AAS Meeting #193 - Austin, Texas, January 1999
Session 102. Binary Stars
Display, Saturday, January 9, 1999, 9:20am-4:00pm, Exhibit Hall 1

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[102.03] Generalized Solution for Binary Star Ephemerides and Apsidal Motion

W. V. Van Hamme (Florida International University), R. E. Wilson (University of Florida)

We demonstrate generalized determination of apsidal motion rates (d\omega/dt's), orbital periods (P's), and period changes (dP/dt's) in binary stars. Our method can use eclipses but is not restricted to eclipse data. A general binary star program solves for d\omega/dt and/or ephemeris parameters together with other binary star quantities, and combines radial velocities and light curves within a coherent analysis. We can use data that may have large timewise gaps and may be far less than optimally distributed over time. The method is particularly useful when the apsidal period is long and eclipse timings cover only a small part of the cycle. We show apsidal motion results for AS Cam and find a d\omega/dt of 18.20±.66\,\arcdeg/100\;{\rm yr}. This result compares to a d\omega/dt of 13.2±.8\,\arcdeg/100\;{\rm yr} obtained from a traditional weighted least squares fit to almost 100 years of times of minima, which is 3.3 times smaller than predicted by theory. Other published estimates for the apsidal motion rate are 15.0±.3\,\arcdeg/100\;{\rm yr} by Maloney, Guinan & Mukherjee (1991, AJ, 102, 256), and 18.3±.6\,\arcdeg/100\;{\rm yr} by Wolf, Sarounová & Diethelm (1996, A&AS, 116, 463). Apsidal motion determined from times of minima depends on the value of the eccentricity e. Our result is for e = 0.1633, obtained from the light and velocity solution. The new d\omega/dt from the general analysis is 2.4 times smaller than theory, with a standard error 3 times smaller than in the traditional method. Our apsidal period of 1978±1 year is based on only 30 years of light and velocity curves, or 1.5% of the cycle. The method also works well in measuring period changes in long period giant binaries (such as symbiotics), considering that these stars are typically observed in fragments and that very few show eclipses that are useful as timing ticks. Our dP/dt results for the symbiotic binary AG Peg have implications for its future evolution. Natural extensions of the idea can include other periodic phenomena, such as polarimetric variation.


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