Astronomy and Astrophysics – Astronomy
Scientific paper
Apr 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997aps..apr.k1307o&link_type=abstract
American Physical Society, APS/AAPT Joint Meeting, April 18-21, 1997, abstract #K13.07
Astronomy and Astrophysics
Astronomy
Scientific paper
Recent substantial improvements in the technique of precision Doppler measurements (PDM) make it possible to measure the relativistic correction to the ordinary Doppler effect [^1]. The quadratic Doppler term frac1 2β^2 is measurable if the PDM accuracy (1σ) is as high as δ v~= 60 m/s for halo stars (v~= 200 km/s); δ v~= 15 m/s for bulge stars (v~= 100 km/s), and δ v~= 1.7 m/s for disk stars (v~= 30 km/s). Motion of the visible star in the binary (with variable velocity β) and motion of the binary's barycenter (with constant velocity b) result in a (variable) total Doppler shift fracν_0tildeν= frac 1-β_r√ 1-β^2frac1-b_r√ 1-b^2 ≈ (1-βr )(1-b_r+1/2b^2+1/2β^2 ). At the instant when β_r=0, observations bring us an approximate value of br (by neglecting the higher order terms 1/2b^2+ 1/2β^2). Measurements of the binary's proper motion and distance yield the transverse velocity of the binary bt and thus enable one to evaluate b^2=b_r^2+ b_t^2. The difference between ν_0/tildeν and (1-b_r+1\over 2b^2 ) yields an approximate value of 1\over 2β^2. By applying the iteration method, the procedure is repeated until it converges to give accurate values of br and β^2. Knowledge of both β_r=β sin i and β^2 allows us to evaluate sin i. This principal opportunity to disentangle β_r, β_t, and inclination angle i for binary stars opens new opportunities for astronomy. A detailed relativistic theory of binary star orbits, with accounting for effects of general relativity, is given in ref. [^2]. renewcommand baselinestretch0.3 ^1L.M. Ozernoy, Mon. Not. R.A.S. 1997 (in press) ^2S.M. Kopeikin & L.M. Ozernoy Ap. J. 1997 (to be submitted)
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