WHEN IS ROTATION EXPECTED TO BE IMPORTANT?

Rotation may be important during transient phases of a star's life; for example, during the star birthing process (the collapse and formation phase), and, perhaps, near the end of the normal life of a star (that is, during the collapse to a white dwarf, neutron star, or the black hole condition).

Rotation rotation may become important during these phases if angular momentum is conserved.

In this event, we can argue that

I (6.28/P) = J_o = constant ===> (P/P_o) = (R/R_o)² where I is the moment of inertia of the star, P is the rotation period of the star, and J is the angular momentum of the star.

We see that the centrifugal force increases with a decrease in the radius of the star R faster than does gravity.

Astrophysical Scenarios:

• Star Formation: A low density interstellar medium cloud compresses from a density of 10^-20 g/cc to 100 g/cc with a predicted humongous increase in spin rate. This raises another question, Since stars are essentially nonrotating, where's the angular momentum? The clear answer is that it goes in to orbital motion either through binary formation, planetary formation, or disk formation. We return to this issue later.

• Collapse of the cores of massive stars and the formation of compact objects such as neutron stars or black holes. Central cores of massive stars (with initial radius 1,000 km) collapse to form compact objects with radius < 10 to 20 km. If any rotation is present, the outcome of the collapse is severely affected; e.g., Fizzlers.

• Merger of Close Binary Systems: In merger of close binaries (New & Tohline), the merging object, by necessity, contains a large amount of angular momentum which affects how the merger process takes place. Binary merger in systems with compact objects (neutron stars and white dwarfs) have been proposed as explanations for many exotic phenomena, gamma-ray burst sources, Type I Supernovae, sources of GR (for LIGO), ... .

All of the above are complex physical problems whose study is feasible only through the use of supercomputers. Even then, one works right on the edge of what is do-able (technologically speaking) because of the physical complexity of the problem ==> mistakes are easily made (and, in fact, bound to be made).