# On the Helium fingers in the intracluster medium

## TL;DR

This paper explores a double diffusive convection instability in the intracluster medium, driven by magnetic field-mediated anisotropic diffusion of Helium ions, leading to the formation of Helium fingers and modified buoyancy instability criteria.

## Contribution

It introduces the concept of Helium fingers as a new form of double diffusive convection in galaxy clusters, extending salt finger instability theory to astrophysical plasmas.

## Key findings

- Helium fingers' width scales as the one-fourth power of the inner region radius.
- Derived the mathematical criterion for heat-flux-driven buoyancy instability with Helium inhomogeneity.
- Identified the formation of vertical Helium-rich filamentary structures 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.