Acta Polytechnica doi:10.14311/AP.2013.53.0698 Acta Polytechnica 53(Supplement):698–702, 2013 © Czech Technical University in Prague, 2013 available online at http://ojs.cvut.cz/ojs/index.php/ap THE MASS COMPOSITION OF ULTRA HIGH ENERGY COSMIC RAYS Aurelio F. Grillo∗ INFN – Laboratori Nazionali del Gran Sasso, SS 17 bis, 67100 Assergi (AQ), Italy ∗ corresponding author: grillo@lngs.infn.it Abstract. The status of the Mass Composition measurements of Ultra High Energy Cosmic Rays is presented, with emphasis on the results from the Fluorescence Detector of the Pierre Auger Observatory. Possible consequences of the present measurements are discussed, both on the particle physics and astrophysics aspects. 1. Introduction At the highest energies (log10 E > 18.5) Ultra High Energy Cosmic Rays (UHECRs) are very likely of extra-galactic origin. Measurements of the moments of their mass distribution when they hit the Earth’s atmosphere are likely to give important clues on their sources, propagation and interaction at (center of mass) energies that are around 100 TeV. The zeroth moment (all particle spectrum) by definition does not explicitly distinguish between different nuclear components, although its interpretation can be easily connected to those (see the report by R. Aloisio at this conference). Higher moments are starting to discriminate between different hypotheses, although of course they are more and more affected by statistical and systematic errors. The most used shower observables for studying the composition of Ultra High Energy Cosmic Rays (UHECR) are the mean value of the depth of shower maximum, 〈Xmax〉, and its dispersion, σ(Xmax). Infer- ring the mass composition from these measurements is subject to some level of uncertainty. This is because their conversion to mass relies on the use of shower codes which include the assumption of a hadronic interaction model. These interaction models [1] have in common the ability to fit lower energy accelerator data. However, they are based on different physical as- sumptions to extrapolate these low energy interaction properties to higher energies. Consequently they pro- vide different expectations for 〈Xmax〉 and σ(Xmax). In the following we will mainly discuss the different roles of the two observables, 〈Xmax〉 and σ(Xmax), with respect to mass composition. On the basis of the superposition model [2] 〈Xmax〉 is proportional to 〈ln A〉 and therefore it actually mea- sures (average) mass composition for both pure and mixed compositions. The behaviour of σ(Xmax) is however more complex, and gives indications on mass distributions corresponding to the same 〈ln A〉. 2. General ideas As observed above 〈Xmax〉 can be directly connected to the average composition of the nuclear cosmic rays in the beam when they hit the atmosphere (the average being performed within reconstructed energy bins): 〈Xmax〉 = X0 + X1〈ln A〉 (1) where the coefficients depend on details of the interac- tion of the beam with the atmosphere and generally depend logarithmically on its energy. For a given combination of nuclear species with nor- malized (generally energy dependent) weights {wi}1 〈ln A〉 = Σ wi (ln Ai) Here we remark that the nuclear weights at the Earth’s atmosphere will be in general different from the corre- sponding fractions at the sources, since, at the energies we are considering, nuclei will suffer photodisintegra- tion γA → (A−n) + nN interacting with the universal radiation backgrounds in the extra-galactic space through which they prop- agate. This implies that even in the extreme case of sources producing pure compositions of nuclei (apart from protons) the detected composition will be in general mixed. The variance of Xmax is σ2(Xmax) = X21 σ 2 ln A + 〈σ 2 shower〉 (2) σ2ln A = Σ wi (ln Ai −〈ln A〉) 2 while 〈σ2shower〉 = Σ wiσ 2 shower(A) describes the intrinsic fluctuations of Xmax for dif- ferent nuclei, and as such depends on details of the interactions, but generically decreases with increasing A, being maximum for protons and minimum for Iron nuclei [3]. Notice that the first factor in Eq. 2 is trivially zero for a pure composition, while the second factor is obvi- ously larger than zero. Equation 1 describes how the measurement fixes the average (logarithmic) mass, but 1Given the low statistics at highest energies it is customary to group the nuclei into mass groups. 