In this section, we briefly describe the data sets of KCDC. More detailed information can be found in Ref. [24].
Air-shower data
The air showers measured by KASCADE-Grande are analyzed using the reconstruction program KRETA (KASCADE Reconstruction for ExTensive Air showers). Starting from the energy deposits and the individual time stamps in all detectors of all components KRETA determines physical quantities like the total number of electrons, muons, hadrons in the shower or the shower direction. KRETA reads the raw data, performs calibrations and reconstructs the basic shower observables, and stores all results in histograms and vectors of parameters. KRETA is written in FORTRAN using CERN library packages and CERN’s HEPDB database to hold time dependent calibration and status parameters for all detector components.
From the various observables obtained in the analysis we choose 22 for 158 million events to be published in the first revision of KCDC in November 2013. With the version released early 2017 we published more than 433 million events from the detector components KASCADE, Grande and Hadron Calorimeter with 24 quantities on which cuts can be applied via the KCDC Data Shop and 5 arrays of data from the local station measurements. Based on data generation and data handling we distinguish between:
Measured Data corresponding to data which are directly measured or reconstructed by the KASCADE analysis software like energy deposit and arrival directions.
Calibration Data used to calibrate and reconstruct the data sets on an event-by-event basis like temperature and air pressure.
Event Information used to uniquely characterize an event like event time and run or event number.
What follows is a brief description of the available KCDC quantities and procedures of how they were obtained:
Primary energy (KASCADE) One of the main goals of the air shower measurement is to determine the energy spectrum of the cosmic rays. Due to uncertainties in the hadronic interactions and the shower-to-shower fluctuations due to the stochastic process in the shower development, the determination of energy and mass is challenging. In KASCADE, we measure the electromagnetic and muonic components of air showers separately. By using both observables, we perform a transformation matrix in order to convert the number of electrons and muons to the energy of primary particles taking into account the angle-of-incidence. The parameters of the formula of the energy estimator are derived from air-shower simulations using the simulation program CORSIKA applying the hadronic interaction model QGSjet-II-02 (Quark-Gluon-String Model, version II-02 [25]) for laboratory energies above \(200\,\hbox {GeV}\) and the low energy model FLUKA 2002.4 [26] below. This first order rough energy estimation is given by the formula:
$$\begin{aligned} \begin{aligned} lg(E_0/\mathrm {GeV})&= 1.93499 + 0.25788 \cdot lg(N_{e}) + 0.66704 \\&\quad \cdot lg(N_{\mu }) + 0.07507 \cdot lg(N_{e})^{2}\\&\quad + 0.09277 \cdot lg(N_{\mu })^{2} \\&\quad - 0.16131 \cdot lg(N_{e}) \cdot lg(N_{\mu }) \end{aligned} \end{aligned}$$
where lg(\(N_{e}\)) and lg(\(N_{\mu }\)) are corrected for atmospheric depth and angle-of-incidence.
Shower core (KASCADE) The core position is the reconstructed location of the shower centre derived from the energy deposits of each detector station of one event. By means of a neural network algorithm which combines high efficiency for the identification of the shower core with good rejection capability for showers that fall outside the fiducial volume, the core can be determined to a precision of about \(1\,\hbox {m}\). Extensive air showers with a core position outside the detector area have a great probability for being incorrectly reconstructed. Therefore, it is recommended to cut showers with a core distance larger than \(91\mathrm m\) from the centre of the detector area.
Shower direction (KASCADE) The KASCADE detectors measure the arrival time and the energy deposit of air shower particles. The shower directions are determined by evaluating the arrival times of the first particle in each detector station. To increase the accuracy, the energy deposits are taken into account when the direction of the shower disk is calculated in a second order correction. By this, an angular resolution of \(0.1^\circ \)–\(1^\circ \) depending on the shower size \(N_{e}\) is reached. The angular resolution drops significantly above \(\theta > 40^\circ \), caused by the fact that the reconstruction algorithms has been fine-tuned to zenith angles below \(40^\circ \). In KASCADE coordinates, the zenith angle is measured against the vertical direction, which means that \(\theta = 0^\circ \) is pointing upwards and \(90^\circ \) denotes a horizontally arriving shower. The azimuth is defined as an angle measured clockwise starting in northern direction (\(90^\circ \) is east). The regular local orientation of the KASCADE array at KIT had an offset of about \(+15^\circ \) against the real North, which is corrected for in the data analysis.
