The Lutz-Kelker bias in trigonometric parallaxes

Abstract

The theoretical prediction that trigonometric parallaxes suffer from a statistical effect, has become topical again now that the results of the Hipparcos satellite have become available. This statistical effect, the so-called Lutz-Kelker bias, causes measured parallaxes to be too large. This has the implication that inferred distances, and hence inferred luminosities are too small. Published analytic calculations of the Lutz-Kelker bias indicate that the inferred luminosity of an object is, on average, 30% too small when the error in the parallax is only 17.5%. Yet, this bias has never been determined empirically. In this paper we investigate whether there is such a bias by comparing the best Hipparcos parallaxes which ground-based measurements. We find that there is indeed a large bias affecting parallaxes, with an average and scatter comparable to predictions. We propose a simple method to correct for the LK bias, and apply it successfully to a sub-sample of our stars. We then analyze the sample of 26 `best' Cepheids used by Feast & Catchpole (1997) to derive the zero-point of the fundamental mode pulsators and leads to a distance modulus to the Large Magellanic Cloud - based on Cepheid parallaxes- of 18.56 +/- 0.08, consistent with previous estimates.Comment: MNRAS Letters in press; 6 pages LaTeX, 6 ps figure

Stellar and wind parameters of Galactic O-stars

“…We have estimated the correction using Fig. 2 in Oudmajier et al (1998) and have found that the resulting value agrees well with existing calibrations of absolute magnitude versus spectral classification (e.g., Massey 1998or Walborn 1972. Therefore, we have adopted this resulting value and corresponding uncertainty (i.e., ±0.43 mag which is larger than the uncertainty adopted for most of the stars).…”

MAXI J1957+032: An Accreting Neutron Star Possibly in a Triple System

“…Following Figure3 of Perryman et al (1997), I extracted the V-band magnitude and parallax measurements for all M0V stars with fractional errors in the parallax of <10%, calculated absolute magnitudes, and found a 1s uncertainty of 0.8 magnitudes. An exact estimate of the absolute magnitudes of M0V stars from the parallax data is beyond the scope of this work, as such estimates are subject to significant biases (e.g., Oudmaijer et al 1999). I therefore adopt an absolute (color-corrected) R-band magnitude for the J1957 counterpart of 7.5(8).…”

Luminosity calibration and distance scale

“…For example, Oudmaijer et al (1999) show that a sample of stars selected from the Michigan Spectral Survey to be KOV stars were (1) shown by Hipparcos observations to be 0.2 mag brighter than given previously (Schmidt-Kaler 1982) and (2) were contaminated by about 20 % of K0IV stars. Domingo & Figueras (1999) use a sample of main-sequence A3-A9 stars, normal and chemically peculiar Am stars, to revise the calibration of absolute magnitudes with respect to temperature, evolution and metallicity effects as obtained from Stromgren photometric indices, and to rotational velocities.…”

“…The only very firm result is the complete three-dimensional study of the Hyades open cluster for which more than 200 members were individually observed with a good accuracy ). The number of other stellar candles, observed with high accuracy, was not large enough to avoid further divergent analysis, and to reliably explore, for example, the effect of metallicity on the position of open cluster main sequences (van Leeuwen 1999, Robichon et al 1999, Pinsonneault et al 1998 or on period-luminosity relations for pulsating variable stars (Feast k Catchpole 1997, Oudmaijer et al 1998, Luri et al 1998, Fernley et al 1998, Tsujimoto et al 1998and Bergeat et al 1998 Gaia would provide such accurate distances (and proper motions) for such huge numbers of each category of stellar candles that, again in this domain, the analysis methods should have to be drastically changed. Some illustrative figures are given in Table 3.…”