FISSION FUNDAMENTALS FROM STUDIES OF INCOMPRESSIBLE FLUIDS

After the dynamic collapse slows, the optically thick cloud quasi-statically contracts (the upper right hand corner) (see figure from Lebovitz 1972 at right); the evolution now driven by the slow increase of its mass and angular momentum due to accretion and through radiative cooling. The core spins-up secularly and moves down the right hand vertical axis. If viscosity is efficient then when the core reaches a3/a1 ~ 0.6, a bifurcation occurs--a lower energy equilibrium exists for J above this threshold, the Jacobi sequence. If the core is inviscid, then this bifurcation is bypassed and the core evolves to a3/a1 ~ 0.3; the dynamic bar mode instability threshold. Conceivably, at this point, a bifurcation may occur to the Lower Self-Adjoint (LSA) Riemann sequence.

LEBOVITZ CONJECTURE The bar cools and spins-up during the secular stage of evolution. The fissiion theory then imagines that the cooling bar encounters a series of m-fold bifurcations. For the viscous case, the Jacobi sequence case, the first instability encountered is the m = 3 mode (the pear mode). The instability is not secular, however; it is dynamic and it is not clear that the higher-oder m-fold instabilities can be reached. This was the original Jeans form of the fission hypothesis and does not appear to be viable. For the inviscid case, the LSA Riemann sequence case, the first instability encountered is the m = 4 mode (the dumbbell mode), not the pear mode. Lebovitz postualted that the dumbbell eventually grew to the point where it pinched-off at its center and a binary star system formed.