Model-independent Determination of Mass Composition and Energy Spectra of the Primary Flux, Based on Extensive Air Shower Observations

 

Measurements of the high energy particles flux incident on Earth brings us information about the possible particle sources, about the nontermal processes in which particles are accelerated to relativistic energies, about the role of the particles and natural accelerators in driving dynamical processes in our galaxy and beyond, also - about the distribution of matter and fields in interstellar space.

This information is complementary to astronomy with photons in various wavelength bands and investigation of nontrivial correlation in multidimensional obsevations of same object in  energy range of  2.5 decades will spread new light on origin and development of numerous exotic objects in Universe.
Observation of blazars (subclass of AGN, Mrk 421, 3C279, etc...) is covered by radio, millimeter, submillimeter, infrared, optical, x-ray, and gamma ray bands and    there is more energy emitted in high energy particles bands, than in all other wavelength bands combained [1].  The observation of a simultaneous flare in the optical and gamma ray bands can discriminate between various existent models of luminosity production.

 Despite enormous efforts by many researchers in this field, many important questions still have to be answered, among them are followings:  

• What is the interpretation of the ?knee? in the cosmic ray spectrum above 3*10**15 eV?
  
• What is the maximum energy to which supernovae blast waves can accelerate particles?
  
• Is there a high-energy component of protons or nuclei from distant, extragalactic sources ?
  
• Can we find specific point sources of high-energy cosmic rays?

In order to answer these and many other questions it is necessary to measure relative contribution of the different group of nuclei and their energy.  The elemental composition of the high energy cosmic rays is a powerful constraint on theories of their origin and propagation. To distinguish among models of cosmic ray origin the nuclear composition should be determined at all energies.

Direct measurements of cosmic ray fluxes are carried out with aircraft, balloons and satellites covered the energies up to 10**14 eV. Chemical composition and energy spectrum of cosmic rays at these energies were determined rather definitely, mainly consisting of light nuclei.
But at the energies higher than 10**15eV an essential change in extrapolated from lower energies composition occurs. Different theories of cosmic ray generation, propagation and acceleration in interstellar space predict different elemental composition and different behavior of energy spectrum.
However, direct measurements in the mentioned energy range are impossible due to the low particle fluxes.

Thus, methods based on the registration of the secondary products of intense hadronic-electromagnetic cascade initiated by interaction of primary particle with atmosphere nuclei, so called Extensive Atmospheric Showers (EAS), are only possible for these energies.
Due to the highly indirect character of the EAS measurements and steeply fallen fluxes, despite of long time study, the element composition for that energy region was not determined with proper accuracy up to now. Progress toward the goals of measuring energy spectra of different species of primary flux and their relative abundance is very slow and difficult.

The mass and the energy of the primary particle have to be deduced from the measurable parameters of EAS. Of course shower development depends on primary type and energy and from measured EAS characteristics one can construct relevant primary estimators. Among these EAS features are:
 

• The atmospheric depth at which the maximum shower development occurs (the most important feature of shower longitudinal development);
• The muon/electron ratio is another powerful indicator of the primary particle nuclear identity;
• Third quantity which correlates with primary mass is the rise time of the all particles pulse far from shower core (especially the arriving time distribution of EAS muons).

New experiments, measuring as much independent characteristics of EAS with better accuracy [2,3], coupled with a better understanding of hadronic interaction models at superaccelerator energies [4] and advanced multivariate statistical techniques [5] show promise for improving the situation.

In previous experiments registering EAS the mass resolution has been rather poor, and only general trends have been obtained comparing various one- or two-dimensional distributions of observables with simulations.

The main advantage of new installations is the simultaneous measurement of the a large number of observables for each individual event. This is achieved by the combination of the various detection techniques for electrons, muons, and hadrons in EAS.

