The UHE cosmic ray energy spectrum measured by the Pierre Auger Observatory

Nuclear Physics B (Proc. Suppl.) 212–213 (2011) 87–92 www.elsevier.com/locate/npbps

The UHE cosmic ray energy spectrum measured by the Pierre Auger Observatory Bruce R. Dawsona , for the Pierre Auger Collaborationb∗ a

School of Chemistry & Physics, University of Adelaide, Adelaide S.A. 5005, Australia

b

Observatorio Pierre Auger, Av. San Martin Norte 304, 5613 Malarg¨ ue, Argentina

The UHE cosmic ray spectrum has been measured with the Pierre Auger Observatory using two complementary techniques. Those techniques are described, emphasising the advantages and cross-checks afforded by the hybrid nature of the Observatory.

1. Introduction Measurement of the ultra-high energy cosmic ray (UHECR) spectrum is a key part of the quest for understanding the origin of these rare and important particles. Building on the pioneering work of several groundbreaking experiments, the Pierre Auger Observatory brings unique capabilities to the UHECR spectrum measurement. Its surface detector (SD) covering 3000 square kilometres operates 24 hours per day, and provides a huge collecting area with an easily calculable aperture and exposure. Its companion instrument, the fluorescence detector (FD), provides near-calorimetric measurement of cosmic ray energies through observation of the air shower development in the atmosphere. Together, this “hybrid” combination of the SD and FD allows a measurement of the primary particle energy spectrum with a straightforward exposure calculation, and with little resort to simulations of air showers. 1.1. The Pierre Auger Observatory The Observatory was completed in mid-2008 after a 4 year construction period. Data were collected from January 2004 as the Observatory grew in size. The surface detector now consists of over 1600 water Cherenkov detectors arranged on a 1.5 km triangular grid over an area of 3000 square kilometres. Each of the SD stations is a ∗ Full

10 square metre area tank containing a depth of 1.2 m of ultra-pure water. Cherenkov light produced in the water by shower particles is collected by three photomultiplier tubes and signals are digitized in 25 ns bins and time-stamped using a local GPS receiver. Trigger and signal information is transmitted to a central data acquisition system via technology based on mobile telephony. The fluorescence detectors are arranged in 4 stations located on the perimeter of the SD array [1]. Each of the stations contains 6 telescopes covering 180◦ of azimuth and 30◦ of elevation. Each telescope consists of a 11 m2 spherical mirror with a 2.2 m diameter entrance aperture containing a corrector ring for improved image quality, and an optical filter (300-400 nm) appropriate for the nitrogen fluorescence signal. Images are formed on a 440-pixel photomultiplier camera, and signals are digitized with 100 ns resolution. Auger’s hybrid detectors offer complementary strengths. The SD provides a huge aperture, easily calculable, with robust detectors. Arrival directions are measured by the SD with good resolution, and promising mass composition indicators are being developed that use SD information only. The FD provides near-calorimetric energy measurements, a direct measurement of the depth of shower maximum (a mass indicator), and precise arrival directions using the “hybrid” method, but suffers from a low duty cycle of 1015% because of the requirement for clear, moon-

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less nights. Auger is an experiment with many layers of cross-checks, with its hybrid nature being the prime example. The FD and SD can measure the same parameters of air showers but with very different measurement systematics. 2. Methods The SD is used to measure the lateral distribution of water Cherenkov signals for each air shower, and the estimated signal 1000 m from the shower core S(1000) is used as the energy parameter. A calibration of the SD method is performed using events also viewed by the FD. 2.1. The fluorescence technique It has been established in laboratory experiments that the fluorescence emission in an air sample is proportional to the energy deposited there by ionizing particles. Lab measurements have determined the spectrum of the emission and the yield of the various bands in the spectrum, typically in terms of photons per unit of energy deposit (e.g. [2]). So the task of the FD is to determine the fluorescence emission per depth interval along the shower axis in order to reconstruct the shower energy deposited in that interval, dE/dX. The total energy deposited in the atmosphere is the integral of dE/dX over depth. While conceptually simple, the implementation of the technique is somewhat more complex. To estimate the light emitted at the shower track, the position of the shower axis must be known [3], the FD must be well calibrated [4], and all corrections for atmospheric attenuation of the light must be made [5], primarily Rayleigh and aerosol scattering. The fluorescence light emitted from a track segment may be converted to the shower energy deposit in that segment once the pressure and temperature of that part of the atmosphere is estimated from monthly atmospheric profiles appropriate for the site [5], since the fluorescence yield has small dependencies on those parameters [2]. The atmospheric profile is also used to estimate the atmospheric depth (in g/cm2 ) at that point on the axis. One can then reconstruct the dE/dX profile along the viewed part of the shower, fit it with a functional form for shower development,

