Resonant scattering effect on the soft X-ray line emission from the hot
  interstellar medium: I. galactic bulges
  Diffuse soft X-ray line emission is commonly used to trace the thermal and
chemical properties of the hot interstellar medium, as well as its content, in
nearby galaxies. Although resonant line scattering complicates the
interpretation of the emission, it also offers an opportunity to measure the
kinematics of the medium. We have implemented a direct Monte Carlo simulation
scheme that enables us to account for resonant scattering effect in the medium,
in principle, with arbitrary spatial, thermal, chemical, and kinematic
distributions. Here we apply this scheme via dimensionless calculation to an
isothermal, chemically uniform, and spherically symmetric medium with a radial
density distribution characterized by a $\beta$-model. This application
simultaneously account for both optical depth-dependent spatial distortion and
intensity change of the resonant line emission due to the scattering,
consistent with previous calculations. We further apply the modeling scheme to
the OVII and OVIII emission line complex observed in the XMM-Newton RGS
spectrum of the M31 bulge. This modeling, though with various limitations due
to its simplicity, shows that the resonant scattering could indeed account for
much of the spatial distortion of the emission, as well as the relative
strengths of the lines, especially the large forbidden to resonant line ratio
of the OVII He$\alpha$ triplet. We estimate the isotropic turbulence Mach
number of the medium in M31 as $\sim0.17$ for the first time and the
line-emitting gas temperature as $\sim2.3\times10^6$ K. We conclude that the
resonant scattering may in general play an important role in shaping the soft
X-ray spectra of diffuse hot gas in normal galaxies.