Number of electrons and muons (KASCADE) In the 252 \(\hbox {e}/\gamma \)- and 192 \(\mu \)-detectors, electrons and muons as well as other particles are registered. In three steps the number of electrons and muons are reconstructed where the results of the current iteration level serves as starting parameters for the next step. Every level starts with a consistency check and the preparation of the data. Signals inconsistent with those of the neighbouring detectors are discarded as well as signals with a time stamp more than \(200\,\hbox {ns}\) from the shower front. Then the measured energies are corrected for the inclination of the shower axis and the lateral energy correction function is applied. Thereby the \(\hbox {e}/\gamma \)- detector signals are corrected for the contributions from \(\gamma \)-particles and the \(\mu \)-detector signals are corrected for electromagnetic and hadronic punch through. Finally the corrected signals are converted to particle numbers. Finally, the lateral distribution of the densities are fitted with a modified Nishimura-Kamata-Greisen (NKG)-function and integrated to obtain the total particle numbers.
Shower age (KASCADE) Contrary to variables like number of electrons or muons the value of the age parameter has no absolute meaning, as it depends on the choice of the lateral distribution function which is fitted to the shower data. It may also be called lateral shape parameter because it describes the steepness of the lateral electron density distribution. KASCADE uses a modified NKG-function to fit the lateral shower shape. A heavy primary particle with the same energy as a light one gives rise to a flatter lateral distribution, as the shower starts earlier in the atmosphere. When reaching ground, the shower is “older”, which gives the age parameter its name. The age parameter therefore may help (in combination with the ratio of number of electrons to muons) to distinguish between primary particles of different mass.
Energy deposits (KASCADE) The energy deposit in every KASCADE station is recorded separately for the signals of the \(\hbox {e}/\gamma \)-detectors and \(\mu \)-detectors. The energy deposits of the \(\hbox {e}/\gamma \)-detectors are used to calculate the shower core position and the shower energy by means of a lateral density function fit. The mean energy deposit of a minimum ionising particle (mip) is about \(12\,\hbox {MeV}\). Energy deposits equivalent up to 1250 mips can be detected linearly with a threshold of roughly 1/4 mip (\(3\,\hbox {MeV}\)). The mean energy deposit of a minimum ionizing particle in the \(\mu \)-detectors is about \(8\,\hbox {MeV}\), where energy deposits equivalent to 60 mips can be detected linearly with a threshold of roughly 1/4 mip (\(2\,\hbox {MeV}\)). The energy deposits of both detector types are derived from the stored ADC (Analog Digital Converter) values for each detector station by means of a calibration procedure where the influences of electronics and cabling are included. In KCDC, no cuts can be applied to these quantities.
Arrival times (KASCADE) The first particle passing the threshold in every station produces a time stamp called Arrival Time which is recorded separately from the 252 \(e/\gamma \)-detectors. The measured arrival time in each station is calibrated for delays and response times of the individual station and stored with a resolution of \(1\,\hbox {ns}\). Arrival times are mainly used to calculate the shower direction.
Shower core (Grande) The Grande shower core position is reconstructed independently from KASCADE using the energy deposits from the 37 Grande detector stations. The reconstruction method is the same as for KASCADE.
Shower direction (Grande) The shower direction in Grande is reconstructed basically in the same way as for KASCADE, using the arrival times of the first particle from every Grande station, corrected with the energy deposits of the charged particles. The angular resolution is \(0.8^\circ \) with a small dependence on the shower size \(N_{ch}\). The reconstruction algorithm has been fine-tuned to zenith angles below \(40^\circ \).
Number of charged particles and muons (Grande) From the measurements of the energy deposits in the Grande array stations the total number of charged particles in the shower, i.e. the shower size is reconstructed. The reconstruction is performed similar to KASCADE but with different parameters. The number of muons (\(N_{\mu }\)) is derived from the KASCADE detector stations participating in the respective event with a simplified method. As there are normally only few KASCADE detector stations with muon information when Grande has been triggered, the number of detected muons is compared to a shower with a normalised shower size. The average value of the ratio of ‘measured muon number’/‘expected muon number’ over all detectors are formed and stored as \(N_{\mu }\).
Shower age (Grande) Like KASCADE, Grande uses a modified NKG-function to fit the lateral shower shape.