Source Systematic uncertainty Fluorescence yield 14% P,T and humidity 7% effects on yield Calibration 9.5% Atmosphere 4% Reconstruction 10% Invisible energy 4% TOTAL 22% Table 1 Present systematic uncertainties in determining energy by the fluorescence method.

the Gaisser-Hillas function, then integrate to get the total visible energy deposited by the shower,  ∞ dE dX (1) E= dX 0 This is not quite the primary cosmic ray energy, because a fraction of the primary energy does not produce light efficiently in the atmosphere - that fraction carried by high energy muons and neutrinos. This “invisible energy” is of order 10−15% of the primary energy, though dependent on energy and the primary mass [6]. The systematic uncertainty introduced by making a missing energy correction without knowing the primary mass is of order 4% of the primary energy. Other systematic uncertainties in primary energy associated with the fluorescence technique are listed in Table 1. Efforts are underway to reduce the main uncertainties in the fluorescence yield, the absolute calibration, and in the reconstruction method, but our current best estimate of the total systematic error on FD energy is 22%. Typical statistical uncertainties on reconstructed energy are less than 10% [7]. 2.2. The surface detector technique After determining the shower arrival direction, the SD analysis proceeds with a fit of the signals S in triggered stations to a lateral distribution function (LDF) of the form,  r −β  r + 700 −β (2) S(r) = S(1000) 1000 1700

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where the radius r is defined in the plane perpendicular to the shower axis, S(1000) is the signal 1000 m from the shower core, and β is fixed to a value dependent on the shower zenith angle and S(1000). Fitting of this function yields the shower core location and the energy estimator S(1000). The signal 1000 m from the core is used as our energy estimator because for Auger’s array spacing (1500 m) S(1000) is typically measured with the smallest systematic uncertainty, given our lack of knowledge of the true shape of the LDF from event to event [8]. The typical systematic and statistical errors on S(1000) are described in [9]. The quadratic sum of the two ranges from about 12% at 3×1018 eV to 4% at the highest energies for events without any saturated station signals, and from 18% to 12% for events with at least one saturated station. Now to the conversion of S(1000) to primary energy E. The steps, described fully in [7], make this conversion without resort to air shower simulations. First, the attenuation of S(1000) with zenith angle is estimated using the method of constant intensity cuts, which assumes that the rate of events (per unit area and solid angle) above a certain energy threshold should be independent of zenith angle. For Auger this assumption is true for energies E > 3 × 1018 eV and zenith angles θ < 60◦ where the SD is fully efficient [10]. Know-

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Figure 2. FD energies from sample of 795 good quality hybrid events are used to calibrate the SD energy parameter S38◦ [7].

ing the attenuation, one can correct the value of S(1000) to S38◦ , the value of S(1000) expected for the shower if it had arrived at a zenith angle of 38◦ , the median zenith angle for Auger’s dataset. The attenuation curve, shown in Figure 1 is fitted with a quadratic function of the form CIC(θ) = 1 + a x + b x2 , where x = cos2 θ − cos2 38◦ . The curve shown is for the constant intensity cut corresponding to a minimum S38◦ signal of 47 VEM (vertical equivalent muons), but the shape is assumed to be the same for all relevant energies. For each shower we calculate the new energy parameter S38◦ ≡ S(1000)/CIC(θ). Finally, we use a sample of well-measured hybrid events to calibrate S38◦ . Details of the selection of FD events is given in [7]. The selection of SD events requires only that the station with the greatest signal is surrounded by a hexagon of operating stations, and that the zenith angle θ < 60◦ . The resulting calibration curve is shown in Figure 2. The procedure takes advantage of the near calorimetric energy determination by the FD, where the only simulations required are for the small invisible energy correction. The same data from Figure 2 are shown in Figure 3. Here ESD is calculated from S38◦ and the calibration curve, and is compared with EF D . This distribution is centered by construction, but

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Figure 3. Data from Figure 2 with S38◦ converted to the SD estimate of energy ESD , compared with the fluorescence energy EF D . The width of the distribution is consistent with expectations, given the typical statistical uncertainties in S(1000) and the fluorescence energy [7].

