V 



268 The Evolution of Binary and Multiple Stars [CH. xi 



hypothesis can be maintained for systems whose separation is of the order of 

 1000 years' proper motion. 



282. Another hypothesis suggests itself. We identify the density 

 1'3 x 10~ 17 which corresponds to a separation of 1000 years' proper motion with 

 the density in the arms of the original rotating nebula out of which the whole 

 system of stars was evolved. As stars form out of the nuclei in these arms 

 the majority will, as we have supposed, move as separate and independent 

 systems, but there must necessarily be a number of cases in which two ad- 

 jacent nuclei in the nebular arms remain permanently describing orbits about 

 one another. Such a pair of stars is dynamically, so far as Russell's investi- 

 gations go, indistinguishable from a pair which has evolved by fission. It 

 has not evolved by fission but the relations between angular velocity, separation 

 and mass are the same as if it had evolved by fission, and the distribution of 

 momentum between rotational and orbital momentum is the same as if it had 

 evolved by fission. 



Thus we are led to conjecture that wide binary systems of separation less 

 than about 1000 years' proper motion are the remains of adjacent nuclei in the 

 original nebula which have never got out of one another's gravitational at- 

 traction; systems of separation greater than this may perhaps be pairs of 

 stars which have fallen into orbits round one another in the random motion 

 of those stars which had become properly separated. Close binary systems 

 may no doubt have been evolved by fission, but at present it is difficult to 

 draw the line between such systems and systems which have never formed a 

 single mass. 



The most direct evidence we have on this point is provided by the observed 

 distribution of periods. We have found that, briefly speaking, encounters with 

 other systems cause the periods to approximate, on the average, to about one 

 year. Thus binaries with periods of less than one year probably (although 

 not certainly) started life with still shorter periods ; such binaries probably 

 originated by fission. In the same way, binaries with periods greater than 

 one year probably started life with still longer periods, so that the majority 

 of these stars are likely to represent the relics of independent nuclei in the 

 original nebula. Thus we may perhaps conjecture with some confidence that 

 such binaries as a. Centauri, discussed in 271, 272, and with it the vast 

 majority of long-period visual binaries, have not been evolved by fission, but 

 in more doubtful cases, such as W Crucis which figures in the bottom line of 

 Shapley's table (p. 250), the only reason for forming a decision is that supplied 

 by dynamical theory, and this as we have seen leads to very indefinite results. 



