On the construction of Brownian house-moving and its properties

The purpose of this paper is to construct a new stochastic process "Brownian house-moving," which is a Brownian bridge that stays between its starting point and its terminal point. To construct this process, statements are prepared on the weak convergence of conditioned Brownian motion, a conditioned Brownian bridge, a conditioned Brownian meander, and a conditioned three-dimensional Bessel bridge. Also studied are the sample path properties of Brownian house-moving and the decomposition formula for its distribution.Comment: 78 page

MHD Simulation of The Inner Galaxy with Radiative Cooling and Heating

We investigate the role of magnetic field on the gas dynamics in the Galactic bulge region by three dimensional simulations with radiative cooling and heating. While high-temperature corona with $T>10^6\ {\rm K}$ is formed in the halo regions, the temperature near the Galactic plane is $\lesssim 10^4\ {\rm K}$ following the thermal equilibrium curve determined by the radiative cooling and heating. Although the thermal energy of the interstellar gas is lost by radiative cooling, the saturation level of the magnetic field strength does not significantly depend on the radiative cooling and heating. The magnetic field strength is amplified to $10\ {\rm \mu G}$ on average, and reaches several hundred ${\rm \mu G}$ locally. We find the formation of magnetically dominated regions at mid-latitudes in the case with the radiative cooling and heating, which is not seen in the case without radiative effect. The vertical thickness of the mid-latitude regions is $50-150\ {\rm pc}$ at the radial location of $0.4-0.8 \ {\rm kpc}$ from the Galactic center, which is comparable to the observed vertical distribution of neutral atomic gas. When we take the average of different components of energy density integrated over the Galactic bulge region, the magnetic energy is comparable to the thermal energy. We conclude that the magnetic field plays a substantial role in controlling the dynamical and thermal properties of the Galactic bulge region.Comment: Submitted to ApJ; 21 pages, 18 figures 3 tables. Comment are welcom