Indirect Estimation of Distance of a Star from Apparent Magnitude

The space observatory Gaia has compiled an extensive catalogue containing nearly one billion astronomical objects, primarily stars, but also including planets, comets, asteroids and quasars. In this catalogue, parallaxes are measured instead of direct distances ( r ). Bailer-Jones 2015, Publications of the Astronomical Society of the Pacific , 127, 956, 994–1009 demonstrated that estimating distances from parallaxes becomes challenging when the fractional parallax error exceeds approximately 20 per cent, a situation that applies to nearly 80 per cent of the stars in the Gaia catalogue. In the present study, distance estimation is performed using a Bayesian framework that incorporates apparent magnitudes, which are distance-dependent intrinsic stellar properties. The proposed model is formulated using an apparent magnitude–limited distribution (denoted by ϕ( m )), developed by combining the probability density function of an absolute magnitude–limited distribution Φ( M ) with an appropriate prior. The absolute magnitude distribution is constructed using real Gaia data consisting of apparent magnitudes corrected for extinction and parallaxes from a large stellar sample. The resulting posterior distribution of the estimated distances exhibits controlled variance and bias, even for significantly large fractional parallax errors (exceeding 80 per cent compared to earlier studies), thereby enabling reliable distance estimation for stars located at greater distances. AMS Subject Classification (2000): 62F10