The mass-ratio distribution of spectroscopic binary stars

In order to determine the mass-ratio distribution of spectroscopic binary stars, the selection effects that govern the observations of this class of binary systems are investigated. The selection effects are modelled numerically and analytically. The results of the models are compared to the data inThe Eighth Catalogue of the Orbital Elements of Spectroscopic Binary Stars (DAO8) compiled by Battenet al. (1989). The investigations involve binary systems with Main-Sequence primary components only, in order to avoid confusion of evolutionary and selection effects.For single-lined spectroscopic binaries (SBI) it is found that the mass ratios (q=Msec/Mprim) in general adhere to a distributionψq∝q-2 forq>q0, withq0=0.3. The observations are consistent with a distribution that is flat forq<q0. The turn-over value varies fromq0=0.3 for systems with B-type primaries, toq0=0.55 for systems with K-type primaries. The semi-major axesa1 are distributed according toψa(a1)∝a1-αa with an average value of αa=1.3. The power varies from αa=1.7 for systems with B-type primaries to αa=0 for systems with K-type primaries. The eccentricitiese of the orbits of SBI systems are distributed according toψe(e)∝e-1.For double-lined spectroscopic binary stars (SBII) it is found that the shape of theq-distribution, as derived from observations, is almost entirely determined by selection effects. It is shown that the distribution is compatible with theq-distribution found for SBI systems. A sub-sample, consisting of the SBII systems from DAO8 with magnitudesmV≤5m, is less hampered by selection effects, and shows the same shape of theq-distribution as the SBI systems, at theq-interval (0.67, 1).It is estimated that 19–45% of the stars in the solar neighbourhood are spectroscopic binary systems.

[1]  V. Trimble On the distribution of binary system mass ratios , 1974 .

[2]  W. Heintz,et al.  Fourth catalog of orbits of visual binary stars , 1985 .

[3]  H. Abt The frequencies of binaries on the main sequence. , 1978 .

[4]  G. Kuiper PROBLEMS OF DOUBLE-STAR ASTRONOMY. I , 1935 .

[5]  L. R. Yungelson,et al.  Study of physical properties of spectroscopic binary stars , 1982 .

[6]  P. Paolicchi,et al.  Statistics of binary stars. I - Multivariate analysis of spectroscopic binaries , 1983 .

[7]  V. Trimble Q-(ALPHA) RECONSIDERED , 1978 .

[8]  C. Tout On the relation between the mass-ratio distribution in binary stars and the mass function for single stars , 1991 .

[9]  P. Conti,et al.  Spectroscopic studies of O type stars. IX - Binary frequency , 1980 .

[10]  The mass-ratio distribution of Visual Binary Stars , 1990 .

[11]  J. M. Fletcher,et al.  Seventh catalogue of the orbital elements of spectroscopic binary systems , 1967 .

[12]  S. J. Hogeveen Statistical properties of spectroscopic binary stars , 1992 .

[13]  J. Halbwachs Binaries among bright stars: systems with evolved primary components and their relation to the properties of main-sequence binaries , 1986 .

[14]  H. Abt,et al.  Multiplicity among solar-type stars. , 1976 .

[15]  H. Abt Normal and abnormal binary frequencies , 1983 .

[16]  V. Trimble The distributions of binary system mass ratios: a less biased sample , 1990 .

[17]  D. Clayton Principles of stellar evolution and nucleosynthesis , 1983 .

[18]  L. Lucy,et al.  The significance of binaries with nearly identical components. , 1979 .

[19]  Determination of the mass-ratio distribution, II: Double-lined spectroscopic binary stars , 1992 .

[20]  V. Trimble,et al.  The angular momentum-vs-mass relation and the distribution of mass ratios for visual binary systems , 1986 .

[21]  H. Abt,et al.  Binaries among B2 - B5 IV, V absorption and emission stars. , 1978 .

[22]  S. Wolff Duplicity of late B-type stars , 1978 .

[23]  William H. Press,et al.  Numerical recipes , 1990 .