The distributions of binary system mass ratios: a less biased sample

5 :1§9:0_|vF\i|§A_s_. 255.q. 75+. Mon. Not. R. astr. Soc. (1990) 242, 79-87 The distributions of binary system mass ratios: a less biased sample Virginia Trimble Astronomy Program, University of Maryland, College Park, MD 20742, USA and Department of Physics, University of California, Irvine, CA 92717, USA Accepted 1989 June 2. Received 1989 February 27; in original form 1988 November 7 SUMMARY Different investigators have obtained very different forms for the distribution func- tion, N(q), of the ratios of the masses of stars in binary systems, q = M2 /M1. Some are consistent with the component stars having been drawn at random from a stand- ard initial mass function; others are not. The difference arises more from the selection of systems to be analysed than from the methods of analysis. The present sample includes 132 SB1s and 32 SB2s, whose orbits have been obtained by R. F. Griffin and his colleagues using radial velocity spectrometers. Many of them (about 106) are Ki giants. The systems have smaller velocity amplitudes (median 9 km s“) and longer periods (median 590 d) than samples previously analysed. The distribution of their mass ratios has been derived both directly, assuming an average value of sin3 i, and indirectly, using a mathematically more correct model-fitting approach. The distribu- tion, N (q), in both cases is best fit by a power law near q‘ 1 over the range q = 0.1-1.0, after allowance is made for observational selection proportional to the sin or sin2 of the angle of inclination. This is rather ﬂatter than the slope of around two generally found for initial mass functions of 0.8-5 MO stars. A somewhat peculiar pattern of mass loss by the Kill primaries would be required to account for the difference. Models of binary formation by the fragmentation process can account for a wide range of mass ratios, but do not yet predict a unique initial distribution function. 1 INTRODUCTION Since Kuiper’s (1935) pioneering work, the statistical pro- perties of binary systems — average values and distributions of periods, separation, eccentricities and mass ratios - have generally been regarded as at least a potential guide to how binaries form and evolve. Thus, concerning mass ratios, questions have been asked in the forms: (i) what is the distri- bution function for all systems, and how has evolution (of component or systems) changed it from the initial one; (ii) does the initial distribution function indicate that the binary stars constitute one or more than one population, and (iii) can the members of unevolved systems be regarded as having been drawn at random from the initial mass function (IIVIF) for single stars? Fairly numerous past investigations have not, so far, pro- vided undisputed answers to any of these questions. Neither does the present work, of which the principal conclusion is that choice of systems to be considered is more important than the method of analysis adopted. Previous work can be roughly divided into four historical periods, during which investigators found, after widely vary- ing attempts to correct for observational selection effects, (1) a distribution function, N(q), rising toward low mass ratio (q =M2/M1), (2) a bimodal N(q) with peaks near 1.0 and 0.3, (3) N(q) rising toward high mass ratios and (4) a certain degree of chaos. The ﬁrst period began with Kuiper (1935) looking at all the then-known single-line spectroscopic binaries and con- cluding that they were best fit by a distribution N(q)=2(1 +q)‘2. Jaschek & Ferrer (1972) pioneered a model-fitting approach in which assumed forms of N (q) were convolved with selection effects in sini (the angle of incli- nation of the orbit) until the result matched the actual distri- bution of the quantity Y= f (M ) /M 1 = q3 sin3 i /( 1 + q)2, where f (M) is the observed mass function of a single—line SB and M, is the primary mass assumed from its spectral type. Double-line systems were included by using the primary f(M) and M, in exactly the same way as for SB1s. The method requires the assumption that N(q) decreases with increasing q, and the best fitting of the forms they tried was q‘7/3. Peaks at the lowest detectable mass ratio (q = 0.4-0.5) also turned up in investigations by Bettis (1975) and J aschek (1976) of the scattering of stars above the zero-age main sequence (ZAMS) for single stars in HR diagrams of open clusters. The present author accidentally inaugurated the second period by considering all the SB orbits then catalogued in © Royal Astronomical Society - Provided by the NASA Astrophysics Data System