We present a new algorithm to derive the mass-ratio distribution of an observed sample of spectroscopic binaries. The algorithm replaces each binary of unknown inclination by an ensemble of virtual systems with a distribution of inclinations. We show that contrary to a widely held assumption the orientations of each virtual ensemble should not be distributed randomly in space. A few iterations are needed to find the true mass-ratio distribution. Numerical simulations clearly demonstrate the advantage of the new algorithm over the classical method. We have applied the new algorithm to the recent large sample of G-dwarf spectroscopic binaries, and got a uniform or perhaps a slightly rising linear mass-ratio distribution. This result suggests that the mass-ratio distributions of short-period and long-period binaries are substantially different. It also indicates that the mass distribution of the secondary stars is not the same as that of the single stars.

Even though various types of data for binary stars are being obtained in unprecedented quantities there is still a lack of completeness. Because the reduction of combinations of these data adds to the fundamental concepts in astronomy it is advantageous to have available a general self-consistent method whereby all the elements of the orbits of a binary or multiple system may be solved simultaneously. Such a method is reviewed in this paper and an emphasis is placed on the specification of meaningful errors attached to the orbital elements.

We have constructed a new facility at the Georgia State University Hard Labor Creek Observatory, consisting of a telescope and a fiber-fed spectrograph and detector. The Multi-Telescope Telescope (MTT) is an inexpensive one-meter light-collecting telescope whose ‘primary’ mirror consists of nine 33.3 cm mirrors. Each mirror of the MTT focuses light into a separate optical fiber, thus avoiding light losses of conventional fiber bundles. The optical fibers feed a modified ‘slightly’ off-plane Ebert-Fastie spectrograph. The detector is a CCD with low thermal noise characteristics, cooled to 200 K. The CHARA spectroscopic facility will be used for high precision radial velocity observations of binary orbits, tomographic separation of binary spectra, and observations of nonradial pulsations of Be stars.

We have analyzed UV photospheric lines of three O-type binaries (AO Cas, Plaskett’s Star, and 29 UW CMa) by means of tomographic and cross-correlation analyses, with the goal of estimating the physical properties of the individual stars. The tomographic techniques allowed us to estimate Teff and log g the luminosity ratio, and rotational velocities. The mass ratios were obtained from a cross-correlation technique, applied to spectral regions in which preliminary tomography shows the secondary has strong photospheric line features.

When velocities can be determined for both members of a double-lined spectroscopic binary, then the mass ratio can be calculated immediately. With the goal of measuring velocities for faint secondaries in single-lined spectroscopic binaries, we have experimented with a technique of first subtracting the spectrum of the primary using synthetic spectra calculated from Kurucz model stellar atmospheres and then correlating to get the velocity of the secondary. For half a dozen of the single-lined spectroscopic binaries in the Carney-Latham survey of proper-motion stars we have been able to extract velocities for the secondaries and to solve for double-lined orbits.

In close binary systems of O-type stars, the individual stellar winds will collide between the stars to form shock fronts (Stevens et al. 1992). Binaries with equally luminous stars will have winds of comparable strength, and the shock will occur near the mid-plane between the stars, but in binaries of unequal luminosity, the interaction will occur along a bow shock wrapped around the star with the weaker wind. The presence of the shock region can be detected through excess X-ray emission (Chlebowski & Garmany 1990), and orbital phase-related variations in the UV P Cygni lines (Shore & Brown 1988) and optical emission lines (formed in high density regions of circumstellar gas).

We have begun a search for colliding winds through a study of the optical emission lines and UV P Cygni lines in four massive binaries, AO Cas (Gies & Wiggs 1991), Plaskett’s star = HD 47129 (Wiggs & Gies 1992), 29 UW CMa and ι Ori. The optical observations consist of high S/N spectra of the Hα and He I λ6678 region obtained with the University of Texas McDonald Observatory 2.1-m telescope and coudé Reticon system. The UV observations were culled from archival IUE high dispersion spectra of several P Cygni features (N V λ1240, Si IV λ1400, C IV λ1550).

Up to this time infrared spectroscopy has been only occasionally used in binary star research due to both the insensitivity of infrared spectrographs and the difficulty of getting observing time on a limited number of spectrographs. However, infrared spectroscopy has a number of interesting applications in binary star research. We present an example of an application to the long-period symbiotic system CH Cyg. Due to the recent development of infrared arrays, infrared spectroscopy (1) is becoming available at a much larger number of telescopes and (2) in the 1.0-2.5 μm region is capable of going to limiting magnitudes nearly as faint as those reached by CCD’s.

