Pierre Auger Observatory

Cosmic Ray Energy Spectra

The cosmic ray energy spectra measured by the Pierre Auger Collaboration are shown on this web page. The data are from papers submitted to the ICRC07 conference. The differential cosmic ray flux J = dN/(dA dΩ dt dE) is expressed in units of [m-2s-1eV-1].

Figures

Click on thumbnails to get larger image


Figures from T. Yamamoto, "The UHECR spectrum measured at the Pierre Auger Observatory and its astrophysical implications," ICRC'07
Figure 1: The energy spectrum multiplied by E3 derived from SD using showers at zenith angles above 60° (filled triangles) and below 60° (open triangles) , together with the spectrum derived from the hybrid data set (red circles). Arrows indicate 84% CL upper-limits.
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Figure 2: Upper panel: Spectral index as a function of minimum energy in the fit. Lower panel: significance (in sigma) of the deviation from power-law distribution with spectral index from upper panel based on the TP statistics.
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Figure 3: The combined energy spectrum multiplied by E3, together with a fit to Eq. 1 (black line), and the predictions of two astrophysical models (blue and red lines). The input assumptions of the models (mass composition at the sources, the source distribution, spectral index and exponential cutoff energy per nucleon at the acceleration site) are indicated in the figure.

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Figures from M. Roth, "Measurement of the UHECR energy spectrum using data from the Surface Detector of the Pierre Auger Observatory," ICRC'07
Figure 1: Integral number of events vs cos2 θ for the indicated minimum value of S(1000). Using the constant intensity method, the signal flux atmospheric attenuation curve may be derived from the non-flatness of these distributions.
    Link to eps file
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Figure 2: The derived signal attenuation curve, CIC(θ), fitted with a quadratic function.
    Link to eps file
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Figure 3: Correlation between the measured fluorescence energy EFD and the measured ground flux parameter S38° for the 387 hybrid events used in the fit. The full line is the best fit to the data and provides the empirical calibration of the surface detector energy measurement. To avoid fitting biases, events below the dashed line were not included in the fit.
   
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Figure 4: The energy resolution is measured as the fractional difference between the FD and SD energy for the 387 selected hybrid events.
    Link to eps file
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Figure 5: Auger spectrum J as a function of energy. Vertical error bars represent the statistical uncertainty only. The statistical and systematic uncertainties in the energy scale are of the order of ≈ 6% and ≈ 22%, respectively.
    The individual systematic uncertainties in determining ESD sum up to 22%. The largest uncertainties are given by the absolute fluorescence yield (14%), the absolute calibration of the FD (9.5%) and the surface event reconstruction method (10%). The uncertainty due to the dependence of the fluorescence spectrum on pressure (1%), humidity (5%) and temperature (5%) are taken into account as well as the wavelength dependent response of the FD, the aerosol phase function, invisible energy and others, which are well below 4%. The spectrum shown is the raw spectrum, uncorrected for possible biases due to energy-dependent and/or primary-composition-dependent systematic effects.
    Link to eps file
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Figure 6: Fractional difference between the derived spectrum and an assumed flux proportional to -2.6 as a function of energy.
    Link to eps file

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Tables

  1. Combined spectrum
  2. SD vertical spectrum
  3. SD inclined spectrum
  4. Hybrid spectrum
Because the data are binned in logarithmic bins of energy, we tabulate the energy flux:
dN/(dln(E) dA dΩ dt) = E * dN/(dE dA dΩ dt) [m-2s-1]


Table 1: Combined spectrum from 3 datasets
(Surface detector vertical + inclined + hybrid)
log(E [eV]) dN/
  (dln(E) dA dΩ dt)
Num. of events
18.05 1.13e-12 7.68e-14 7.82e-14 --
18.15 6.26e-13 4.52e-14 4.58e-14 --
18.25 3.63e-13 2.96e-14 2.99e-14 --
18.35 2.46e-13 2.14e-14 2.16e-14 --
18.45 1.46e-13 1.47e-14 1.49e-14 --
18.55 7.33e-14 9.42e-15 9.49e-15 --
18.65 4.37e-14 1.07e-15 1.07e-15 --
18.75 3.14e-14 9.04e-16 9.04e-16 --
18.85 2.04e-14 7.27e-16 7.27e-16 --
18.95 1.49e-14 6.22e-16 6.23e-16 --
19.05 9.82e-15 5.01e-16 5.02e-16 --
19.15 7.54e-15 4.42e-16 4.42e-16 --
19.25 4.90e-15 3.43e-16 3.44e-16 --
19.35 3.25e-15 2.95e-16 2.95e-16 --
19.45 2.10e-15 2.33e-16 2.33e-16 --
19.55 1.50e-15 1.65e-16 1.69e-16 --
19.65 6.92e-16 1.12e-16 1.16e-16 --
19.75 3.92e-16 8.32e-17 9.69e-17 --
19.85 1.24e-16 4.39e-17 5.76e-17 --
19.95 1.33e-16 5.98e-17 7.49e-17 --
20.05 2.67e-17 1.68e-17 4.68e-17 --
20.15 0.0 0.0 3.42e-17 0
20.25 2.67e-17 1.68e-17 4.68e-17 --
20.35 0.0 0.0 3.42e-17 0

