Gravitational compression

Abstract: In a crystallized suspension of polystyrene spheres, the earth9s gravitational field, acting on a vertical column of material several centimeters high, produces an elastic deformation that can be readily observed through its effect on the crystal lattice constant. This effect has been used to determine that Young9s modulus for the crystalline material ranges from 1 to 3 dynes per square centimeter, depending on the concentration of spheres.

Abstract: We explore the amplification of magnetic seed fields during the formation of the first stars and galaxies. During gravitational collapse, turbulence is created from accretion shocks, which may act to amplify weak magnetic fields in the protostellar cloud. Numerical simulations showed that such turbulence is sub-sonic in the first star-forming minihalos, and highly supersonic in the first galaxies with virial temperatures larger than 10^4 K. We investigate the magnetic field amplification during the collapse both for Kolmogorov and Burgers-type turbulence with a semi-analytic model that incorporates the effects of gravitational compression and small-scale dynamo amplification. We find that the magnetic field may be substantially amplified before the formation of a disk. On scales of 1/10 of the Jeans length, saturation occurs after ~10^8 yr. Although the saturation behaviour of the small-scale dynamo is still somewhat uncertain, we expect a saturation field strength of the order ~10^{-7} n^{0.5} G in the first star-forming halos, with n the number density in cgs units. In the first galaxies with higher turbulent velocities, the magnetic field strength may be increased by an order of magnitude, and saturation may occur after 10^6 to 10^7 yr. In the Kolmogorov case, the magnetic field strength on the integral scale (i.e. the scale with most magnetic power) is higher due to the characteristic power-law indices, but the difference is less than a factor of 2 in the saturated phase. Our results thus indicate that the precise scaling of the turbulent velocity with length scale is of minor importance. They further imply that magnetic fields will be significantly enhanced before the formation of a protostellar disk, where they may change the fragmentation properties of the gas and the accretion rate.

Abstract: We study the influence of initial conditions on the magnetic field amplification during the collapse of a magnetized gas cloud. We focus on the dependence of the growth and saturation level of the dynamo-generated field on the turbulent properties of the collapsing cloud. In particular, we explore the effect of varying the initial strength and injection scale of turbulence and the initial uniform rotation of the collapsing magnetized cloud. In order to follow the evolution of the magnetic field in both the kinematic and the non-linear regime, we choose an initial field strength of with the magnetic to kinetic energy ratio, Em/Ek∼ 10−4. Both gravitational compression and the small-scale dynamo initially amplify the magnetic field. Further into the evolution, the dynamo-generated magnetic field saturates but the total magnetic field continues to grow because of compression. The saturation of the small-scale dynamo is marked by a change in the slope of B/ρ2/3 and by a shift in the peak of the magnetic energy spectrum from small scales to larger scales. For the range of initial Mach numbers explored in this study, the dynamo growth rate increases as the Mach number increases from vrms/cs∼ 0.2 to 0.4 and then starts decreasing from vrms/cs∼ 1.0. We obtain saturation values of Em/Ek= 0.2–0.3 for these runs. Simulations with different initial injection scales of turbulence also show saturation at similar levels. For runs with different initial rotation of the cloud, the magnetic energy saturates at Em/Ek∼ 0.2–0.4 of the equipartition value. The overall saturation level of the magnetic energy, obtained by varying the initial conditions, is in agreement with previous analytical and numerical studies of small-scale dynamo action where turbulence is driven by an external forcing instead of gravitational collapse.

Abstract: Gravitational effect in colloidal suspensions is examined both theoretically and experimentally by light scattering. In contrast to the previous theory the present theory predicts the cube of the nearest-neighbour distance to vary linearly as a function of height of the suspension. The position of the first peak in the static structure factor of the suspension having liquid-like order is used to obtain average nearest-neighbour distance. The experimental data fit well to the present theory. The bulk modulus of the liquid order estimated for the first time by this method is found to evolve as a function of time. The time taken for the colloidal suspension to reach gravitational equilibrium as well as deionisation equilibrium is obtained. The time to reach gravitational equilibrium is found to be much less than earlier theoretical estimates based on a simple model. A possible mechanism for this is proposed. Concentration dependence of the saturation bulk modulus is obtained and discussed.