286 
Rotation and Fission of Stars 
[ch. x 
surface must always remain smooth. It can never acquire a sharp edge, but 
may acquire a more and more drawn out equatorial cross-section. Apart from 
this, the star is in most respects similar to the modified Roche’s model 
discussed in § 234, which consisted of an approximately incompressible core 
surrounded by a tenuous envelope. A star with a sufficiently incompressible 
core may behave in the way in which we found the modified Roche’s model to 
behave. With increasing angular momentum the core may depart from the 
spheroidal configuration; it may become first ellipsoidal, then pear-shaped, 
and may end by fission into two detached masses rotating about one another. 
During this process the envelope, owing to its small mass, exerts only 
a negligible influence on the dynamics of the core. The rôle of the envelope 
is merely that of adjusting itself to the changes going on in the core ; it will 
arrange itself so that its outer surface always forms an equipotential in the field 
formed jointly by its own rotation and the ever-changing gravitational field of 
the core. When the core finally breaks into two detached masses, the envelope 
may either form a continuous surface surrounding both masses, or may itself 
divide into two envelopes, one surrounding each of the two masses. Or, to put 
the matter in a slightly different form, the final result will be two detached 
masses surrounded by two envelopes which may or may not overlap. 
The Sequence of Configurations of a Shrinking Star. 
254. Our discussion has so far supposed that the rotating mass continually 
acquires more and more angular momentum. The separate stars in the sky 
are so widely spaced that their mutual gravitational influence on one another 
is quite negligible under normal circumstances, and no agency is known by 
which the angular momentum of a star can increase under normal circumstances. 
The emission of radiation from a rotating star, by carrying away angular 
momentum, will cause a decrease in the total angular momentum residing in 
the star, but apart from this the angular momentum must remain constant. 
On the other hand, our discussion has also supposed that the density of 
the rotating mass remains constant, and this supposition also is equally un 
fulfilled in nature. In discussing the evolution of the stars in Chapter vi, we 
saw how a star on any one series (AT-ring, Z-ring, or A - -ring) might at any 
instant reach the limit of stable configurations, and start to contract with 
comparative rapidity until it reached the next lower series as a star of far 
higher density. 
During such a contraction the angular momentum of the whole star will 
remain approximately constant, so that its average angular velocity must 
increase. Since the effect of viscosity is negligible in the core, the motion of 
the core will conform to the well-known hydrodynamical equation* 
A L J P JA 
* Lamb, Hydrodynamics , Equation (2), p. 34.