Along with measuring as much as possible EAS secondary particles, the simulation studies of EAS development are of crucial importance. Primary mass identification requires absolute calibration with sophisticated Monte Carlo (M.C.) code.
The challenge of experimental EAS physics is to understand the shower development and the detector performance well enough to enable reliable reconstruction of the mass and energy of the primary particle starting from the measuring energy deposits and time signals in the single detector element without being able to calibrate experiment in a suitable test beam [6].

The major systematic uncertainties in EAS analysis arise from the lack of knowledge of the total cross sections and the details of particle production for hadronic reactions with small momentum transfer. The proton collider results have to be extrapolated over many orders of magnitude, to small emission angles and to nuclear projectiles and targets.
The systematic comparative study of existent M.C. codes were performed recently by J.Knapp [7], giving firm basis for mutual calibration of EAS experiments.
The actuality of having reference M.C. code for CR community can be illustrated by contradictions between physical inference on elemental composition made by different experimental groups based on various simulations.

Based on the experimental measured intensity of gamma-families detected by emulsion chambers at high mountain altitudes [8], The Fudji-Kanbala group decided that after "knee" the iron primary is dominated in primary flux[9], on the other hand based on the approximately same data, Chakaltaya and Pamir collaborations[10] insist that it is due to change of characteristics of hadronic interaction and composition didn?t change dramatically.

The Fly's Eye detector group publish a number of papers [11] climbing the change of primary composition to approximately pure protons after 10**17 eV,  in contradiction the Akeno group didn't notice significant change in composition at these energies[12].

In both cases different conclusions just reflect the difference in the simulation codes used.
We agree, as it was mentioned in [7], that it is vitally important to make a common effort towards a reference simulation program that contains the best and most detailed treatment of all physical processes relevant to EAS and that is used and tested by different groups without adapting the physics parameters for each experiment in different way.
There exists very good example of such program, also heavily used in CR community for detector response calculations. The CERN detector simulation package GEANT [13] is nowadays the de facto standard for the simulation of detector response function in complex setups in presence of all kind radiation sources.

Along with experimental installation measuring as much as possible EAS parameters and detailed and properly tested reference M.C. code it is necessary to develop coherent statistical methods for dealing with such multivariate, nonlinear cases.
To make the conclusions about the investigated physical phenomenon more reliable and significant, a unified methodology of statistical inference, based on nonparametric models,   was worked out in CRD YeRPhI (ANI package[http://crdlx5.yerphi.am/ani/conference.htm ].)

The most important part of the advocated approach is the quantitative comparison of multivariate distributions and use of a nonparametric technique to estimate the probability density in the multidimensional feature space. As compared to the earlier used methods of  inverse  problem  solving, the object of analysis is each particular event (a point in the multivariate space of measured  parameters .  That is why, along with the averaged characteristics, the belonging of each event to a certain class is determined (shower-by-shower analysis).
This approach was first used to estimate the upper limit of the iron nuclei fraction  according  to  the   gamma - family characteristics, registered  by  PAMIR  collaboration  [14]. Obtained results allows to reject the hypothesis of dominance of iron nuclei in PCR just after "knee".

The potential difficulties and limitations of the ANI package are connected with model dependence  of  statistical inference. The question of correctness of the model itself is always open and we need a more general procedure  to check the model validity and obtain  physical  results  not  so crucially depending on the prechosen models. Such procedures will be constructed using ANI different ANI modes in the framework of proposed project.

Also in the framework of the project new characteristics of EAS, allowing more precise determination of energy and primary type, will be investigated and measured with modernized experimental facilities of Aragats research station (ANI experiment). First of all they are precise measurement of the longitudinal structure of EAS by observing the arrival time distribution of muons [17] and the measurement of the shower soft component density at the distance of 120 m. from shower axes [15,16].

