|
Abstract
|
In this paper, we use the quantum hydrodynamics and its hydrostatic limit to investigate the newly
posed problem of Jeans instability in quantum plasmas from a different point of view in connection
with the well-known Chandrasekhar mass-limit on highly collapsed degenerate stellar configurations. It is shown that the hydrodynamic stability of a spherically symmetric uniform quantum
plasma with a given fixed mass is achieved by increase in its mass-density or decrease in the radius
under the action of gravity. It is also remarked that for masses beyond the limiting Jeans-mass, the
plasma becomes completely unstable and the gravitational collapse would proceed forever. This
limiting mass is found to depend strongly on the composition of the quantum plasma and the
atomic-number of the constituent ions, where it is observed that heavier elements rather destabilize
the quantum plasma hydrodynamically. It is also shown that the Chandrasekhar mass-limit for
white dwarf stars can be directly obtained from the hydrostatic limit of our model.
|