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. One of the most puzzling problems of astrophysical origin is the condition of star birth 1 in the Universe. Stars are believed to form in nebulaes, interstellar clouds of dust and gases, mostly hydrogen. One of the possible mechanisms for agglomeration and globule formation in nearly homogeneous interstellar medium is known as the gravitational collapse due to the well-known Jeans instability.2 In the force balance condition on a massive interstellar cloud, beyond a mass-limit called the Jeans-mass, the gravity force happens to win the battle against the internal gas pressure caused by the thermal radiation. However, it is supposed that as the interstellar cloud cools-down in an appropriate manner, the gravitational collapse to lead to the structure formation and star birth. While it seems a simple mechanism, the Jeans instability has recently attracted increased attention due to the fact that other phenomena such as the multi-fluid presence, 3 degree of ionization, 4 fluid viscosity, 5,6 rotation, 7 effect of magnetic fields, 8 and many other parameters, significantly influence the Jeans criteria. In recent years, many researchers have incorporated the quantum statistics, electron diffraction, spin-1/2 magnetization, and dust effects into the Jeans instability mechanism, 9-14 using the quantum hydrodynamics (QHD) [15][16][17][18][19][20] and quantum magnetohydrodynamics (QMHD) 21-23 approaches. It is well-known that quantum effects appear as the inter-particle distances (d ' 1=n 1=3 0 with n 0 being the number-density of particles) approach the particle (usually electron) de Broglie wavelength K D ¼ h=mv th , where h, m, and v th ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi ffi k B T=m p are Planck constant, particle mass, and its thermal velocity, respectively. This condition requires a number-density equal to or greater than the value of n 0 ' 10 18 cm À3 for degenerate plasma density. It is apparent, however, that the number-density of a typical interstellar cloud is much lower 24 ...