Figure 4. The UHECR energy spectrum determined using the SD [11]. The flux has been multiplied by E 3 to emphasize spectral features. The number of events contributing to each energy bin is indicated.

its width is pleasingly consistent with the convolution of the expected statistical resolution of the SD and FD energy parameters. Calculation of the energy spectrum requires the determination of the experiment’s exposure. For the SD spectrum the exposure calculation is simple and robust [10]. The exposure is uniform with energy above the SD threshold of 3 × 1018 eV for showers of θ < 60◦ . The number of operating array “unit cells” (a centered hexagon of 7 stations) is calculated for every second of the SD operation. Given that each cell has an aperture of 4.59 km2 sr for showers within this zenith range, this method easily results in the exposure in units of km2 sr y.

The spectral shape has been corrected for the effects of finite energy resolution of ∼ 15% at the lower energies improving to ∼ 10% at the highest energies. There is clear evidence for a suppression in the flux at the highest energies. Compared with an extrapolation of the power law spectrum above 1018.6 eV, the flux drops to 50% of the expectation at 1019.6 eV. The significance of the deficit is ∼ 20σ and confirms (with superior statistical power) the result reported by the HiRes Collaboration [12]. Such a spectral suppression is consistent with that expected from the GZK effect [13] where a high energy protonic flux is attenuated through interactions with photons of the cosmic microwave background.

3. Results 3.1. The surface detector energy spectrum The energy spectrum derived from SD data is displayed in Figure 4 [11]. It is derived from data collected from the beginning of the operations in January 2004 through to the end of December 2008. The exposure is 12,790 km2 sr y. As is traditional, the flux axis is multiplied by E 3 to emphasise features of the rapidly falling spectrum.

3.2. The hybrid energy spectrum The SD spectrum already discussed begins at 3 × 1018 eV, the threshold energy for full efficiency of the SD. Auger has also produced a “hybrid” spectrum [11], consisting of FD observed events. (The “hybrid” title refers to the method for determining the axis geometry of FD events, which uses the shower arrival time at the ground measured by one station of the SD [3]). The cal-

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Figure 5. The hybrid energy spectrum, clearly showing the spectral “ankle” [11].

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Figure 6. The combined hybrid and SD spectra from Auger [11] are compared with the stereo spectrum from the HiRes experiment [15].

4. Discussion culation of the energy-dependent hybrid exposure is challenging, and requires a detailed simulation that takes into account measured atmospheric and detector conditions [14]. Quality and anti-bias cuts are applied to the events to minimize the influence of mass composition on the expected exposure. The results are shown in Figure 5. While the statistics are poorer than the SD spectrum, we can now view lower energies. The spectral ankle, hinted at in the SD spectrum, is clearly seen. The hybrid and SD spectra are combined in Figure 6, where there is a comparison with the HiRes stereo spectrum [15]. A systematic error in energy will shift a spectrum diagonally on such a plot. The reported systematic errors of Auger (22%, indicated on plot) and HiRes (17%) suggest that the two spectra are consistent. Fits have been made to the Auger spectrum, details in [11]. For example, simple power law fits indicate that the ankle is located at log(E) = 18.61 ± 0.01, with the spectral break at log(E) = 19.46 ± 0.03. The power law indices (J(E) ∝ E −γ ) are γ = 3.26 ± 0.04 below the ankle, γ = 2.59 ± 0.02 above the ankle, and γ = 4.3 ± 0.2 at energies above the break.

