins (25 ns) ) s t i n u . b r a ( l a n g i s r

  • t

c e t e D

r [m]

500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10 500 1000 1500 2000 2500

Signal [VEM]

1 10

2

10

3

10

4

10

Time structure Lateral distribution

S1000 ∝ E S1000

Pierre Auger Coll., JCAP 1408 (2014) 019

slide-20
SLIDE 20

Muon Production Depth 
 distribution (MPD) in a nutshell

20 ]

  • 2

[g cm

µ

X

200 400 600 800 1000 1200

/dX [a.u.]

µ

dN

5 10 15 20 25 30 35 40

  • θ = 59.06 ± 0.08

E = 92 ± 3 EeV

Geometric delay of arriving muons: Mapped to muon production depth:

Inclined events to avoid 
 EM contamination:

c · tg = l − (z − ∆) = p r2 + (z − ∆)2 − (z − ∆) z = 1 2 ✓ r2 ctg − ctg ◆ + ∆

slide-21
SLIDE 21

Muon Production Depth 
 distribution (MPD) in a nutshell

21 3 3RD INTERN

]

  • 2

[g cm

µ

X

2 4 6 8 1 1 2

/dX [a.u.]

µ

dN

5 1 1 5 2 2 5 3 3 5 4

Figure 2: Real reconstructed MPD, = (59.06 = (92 ± 3) EeV, with the fit to a Gaisser function.

  • chosen. Therefore

a trade off and reconstruction

µ

(rec) - X

m a x µ

X

20 40

Geometric delay of arriving muons: Mapped to muon production depth:

c · tg = l − (z − ∆) = p r2 + (z − ∆)2 − (z − ∆) z = 1 2 ✓ r2 ctg − ctg ◆ + ∆

slide-22
SLIDE 22

Muon Production Depth

22

EPOS-LHC 30 EeV 55°-65°

Data set: 01/2004 - 12/2012
 E > 1019.3 eV (more muons/event)
 Zenith angles [55°,65°] (low EM contamination) 
 Distances from the core [1700 m, 4000 m]
 481 events after quality cuts
 Systematic uncertainties: 17 g/cm2 Resolution:
 100 (80) g/cm2 at 1019.3 eV for p (Fe) 
 50 g/cm2 at 1020 eV QGSJetII-04: data bracketed by predictions 
 EPOS-LHC: predictions above data

slide-23
SLIDE 23

Comparison of ⟨ln A⟩ from Xmax and Xmax

23

E [eV]

18

10

19

10

20

10 ! lnA "

1 2 3 4 5 6 7 8

max µ

X

max

X

QGSJetII-04

Fe p E [eV]

18

10

19

10

20

10 ! lnA "

1 2 3 4 5 6 7 8

Epos-LHC

Fe p

lnA (FD) from Phys. Rev. D 90 (2014) 12

QGSJetII-04: Compatible values within 1.5 σ
 EPOS-LHC: Incompatibility at a level of at least 6 σ

μ

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SLIDE 24

Muons in highly 
 inclined events

24

  • Data set: 01/2004 - 12/2013
  • E > 4 x 1018 eV 


(100% SD trigger)

  • Zenith angles [62°, 80°] 


(low EM contamination)

  • 174 hybrid events after quality cuts
  • Systematic uncertainty on Rμ: 11%
slide-25
SLIDE 25

Hadronic interactions 
 Data at variance with simulations

25

Pierre Auger Collaboration, PRD91 (2015) 3, 032003

680 700 720 740 760 780 800 820

⟨Xmax⟩ / g cm−2

0.0 0.2 0.4 0.6 0.8 1.0

⟨ln Rµ⟩

Auger data p He N Fe

E = 1019 eV, θ = 67◦ EPOS LHC QGSJet II-04 QGSJet II-03 QGSJet01

1019 1020 E/eV 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4

Rµ/(E/1019 eV)

