Volume 555, July 2013
|Number of page(s)||10|
|Section||Planets and planetary systems|
|Published online||04 July 2013|
In the case of a visual binary star system, one might not have any information about the orbit other than the current separation. In this case, one can still calculate the maximum RV change of any orbit in that configuration, as long as the distance to the system is known.
Diagram of binary star system. The star of interest is on the right and the companion is on the left. The observer is below the system in the plane of the page, so that the separation r can be broken into the component along the line of sight, z, and the projection of the separation visible to the observer, x.
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Figure A.1 shows the orientation of our system. The star and companion are separated by distance r. If we assume the observer is in the plane of the page, then we can break that distance into the x component, the projection of the separation visible to the observer, and the z component along the line of sight. We know that the acceleration of our star of interest, due to the gravitational interaction with its companion, is (A.1)where G is the gravitational constant, mc is the companion mass, and r is the physical separation between them. Since we do not know the physical separation, but instead only have the projection of this separation, we must find the acceleration in terms of the projected separation x and the component of the separation along our line of sight, z. Here we are only concerned with the acceleration along our line of sight, which is (A.2)To find the maximum value for the acceleration we must differentiate, (A.3)then set this equal to zero. This gives (A.4)which is the condition at the maximum acceleration. Inserting this back into Eq. (A.2), and putting the projected separation x in terms of the observed angular separation ρ and the parallax ϖ, gives the maximum acceleration along the line of site (A.5)for any orbit of a star with a companion of given mass.
RV data for τ Gem.
RV data for 91 Aqr.
CRIRES data for τ Gem.
CRIRES data for 91 Aqr.
© ESO, 2013
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