Tomaschitz, R. (2016). Partition function and thermodynamic parameters of the all-particle cosmic-ray flux, Astroparticle Physics 84, 36–51, DOI: 10.1016/j.astropartphys.2016.08.003


Abstract (ScienceDirect, SAO/NASA ADS)

The all-particle cosmic-ray energy spectrum is studied in the 1 GeV–1011 GeV interval, the relativistic nuclei being treated as a free multi-component gas in stationary non-equilibrium. A phase-space derivation of the spectral number density, partition function and entropy is given, and an analytic expression for the flux density of the all-particle spectrum is semi-empirically obtained from a wideband spectral fit. The all-particle spectrum is the additive superposition of four strongly overlapping peaks with exponential cutoffs at the spectral breaks. The analytic flux density covers the mentioned interval ranging over eleven decades and accurately reproduces the spectral fine-structure, such as two weak spectral breaks between knee and ankle emerging in the IceTop-73 and KASCADE-Grande data sets. In the low-energy range below 104 GeV, the all-particle flux is approximated by adding the proton and helium flux densities obtained from fits to the AMS-02 and CREAM spectra, the contribution of heavier nuclei being negligible in this energy range. Estimates of the thermodynamic parameters (number count, internal energy, entropy and pressure) of the all-particle flux and the partial fluxes generating the spectral peaks are derived.



05.20.Gg Classical ensemble theory

05.30.Ch Quantum ensemble theory

05.70.Ce Thermodynamic functions and equations of state

98.70.Sa Cosmic rays



description: Roman Tomaschitz (2016) Partition function and thermodynamic parameters of the all-particle cosmic-ray flux, Astropart. Phys. 84, 36.


Keywords: Spectral breaks in the all-particle cosmic-ray flux; Wideband spectral fits with multiplicative flux densities; Decomposition of wideband spectra into spectral peaks; Partition function of relativistic stationary non-equilibrium ensembles; Entropy of cosmic-ray nuclei; Flux densities of proton and helium spectra



The all-particle cosmic-ray spectrum is generated by the flux density of a stationary non-equilibrium gas of relativistic nuclei.

Reconstruction of the phase-space probability distribution and partition function from wideband spectral fits in the 1 GeV–1011 GeV interval.

An analytic expression for the spectral flux density is obtained, exhibiting two weak spectral breaks between knee and ankle.

Decomposition of the all-particle energy spectrum into four exponentially decaying spectral peaks with crossovers at the spectral breaks.

Thermodynamic parameters of cosmic-ray fluxes: temperature, specific number, energy and entropy densities, pressure.


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