The mass ratio and the orbital parameters of the sdOB binary AA Doradus

The time sequence of 105 spectra covering one full orbital period of AA Dor has been analyzed. Direct determination of Vsini for the sdOB component from 97 spectra outside of the eclipse for the lines MgII 4481 A and SiIV 4089 A clearly indicated a substantially smaller value than estimated before. Detailed modelling of line profile variations for 8 spectra during the eclipse for the MgII 4481 A line, combined with the out-of-eclipse fits, gave Vsini = 31.8+/-1.8 km/s. The previous determinations of Vsini, based on the HeII 4686 A line, appear to be invalid because of the large natural broadening of the line. With the assumption of the solid-body, synchronous rotation of the sdOB primary, the measured values of the semi-amplitude K1 and Vsini lead to the mass ratio q = 0.213+/-0.013 which in turn gives K2 and thus the masses and radii of both components. The sdOB component appears to be less massive than assumed before, M1 = 0.25+/-0.05 Msol, but the secondary has its mass-radius parameters close to theoretically predicted for a brown dwarf, M2 = 0.054+/-0.010 Msol and R2 = 0.089+/-0.005 Rsol. Our results do not agree with the recent determination of Vuckovic et al. 2008 based on a K2 estimate from line-profile asymmetries.Comment: Accepted by MNRA

Hyperbolic formulations of General Relativity with Hamiltonian structure

With the aim of deriving symmetric hyperbolic free-evolution systems for GR that possess Hamiltonian structure and allow for the popular puncture gauge condition we analyze the hyperbolicity of Hamiltonian systems. We develop helpful tools which are applicable to either the first order in time, second order in space or the fully second order form of the equations of motion. For toy models we find that the Hamiltonian structure can simplify the proof of symmetric hyperbolicity. In GR we use a special structure of the principal part to prove symmetric hyperbolicity of a formulation that includes gauge conditions which are very similar to the puncture gauge.Comment: Our mathematica scripts are available at http://na.mathematik.uni-tuebingen.de/~richter