Abstract

In 1930, Trumpler noticed that linear diameters (LD) of open clusters increase with distance (D) from the Sun. As the anthropocentric concept had been abandoned for a long time, he concluded that this apparent increase was caused by the unaccounted interstellar extinction that makes photometric distances to the OCL greater that they are in reality.

Since that time, the interstellar absorption has become one of the best studied factor in astrophysics, and we may hope that current OCL distance scales are free from this LD-D correlation. To verify if this is the case we have chosen several modern OCL distance scales and test them with the same clusters and the same angular diameters that Trumpler had used back in 1930. These scales are Pylskaya & Barkhatova (1980), Danilov & Seleznev (1994), Loktin & Beshenov (2000), Dambis (1999), Lynga (1987), and Robichon et al. (1999). When preparing these scales we used the Catalogue of Open Clusters and Associations (Pylskaya 1998), which is being maintained at the Urals State University for several decades, and the open cluster database WEBDA (Mermilliod 1998).

We have found that the scales of Barkhatova & Pylskaya (1980) and Dambis (1998) are slightly shorter than the Lynga scale, but in general they agree very well. The Loktin & Matkin (1994) scale is formally less consistent with the Lynga's one, but in general these two catalogues disagree only at large distances. And again, Loktin & Matkin (1994) distances tend to be slightly shorter than those in Lynga's Catalogue. Danilov & Seleznev (1994) distances seem to be significantly smaller than any other scale.

Comparison of pre-Hipparcos scales with Hipparcos distances according to Robichon et al (1999) also have shown that the agreement between photometric and geometric distances is quite good, except for Danilov & Seleznev (1994). Thus, we might expect that the presented photometric scales give a reasonable estimation of the OCL distances in the Galaxy.

Then, we used these distances to calculate the OCL linear sizes from their angular diameters (AD) taken from the Trumpler sample. This revealed a surprising fact: for all modern photometric scales linear diameters appear to increase with distance even stronger than in the original Trumpler (1930) paper.

As Kholopov (1981) noted, the Trumpler LD-D correlation is caused partially not by the overestimated distances influenced by interstellar extinction, but by the effect of the interstellar extinction on the angular diameter measurements. However, if we use angular diameters taken from Lynga's catalogue to compute OCL linear sizes, the LD-D correlation, though not that strong, still persists in all photometric scales. This may be caused by selection effects (at larger distances we see larger complexes and miss or misidentify smaller stellar groups) or be related somehow to the inhomogeneous distribution of the absorbing matter in the Solar vicinity.