Astrometric binaries manifest themselves through the presence of systematic irregularities in the tangential motion of the primary star. Sirius B was the first "invisible" companion discovered in this manner, revealed by Friedrich Bessel's analysis of proper motion data for the primary spanning a 6-year period from 1836 to 1842. In this case, the system lies near the Sun, the two components have similar masses and are separated by ~ 7.5 AU. Consequently, Sirius A exhibits an astrometric "wobble" of several arcseconds, an excursion readily detectable via accurate 19th-century visual observations. Brown-dwarf and planetary mass companions produce much smaller reflex motions, and require correspondingly more precise measuring techniques.
The motion produced by a single companion in a circular orbit has a semiamplitude given by the following relation:
where mc is the mass of the companion in Jupiter masses, M* the mass of the primary star in solar masses, r the distance in parsecs, and P the period in years (Gatewood, 1976). Thus, as viewed from a distance of 1 parsec, the Sun has an astrometric wobble of ~ 0.5 milliarseconds due to Jupiter alone; Saturn contributes an additional 0.27 milliarcsecond. As another example, a 50Mjup brown dwarf companion in a Jupiter-like orbit would produce a 2.5 milliarcsecond wobble in a sun-like star as viewed from a distance of 10 parsecs.
Precision astrometry is therefore an alternative to radial velocity in searching for sub-stellar companions to main sequence stars. However, astrometry is most effective in a different regime of orbital parameter space. Astrometric surveys are best suited to detecting sub-stellar secondaries in wide, face-on orbits, since those systems induce larger amplitude (and longer period) reflex motion on the host star. In contrast, radial velocity surveys are optimal for detecting close-in companions in edge-on orbits.
Astrometric searches for sub-stellar companions have had a chequered career, at least until recently. Reuyl & Holmberg (1943) were the first to enter the lists, with the claimed detection of a ~ 0.01M© companion of 70 Ophiuchi (which actually has an unrelated ~ 1.5MJup planetary companion). Subsequent investigations over the succeeding four decades led to claims of planetary-mass companions around almost a dozen other stars, notably Barnard's star (van de Kamp, 1982). None has survived detailed scrutiny. Recently, however, Pravdo et al (2005) announced the discovery of the brown dwarf Gl 802B, the first and, so far, the only astrometrically discovered sub-stellar companion. The longer orbital periods of the sub-stellar companions sought through astrometric surveys mean that a decade may pass before a large number of brown dwarfs and extrasolar planets are discovered through astrometry.
Although astrometric monitoring has yet to produce many new brown dwarf and planet discoveries, it has proven effective in refining the dynamical masses of known sub-stellar binaries and extrasolar planets. Astrometry allows accurate measurement arcsec arcsec
of the total mass and orbital inclination of a binary. If both components are visible, then measurement of the absolute motions allows one to deduce all the orbital parameters directly from the astrometry alone. Alternatively, if only one component is visible (as is the case with planetary companions), the relative astrometry of the host star can be combined with radial velocity data for the same system to uniquely resolve the sin i ambiguity inherent in measurements of single-lined spectroscopic binaries (Sect. 5.3.2). This allows an exact determination of the mass of the radial velocity planet.
The first sub-stellar objects to have astrometrically determined masses were the components of the binary Gl 569Bab (Lane et al., 2001). Gl 569B is a distant companion of Gl 569A, and its components were originally resolved through AO observations (Martin et al., 2000). It has recently been hypothesized (Simon et al., 2006) that Gl 569Ba is itself a binary (i.e., composed of Gl 569Baa and Gl 569Bab), based on high-resolution spectroscopic observations that suggest two distinct components, as in a double-lined spectroscopic binary (Sect. 5.3.2). Gl 569, a candidate quadruple system is thus an excellent example of how different approaches (direct imaging, astrometric, and radial velocity monitoring) depict complementary pieces of the same larger picture. Several other binary brown dwarfs have had their total masses measured astrometrically in recent years, and a number of astrometric campaigns to measure more dynamical masses are currently underway.
Dynamical masses of brown dwarfs are crucial to understanding sub-stellar evolution. Brown dwarf astrometric binaries with known ages and heliocentric distances (e.g., through physical association with a star of a well-determined age and distance, or membership of star clusters or associations) allow us to constrain sub-stellar properties by disentangling the degeneracies between the mass, age, and luminosity of a sub-stellar object (see Sect. 5.2.1).
More recently, astrometric monitoring has been successfully applied to measure the exact dynamical masses both of extrasolar planets (Benedict et al., 2002, 2006) and of brown dwarfs (Reffert et al., 2006) known from radial velocity surveys. The combination of astrometric and radial velocity data thus depict a unique picture of systems with known radial velocity sub-stellar companions.
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