The Perseus galaxy cluster was observed by the MAGIC Cherenkov telescope for a total effective time of 24.4 hr during 2008 November and December. The resulting upper limits on the gamma-ray emission ...above 100 GeV are in the range of 4.6-7.5 x 10{sup -12} cm{sup -2} s{sup -1} for spectral indices from -1.5 to -2.5, thereby constraining the emission produced by cosmic rays, dark matter annihilations, and the central radio galaxy NGC 1275. Results are compatible with cosmological cluster simulations for the cosmic-ray-induced gamma-ray emission, constraining the average cosmic ray-to-thermal pressure to <4% for the cluster core region (<8% for the entire cluster). Using simplified assumptions adopted in earlier work (a power-law spectrum with an index of -2.1, constant cosmic ray-to-thermal pressure for the peripheral cluster regions while accounting for the adiabatic contraction during the cooling flow formation), we would limit the ratio of cosmic ray-to-thermal energy to E{sub CR}/E{sub th} < 3%. Improving the sensitivity of this observation by a factor of about 7 will enable us to scrutinize the hadronic model for the Perseus radio mini-halo: a non-detection of gamma-ray emission at this level implies cosmic ray fluxes that are too small to produce enough electrons through hadronic interactions with the ambient gas protons to explain the observed synchrotron emission. The upper limit also translates into a level of gamma-ray emission from possible annihilations of the cluster dark matter (the dominant mass component) that is consistent with boost factors of {approx}10{sup 4} for the typically expected dark matter annihilation-induced emission. Finally, the upper limits obtained for the gamma-ray emission of the central radio galaxy NGC 1275 are consistent with the recent detection by the Fermi-LAT satellite. Due to the extremely large Doppler factors required for the jet, a one-zone synchrotron self-Compton model is implausible in this case. We reproduce the observed spectral energy density by using the structured jet (spine-layer) model which has previously been adopted to explain the high-energy emission of radio galaxies.
We study a random bisection problem where an interval of length x is cut into two random fragments at the first stage, then each of these two fragments is cut further, etc. We compute the probability ...P(n)(x) that at the nth stage, each of 2(n) fragments is shorter than 1. We show that P(n)(x) approaches a traveling wave form, and the front position x(n) increases as x(n) approximately n(beta)rho(n) for large n with rho = 1.261 076ellipsis and beta = 0.453 025ellipsis. We also solve the m-section problem where each interval is broken into m fragments and show that rho(m) approximately m/(lnm) and beta(m) approximately 3/(2lnm) for large m. Our approach establishes an intriguing connection between extreme value statistics and traveling wave propagation in the context of the fragmentation problem.
We consider a particle moving in a one-dimensional potential which has a symmetric deterministic part and a quenched random part. We study analytically the probability distributions of the local time ...(spent by the particle around its mean value) and the occupation time (spent above its mean value) within an observation time window of size t. In the absence of quenched randomness, these distributions have three typical asymptotic behaviors depending on whether the deterministic potential is unstable, stable, or flat. These asymptotic behaviors are shown to get drastically modified when the random part of the potential is switched on, leading to the loss of self-averaging and wide sample to sample fluctuations.
We study the phenomenon of real space condensation in the steady state of a class of one-dimensional mass transport models. We derive the criterion for the occurrence of a condensation transition and ...analyze the precise nature of the shape and the size of the condensate in the condensed phase. We find two distinct condensate regimes: one where the condensate is Gaussian distributed and the particle number fluctuations scale normally as L(1/2) where L is the system size, and the second regime where the particle number fluctuations become anomalously large and the condensate peak is non-Gaussian. We interpret these results within the framework of sums of random variables.
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