Direct distance determination using parallax: Techniques, promises and limitations

Abstract

Abstract. Determination of trigonometric parallaxes is one of the very few direct methods available for measuring cosmic distances, and the only one capable of reaching beyond the Solar System. It is fundamental both to determine the intrinsic properties of astrophysical objects and as the first step on the cosmic distance ladder. Steady improvements of instruments and techniques have extended the applicability of the parallax method to ever greater distances. However, it is not correct to say that the method is independent of physical assumptions. This review covers ground-based optical techniques, from Bessel's time to the present, as well as space observations and radio interferometry. Some emphasis is put on the physical limitations of the method, in particular its sensitivity to source structure and photocentric variability on different timescales.Keywords. astrometry, stars: distances, solar neighborhood, Galaxy: general What is parallax?If the stars were fixed in space, relative to the Sun, each would appear to describe a small ellipse as seen by an observer on the Earth. This parallax ellipse mirrors the Earth's orbit as seen from the star: the semi-major axis equals the angle subtended by the astronomical unit (au) at the distance of the star: that is the parallax ; the axis ratio equals sin β, where β is the ecliptic latitude of the star; and the phase of the parallax motion varies with the ecliptic longitude of the star. Real stars are in motion, however, which usually can be modelled quite accurately over several years as a constant angular velocity or proper motion, μ. Combining the two effects, it is found that the variation in any angular coordinate θ (such as α or δ) can be modelled as( 1.1) where θ 0 is the coordinate at reference time t 0 and F θ (t, α, δ) is a known function representing the projection of the unit parallax ellipse in the measurement direction, i.e. along θ. Note that F θ depends on the position of the star as well as on time because of the varying shape and phase of the parallax ellipse across the celestial sphere. From a series of accurate positional measurements, covering θ(t) over the course of at least one year, it is in principle trivial to determine the three model parameters θ 0 , μ and by least-squares fitting of Eq.(1