  We examine the linear stability analysis of a hot, dilute and differentially
rotating plasma by considering anisotropic transport effects. In the dilute
plasmas, the ion Larmor radius is small compared with its collisional mean free
path. In this case, the transport of heat and momentum along the magnetic field
lines become important. This paper presents a novel linear instability that may
more powerful and greater than ideal magnetothermal instability (MTI) and ideal
magnetorotational instability (MRI) in the dilute astrophysical plasmas. This
type of plasma is believed to be found in the intracluster medium of galaxy
clusters and radiatively ineffective accretion flows around black holes. We
derive the dispersion relation of this instability and obtain the instability
condition. There is at least one unstable mode that is independent of the
temperature gradient direction for a helical magnetic field geometry. This
novel instability is driven by the gyroviscosity coupled with differential
rotation. Therefore we call it as gyroviscous modified magnetorotational
instability (GvMRI). We examine how the instability depends on signs of the
temperature gradient and the gyroviscosity, and also on the magnitude of the
thermal frequency and on the values of the pitch angle. We provide a detailed
physical interpretation of obtained results. The GvMRI is applicable not only
to the accretion flows and intracluster medium but also to the transition
region between cool dense gas and the hot low-density plasma in stellar
coronae, accretion disks, and the multiphase interstellar medium because of
being independent of the temperature gradient direction.