Energy deposits (Grande) The energy deposits of the charged particles are used to calculate the shower core position and the shower energy using a lateral density function fit similar to KASCADE but with different parameters. The energy deposits are derived from the stored ADC values for each detector station by means of a calibration procedure where the influences of electronics and cabling are included.
Arrival times (Grande) The arrival time is the first time stamp at each detector station that has been hit by a charged particle.
Number of hadrons (Calorimeter) The hadrons and their interactions are important for the understanding of the shower development within the atmosphere. Due to the fine lateral segmentation and the read-out of the KASCADFE hadron calorimeter, hadrons with an energy \(E_{had} >20\,\hbox {GeV}\) can be measured. They can be separated from each other when the distance of their axis is above \(40\,\hbox {cm}\). The spatial resolution of the calorimeter is about \(11\,\hbox {cm}\) and the energy resolution is 30% for hadrons with \(100\,\hbox {GeV}\) decreasing to 15% for \(E_{had}=25\,\hbox {TeV}\).
Hadron energy sum (Calorimeter) The energy sum of all reconstructed hadrons ranges between \(20\,\hbox {GeV}\) corresponding to the lower threshold, and about \(10^{7}\,\hbox {GeV}\).
Air temperature and air pressure The condition of the Earth’s atmosphere has an influence on the development of the extensive air showers and thus cannot be neglected, in particular for anisotropy studies of cosmic rays. The variation of the air pressure of about 1 hPa corresponds to a change in the measured rate of about 1%, while the effect of the temperature is significantly smaller. The fluctuation of the rate because of the pressure variation can be up to 20%. The meteorological data are provided by the Institute of Meteorology and Climate Research at KIT. The measurements of the temperature and the air pressure are taken from sensors placed \(2\,\hbox {m}\) above ground level for the temperature readings and \(1.5\,\hbox {m}\) above ground for the air pressure measurements on site of KIT, in about \(1\,\hbox {km}\) distance from the KASCADE experiment. All climate observables were recorded every 10 min.
Event time An event is stored when a pre-defined trigger condition of any detector component is fulfilled. The time of the first trigger is stored as the ‘Event Time’ and distributed to all other detector components. The event time (DateTime) is always given in UTC. As a redundant time information we use in KASCADE the Unix Time, a system time stamp counting the number of seconds elapsed since January, 1st 1970 (midnight UT), which is internally referenced as Global Time (GT). To get a high precision time stamp the Micro Time information (MT) is used. Based on the cycle of a \(5\,\hbox {MHz}\) clock which is reset and synchronized every second, we obtain an accuracy of \(\pm 200\,\hbox {ns}\) for the event time.
Run and event number Run number and event number are two parameters which characterize an event uniquely. They are always supplied with the data sets. A run is defined as a set of events recorded under the same hardware conditions. The event number starts at one for each run and is increased with every valid hardware trigger which invokes data recording. Run numbers and event numbers are not necessarily in increasing order for the selected event sample in KCDC.
Simulations
Analysing experimental data of air showers in terms of parameters of the impinging primary particle or nucleus requires a detailed theoretical modeling of the entire cascade. This can only be achieved by Monte-Carlo calculations taking into account all knowledge of particle interactions and decays. With KASCADE we have not only reconstructed energy spectra for five mass groups using 6 different high-energy hadronic interaction models, but also tested the validity of these models by studying correlations of various individual observables. This helped the model builders to improve their models. All the models are implemented in the CORSIKA simulation package. CORSIKA has been written especially for KASCADE and extended since then to become the standard simulation package in the field of cosmic ray air shower simulations [17].
At KASCADE, the entire simulation chain consists of three parts: (1) air shower simulation performed by CORSIKA; (2) detector simulation performed by CRES (Cosmic Ray Event Simulation); (3) data reconstruction performed by KRETA. Figure 9 illustrates the parallel workflow of measurements and simulations as applied in KASCADE (and Grande).
CORSIKA is a detailed Monte Carlo program to study the evolution and properties of extensive air showers in the atmosphere. Protons, light nuclei up to iron, photons, and many other particles can be treated as primaries. The particles are tracked through the atmosphere until they undergo reactions with the air nuclei or – in the case of non-stable secondaries – decay. A variety of high- and low-energy hadronic interaction models is implemented. In KASCADE we were using six high energy models from three different model families (for a comparison of the models see [27] and references therein) – QGSjet-II-02 and QGSjet-II-04; EPOS 1.99 and EPOS-LHC; SIBYLL 2.1 and SIBYLL 2.3 – and one low energy model in different versions, named FLUKA.
