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Special Cases: Supernova Explosion and the Common Envelope


Supernova explosion  in a binary is treated as an instantaneous mass loss of the exploding star. We assume that an additional kick velocity  is imparted to young neutron stars due to possible asymmetry of the collapse  (see Section 5 for further discussion). In this case, the eccentricity and semi-major axis of the binary after the explosion can be straightforwardly calculated (Boersma, 1961[21]). We do this using the following scheme.

  1. First, velocities and locations of the components in orbit prior to the explosion are calculated,
  2. Then, the changing mass of the exploding star tex2html_wrap_inline9321 is calculated and kick vwlocity tex2html_wrap_inline9323 arbitrarily oriented in space is added to the orbital velocity,
  3. Then, the transition to a new system barycenter frame is made (at this point the spatial velocity of the new center of mass of the binary is computed),
  4. Now in this new reference frame, the new total energy tex2html_wrap_inline9325 and orbital angular momentum tex2html_wrap_inline9327 are computed; if the new total energy is negative, then the new semimajor axis a' and eccentricity e' are calculated by using the new tex2html_wrap_inline9327 and tex2html_wrap_inline9325 ; if the total energy is positive (that is, the binary is unbound) spatial velocities of each component are calculated.

During the CE stage, an effective spiral-in  of the binary components occurs. This complicated process (first introduced by Paczynsky, 1976[151]) is not fully understood as yet, so we use the conventional energy consideration to find the binary system parameters after the CE by introducing a parameter tex2html_wrap_inline8879 measuring what fraction of the system's orbital energy (between the beginning and the end of the spiralling-in process) is transformed into the binding energy (gravitational minus thermal) of the ejected envelope. Thus


where tex2html_wrap_inline9339 is the mass of the core of the mass losing star of initial mass tex2html_wrap_inline9341 and radius tex2html_wrap_inline9343 (which is simply a function of the initial separation tex2html_wrap_inline9345 and the initial mass ratio tex2html_wrap_inline9347 ), and no substantial mass growth is assumed for the accretor (see, however, Chevalier, 1993[31]). The lower tex2html_wrap_inline8879 is, the closer the binary becomes after the CE stage. We will show below that the evolutionary scenario allows values of tex2html_wrap_inline8879 over a wide range, tex2html_wrap_inline9353 -10.

next up previous contents index
Next: ``Ecology'' of Magnetic Rotators Up: Evolutionary Scenarios of Binary Previous: Semi-major axis change

Mike E. Prokhorov
Sat Feb 22 18:38:13 MSK 1997