We plan to combine the enlarged possibilities of the installations, observing EAS on mountain altitude (ANI experiment with it?s most developed detector - GAMMA installation, combining the EAS surface array with extended muon detection facility) with another big installation operating on sea level with unique possibilities of sampling muon, hadron  and soft component - KASCADE [3]. The mutual analyses of both experiments will provide unique possibility for exploring energy region around knee. The minor fluctuations of EAS parameters on the Aragats level (700 g/cm.sq.) provide a unique possibility for calibration CORSIKA simulation code used for KASCADE data analysis

Previously used methods, where only the distributions (histograms) summarized over experiment and simulation respectively are compared, lead mostly only to qualitative conclusions. New techniques proposed here provide possibility to analyze EAS data on event-by-event basis and therefore derive mass composition and energy spectra of primary flux with reliability and accuracy compatible with ones achieved on man-made accelerators [18,19].
By the classification method one can obtain the ?cosmic accelerator beams? and subsequently address the problem of tuning strong interaction parameters (cross sections, multiplicities, inelasticity coefficients).

EXPECTED RESULTS

1. Construction of the experimental installation for precise measurement of the  different independent characteristics of EAS;
2. Detailed investigation of the mass composition of primary cosmic ray flux in "knee" region - mass spectroscopy of "knee" region;
3. Measurements of the energy spectra of all particle flux and separately for different species of primary flux (5 groups of nuclei), search for diffuse flux of gamma-quanta;
4. Estimation of some phenomenological parameters of strong interactions of protons and nuclei with air nitrogen at energies not achievable for man-made accelerators;
5. Development of a new unified methodology of model-independent inference.

SCOPE OF ACTIVITIES

1a.  Investigations of the time characteristics of scintillators, hausings, phototubes ans front-end electronics.
1b.  Commissioning  of electronics, mechanical parts for fast timing  muon detectors.
1c.  Testing of the new muon detector performance.

2a. Installation of fast timing facilities for accurate experimental investigations of the temporal structure of EAS muon component.
2b. Development of the relational data bases structures for raw data storage and fast access, validation of the estimated by M.C. simulations actual values of detector performance.
2c. Data analysis, comparison of simulations and experimental data.

3a. Continuous operation of the  installation, data acquisition.
3b. Precise calculation of detector response function, comparisons of different array triggers, reconstruction of the primary flux intensity.
3c.  Classification of the detected events according to 5 nuclei groups, estimation of the energy of the primaries, elaborating of the necessary corrections due to finite resolution and energy-dependent threshold of installation.

4a. Search for EAS parameters informing about the nature of the primary particle and study of significant relations between EAS characteristics on the mountain altitude and sea level for unambigious physical inference on elemental composition.
4b. Selection of events corresponding to the ?heavy? and "light" nuclei.
4c. Estimation of the cross sections and elasticity coefficients for different nuclei groups.

5a. Simulation of the electron-nuclear cascade in the atmosphere and of the response function of apparatus for different primary nuclei, preparation of the data bases with EAS simulations and experimental data from ANI and KASCADE installations.
5b. Development of the multivariate analysis methods for  joint analysis of simulation and experimental data and - for  model independent inference.
5c. Development of the program package with friendly user interface for on-line and off-line data analysis.

TECHNICAL APPROACH AND METHODOLOGY

The theoretical base of the project is comprised of:

• Detailed investigations of the optimal subset of EAS measurable characteristics for primary type and energy estimation [20].
• A special data analysis methodology developed for EAS experiments, proved to be reliable and powerful in a number of astroparticle physics applications [21-23].

- the total soft component particle number : 10%
- the coordinates of shower axis : 3m
- the total muon number : 20%
- zenith angle of shower axis : 1.50 degrees.

In the framework of present project the GAMMA array will be significantly modernized. The new fast timing system will be installed, providing time resolution approx. 2 nsec.
More precise and reliable flash ADCs and new data acquisition system will provide reliable measurement of time profile of scintillation detector response.

• Dedicated infrastructure of station providing possibilities of nonstop operation on the altitude 3200 m above sea level.
• Advanced electronics to be delivered by partner.

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