Binary star statistics: the mass ratio distribution for very wide systems

Binary star statistics: the mass ratio distribution for very wide systems V. TRIMBLE, Irvine, USA Department of Physics, University of California and Astronomy Program, University of Maryland Received 1987 April 21 The distribution of mass ratios for a sample of common proper motion (CPM) binaries is determined and compared with that of 798 visual binaries (VB's) studied earlier, in hopes of answering the question: Can the member stars of these systems have been drawn at random from the normal initial mass function for single stars? The observed distributions peak strongly toward q = 1.0 for both kinds of systems, but less strongly for the CPM's than for the VB's. Due allowance having been made for assorted observational selection effects, it seems quite probable that the CPM's represent the observed part of a population drawn at random from the normal IMF, while the VB's are much more difficult to interpret that way and could, perhaps, result from a formation mechanism that somewhat favors systems with roughly equal components. Die Verteilung der Massenverhiiltnisse fiir eine Auswahl von Doppelsternen mit gemeinsamer Eigenbewegung (CPM) wird bestimmt und mit der von 798 schon friiher untersuchten visuellen Doppelsternen (VB) verglichen in der Hoffnung, die Frage beantworten zu konnen, ob die Mitglieder dieser Systeme nach der normalen urspriinglichen Massefunktion (IMF) fiir Einzelsterne verteilt sind. Beide Systeme haben eine deutliche Spitze bei q = 1.0, jedoch weniger ausgepriigt fiir die CPM als fiir die VB. Nach Beriicksichtigung von Auswahleffekten <lurch die Beobachtung scheint es wahrscheinlich, daLl die CPM eine zufallsverteilte Teilpopulation der normalen IMF repriisentieren, wiihrend die VB auf diese Weise wesentlich schwieriger zu erkliiren sind und vielleicht das Ergebnis eines Bildungsmechanismus darstellen, der Systeme mit anniihernd gleichen Komponenten bevorzugt. Key words: binaries -mass distribution -initial mass function Introduction: binary star statistics The processes of binary star formation are still not at all well understood, and the hope of probing or constraining them has provided the primary motivation for study of binary star statistics (BATTEN 1973) from the time of KUIPER 's (1935) pioneering investigations to the present. Studies of the distributions of separations and periods are still capable of yielding surprises in the form, for instance, of a large number of systems with separations of 10-100 AU and periods of 30-300 yr which are not easily found by either spectroscopic or visual methods (McAusTER et al. 1986; SHARA et al. 1987). It is possible that this range constitutes a preferred scale for binary system formation. Investigations of the mass ratio distribution normally address the question : can this population have been drawn at random from a Salpeter-type mass distribution (SALPETER 1955; ScALo 1986), or do we need to invoke more complex assumptions? The hypothesis of selection at random from an initial mass function of stars with N( M) = N 0 M - x automatically predicts a population of binaries with an initial mass ratio distribution N( q = M 2 /M 1) = N q- x. Observed distributions have been reported both for small samples of stars thoroughly searched (ABT and LEVY 1976, 1978 ; WOLFF 1978; GARMANY et al. 1980) and for larger samples of binaries catalogued as eclipsing (TRIMBLE and WALKER 1986), spectroscopic (STANIUCHA 1979; KRAJCHEVA et al. 1977; TRIMBLE 1978; LUCY and RICCO 1979; HALBWACHS 1987), or visual (JORISSEN 1984; HALBWACHS 1986; TRIMBLE and w ALKER 1986) systems. Unfortunately, before comparing the prediction with observations, it is necessary to correct one or the other for the effects both of post-formation evolution and of observational selection, which discriminates strongly against small mass ratios, no mat ter how one thinks of trying to identify the systems. Evolutionary processes in the form of mass, energy, and angular momen- tum exchange (SHU and LUBOW 1981) entirely dominate the interacting and contact systems that predominate among eclipsing binaries and thereby fully account for their preponderance of mass ratios of 0.5-0.7 (TRIMBLE and WALKER 1986). Mass t ransfer is also important for at least the closer spectroscopic systems and is, perhaps, responsible for many of the late BV stars wit h low-mass (white dwarf ?) companions (WOLFF 1978). Even for the visual systems, it has been suggested (JORISSEN 1984) that the statistical properties cannot be understood without allowance for mass loss from the individual stars large enough to affect the separations as well as the mass ratios significantly. Against this background, it is perhaps not surprising that rather similar data bases have suggested very different conclusions to different authors. KUIPER (1935) found the spectroscopic binary population consistent with random selection from a normal initial mass function (though he ignored double line systems in order to do it). KRAJCHEVA et al. (1977) and TRIMBLE (1974, 1978) found a bimodal distribution for the complete spectroscopic sample, with peaks at mass ratios of 1 and 0.3 (the latter being presumably an observational cutoff of a real distribution rising still higher at smaller ratios). Concentrating on very close systems, Lucv and Ricco ( 1979) and GARMANY et al. (1980) found only the q = 1 peak, while WOlH (1978) thought it was, at any rate, the dominant feature for unevolved systems. A tendency at least for close systems to favor q = l turns up also in the data of ABT and LEVY (1976, 1978) and TRIMBLE and CHEUNG (1976). But HALBWACHS (1987) has looked yet again at the catalogued spectroscopic systems and found only the \ow-q peak. Meanwhile, his 1986 analysis of visual systems concurs with that of TRIMBLE and WALKER (1986) in finding so large an excess of large mass ratios that it is hard to attribute it entirely to observa- tional selection.