ON THE WAY TO THE DETERMINATION OF THE COSMIC RAY MASS COMPOSITION BY THE PIERRE AUGER FLUORESCENCE DETECTOR: THE MINIMUM MOMENTUM METHOD M. AMBROSIO 1,C.ARAMO 1,2, C. DONALEK 2,3,D.D URSO 4,5,A.D.ERLYKIN 1,6, F. GUARINO 1,2,A.INSOLIA 4,5,G.LONGO 1,2, R. TAGLIAFERRI 7 (1) INFN, Sezione di Napoli, Napoli, Italy (2) Department of Physics, University of Napoli, Napoli, Italy (3) Department of Mathematics and Applications, University of Napoli, Napoli, Italy (4) Department of Physics and Astronomy, University of Catania, Catania, Italy (5) INFN - Sezione di Catania, Catania, Italy (6) P. N. Lebedev Physical Institute, Moscow, Russia (7) Department of Mathematics and Informatics, University of Salerno, Baronissi, Italy We propose a possible approach for the determination of very high energy cosmic ray primary mass A based on the information provided by the longitudinal development of the shower in the Earth atmosphere. We refer to an apparatus such as the Pierre Auger Observatory, which is a unique hybrid UHECR detector. The surface detector (SD) and air fluorescence detector (FD) of the observatory are designed for observation of cosmic ray showers in coincidence, with a 10% duty cycle, with resulting data expected to be superior in quality especially for the primary energy E 0 which is determined with a 5 % accuracy. We present results obtained using an approach for the determination of A in the individual event based on only FD information (MMM - Minimum Momentum Method ). This approach shows that, if the entire information contained in the longitudinal profile is exploited, reliable results may be obtained. 1. Introduction The study of the longitudinal profile of individual atmospheric cascades started with the development of the fluorescent light detection technique implemented for the first time in the Fly s Eye experiment 1. After this pioneeristic efforts, the HiRes 5 array continued detection of UHE cosmic rays using their fluorescent track in the atmosphere. Only recently a new and much more powerful detector has started to collect data: the Fluorescent Detector (FD) of the Pierre Auger Observatory 2. This instrument will produce a large data flow over the next decades and is therefore calling for new and accurate data analysis procedures capable to fully exploit the large amount of information contained in the FD data. Indeed all the groups analyse the distribution of X max - the depth of the maximum cascade development 3 and derive the observed mean mass composition as a function of the primary energy. This approach does not require the identification of the primary particle for each 1
2 individual cascade. Though X max is the most sensitive parameter to the mass of the primary particle in the longitudinal profile, its sensitivity is still weak. There are other parameters which could be used for the discrimination of cascades having a different origin. Among them N max - the number of particles (mostly electrons) in the maximum of the cascade, the speed of rise in the particle number etc. In any case the approach described below attempts to use the complete information contained in the cascade curves for individual event. This method, based on only FD information, and called MMM ( Minimum Momentum Method ), identifies the origin of the cascade by its comparison with simulated cascade of known origin and the estimation of their fraction which have just like shape. It is shown that, to get the best mass resolution, one has to use the entire information contained in the longitudinal profile. We consider them as just the first step on the way to the more sophisticated approach with the use of the information from SD too. 2. The simulation data set The simulation data used for the development of method for the primary mass determination is a set of 4000 vertical cascades at the fixed energy of 1 EeV simulated by the CORSIKA program (version 6.004) 4 with the QGSJET interaction model developed in the Lyon Computer Centre. The primary nuclei comprising this set are P, He, O and Fe, each of them amounts 1000 cascades. CORSIKA output provides the number of charged particles at the atmospheric depths separated by 5 gcm 2. For the development of parametric methods we used the data starting from the depth of 200 gcm 2, since the detection threshold of FD apparatus does not allow to detect the weak signals from the very beginning of the cascade development. The maximum atmospheric depth taken in the analysis is 870 gcm 2 corresponding to the level of the Pierre Auger Observatory. Samples of 50 cascades of the different origin are shown in Figure 1 for the illustration. The same set of simulation has been used for a different analysis based on the use of a neural net, as reported in these proceedings 6. 