698 http://dx.doi.org/10.14311/AP.2013.53.0698 http://ojs.cvut.cz/ojs/index.php/ap vol. 53 supplement/2013 The Mass Composition of Ultra High Energy Cosmic Rays Figure 1. The relation between 〈ln A〉 and σ2(Xmax), here for four mass groups (Figure provided by M. Unger). cannot discriminate the real composition. Equation 2 starts to help in this task because for each average mass there is a spread of corresponding allowed values of the variance – so a given measurement can hopefully exclude possible contributions to the average mass. This is beautifully expressed in a plot, originally pro- posed by Linsley (Fig. 1) [4]. In the original plot the σln A was plotted, here we use σ2(Xmax), introducing a dependence on the propagation model. It is instruc- tive to elaborate on this plot. The figure describes the possible range of σ2(Xmax) for a given value of 〈ln A〉. Clearly the cusps correspond to pure mass composi- tions: here the σ2 reaches a minimum consistent with a given average mass since the first term in Eq. 2 vanishes. For the same reason the transition from a pure composition to the next one (e.g. from proton to helium) bounds its minimum variation. On the other hand a superposition of the two extreme masses, here proton and iron, gives the largest variance. In fact, for a given 〈ln A〉 this combination requires a proton fraction larger than any other combination, and pro- tons give the largest contribution to both terms of Eq. 2. 3. The data from the Pierre Auger Observatory Figure 2 shows the all-particle spectrum obtained by the Pierre Auger Observatory. The cut-off of the spectrum at high energies has a significance of ≈ 20σ. The composition data from the Pierre Auger Ob- servatory discussed below are obtained from hybrid events, which are events detected by the Fluorescence Detector (FD) of the Observatory, with at least a signal in one of the water Cherenkov stations of the Surface Detector (SD) measured in coincidence2. Considering the data from December 2004 up to September 2010, after the FD quality cuts [5] 15 979 events remain. For the composition analy- sis additional cuts are used to ensure that no bias 2The data are those described in Ref. [5] as updated in [6]. E[eV] 18 10 19 10 20 10 ] 2 e V -1 s r -1 y r -2 J (E ) [k m 3 E 37 10 38 10 (E/eV) 10 log 18 18.5 19 19.5 20 20.5 Auger power laws power laws + smooth function Figure 2. The Pierre Auger Observatory All-particle spectrum. See [7] for details. with respect to the cosmic ray composition is intro- duced in the data sample. Specifically, it is required that the trigger probability of the SD station be sat- urated both for proton and iron primaries and only FD reconstructed geometries are kept for which the full range of Xmax is observable. After these cuts, 6 744 events remain. The systematic uncertainty in the energy reconstruction of the FD events is 22 % The average resolution is ≈ 20 g/cm2 over the energy range considered. Furthermore, the RMS(Xmax) has been corrected for the detector resolution. Therefore the Auger data are detector independent and can be directly compared with simulations. Let us first consider the plot of 〈Xmax〉 in Fig. 3. Its energy dependence has been fitted with a broken line, showing an increase up to log10 E ≈ 18.4 up to a value compatible with a pure proton composition, then a much milder increase consistent with a com- pensation of the logarithmic increase with energy by a (logarithmic) increase of average mass. As is also indicated by the expectations from interaction models the composition appears to become increasingly heavy with energy. We can therefore conclude that 〈Xmax〉 data are consistent with 〈ln A〉 increasing with energy, at least above log10 E > 18.4. Let us now discuss the plot of fluctuations, the lower panel of Fig. 3. Let us first note that this plot can lead to misleading interpretation in the way it is customarily presented. The lines of the predictions of interaction models are only for pure compositions. While in the 〈Xmax〉 plot they have the generic mean- ing of the possible range of values of Xmax, this is not true here and, as for instance indicated in Fig. 1, the fluctuations can be larger than those corresponding to the upper lines, i.e. pure proton compositions, while they cannot be smaller than those of pure iron com- position. To take an example, if the composition is proton dominated at some energy and then evolves to- ward larger mass through a proton–iron combination, then in general in some energy range the fluctuations can be larger than those of pure protons. 