Magnetic structure of our Galaxy: A review of observations

The magnetic structure in the Galactic disk, the Galactic center and the Galactic halo can be delineated more clearly than ever before. In the Galactic disk, the magnetic structure has been revealed by starlight polarization within 2 or 3 kpc of the Solar vicinity, by the distribution of the Zeeman splitting of OH masers in two or three nearby spiral arms, and by pulsar dispersion measures and rotation measures in nearly half of the disk. The polarized thermal dust emission of clouds at infrared, mm and submm wavelengths and the diffuse synchrotron emission are also related to the large-scale magnetic field in the disk. The rotation measures of extragalactic radio sources at low Galactic latitudes can be modeled by electron distributions and large-scale magnetic fields. The statistical properties of the magnetized interstellar medium at various scales have been studied using rotation measure data and polarization data. In the Galactic center, the non-thermal filaments indicate poloidal fields. There is no consensus on the field strength, maybe mG, maybe tens of uG. The polarized dust emission and much enhanced rotation measures of background radio sources are probably related to toroidal fields. In the Galactic halo, the antisymmetric RM sky reveals large-scale toroidal fields with reversed directions above and below the Galactic plane. Magnetic fields from all parts of our Galaxy are connected to form a global field structure. More observations are needed to explore the untouched regions and delineate how fields in different parts are connected.Comment: 10+1 pages. Invited Review for IAU Symp.259: Cosmic Magnetic Fields: From Planets, to Stars and Galaxies (Tenerife, Spain. Nov.3-7, 2009). K.G. Strassmeier, A.G. Kosovichev & J.E. Beckman (eds.

First- and Second-Order Hypothesis Testing for Mixed Memoryless Sources with General Mixture

The first- and second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to epsilon, is called the epsilon-optimum exponent. In this paper, we first give the second-order epsilon-exponent in the case where the null hypothesis and the alternative hypothesis are a mixed memoryless source and a stationary memoryless source, respectively. We next generalize this setting to the case where the alternative hypothesis is also a mixed memoryless source. We address the first-order epsilon-optimum exponent in this setting. In addition, an extension of our results to more general setting such as the hypothesis testing with mixed general source and the relationship with the general compound hypothesis testing problem are also discussed.Comment: 23 page