Cosmic Distances and Selection Biases

Abstract

Our ability to travel in space is badly limited. This is much felt in the process of extending distance measurements into deep space. Paul Hodge (1981) once began his review: "The determination of the extragalactic distance scale, like so many problems that occupy astronomers' attention, is essentially an impossible task". In fact, he was quite optimistic, and how else, the life is full of impossible things that nevertheless have been done.Various types of Gregory's standard candles are still the main method to measure extragalactic distances, and also used in cosmological tests. One should be aware of fundamental difficulties accompanying this method. Here we give an overview of problems appearing in distance determination, when the astronomer works, as usually, with samples gathered from the sky (magnitude-limited), instead of samples obtained unrestricted from space. Errors and BiasesAll determinations of a physical quantity, including a cosmic distance, contain some error. In fact, one may speak about (1) random errors, (2) systematic errors, and (3) crude errors. A supposed distance indicator may be simply erroneous, leading to crude errors, an example being Hubble's brightest stars in galaxies, which were actually HII regions. Evolution of standard candles or their classes may cause systematic errors. And even if there were no inherent differences in the objects in different places and epochs, a sample of the observed objects may be much deformed by selection effects, leading to systematic errors in the inferred average distances.Random peculiar velocities change the redshift from its ideal cosmological value, and generally these motions are not known for any individual galaxy. This adds always some error to the redshift distance.Sometimes the method is sensitive to a factor whose effect must be modelled. Thus when using the time delay in gravitational lenses to derive the Hubble constant, one has to use a model for the mass distribution of the lensing galaxy. It also happens that a distance indicator may be made better when one notes the influence of an extra factor. For instance, the peak luminosity of the supernovae SN Ia is correlated with the decay rate of their light curves. Before such effects are known, they may give rise to errors that are not simply random, but systematic and distance-dependent.Naturally, astronomer wants to see some measurable effect indicating the distance. Even if the observations are too inaccurate something is often seen and this is taken as a distance effect-usually leading to an underestimate.An early example is the derivation of the Sun's distance by . He knew that when the Moon appears exactly half full, then the Earth, the Moon and the Sun form a right-angled triangle with 90°at the Moon. He took the Moon-Sun angle to be 87 degrees and proved from the triangle that the ratio of the Sun's and the Moon's distances is between 18 and 20. In fact, the Moon-Sun angle in the half moon triangle is so close to 90 degrees (89.85°) that it was impossible to measure it and Aristarch...