ASCII file for the combined spectrum

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Table 2: Surface Detector vertical spectrum (θ < 60°)
log(E [eV]) dN/
  (dln(E) dA dΩ dt)
Num. of events
18.45 1.10e-13 1.71e-15 1.71e-15 4128
18.55 6.53e-14 1.32e-15 1.32e-15 2450
18.65 4.35e-14 1.08e-15 1.08e-15 1631
18.75 3.16e-14 9.17e-16 9.17e-16 1185
18.85 2.03e-14 7.35e-16 7.35e-16 761
18.95 1.49e-14 6.31e-16 6.31e-16 560
19.05 9.78e-15 5.10e-16 5.10e-16 367
19.15 7.57e-15 4.49e-16 4.49e-16 284
19.25 4.74e-15 3.55e-16 3.55e-16 178
19.35 3.33e-15 2.98e-16 2.98e-16 125
19.45 2.10e-15 2.37e-16 2.37e-16 79
19.55 1.44e-15 1.96e-16 1.96e-16 54
19.65 6.66e-16 1.33e-16 1.33e-16 25
19.75 3.73e-16 9.85e-17 1.15e-16 14
19.85 1.33e-16 5.98e-17 7.49e-17 5
19.95 1.33e-16 5.98e-17 7.49e-17 5
20.05 2.66e-17 1.68e-17 4.68e-17 1
20.15 0.0 0.0 3.41e-17 0
20.25 2.66e-17 1.68e-17 4.68e-17 1
20.35 0.0 0.0 3.41e-17 0

ASCII file for the SD spectrum

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Table 3: Surface Detector inclined spectrum (60° < θ < 80°)
log(E [eV]) dN/
  (dln(E) dA dΩ dt)
Num. of events
18.85 2.24e-14 1.43e-15 1.43e-15 246
18.95 1.40e-14 1.13e-15 1.13e-15 153
19.05 1.11e-14 1.01e-15 1.01e-15 122
19.15 7.11e-15 8.05e-16 8.05e-16 78
19.25 4.74e-15 6.58e-16 6.58e-16 52
19.35 2.64e-15 4.91e-16 4.91e-16 29
19.45 1.92e-15 4.18e-16 4.18e-16 21
19.55 1.64e-15 3.82e-16 4.40e-16 18
19.65 8.21e-16 2.43e-16 3.46e-16 9
19.75 4.56e-16 2.05e-16 2.56e-16 5
19.85 9.12e-17 5.75e-17 1.60e-16 1

ASCII file for the inclined spectrum

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Table 4: Hybrid spectrum
log(E [eV]) dN/
  (dln(E) dA dΩ dt)
Num. of events
18.05 1.10e-12 7.56e-14 7.56e-14 245
18.15 6.11e-13 4.44e-14 4.44e-14 209
18.25 3.54e-13 2.90e-14 2.90e-14 160
18.35 2.40e-13 2.10e-14 2.10e-14 140
18.45 1.42e-13 1.44e-14 1.44e-14 102
18.55 7.15e-14 9.22e-15 9.22e-15 62
18.65 4.70e-14 6.87e-15 6.87e-15 48
18.75 2.54e-14 4.75e-15 4.75e-15 29
18.85 2.36e-14 4.35e-15 4.35e-15 30
18.95 1.22e-14 3.85e-15 4.77e-15 17
19.05 1.01e-14 3.26e-15 4.46e-15 15
19.15 6.36e-15 2.45e-15 3.58e-15 10
19.25 8.20e-15 2.87e-15 3.61e-15 14
19.35 1.50e-15 9.50e-16 1.80e-15 3
19.45 1.75e-15 1.11e-15 2.09e-15 3
19.55 1.82e-15 1.15e-15 1.85e-15 4
19.65 4.82e-16 3.98e-16 1.24e-15 1
19.75 0.0 0.0 8.56e-16 0
19.85 0.0 0.0 7.50e-16 0
19.95 0.0 0.0 8.92e-16 0

ASCII file for the hybrid spectrum

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