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We have determined a spectroscopic orbit for SAO 167450, which is the visual secondary of the W UMa-type eclipsing binary AA Cet, and so the system is quadruple. Radial velocities from the coudé feed and 4 m telescopes at Kitt Peak National Observatory produce an orbit with a period of 25.68 days and an eccentricity of 0.50. We classify both the primary and secondary as G0 subgiant/dwarf stars and find that they are somewhat metal rich relative to the Sun. The high lithium abundances of both components argue that the stars are less than 1 Gyr old. If the components are dwarfs, they are pseudosynchronously rotating, while if they are subgiants, they are rotating more slowly than pseudosynchronous. We very roughly estimate a period of 5,000–15,000 yr for the visual pair. Although it has been suggested that in a multiple system, the combination of Kozai cycles and tidal friction may produce contact binaries, the separation between the visual components in this system appears to be much too large to accomplish that result.