arXiv:astro-ph/0303634astro-ph
The diameters of Alpha Centauri A and B - A comparison of the asteroseismic and VINCI/VLTI views
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Abstract
We compare the first direct angular diameter measurements obtained on our closest stellar neighbour, Alpha Centauri, to recent model diameters constrained by asteroseismic observations. Using the VINCI instrument installed at ESO's VLT Interferometer (VLTI), the angular diameters of the two main components of the system, Alpha Cen A and B, were measured with a relative precision of 0.2% and 0.6%, respectively. Particular care has been taken in the calibration of these measurements, considering that VINCI is estimating the fringe visibility using a broadband K filter. We obtain uniform disk angular diameters for Alpha Cen A and B of UD[A] = 8.314 +/- 0.016 mas and UD[B] = 5.856 +/- 0.027 mas, and limb darkened angular diameters of LD[A] = 8.511 +/- 0.020 mas and LD[B] = 6.001 +/- 0.034 mas. Combining these values with the parallax from Soderhjelm (1999), we derive linear diameters of D[A] = 1.224 +/- 0.003 Dsun and D[B] = 0.863 +/- 0.005 Dsun. These values are compatible with the masses published by Thevenin et al.(2002) for both stars.
It's a lot easier to reason about this using angular resolution, because that's normally what the diffraction limit formula is in reference to. If you know the angular diameter of the system (α) and the wavelength (say λ=500 nm for visible), you can use α ≈ λ/d and solve for the…
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