Measurement of the energy spectrum of ultra-high energy cosmic rays using the

Pierre Auger Observatory

1

Valerio Verzi1 for the Pierre Auger Observatory2 1 INFN, Sezione di Roma “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italia 2 Observatorio Pierre Auger, Av. San Martín Norte 304, 5613 Malargüe, Argentina

Full author list: http://www.auger.org/archive/authors_icrc_2019.html

Hybrid Observatory

Fluorescence Detector (FD) 27 telescopes in 4 sites (-) duty cycle ~ 15% (+) calorimetric measurement of E

Surface Detector array (SD) 1661 water-Cherenkov detectors on 1500 m and 750 m triangular grid (+) duty cycle ~ 100% (-) shower size at ground ∝ E (systematics)

•  energy scale of the Observatory set by the FD with a 14% systematic uncertainty

•  precise measurement of the flux up to 1020 eV

B. Dawson #231 A. Coleman #225

SD

FD

3000 km2

2

A. Castellina highlight

energy spectrum over 4 decades in energy

SD 1500 m θ < 600

E > 1018.4 eV

SD 1500 m

600 < θ < 800

E > 1018.6 eV signal ~ Nµ

FD + SD stat. hybrid

(15% duty cycle)

E > 1018 eV

SD 750 m θ < 400

A. Coleman #225

E > 1017 eV

FD-HEAT Cherenkov

V. Novotny #374

E > 1016.5 eV 3

energy estimation for 1500 m array θ < 600 events

θsec

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2

Attenuation factor

0.4

0.6

0.8

1

1.2

1

I

2

I

3

I

fit the lateral distribution of the signals to get S(1000)

use the CIC method to remove the zenith angle dependence of S(1000). CIC at different intensity thresholds

note: correction determined from data (no use of simulations)

3 EeV 8 EeV 20 EeV

S38

D. Mockler #353

500 1000 1500 2000 2500 3000

Axial Distance [m]

1

10

210

310

Sign

al [V

EM]

Measured Signals

LDF Fit

S(1000)

4

[eV]FDE1910 2010

[VEM

]38S

10

210

B38E = A S 3338 events

eV18 10× 0.003) ±A = (0.186 0.004±B = 1.031

= -0.98ρ

D/n.d.f. = 3419/3336

energy estimation for 1500 m array θ < 600 events

high-quality events triggered independently by SD and FD correlation well described by a power-law relationship maximum-likelihood fit using a “bootstrap” estimate of the p.d.f. and event-by-event uncertainties

5

E [eV]1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E) 3710

3810

(E/eV)10

log18.5 19 19.5 20

rawJ 0 < 60θ1500m

8314

347

500

2865

717

843

1243

587

15 6050 41

1126

2016

9199

162

437

215

683

249 6

measurements done with full trigger efficiency

raw energy spectrum using 1500 m array

θ < 600 events

J = fresJraw = fresN

ε ΔE

ε = (60400±1800) km2sr yr

215030 events with E > 1018.4 eV

6

(E/eV)10

log1810 1910 2010

ener

gy re

solu

tion

[%]

5

10

15

20

25 resolutionSDE resolutionFDE

ESD resolution knowing the EFD one

7 FD/ESDE0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

events

0

5

10

15

20

25

30

35

E ≈10 EeV

FD/ESDE0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

events

0

20

40

60

80

100

120

140

160

180

200E ≈1 EeV

ingredients to calculate fres from hybrid data

also ESD bias and trigger efficiency at lower energies

fres calculated using a forward-folding technique •  new function: sequence of 4 power-laws with 3 inflection points •  previous function: slow transition between ankle and suppression •  fres small at all energies

previous function discarded with a significance of 3.2σ

unfolded spectrum

8

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

< 60 degreesθSD 1500m > 60 degreesθSD 1500m

energy spectra full trigger efficiency exposure (30% more) 17447 km2 sr yr above 1018.6 eV 24209 events similar data-driven approach but completely different reconstruction technique energy resolution 22% - 10%

9

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

< 60 degreesθSD 1500m > 60 degreesθSD 1500m

hybrid

energy spectra

10

13655 events above 1018 eV full time-dependent simulation of FD events exposure [km2 sr yr] 1 EeV 265 km2 sr yr 10 EeV 2248 km2 sr yr energy resolution ≈ 7.4%

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

< 60 degreesθSD 1500m > 60 degreesθSD 1500m

hybridSD 750m

energy spectra

11

full trigger efficiency exposure 105 km2 sr yr 569285 events above 1017 eV data-driven approach similar to the ones of the 1500m array

A. Coleman #225

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

< 60 degreesθSD 1500m

SD 750mCherenkov

> 60 degreesθSD 1500m hybrid

energy spectra

12

69793 events above 1016.5 eV energy deposited from a profile constrained geometry fit and invisible energy correction inferred from muon data exposure from full time-dependent simulation of FD events

V. Novotny #374

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

< 60 degreesθSD 1500m

SD 750mCherenkov

> 60 degreesθSD 1500m hybrid

energy spectra

13

fluxes in good agreement among them once rescaled by normalization factors that are consistent with the systematic uncertainties

0% +5% -9% -1% -1%

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

Auger combined(preliminary)

combined spectrum

γ0 = 2.92 ± 0.05 γ3 = 3.2 ± 0.1

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

Auger combined(preliminary)

‘previous’ function discarded at the 4σ level

errors = stat.+syst

E01 = 0.15 ± 0.02 E12 = 6.2 ± 0.9 E23 = 12 ± 2 E34 = 50 ± 7 (energies in EeV units)

14

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

Auger combined(preliminary)

OUTLOOK

15

•  improved 1500 m array θ < 600 spectrum (no use of simulations) •  independent measurements with 1500 m array θ > 600 and hybrid events •  lower the threshold down to 1016.5 eV with the 750 m and Cherenkov events

Ø  combined spectrum with a common energy scale: -  second knee and ankle -  an indication of a further

inflection point at E ~ 10 EeV -  abrupt suppression at the

highest energies

THANKS

16

E [eV]1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E) 3710

3810

ICRC 20190 < 60θ1500m ICRC 20170 < 60θ1500m

E [eV]1910 2010

ICRC

2017

/JIC

RC20

19J

0.6

0.8

1

1.2

1.4

17

1500 m array θ < 600 spectrum: ICRC2019 vs ICRC2017

E [eV]1710 1810 1910 2010

]2 e

V-1

sr-1

yr

-2 [k

m3

E×J(

E)

3710

3810

(E/eV)10

log17 18 19 20

Auger combined(preliminary)

18

γ

J ~ E−γ

A. Castellina highlight