Fe p Auger data EPOS LHC QGSJET II-04

  • ⟨Rμ⟩ higher than MC iron predictions
  • Tension between the Xmax and muon measurements
  • Older versions of QGSJet model are at odds with data 


taking into account the large systematic uncertainty

slide-26
SLIDE 26

The average muon content and 
 the muon gain with energy

26

muon deficit from 30% to 80% at 10 eV dep Muon deficit from 30% to 80% at 1019 eV 
 depending on the model: 
 Best case for EPOS-LHC 
 (minimum deviation of 1.4 σ) Deviations from a constant 
 proton (iron) composition 


  • bserved at the level of 2.2 (2.6) σ
slide-27
SLIDE 27

Muon number in hybrid events 
 with θ<60°

27

5 10 15 20 200 400 600 800 1000 1200 dE/dX [PeV/g/cm2] Depth [g/cm2] Energy: 8.8 ± 0.5 EeV Zenith: 34.7 ± 0.4o Xmax: 697 ± 7 g/cm2

2/d.o.f. (p): 0.75 2/d.o.f. (Fe): 0.76

Data QII 04 p QII 04 Fe

s l a n t d e p t h [ g / c m ]

1000 500 40 30

dE/dX [PeV/(g/cm )]

20 10

ML fit adjusting 
 EM and muonic 
 contribution to 
 S1000

1 10 100 500 1000 1500 2000 S1000 [VEM] Distance [m] Data QII 04 p QII 04 Fe

Ratio Rhad

Auger Preliminary 2015

Data set: 01/2004 - 12/2012

  • E = 1018.8 - 1019.2 eV
  • Zenith angles [0°, 60°]
  • 411 hybrid events after 


quality cuts

  • Systematic uncertainties 

  • n RE and Rhad: 10 %
slide-28
SLIDE 28

680 700 720 740 760 780 800 820

⟨Xmax⟩ / g cm−2

0.0 0.2 0.4 0.6 0.8 1.0

⟨ln Rµ⟩

Auger data p He N Fe E = 1019 eV, θ = 67◦ EPOS LHC QGSJet II-04 QGSJet II-03 QGSJet01

Summary

  • Xmax:
  • Measured in ∼ 3 decades of energy down to 1017 eV
  • ⟨lnA⟩ vs log10(E/eV): Non-constant composition;


Lightest at ∼ 1018.4 eV

  • Muon measurements:
  • Muon deficit in simulations
  • Strong model dependence
  • Conclusions on composition cannot be drawn


but discrepancy with models large enough to put new constrains on hadronic interactions

28

None of the interaction models recently tuned to LHC data provides a consistent description of both the EM and muonic shower profiles as measured by Auger

E [eV]

18

10

19

10

20

10 ! lnA "

1 2 3 4 5 6 7 8

Epos-LHC

Fe p

Xmax

μ

Xmax Xmax Auger is going to extend the composition measurements
 up to highest energies by means of SD: AugerPrime
 ⇒ Refined analysis procedures needed

slide-29
SLIDE 29

Upgrade of the 
 Pierre Auger Observatory

29

(E/eV)

10

log

18.8 19 19.2 19.4 19.6 19.8 20

]

2

[g/cm

max

  • X

max, rec

X

  • 80
  • 60
  • 40
  • 20

20 40 60 80

p He N Fe

(E/eV)

10

log

18.8 19 19.2 19.4 19.6 19.8 20

µ

)/N

µ

  • N

, rec µ

(N

  • 0.3
  • 0.2
  • 0.1

0.1 0.2 0.3

p He N Fe

  • Additional scintillators (4 m2)
  • Event-by-event mass estimate 


with 100% duty cycle instead of 15% for FD Xmax reconstruction Nµ reconstruction

slide-30
SLIDE 30

Universality fitting procedure Fitting of a single event

30

500 750 1000 1250 1500 1750 2000

r/m

100 101 102 103

S/VEM

lg E/eV = 19.5 Nµ = 1.25 θ = 36° µ eγ eγ(µ) eγ(had)

