Determining Gravitational Masses of Galaxy Clusters With (1)Virial Equilibrium And (2)Arc-like Images

The mass derived from gravitational lensing reflects the total mass contained in the lensing system, independent of the specific matter contents and states. A comparison of the dynamical masses from hydrostatic equilibrium with the gravitational masses from arc-like images of background galaxies is made for four clusters of galaxies at intermediate redshits. It is found that virial analysis has underestimated the total cluster masses (from lensing) by a factor of $3\sim6$ within a radius of $\sim0.3$ Mpc $h_{50}^{-1}$ around the cluster centers, indicating that clusters of galaxies might not be regarded as the well relaxed virialized systems. The increase of the total cluster masses obtained from lensing leads to the decrease of the baryon fractions of clusters of galaxies, which provides a crue for solving the ``$\Omega_0$ disprepancy puzzle" in cosmology.Comment: 11 pages plus 1 Table. LATEX style, submitted to ApJ, BAO-BGGC-940

Gravitational Microlensing by the MACHOs of the LMC

The expected microlensing events of the LMC by the MACHOs of the LMC itself are calculated and compared with analogue events by objects in the Galactic halo. The LMC matter distribution is modelled by a spherical halo and an exponential disk while a face-on exponential disk is used for the stellar distribution of the LMC. Among the microlensing events discovered by the MACHOs and EROS projects, a fraction of $22\%$ could be caused by the lenses near the center of the LMC or $13\%$ from lenses at $5^o$ from the LMC center. Therefore, any statistical study of these microlensing events must take the LMC lenses into account.Comment: 12 pages, 6 figures (not included) by fax, ApJ submitted, DAEC-OPM-9

The Single Flavor Color Superconductivity in a Magnetic Field

We investigate the single flavor color superconductivity in a magnetic field. Because of the absence of the electromagnetic Meissner effect, forming a nonspherical CSC phase, polar, A or planar, does not cost energy of excluding magnetic flux. We found that these nonspherical phases do occupy a significant portion of the phase diagram with respect to magnetic field and temperature and may be implemented under the typical quark density and the magnetic field inside a compact star.Comment: 4 pages minor changes, typos fixed, figures redraw