Soft X-ray excess of clusters: a thermal filament model, and the strong
  lensing of background galaxy groups
  The observational and theoretical status of the search for missing
cosmological baryons is summarized, with a discussion of some indirect methods
of detection. The thermal interpretation of the cluster soft X-ray and EUV
excess phenomenon is examined in the context of emission filaments, which are
the higher density part of the warm hot intergalactic medium (WHIM) residing at
the outskirt of clusters. We derived an analytic radial profile of the soft
excess surface brightness using a simple filament model, which provided us a
means of observationally constraining the WHIM parameters, especially the total
mass budget of warm gas associated with a cluster. We then pointed out a new
scenario for soft excess emission, viz. a cluster that can strongly lens the
soft X-rays from background WHIM knots. If, as seems quite likely, the missing
baryons are mostly in the WHIM halos of galaxy groups, the lensing probability
will be quite high ($\sim$ 10 %). This way of accounting for at least part of a
cluster's soft excess may also explain the absence of O VII absorption at the
redshift of the cluster.