The detector simulation is performed with CRES, a code package for the simulation of the signals and energy deposits in all detector components of KASCADE-Grande as response to an extensive air shower as simulated with CORSIKA. CRES has been developed, based on the GEANT3 [28] package accepting simulated air shower data from (unthinned) CORSIKA as input delivering simulated detector signals. The data structure of the CRES output is the same as from the KASCADE measurements, which means that both are analysed using the same reconstruction program KRETA. Unlike for measured data where we have calibration parameters like air temperature and event specific information like the event time, we have here some additional information on the shower properties like true primary energy and particle ID derived directly from CORSIKA or from CRES. It was one of our main goals to publish the simulation data in the same format as the measured data published with the release NABOO, to make it as easy as possible for the users.
From about 200 observables obtained in the analysis of the simulated data we choose 34 to be published in KCDC. Some of these parameters are representing the true shower information, which are described as:
True primary energy The energy of the particle inducing the air shower is an input for the CORSIKA air shower simulation code. In our case we simulated showers with a primary energy between \(10^{14}\) and \(3.16 \cdot {10}^{17}\,\hbox {eV}\) following a power law spectrum with an index of −2.
True primary particle ID The ID of the particle inducing the air shower is an input for the CORSIKA air shower simulation code. We simulated 5 primaries representing 5 different mass groups. These primaries and their respective IDs are:
Proton
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ID =
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14
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Representing the lightest mass group
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Helium
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ID =
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402
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Representing a light mass group
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Carbon
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ID =
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1206
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Representing the CNO-group
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Silicon
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ID =
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2814
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Representing a medium heavy mass group
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Iron
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ID =
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5626
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Representing a heavy mass group
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True shower direction The zenith angle and the azimuth angle of the incident particles are input parameters for the CORSIKA air shower simulation code. The zenith angle spectrum reaches from \(0^\circ \) to \(42^\circ \) in simulation. The zenith angle is selected at random in this interval to match equal particle fluxes from all solid angle elements of the sky and a registration by a horizontal flat detector arrangement. The azimuth angle is always simulated between \(0^\circ \) and \(360^\circ \), where \(0^\circ \) corresponds to an shower axis pointing to the North and \(90^\circ \) to the East.
True numbers of electrons The true number of electrons is derived from the CORSIKA output as the number of electrons tracked down to the observation level of KASCADE at \(110\,\hbox {m}\) asl. Only electrons above \(3\,\hbox {MeV}\) low energy cut-off are taken into account.
True numbers of muons The true number of muons is derived from the CORSIKA output as the number of muons tracked down to the observation level. Only muons above \(100\,\hbox {MeV}\) low energy cut-off are taken into account.
True numbers of photons The true number of photons is derived from the CORSIKA output as the number of photons (and \(\pi ^{0}\)!) above \(3\,\hbox {MeV}\) tracked down to the observation level.
True numbers of hadrons The true number of hadrons is derived from the CORSIKA output as the number of hadrons tracked down to the observation level and above \(100\,\hbox {MeV}\).
True shower core position The true shower core position is derived from the detector simulation (CRES) output defined as the position within the detector area where the shower centre is located. In CRES this centre can be chosen when initializing the detector simulation. The core positions are uniformly distributed over an area slightly larger than the detector array, without any fiducial area cuts applied.
Sample of cosmic-ray spectra
With the latest release, spectra data sets from a number of experiments in the cosmic ray field are available for download. Currently 88 data sets are provided from 21 different experiments published between 1984 and 2017 in the energy range \(E_0=10^{14}\)–\({10}^{20}\,\hbox {eV}\). In case of KASCADE and KASCADE-Grande we published as well the data sets from the different mass groups derived from the unfolding procedure for different high-energy interaction models like QGSJet, EPOS and SIBYLL. All data sets are basically stored with a spectral index \(\gamma =0\), but the index for the download data can be chosen as well as the format settings. The errors given comprise only statistical errors as published by the authors.
Figure 10 shows an example of the KCDC spectra selection and download page.