500 1000 1500 2000 2500 r/m 200 400 600 800 1000 1200 1400 Difference to plane front / ns

standard curvature fit time model median ±1σ start time + var. model

100 200 300 400 500 600 700

t/ns

10 20 30 40 50 60 70 80

S/VEM

Sµ Seγ Seγ(µ) Seγ(had) Stotal

Station closest to core

Colored bands indicate corrections for up- and downstream asymmetry, e.g. different ΔX, ground screening, detector response

slide-31
SLIDE 31

The world‘s largest cosmic ray observatory

31

About 500 members from 16 countries Argentina Australia Brazil Colombia* Czech Republic France Germany Italy Mexico Netherlands Poland Portugal Romania Slovenia Spain USA

*Associated

  • Full members
  • Associate member

★ Auger site

slide-32
SLIDE 32
  • 0.2

0.4 0.6 0.8 1

p fraction

0.2 0.4 0.6 0.8 1

He fraction

0.2 0.4 0.6 0.8 1

N fraction

0.2 0.4 0.6 0.8 1

Fe fraction

Sibyll 2.1 QGSJET II-4 EPOS-LHC 1018 1019 1020

E [eV]

Pierre Auger Collaboration, Phys. Rev. D90 (2014) 122006

Composition Fit (Xmax distribution)

35

Pierre Auger Collaboration, PRD 90 (2014) 12, 122006

Data available


  • nly up to


< 5x1019 eV Hic sunt
 leones

slide-33
SLIDE 33

Unambiguously detected flux suppression

36

Energy (eV/particle)

13

10

14

10

15

10

16

10

17

10

18

10

19

10

20

10

21

10

)

1.5

eV

  • 1

sr

  • 1

s

  • 2

J(E) (m

2.5

Scaled flux E

13

10

14

10

15

10

16

10

17

10

18

10

19

10

(GeV)

pp

s Equivalent c.m. energy

2

10

3

10

4

10

5

10

6

10

  • p)

γ HERA ( RHIC (p-p) Tevatron (p-p) 14 TeV 7 TeV LHC (p-p)

ATIC PROTON RUNJOB

KASCADE (SIBYLL 2.1) KASCADE-Grande 2012 Tibet ASg (SIBYLL 2.1) IceTop ICRC 2013

HiRes-MIA HiRes I HiRes II Auger ICRC 2013 TA SD 2013

Energy scale 
 uncertainty ~20%

Courtesy R. Engel

slide-34
SLIDE 34

Flux suppression due to GZK energy-loss?

37

17.5 18.0 18.5 19.0 19.5 20.0 20.5

log10(E/eV )

1036 1037 1038

E 3J(E) eV 2 km − 2 sr− 1 yr − 1

∆E/ E = 14 %

Proton, Ecut = 1020 eV Proton, Ecut = 1020.5 eV Iron, Ecut = 1020 eV Iron, Ecut = 1020.5 eV

1018 1019 1020

E [eV]

Auger ICRC 2013

Proton dominated flux Ankle: e+e– pair production 
 Suppression: delta resonance

(Dip model by Berezinsky et al.)

Iron dominated flux Ankle: transition to galactic sources Suppression: giant dipole resonance Spectral information is not enough to decide upon

slide-35
SLIDE 35

(GeV) s

1 10

2

10

3

10

4

10

5

10 (mb)

p-p

σ 50 100 150 200 250 300 350

Fly’s Eye Akeno HiRes Auger This work pbar-p pp even (QCD-Fit)

nn

σ Telescope Array

log Energy [E/eV]

[mb]

P-air

σ

200 300 400 500 600 700 800

EPOS-LHC QGSJETII-04 SIBYLL-2.1 Nam et al. 1975 Siohan et al. 1978 Baltrusaitis et al.1984

