arXiv subjects
Publications and source records attributed to M. Hirayama.
The non-Abelian Stokes theorem for loop variables associated with nontrivial loops (knots and links) is derived. It is shown that a loop variable is in general different from unity even if the field strength vanishes everywhere on the surface surrounded by the loop.
A simple analytic proof of the formula known as the non-Abelian Stokes theorem is given. It is explicitly shown that the consistency of the formula is guaranteed by the Bianchi identity for the gauge field. An attempt is made to construct the Lagrangian for the gauge field in terms of loop variables.
The temperature and abundance structure in the intracluster medium (ICM) of the Hydra-A cluster of galaxies is studied with ASCA and ROSAT. The effect of the large extended outskirts in the point-spread function of the X-Ray Telescope on ASCA is included in this analysis. In the X-ray brightness profile, the strong central excess above a single beta-model, identified in the Einstein and ROSAT data, is also found in the harder energy band (>4keV). A simultaneous fit of five annular spectra taken with the GIS instrument shows a radial distribution of the temperature and metal abundance. A significant central enhancement in the abundance distribution is found, while the temperature profile suggests that the ICM is approximately isothermal with the temperature of ~3.5keV. The ROSAT PSPC spectrum in the central 1'.5 region indicates a significantly lower temperature than the GIS result. A joint analysis of the GIS and PSPC data reveals that the spectra can be described by a two temperature model as well as by a cooling flow model. In both cases, the hot phase gas with the temperature of ~3.5keV occupies more than 90% of the total emission measure within 1'.5 from the cluster center. The estimated mass of the cooler (0.5-0.7keV) component is ~2-6 x 10^9 M_solar, which is comparable to the mass of hot halos seen in non-cD ellipticals. The cooling flow model gives the mass deposition rate of 60+-30 M_solar/yr, an order of magnitude lower than the previous estimation.