New observational spectroscopic methods have made it possible to obtain radial velocities of eclipsing binary star components with unprecedented accuracy. Most of the improvement in accuracy is due to two techniques: (1) The use of optical fibers to scramble the spatial distribution of stellar brightness at the input end of the spectrometer, and to allow the spectrometer to be located off the telescope where its temperature and position can be stabilized. (2) The simultaneous exposure of the comparison emission-tube light through a separate fiber or pair of fibers adjacent to the stellar fiber continuously during the stellar exposure. Any changes in the response of the spectrometer during the exposure then affect the stellar and adjacent comparison spectra in almost exactly the same way.

For almost 400 members of M67 we have accumulated about 5,000 precise radial velocities. Already we have orbital solutions for more than 32 spectroscopic binaries in M67. Many of these orbits were derived by combining the Palomar and CfA observations, thus extending the time coverage to more than 20 years. The distribution of eccentricity versus period shows evidence for tidal circularization on the main sequence. The transition from circular orbits is fairly clean. Excluding the blue stragglers, the first eccentric orbit has a period of 11.0 days, while the last circular orbit has a period of 12.4 days. For longer periods the distribution of eccentricity is the same as for field stars. The blue straggler S1284 has an eccentric orbit despite its short period of 4.2 days.

For almost 1500 stars in the Carney-Latham survey of proper-motion stars we have accumulated about 20,000 precise radial velocities. Already we have orbital solutions for more than 150 spectroscopic binaries in this sample, and about 100 additional binary candidates with variable velocity. We find that among the metal-poor halo field stars in this sample the frequency of short-period spectroscopic binaries is indistinguishable from that of the disk. The distribution of eccentricity versus period shows evidence for tidal circularization on the main sequence. For the binaries more metal poor than [m/H] = −1.6 there is a clean transition from circular to elliptical orbits at a period of about 19 days. For longer periods the distribution of eccentricity is the same as for stars in the disk of the Galaxy.

Several binary stars detected by the Center for Astrophysics (CfA) radial-velocity surveys were found to be members of triple systems. We present two examples, each requires a different analysis to discover its multiplicity.

One example is G176-46, a double-lined halo star of the Carney & Latham (1987) high proper-motion survey. The secondary star (G176-46b) displays large radial velocity variations, in contrast with the primary (G176-46a), which is constant within the error limits. Figure 1 shows two cross correlations of the stellar spectra against the same calculated template taken at different times, which indicate that only the secondary’s peak changes its position. A similar variation was observed previously for ADS 8811 (Mazeh & Latham 1988).

We have found the secondary radial velocity to vary with a period of 10.44 days, and therefore conclude that Gl76-46b is a member of a short-period binary system. The orbital solution has an amplitude of 38 km s−1 and eccentricity of 0.05.

Cross correlation is a frequently used technique to obtain the Doppler shifts of digitized celestial spectra. This method, suggested by Tonry & Davis (1979), cross correlates the observed spectrum against an assumed template, and obtains the stellar radial velocity by the location of the correlation maximum (Wyatt 1985). The technique finds the correct radial velocity even for extremely low S/N spectra.

Spectra composed of two components present a potential difficulty to this technique. The cross correlation of these spectra usually displays a double peak which can not be resolved whenever the relative velocity of the two components is small. To overcome this difficulty, we developed TODCOR — a new TwO-Dimensional CORrelation algorithm which can simultaneously derive the Doppler shifts of the two components.

TODCOR assumes that the observed spectrum is a combination of two known spectra with unknown shifts. Following the one-dimensional technique, the algorithm calculates the correlation of the observed spectrum against a set of combinations of two templates, with all possible shifts. The correlation, thus, is a two-dimensional function, whose two independent variables are the radial velocities of the two components. The location of the maximum of this function corresponds to the actual Doppler shifts of the two components.

With a small telescope and conventional techniques we have achieved external radial-velocity errors for bright stars of only ±50 m/s by using an optical fibre feed between telescope and spectrograph. In a search for low-mass companions to solar-type dwarf stars, intrinsic radial-velocity variability was detected in some IAU radial-velocity standard stars but no convincing evidence was found of the presence of low-mass companions to the dwarfs.

The Hamilton CCD-echelle spectrometer at the coudé focus of the 3-m Shane telescope of the Lick observatory has been described by Vogt (1987). Illustrations of some binary star spectra obtained with this instrument are given by Popper & Nelson (1990, B-type binaries with large magnitude differences) and by Popper (1992, G-type eclipsing binaries), where typical cross-correlation functions are also shown.

In this progress report, I give some initial preliminary orbital results. First is the bright early B binary, VV Ori, the orbits of which have been the subject of considerable controversy (Duerbeck 1975, Andersen 1976, Popper 1981). According to Chambliss & Leung (1982) and to the line ratios, the secondary component contributes about 10% of the light of the system in the visual region. Multiple (2 to 4) exposures of VV Ori have been obtained with the Hamilton on 7 nights. Velocities of the primary are determined from 13 lines, primarily of OII and HeI between 440 and 590 nm. The only lines found to be useful for the secondary are HeI 597.5 and 492.1. Analysis of the velocities is complicated by the poorly determined variation of the center-of-mass velocity, with a range of roughly 26 km s−1 and a period of roughly 120 days (e.g., Duerbeck 1975). Preliminary orbits based on this material lead to masses 11.1 and 4.7.M⊙, to be compared to Duerbeck’s values of 7.7 and 3.4. It is primarily the high signal/noise ratio, over 600, that enables this study to be carried out satisfactorily.

