Mathematics – Probability
Scientific paper
Dec 1971
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971natur.234..342g&link_type=abstract
Nature, Volume 234, Issue 5328, pp. 342-343 (1971).
Mathematics
Probability
9
Scientific paper
IT would be of great interest to discover a collapsed object (neutron star or black hole) as one component of a binary star system. Trimble and Thorne1 have compiled a list of fifty candidate systems from Batten's2 catalogue. These are non-eclipsing single-line spectroscopic binaries in which the unseen companion has a mass estimated to be greater than 1.4 Msolar. These unseen companions are thus too massive to be non-rotating white dwarfs (although the possibility that they are rapidly, differentially rotating white dwarfs cannot be completely excluded as Ostriker and Bodenheimer3 have shown). In principle, some of these unseen companions could be neutron stars or black holes. In most cases, including all those to be considered here, the unseen companion is less massive than the observed primary star and can be a normal main-sequence star, which is not observed simply because it is considerably less luminous than the primary. Recently, however, Gibbons and Hawking4 have presented evidence that suggests that one or more of the systems on the Trimble and Thorne list contain collapsed objects. Their argument is as follows. Let the initial binary system consist of two stars with masses M 1 and M 2. Let the more evolved star (M 1) eject some of its mass and collapse to form a neutron star or black hole with gravitational mass M N1. The ejected mass-energy can be in the form of a shell of matter or gravitational radiation, for example. If the initial orbit is circular and the mass loss can be treated as instantaneous and spherically symmetric, then the resultant binary system (M 2, M N1) will have an orbital eccentricity given by (Note: the notation for the star masses above is not the usual notation for spectroscopic binaries.) Three of the seven systems from the Trimble and Thorne list with P<5 days were found to have e>0.08. By a comparison with short-period double-line binaries Gibbons and Hawking concluded that the probability of this occurring by chance is only 8%. This suggests that in one or more of the three systems, the eccentricity arises from a sudden mass loss and that the unseen companion is a collapsed object rather than a main-sequence star.
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