Chandra detection of diffuse hot gas in and around the M31 bulge

We report the detection of diffuse hot gas in M31, using archival Chandra observations which allow us to map out a 30' by 30' field (covering a galactocentric radius up to 4.5 kpc) and to detect sources in the galaxy down to a 0.5-8 keV luminosity limit of ~10^35 ergs/s. We estimate the remaining stellar contribution from fainter X-ray sources (primarily cataclysmic variables and coronally active binaries), assuming that they spatially follow the stellar distribution. Indeed, the near-IR K-band light of the galaxy closely traces the 2-8 keV unresolved X-rays, indicating a collective stellar X-ray emissivity consistent with those determined for the Galactic ridge and M32, whereas the amount of the 0.5-2 keV unresolved emission is significantly greater than the expected stellar contribution, especially within a galactocentric radius of ~2 kpc. Morphologically, this soft X-ray excess appears substantially rounder than the bulge as seen in K-band and is elongated approximately along the minor-axis at large radii. The excess thus most likely represents the emission of diffuse hot gas in and around the galactic bulge. Furthermore, the near side of the M31 disk casts an apparent shadow against the soft X-ray excess, indicating that the hot gas extends to at least 2.5 kpc from the galactic plane. We briefly discuss the implications of these results on the energy balance in the M31 bulge and on understanding the large-scale soft X-ray enhancement observed toward the inner region of our own Galaxy.Comment: 10 pages, 2 figures, accepted by ApJ

General covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

For a particle that is constrained on an ($N-1$)-dimensional ($N\geq2$) curved surface, the Cartesian components of its momentum in $N$-dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the $su(2)$ algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion.Comment: 8 pages, no figure. Presentation improve