## 2. Runaway velocities from symmetric SNeConsider a circular pre-SN orbit consisting of a helium star with
mass (the progenitor of the black
hole) and a companion star with mass where we define and subscripts And similarly . Here we have ignored the effects of the impact of the ejected shell on the companion star and assume there is no mass loss or transfer during the re-circularization phase. From conservation of momentum one finds an expression for the resulting runaway velocity (recoil) of the system where is the pre-SN orbital velocity of the exploding helium star in a centre-of-mass reference frame. Together with Keplers third law we find For convenience this equation can be expressed as If we know the masses of the stellar components and the orbital period after the re-circularization () we can calculate from the observed runaway velocity, . However, we observe mass-transferring binaries which might have evolved due to loss of angular momentum by gravitational radiation or magnetic braking before the mass transfer started and/or might have transferred already a significant amount of mass from the donor to the black hole. Before applying Eq. (7) to the observed systems we have to correct for these effects. Also, one has to check whether the binary before the SN would be detached, i.e. that both stars do not fill their Roche lobes at the moment the SN explodes. © European Southern Observatory (ESO) 1999 Online publication: December 2, 1999 |