Hydrostatic gas distributions: global estimates of temperature and abundance

Estimating the temperature and metal abundance of the intracluster and the intragroup media is crucial to determine their global metal content and to determine fundamental cosmological parameters. When a spatially resolved temperature or abundance profile cannot be recovered from observations (e.g. for distant objects), or deprojection is difficult (e.g. due to a significant non-spherical shape), only global average temperature and abundance are derived. After introducing a general technique to build hydrostatic gaseous distributions of prescribed density profile in potential wells of any shape, we compute the global mass-weighted and emission-weighted temperature and abundance for a large set of barotropic equilibria and an observationally motivated abundance gradient. We also compute the spectroscopic-like temperature that is recovered from a single temperature fit of observed spectra. The derived emission-weighted abundance and temperatures are higher by 50 to 100 per cent than the corresponding mass-weighted quantities, with overestimates that increase with the gas mean temperature. Spectroscopic temperatures are intermediate between mass and luminosity-weighted temperatures. Dark matter flattening does not lead to significant differences in the values of the average temperatures or abundances with respect to the corresponding spherical case (except for extreme cases).