Formation of Binary Stars

The idea was put forward in the 1800's that binary stars were formed in the following rather simple manner. Suppose that we have a slowly rotating cloud which is contracting to form a star.

• Initially we have that
  • Gravitational acceleration at the surface = - GM/R**2
  • Centrifugal acceleration at the Equator = v**2/R
• In general, gravity starts much larger than the centrifugal term and the collapse just goes.

  However, what happens as the cloud shrinks?

  • Gravity increases as 1/R**2
  • What about the centrifugal term? Well because of the conservation of angular momentum, v increases as 1/R, that is, if the cloud becomes half as large, the velocity becomes twice as large.

    So, the centrifugal term also strongly increases as the cloud gets smaller. We have that since v ~ 1/R ===> centrifugal term ~ 1/R**3

  • What we see is that the centrifugal term increases faster than gravity. If the cloud halves in size, gravity becomes 4 times stronger while the centrifugal acceleration becomes 8 times stronger.

    Even if gravity is initially dominant, because the cloud has to collapse by such huge amounts, the centrifugal term always wins unless we start with a non-rotating cloud.

  Based on this observation, people in the 1800's suggested that it was easy to form double star systems. All you needed to do was to start with a rotating cloud and let it collapse. Eventually the centrifugal term would cause the cloud to break apart into two lumps.

  This is a very appealing idea and in some form or another is probably correct! However, .... .