Orbital solutions are now available for 46 binaries which are members of the Hyades. The distribution of eccentricity versus period shows evidence for tidal circularization of the short-period binaries. However, the transition from circular to eccentric orbits is not clean. The first eccentric orbit has a period of 5.75 days, while the last circular orbit has a period of 8.50 days. For longer periods the distribution of eccentricity is the same as for solar-type stars in the field.

By the time a binary arrives on the main sequence, its dynamics have essentially become those of a simple two-body system, so that its orbital parameters are constants of the motion thereafter. This statement of course needs to be modified under several circumstances, such as where tidal effects, mass exchange or interactions with field stars come into play. For the majority of binaries, however, orbital evolution is all but over by the main sequence. Therefore, in order to explain the distribution of binary orbital parameters one has to look to earlier times (prior to 107 years) when the more complicated dynamics can drive the orbital evolution that establishes these parameters.

We review recent work on gravitational instabilities in circumstellar disks and discuss implications for the possibility of forming binary companions within these disks. Linear stability analysis indicates that self-gravitating modes with azimuthal wavenumber m = 1 will grow strongly in star/disk systems with the physical properties observed in astrophysical systems. Smooth particle hydrodynamic simulations indicate that these self-gravitating instabilities (with m = 1 and higher) will grow into the nonlinear regime. In many cases, a spiral arm will collapse into a gravitationally bound “knot” of gas; these knots typically contain 1% of the mass of the disk and travel on elliptical orbits about the central star.

Binary and multiple star systems may form by fragmentation, that is, through break-up of a dense molecular cloud core during the dynamical collapse phase that leads to the formation of protostellar objects. This review concentrates on theoretical models of fragmentation based on numerical hydrodynamical calculations in three spatial dimensions, using both finite-difference and smoothed particle hydrodynamics techniques. A variety of recent results are described, including calculations of the fragmentation of bar-like (prolate) clouds, fragmentation in clouds with initial power-law density and angular velocity distributions, tidally-induced fragmentation, fragmentation in cooling clouds, formation of hierarchical systems, and the dividing line between clouds that fragment and those that appear to form single protostars. A brief comparison of the predicted physical and dynamical properties of the theoretical fragments with the observed properties of main-sequence and pre-main-sequence binary stars lends supports to the hypothesis that fragmentation is the dominant formation mechanism for binary and multiple star systems. The major uncertainties regarding fragmentation are the extent to which precollapse clouds are susceptible to fragmentation, and the degree to which binary fragments undergo orbital decay and possibly mergers through interactions with the enveloping disk.

Calculations of the formation of non-equal mass binary and multiple systems are presented. Binary formation results from the elongated shape of the initial cloud, one fragment forming on each side of the equatorial plane. Slight linear density gradients along the cloud’s major axis are sufficient to form non-equal mass fragments. Resultant mass ratios range from 0.1 to 1.0, in agreement with observations.

In the presence of rotation, the fragments form with surrounding disks. The primary forms with a larger disk than does the secondary. Due to it’s orbital motion around the primary, the secondary can directly accrete the matter that has gathered in the primary’s disk. The secondary is thus less likely to have an appreciable disk, accounting for a redder primary. The binary system’s initially high eccentricity decreases with the continued accretion of higher specific angular momentum at apastron and lower specific angular momentum matter at periastron. Non-coplanar multiple systems with unequal mass components are also formed. The systems are composed of an inner binary and a more distant companion. The mass ratio of the companion binary system is usually less than that of the binary.

This is not going to be an exhaustive review of all of the literature on the subject of multiple star dynamics, although I will call your attention to the very recent review by Valtonen & Mikkola (1991) entitled “The Few-Body Problem in Astrophysics”. After all, from a dynamical point of view a multiple-star system is the physical realization of the n-body problem of celestial mechanics, and an enormous literature exists for that subject. Rather, this will be some personal thoughts on aspects of the few-body problem that are particularly relevant to the multiple-star astronomer.

One should not forget the case of n=2. Although the problem is completely solvable and contains no surprises, it is one of our reasons to exist. Especially if a binary is on a photographic program, which can yield a parallax, a total mass, and a mass-ratio, and if photometry exists, as is usually the case now for parallax stars, a real contribution is possible. Do an orbit, which is the dynamical problem, and you have two more good points for the empirical mass/luminosity relationship, which is not a bad day’s work for the astrophysicist.