Detection of gamma-ray emission from the Coma cluster with Fermi Large Area Telescope and tentative evidence for an extended spatial structure

Many galaxy clusters have giant halos of non-thermal radio emission, indicating the presence of relativistic electrons in the clusters. Relativistic protons may also be accelerated by merger and/or accretion shocks in galaxy clusters. These cosmic-ray (CR) electrons and/or protons are expected to produce gamma-rays through inverse-Compton scatterings or inelastic $pp$ collisions respectively. Despite of intense efforts in searching for high-energy gamma-ray emission from galaxy clusters, conclusive evidence is still missing so far. Here we report the discovery of $\ge 200$ MeV gamma-ray emission from the Coma cluster direction with an unbinned likelihood analysis of the 9 years of {\it Fermi}-LAT Pass 8 data. The gamma-ray emission shows a spatial morphology roughly coincident with the giant radio halo, with an apparent excess at the southwest of the cluster. Using the test statistic analysis, we further find tentative evidence that the gamma-ray emission at the Coma center is spatially extended. The extended component has an integral energy flux of $\sim 2\times 10^{-12}{\rm \ erg\ cm^{-2}\ s^{-1}}$ in the energy range of 0.2 - 300 GeV and the spectrum is soft with a photon index of $\simeq-2.7$. Interpreting the gamma-ray emission as arising from CR proton interaction, we find that the volume-averaged value of the CR to thermal pressure ratio in the Coma cluster is about $\sim 2\%$. Our results show that galaxy clusters are likely a new type of GeV gamma-ray sources, and they are probably also giant reservoirs of CR protons.Comment: 10 pages, 10 figures, Accepted by Physical Review D, more spatial models for the gamma-ray emission are used, systematic checks on the results are adde

Tourism Flows Prediction based on an Improved Grey GM(1,1) Model

AbstractThis study analyzes the factors affecting the tourist flow. These factors include tourism resources, traffic conditions and so on. In recent years, the grey forecasting model has achieved good prediction accuracy with limited data and has been widely used in various research fields. However, the grey forecasting model still have some potential problems that need to be improved, such as applicate range and prediction accuracy. It is found that original data and background value are main factors affecting the accuracy of the proposed model's application. To solve these problems, this study develops a optimization model for the GM(1,1) model problem which includes optimization of initial and background values. In order to reduce errors caused by back-ground values, the “new information prior using” principle is followed, and a liner function is dopted in the construe of background. Numerical examples verified that the simulation and prediction accuracy of the short-term forcasts is significantly increased. As a result, the newly improved model yields a high prediction capability