3. Minimum Momentum Method (MMM): the motivation and the procedure The Fluorescent Detector of the Pierre Auger experiment allows the reconstruction of longitudinal profile of each atmospheric cascade, i.e. the number of electrons N e as the function of the atmospheric depth X. This profile carries more information than just X max or N max. Therefore the attempt has been made to use the entire profile for the determination of the primary mass composition. Each of the 4000 simulated cascades (trial) was compared consequently with all others (test) using a measure of the distance, which incorporates all the available information. We call this approach the minimum momentum method ( MMM ) and we introduce the measure of the closeness or the distance D lm between trial (l) andtest(m)
3 Figure 1. The examples of the longitudinal development of 1 EeV vertical atmospheric cascades induced by protons P, helium He, oxygen O and iron Fe nuclei. The origin is indicated at the headers of graphs. 50 cascades are shown in each graph. cascades to include the information on: (i) the longitudinal development of cascades, i.e. the function N e (X), where N e is the number of electrons at the atmospheric depth X; (ii) fluctuations of the cascade development; (iii) the mutual position of the compared cascade curves, i.e. whether is the test cascade at the greater or at the lower atmospheric depths with respect to the trial cascade. In this approach we used the following definition of the distance: D lm = abs[σ i (X i Xlm )Nl i N i m ] (1) σ Nm i Here Ni l is the number of electrons in the trial cascade at the depth of X i, Ni m - the number of electrons at the same depth X i in the mean cascade initiated by the primary nucleus m, wherem stands for P,He,O,Fe. σ Nm i is the standard deviation of Ni m at the depth X i. By this way we include the information on the fluctuations of the longitudinal development for test cascades. The mean cascades and the standard deviations of their particle numbers as the function of the atmospheric depth X are shown in Figure 2. Interestingly the minimum fluctuations is not at the mean depth of
4 Figure 2. The mean cascade ( full line ) and the standard deviation of its particle number ( dashed line ) for the vertical cascades initiated by primary protons ( P ), helium ( He ), oxygen ( O ) and iron ( Fe ) nuclei ( indicated in the upper right corner of the graphs ) with the energy of 1 EeV. The abscissa is the atmospheric depth in g/cm 2, the ordinate is the number of particles. the maximum development X max but slightly shifted to the larger depths. It is the consequence of the fact that besides the ordinary fluctuations of the particle number there are also fluctuations of the first interaction points - starting points of the cascade development. In order to include the information about the relative location of the trial and the mean test cascade in the atmosphere, we used the term (X i Xlm )beingx lm the depth at which two cascade curves cross (Figure 3). In panel a of the figure 3 the trial cascade, which is shown by the left full line, is compared with four test cascades. They are the mean cascades induced by P, He, O and Fe nuclei, as those shown in Figure 2. The difference in the particle numbers between the trial and test cascades is shown in the pannel b. It is seen that: (i) the cascades which are to the right of the trial cascade (P, He and O) give a different profile of the difference compared with that to the left (Fe); (ii) the crosing point Xlm moves to the left from P to Fe. The weighted difference in particle numbers N l N m is shown in the pannel c. σ Nm i Since all standard deviations are positive the weighted differences preserve the same sign as the original differences, i.e. they are positive below the crossing point Xlm for the right cascades and negative for the left one. Above the crossing point they change the sign.