699 Aurelio F. Grillo Acta Polytechnica E [eV] 18 10 19 10 ] 2 > [ g /c m m a x < X 650 700 750 800 850 1407 1251 998 781 619 457 331 230 188 143 186 106 47 EPOSv1.99 p Fe QGSJET01 p Fe SIBYLL2.1 p Fe QGSJETII p Fe EPOSv1.99 p Fe QGSJET01 p Fe SIBYLL2.1 p Fe QGSJETII p Fe Figure 3. Xmax (upper panel) and RMS(Xmax) com- pared with predicted values for pure compositions in different interaction models. ] 2 [g/cm〉 Fe max X〈-〉 max X〈 0 20 40 60 80 100 ] 2 [ g /c m F e σ- σ 0 10 20 30 40 50 Fe Si N He p Auger data Auger syst. simulation ] 2 [g/cm〉 Fe max X〈-〉 max X〈 0 20 40 60 80 100 ] 2 [ g /c m F e σ- σ 0 10 20 30 40 50 Fe Si N He p ] 2 [g/cm〉 Fe max X〈-〉 max X〈 0 20 40 60 80 100 ] 2 [ g /c m F e σ- σ 0 10 20 30 40 50 Fe Si N He p ] 2 [g/cm〉 Fe max X〈-〉 max X〈 0 20 40 60 80 100 ] 2 [ g /c m F e σ- σ 0 10 20 30 40 50 Fe Si N He p Figure 4. σ(Xmax) versus 〈Xmax〉 of the data, both normalized to iron, compared with predictions of var- ious interaction models: QGSJET01/II (up left and right), SIBYLL2.1 (bottom left) and EPOSv1.99 (bot- tom right). Energy varies as the dotted line, the highest value being the lower points. The variance reaches a maximum approximately at the same energy as the break of the slope of 〈Xmax〉, then it starts to decrease approximately monotonically with energy. Since 〈ln A〉appears to rise monotonically in log10 E, and considering Eq. 2 and the behaviour of Fig. 1 it appears that the transition of average mass towards larger values happens consistently through almost pure compositions (〈σln A〉≈ 0), in particular with few protons at the higher energies. In [8] a thorough discussion is presented of mass composition measurements in cosmic ray experiments. In particular a discussion of the combined 〈Xmax〉 versus σ(Xmax) of the Auger data is analyzed with the help of a series of plots similar to Fig. 1 for each interaction model considered and for five mass groups ] 2 [ g /c m µ m a x µ Xµ 500 550 600 650 EPOSv1.99 QGSJETII-03 S IB Y L L 2. 1 proton iron Syst. Unc. m a x Θ 1.5 1.55 1.6 energy [eV] 18 10 19 10 20 10 Figure 5. Two composition sensitive observables from SD, compared with expectations from interaction models (for further details see [9]). (proton, helium, CNO, silicon, iron). The main differ- ence from Fig. 1 lies in the use of the experimental observables both for the simulations and for the data. From these plots it appears that the central values of the experimental data (within statistical errors only) have a varying, but generically large, tension towards all the interaction models apart from EPOS, especially at the highest energies. Also, these plots confirm the general idea that the transition to larger masses can be better described by the dominance of different mass groups in different energy intervals, with small mixing between the groups, and in particular little admixture of protons. However, taking into account systematics considerably weakens these conclusions. The Fluorescence Detector of the Pierre Auger Ob- servatory has only a limited duty cycle, while the Surface Detector is continuously active, therefore composition-related observables connected to SD, al- though of less direct interpretation, are a valuable complement for direct longitudinal shower develope- ment measurements. Fig. 5 shows two such measure- ments, relating to muons (and electrons) in Auger showers. This data confirm the FD measurements, especially when systematics is taken into account [9]. 4. Discussion Although a full analysis of the Auger composition data is not yet available, some tentative conclusions can be drawn. But before discussing them, it is important to relate the behaviour of the composition to the data of other large experiments, HiRes [10], Telescope Ar- ray [11] and Yakutsk [12]. The former is no longer in operation. These experiments claim a composition 700 vol. 53 supplement/2013 The Mass Composition of Ultra High Energy Cosmic Rays 1e+32 1e+33 1e+34 1e+35 18 18.5 19 19.5 20 20.5 21 proton nitrogen iron All particle Figure 6. Partial spectra (multiplied by E3, in arbi- trary units) of a mixture of mass groups that would qualitatively reproduce both spectrum and composi- tion data. compatible with pure proton. However their dataset is substantially smaller than that of Auger, and their data are also compatible with Auger data. Moreover, with the cuts described above the Auger data (and, al- though with a different strategy, those from Yakustsk) are free from detector biases and therefore can be directly compared with simulations from interaction models, while for HiRes and TA the detector biases have been applied to the simulations. This makes a direct comparison of the data difficult. It should also be stressed that moving the data within the relatively large band of systematics, espe- cially for the second moment (the variance of Xmax), can greatly influence the conclusions, as can be seen in Fig. 43. Finally, we are implicitely assuming that at least