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Register a new userGeneralized statistical mechanics of cosmic rays: Application to positron-electron spectral indices
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We apply generalized statistical mechanics developed for complex systems to theoretically predict energy spectra of particle and anti-particle degrees of freedom in cosmic ray fluxes, based on a $q$-generalized Hagedorn theory for transverse momentum spectra and hard QCD scattering processes. QCD at largest center of mass energies predicts the entropic index to be $q=frac{13}{11}$, whereas the escort duality of the nonextensive thermodynamic formalism predicts an energy split of effective temperature given by $Delta kT =pm frac{1}{10} kT_H approx pm 18 $ MeV, where $T_H$ is the Hagedorn temperature. We carefully analyse the measured primary cosmic ray data of the AMS-02 collaboration and provide evidence that the predicted temperature split is indeed observed, leading to a different energy dependence of the $e^+$ and $e^-$ spectral indices. Moreover, we observe that at larger energies $E$ the measured $e^+e^-$ flux starts to deviate from our QCD-based statistical mechanics theory, with a crossover scale of $E^*=(50 pm 10)$ GeV, which could be a hint for WIMP decay or other new physics setting in at this mass scale. Fits using linear combinations of the escort and non-escort $q$-generalized canonical distributions yield excellent agreement with the measured data in the entire energy range.
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We isolated the anomalous part of the cosmic electron-positron flux within a Bayesian likelihood analysis. Using 219 recent cosmic ray spectral data points, we inferred the values of selected cosmic ray propagation parameters. In the context of the propagation model coded in GalProp, we found a significant tension between the electron positron related and the rest of the fluxes. Interpreting this tension as the presence of an anomalous component in the electron-positron related data, we calculated background predictions for PAMELA and Fermi-LAT based on the non-electron-positron related fluxes. We found a deviation between the data and the predicted background even when uncertainties, including systematics, were taken into account. We identified this deviation with the anomalous electron-positron contribution. We briefly compared this model independent signal to some theoretical results predicting such an anomaly.
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The basic notions of statistical mechanics (microstates, multiplicities) are quite simple, but understanding how the second law arises from these ideas requires working with cumbersomely large numbers. To avoid getting bogged down in mathematics, one can compute multiplicities numerically for a simple model system such as an Einstein solid -- a collection of identical quantum harmonic oscillators. A computer spreadsheet program or comparable software can compute the required combinatoric functions for systems containing a few hundred oscillators and units of energy. When two such systems can exchange energy, one immediately sees that some configurations are overwhelmingly more probable than others. Graphs of entropy vs. energy for the two systems can be used to motivate the theoretical definition of temperature, $T= (partial S/partial U)^{-1}$, thus bridging the gap between the classical and statistical approaches to entropy. Further spreadsheet exercises can be used to compute the heat capacity of an Einstein solid, study the Boltzmann distribution, and explore the properties of a two-state paramagnetic system.
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.
The AMS-02 collaboration has just released its first result of the cosmic positron fraction $e^+/(e^-+e^+)$ with high precision up to $sim 350$ GeV. The AMS-02 result shows the same trend with the previous PAMELA result, which requires extra electron/positron sources on top of the conventional cosmic ray background, either from astrophysical sources or from dark matter annihilation/decay. In this paper we try to figure out the nature of the extra sources by fitting to the AMS-02 $e^+/(e^-+e^+)$ data, as well as the electron and proton spectra by PAMELA and the $(e^-+e^+)$ spectrum by Fermi and HESS. We adopt the GALPROP package to calculate the propagation of the Galactic cosmic rays and the Markov Chain Monte Carlo sampler to do the fit. We find that the AMS-02 data have implied essential difference from the PAMELA data. There is {rm tension} between the AMS-02 $e^+/(e^-+e^+)$ data and the Fermi/HESS $(e^-+e^+)$ spectrum, that the AMS-02 data requires less contribution from the extra sources than Fermi/HESS. Then we redo the fit without including the Fermi/HESS data. In this case both the pulsars and dark matter annihilation/decay can explain the AMS-02 data. The pulsar scenario has a soft inject spectrum with the power-law index $sim 2$, while the dark matter scenario needs $tau^+tau^-$ final state with mass $sim 600$ GeV and a boost factor $sim 200$.
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