5 Figure 3. The illustration of the Minimum Momentum Method. (a) The trial cascade (left full line) and the mean test cascades, induced by primary P (right full line), He (chain line), O (dotted line) and Fe (dashed line) nuclei, with which the trial cascade is compared. (b) The difference in the particle number between the trial and test cascades. The notations here and in the subsequent graphs are the same as in (a). (c) The difference in particle numbers weighted with the standard deviations σ Nm i shown in Figure 2. (d) The atmospheric depth rescaled with the depth Xlm corresponding to the crossing point of the trial and test cascades. (e) The rescaled atmospheric depth multiplied by the weighted difference in the particle number. (f) The first momentum of the weighted difference, obtained just by an integration of the functions shown in the graph (e). The minimum of the absolute values of these four momenta defines the origin of the trial cascade. In this illustration it is an oxygen (O) nucleus. In a simple integration of these curves the positive and negative parts partly compensate each other and the sensitivity of the such integral to the primary mass is reduced. That is why the integration has been performed for the function which is the product of the weighted difference and the first momentum rescaled to 0 at the crossing point: X Xlm. This rescaled momentum is shown in the pannel d. It also changes its sign at the crossing point. When we multiply these functions then for right ( P, He, O ) cascades the product is negative in the whole range of atmospheric depths, both below and above the crossing point. The same is true for the left (Fe) cascades, but the sign of the product is positive. These product
6 functions (X i Xlm ) N i l N i m are shown in the pannel e. Different signs of the σ Nm i functions for P, He, O and for Fe induced cascades are clearly seen. Integrating these functions the values of the first momentum which have different signs for right and left cascades (pannel f ) are obtained. By this way not only is increased the separation between the trial and different test cascades, but is determined if the test cascade have earlier or later development in the atmosphere with respect to the trial cascade. The final problem is how to use these momenta for the determination of the parent nucleus and consequently the probability to classification (and mis-classification) this nucleus. We define it as the test nucleus which gives the cascade closest to the trial cascade in terms of the distance (1). Therefore we first determine the distance as the absolute value of the momentum (1) and then find their minimum D min = min(d lm ). The nucleus m which gives this minimum is defined as the parent nucleus for the trial cascade. Hence we call this method as the minimum momentum method (MMM). The results for the determination of the observed mass composition in the case of the mixed uniform primary composition are shown in Figure 4. The plot of mean probability for the primary P, He, O and Fe nuclei to be correctly identified as P, He, O and Fe indicates that the MMM method works quite successfully in distinguishing ligth nuclei (P and He) from heavy nuclei (O and Fe). 4. Conclusion The problem of the determination of the primary mass composition using the longitudinal development of the cascades is difficult because of its small sensitivity to the mass of primary nucleus and big fluctuations in the longitudinal profile. The method we developed is principally based on the assumption that in the hybrid events the accuracy of the primary energy estimate is as high as 5%. Maximum information should be used including the information about the shower lateral distribution coming from surface array. In any case the proposed approach, on the basis of comparison with 4000 simulated cascade, gives promising results for P and Fe identification in the individual case as well as for the determination of mean mass composition including the uniform one, which is the most complicated for the reconstruction. Results reported here refer to 1 EeV primary energy vertical cosmic rays. Experimental errors must be also estimated and accounted in the data processing. Acknowledgments Authors thank Dr.M.Risse for the high statistics simulation of cascades used in the this work.
7 Figure 4. The mean probability for the primary P, He, O and Fe nuclei (specified in the headers of the graphs) to be identified as P, He, O and Fe by MMM for the uniform primary mass composition. References 1. Baltrusaitis R.M. et al. 1985, Nucl.Instr.and Meth. A 240, 410 2. Blümer H. 2003, 28th Int. Cosm. Ray Conf., Tsukuba, Highlight Talk 3. Gaisser T.K. et al. 1993, Phys. Rev. D47, 1919 4. Heck D. et al. 1998, FZKA Report Forschungszentrum Karlsruhe 6019 5. Matthews J.N. et al., HiRes Call., 2001, 27th Int. Cosm. Ray Conf., Hamburg, 2, 350 6. M. Ambrosio et al. 2004, These Proceedings