some of the interaction models used are correct at these energies, which in the center of mass are approx- imately two orders of magnitude larger than those in LHC. A change in proton (and nuclei) interactions in these range would have profound consequences on the interpretation of the experimental data. Coming back to the data we have seen that the be- haviour of RMS(Xmax) seems to suggest an evolution of the mass composition toward larger values with little mixing between mass groups. In other words the transition towards large masses in energy is possibly happening through the dominance of a single mass group, as is sketched in Fig. 6 for three mass groups (proton, nitrogen and iron). Although this figure has to be seen as a guide to the eyes, it is clear that a similar behaviour could apply for log10 E > 18.4 given that measurements suggest an increasing 〈ln A〉 plus a decreasing variance, remembering that one expects a decrease of 〈σshower〉 with A. Note however that these are the spectra at Earth. 3However, as is clear from the figures, moving the data towards lower values of fluctuations is inconsistent with any interaction model and would imply profound consequences from a particle/nuclear physics point of view. Nuclei generally interact with universal radiation back- grounds (both CMB and EBL) in their travel in the extra-galactic space, and suffer photodisintegration in wich the original A decreases. If one assumes the simplest model of (extra-galactic) sources of UHE- CRs at these energies: uniformily distributed, with a universal power law spectrum and charge-dependent maximum energy, then it appears that very pecu- liar conditions must be fulfilled in order to reproduce the experimental moments of the mass distribution. In fact, to avoid overpopulating the partial spectra with species produced in the propagation in the extra- galactic space (particularly protons) it appears that a low cut-off energy is needed at the source. This in turn implies very flat spectra (i.e. differential slope < 2) to reproduce the observed data. In this case the observed high energy cut-off of the all-particle spectrum would be a feature of the sources, not of the propagation. These features appear to be at odds with generally accepted ideas of acceleration of UHECRs, but of course this source model can be oversimpli- fied. For instance the spectrum might be dominated by only a few (maybe peculiar) nearby sources (see e.g. [13]). And, of course, the interaction models used to describe the data might be inadequate at these energies. This has been advocated in [14]. In conclusion, a combined, full analysis of UHECR data (spectrum, composition and possibly anisotropy) is needed to get hints of their provenience. Such full analysis is likely to require a modification of the sim- plest models, of particle physics and/or of astrophysics, used up to now to describe the data. Acknowledgements All of the considerations expressed here benefitted from very fruitful work and discussions within the Pierre Auger Collaboration; they in any case represent my personal point of view. I thank K.-H. Kampert and M. Unger for allowing me to use figures from their paper [8]. References [1] For a recent review see e.g. R. Engel, D. Heck and T. Pierog, Annu. Rev. Nucl. Part. Sci., 61, 467 (2011) [2] See e.g. T.K. Gaisser, Cosmic Rays and Particle Physics, Cambridge 249 University Press, Cambridge, 1990 [3] See e.g. J. Matthews, Astropart. Phys., 22, 387 (2005) and references therein [4] J. Linsley, Proc. 19th ICRC 6 (1985) 1 [5] J. Abraham et al. (Pierre Auger Collaboration), Phys. Rev. Lett. 104, 091101 (2010) [6] P. Facal San Luis for the Pierre Auger Collaboration, Proc. 32nd International Cosmic Ray Conference (ICRC 2011), Beijing, China and arXiv:1107.4804v1 [7] F.Salamida (Pierre Auger Collaboration) Proc. 32nd International Cosmic Ray Conference (ICRC 2011), Beijing, China and arXiv:1107.4804v1 [8] K.-H. Kampert and M. Unger, Astropart. Phys. 35, 660 (2012) 701 Aurelio F. Grillo Acta Polytechnica [9] D. Garcia-Pinto et al. (Pierre Auger Collab.) in Proc. 32nd ICRC (Beijing, China, 2011), arXiv:1107.4804v1 [10] R. Abbasi et al. [HiRes Coll.], Phys. Rev. Lett. 104 161101 (2010) [11] C. Jui et al. [TA Coll.], Proc. APS DPF Meeting, arXiv:1110.0133 [12] E. Korosteleva et al., Nucl.Phys.Proc.Suppl. 165 74 (2007) [13] A. M. Taylor, M. Ahlers and F. A. Aharonian, arXiv:1107.2055v1 [14] N. Shaham and T. Piran, arXiv:1204.1488v1 282 702 Acta Polytechnica 53(Supplement):698–702, 2013 1 Introduction 2 General ideas 3 The data from the Pierre Auger Observatory 4 Discussion Acknowledgements References