Abstract
Parallaxes - and hence the fundamental establishment of stellar distances - rank among the oldest, most direct, and hardest of astronomical determinations. Arguably amongst the most essential too. The direct approach to obtain trigonometric parallaxes, using a constrained set of equations to derive positions, proper motions, and parallaxes, has been labelled as risky. Properly so, because the axis of the parallactic apparent ellipse is smaller than one arcsec even for the nearest stars, and just a fraction of its perimeter can be followed. Thus the classical approach is of linearizing the description by locking the solution to a set of precise positions of the Earth at the instants of observation, rather than to the dynamics of its orbit, and of adopting a close examination of the few observations available. In the PARSEC program the parallaxes of 143 brown dwarfs were planned. Five years of observation of the fields were taken with the WFI camera at the ESO 2.2m telescope in Chile. The goal is to provide a statistically significant number of trigonometric parallaxes for BD sub-classes from L0 to T7. Taking advantage of the large, regularly spaced, quantity of observations, here we take the risky approach to fit an ellipse to the observed ecliptic coordinates and derive the parallaxes. We also combine the solutions from different centroiding methods, widely proven in prior astrometric investigations. As each of those methods assess diverse properties of the PSFs, they are taken as independent measurements, and combined into a weighted least-squares general solution. The results obtained compare well with the literature and with the classical approach.