A full astrophysical interpretation of the energy spectrum requires information on the mass composition of the flux and input from anisotropy analysis. The Auger Collaboration is busily working in these areas, and reports were made at this meeting [16,17]. The traditional interpretation of a spectral suppression at the highest energies is the GZK effect [13], but one should note that heavy particles also lose energy via interactions with cosmic photons. In particular, iron suffers photo-erosion interactions with CMB photons, giving an endE ) ergy loss length for the leading particle (E/ dX which drops below 100 Mpc at energies beyond ∼ 1019.5 eV, quite similar to the energy loss length of protons due to the GZK interaction [18]. Some very simple models have been compared to Auger’s spectrum measurement [19], shown here in Figure 7. A uniform distribution of extragalactic sources has been assumed, with a cosmological evolution of source luminosity going as (1 + z)m , a source spectrum of E −β , and a maximum energy of 1020.5 eV. No attempt has been made to optimize agreement with any particular model by shifting the energy scale within the systematic uncertainty. For the pure iron

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Figure 7. The combined Auger spectrum is compared with some simple astrophysical models, as described in the text [19].

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11. model, lower energy particles must be supplied by another set of sources, perhaps galactic. These models are very simple at this stage, but will become more sophisticated as the statistical quality of the spectrum improves, and will be informed by Auger’s measurements of mass composition. The SD spectrum presented here was collected with an exposure of 12,790 km2 sr y. The completed observatory will now accumulate over 7000 km2 sr of exposure every year, so better statistics will flow quickly. At the same time enhancements of the Observatory, including HEAT [20] and an infill area of enhanced SD station density, will allow more detailed investigation of the spectral features and mass composition at energies at and below the spectral ankle.

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REFERENCES 1. J. Abraham et al. [Pierre Auger Collaboration], Nuclear Instruments and Methods in Physics Research A620 (2010) 227. 2. M. Ave, et al., AIRFLY Collaboration, Astropart. Phys. 28 (2007) 41, astroph/0703132. 3. B.R. Dawson, H.Y. Dai, P. Sommers and S. Yoshida, Astropart. Phys. 5, 239 (1996). 4. R. Knapik et al. [Pierre Auger Collaboration], Proc. of 30th International Cosmic Ray

18. 19.

20.

Conference (ICRC 2007), Merida, Yucatan, Mexico (2007). (arXiv:0708.1924 [astro -ph]) J. Abraham et al. [Pierre Auger Collaboration], Astropart. Phys. 33 (2010) 108. H.M.J. Barbosa, et al., Astropart. Phys. 22 (2004) 159, astro-ph/0310234. C. Di Giulio [Pierre Auger Collaboration], Proc. 31th Int. Cosmic Ray Conf. (Lodz, Poland) (2009), arXiv:0906.2189 [astro-ph.HE]. D. Newton et al., Astropart. Phys. 26 (2007) 414. M. Ave [Pierre Auger Collaboration], arXiv:astro-ph/0709.2125v1. J. Abraham et al. [Pierre Auger Collaboration], Nucl. Instrum. Meth. Phys. Res. A613 (2010), 29-39. J. Abraham et al. [Pierre Auger Collaboration], Physics Letters B685 (2010) 239 R. U. Abbasi et al., Phys. Rev. Lett. 100, 101101 (2008). K. Greisen, Phys. Rev. Lett. 16 748 (1966); G.T. Zatsepin a nd V.A. Kuz’min, Pis’ma Zh. Eksp. Teor. Fiz 4 114 (1966) [JETP Lett. f ¯ 4 78 (1966)]. P. Abreu et al. [Pierre Auger Collaboration],”The exposure of the hybrid detector of the Pierre Auger Observatory”, Astropart. Phys. (in press) (2010). R.U. Abbasi, et al., HiRes Collaboration, Astropart. Phys. 32 (2009) 53. S. Riggi [Pierre Auger Collaboration], “Mass Composition Results from the Pierre Auger Observatory”, this conference (2010). P. Ghia [Pierre Auger Collaboration], “Study of the Arrival Directions of Ultra-High Energy Cosmic Rays Detected by the Pierre Auger Observatory”, this conference (2010). D.Allard, Proc. Rencontres de Moriond 2009, arXiv:0906.3156. F. Schuessler [Pierre Auger Collaboration], Proc. 31th Int. Cosmic Ray Conf. (Lodz, Poland) (2009), arXiv:0906.2189 [astro-ph.HE]. M. Kleifges [Pierre Auger Collaboration], Proc. 31th Int. Cosmic Ray Conf. (Lodz, Poland) (2009), arXiv:0906.2354 [astro-ph.HE].