Title: On the Helium fingers in the intracluster medium,
Abstract: In this paper we investigate the convection phenomenon in the intracluster
medium (the weakly-collisional magnetized inhomogeneous plasma permeating
galaxy clusters) where the concentration gradient of the Helium ions is not
ignorable. To this end, we build upon the general machinery employed to study
the salt finger instability found in the oceans. The salt finger instability is
a form of double diffusive convection where the diffusions of two physical
quantities---heat and salt concentrations---occur with different diffusion
rates. The analogous instability in the intracluster medium may result owing to
the magnetic field mediated anisotropic diffusions of the heat and the Helium
ions (in the sea of the Hydrogen ions and the free electrons). These two
diffusions have inherently different diffusion rates. Hence the convection
caused by the onset of this instability is an example of double diffusive
convection in the astrophysical settings. A consequence of this instability is
the formation of the vertical filamentary structures having more concentration
of the Helium ions with respect to the immediate neighbourhoods of the
filaments. We term these structures as Helium fingers in analogy with the salt
fingers found in the case of the salt finger instability. Here we show that the
width of a Helium finger scales as one-fourth power of the radius of the inner
region of the intracluster medium in the supercritical regime. We also
determine the explicit mathematical expression of the criterion for the onset
of the heat-flux-driven buoyancy instability modified by the presence of
inhomogeneously distributed Helium ions.