  • H. Mielke et al.1994

Honda et al.1999 Knurenko et al.1999

  • I. Aielli et al.2009

Telescope Array 2015 Auger PRL2012 This Work 2015

Energy [eV]

13

10

14

10

15

10

16

10

17

10

18

10

19

10

20

10 [TeV]

pp

s Equivalent c.m. energy

  • 1

10 1 10

2

10

Hadronic interactions

38

σp-air σp-p

Glauber
 theory

TA collaboration, arXiv:1505.01860v1
 Pierre Auger Collaboration, PRL 109 (2012) 062002

slide-36
SLIDE 36

18 18.5 19 19.5 20 20.5

37

10

38

10

(E/eV)

10

log ]

  • 1

yr

  • 1

sr

  • 2

km

2

J [eV

3

E

] ]

18 18.5 19 19.5 20 20.5

37

10

38

10

(E/eV)

10

log ]

  • 1

yr

  • 1

sr

  • 2

km

2

J [eV

3

E

]

Protons injected from sources Secondary
 protons

Allard et al. 2011 Hooper-Taylor et al. 2012 (Sergio Petrera et al.)

Fe Fe N N p p

Difference: Scaling with charge Z or mass number A
 Both scenarios: Hard injection spectrum, γ≈ -1 … 1.7, and heavy source composition 
 (Astrophysics: very exotic result!)

(Shaham & Prian, Phys. Rev. Lett. 110, 2013)

Injection: ~70% N or Si (almost no light elements) Injection: Galactic composition with enhanced heavy elements

He He

39

Maximum-energy or GZK energy-loss? Hard injection spectrum?

Emax=Z x 4 EeV

slide-37
SLIDE 37

Flux suppression not universal?

40

(E/eV)

10

log

18.2 18.4 18.6 18.8 19 19.2 19.4 19.6 19.8 20 20.2

) -1

3

E × J/(A

  • 1
  • 0.5

0.5 1 1.5

E[eV]

19

10

20

10

1.070 ) × ) (E

inv

Auger (TA FY and E Telescope Array (6 years)

Using same fluorescence yield and invisible energy + 7% shift


Spectrum working group report, UHECR14

Suppression 
 different in 
 northern and 
 southern 
 hemisphere?

slide-38
SLIDE 38

Average shower maximum and RMS

44

Dip model (ankle due to pure proton flux)
 seems to be ruled out

200 400 600

17.8 ≤ lg(E/eV) < 17.9 N = 3768

200 400 600

17.9 ≤ lg(E/eV) < 18.0 N = 3383

200 400

18.0 ≤ lg(E/eV) < 18.1 N = 2818

200 400

18.1 ≤ lg(E/eV) < 18.2 N = 2425

100 200 300

18.2 ≤ lg(E/eV) < 18.3 N = 1952

100 200 300

18.3 ≤ lg(E/eV) < 18.4 N = 1439

100 200

18.4 ≤ lg(E/eV) < 18.5 N = 1139

100 200

18.5 ≤ lg(E/eV) < 18.6 N = 814

50 100 150

18.6 ≤ lg(E/eV) < 18.7 N = 575

50 100

18.7 ≤ lg(E/eV) < 18.8 N = 413

50 100

18.8 ≤ lg(E/eV) < 18.9 N = 297

20 40 60

18.9 ≤ lg(E/eV) < 19.0 N = 230

20 40 60

19.0 ≤ lg(E/eV) < 19.1 N = 165

20 40

19.1 ≤ lg(E/eV) < 19.2 N = 114

10 20 30

19.2 ≤ lg(E/eV) < 19.3 N = 87

10 20

19.3 ≤ lg(E/eV) < 19.4 N = 63

5 10

19.4 ≤ lg(E/eV) < 19.5 N = 40

10 20

19.5 ≤ lg(E/eV) < ∞ N = 37

Xmax [g/ cm2] events/(20 g/ cm2)

600 800 1000 600 800 1000 600 800 1000

Pierre Auger Collaboration, PRD 90 (2014) 12, 122006