Tidal radii and masses of open clusters^*

¹ Astronomisches Rechen-Institut, Mönchhofstraße 12-14, 69120 Heidelberg, Germany e-mail: [apiskunov;elena;nkhar;roeser]@ari.uni-heidelberg.de
² Institute of Astronomy of the Russian Acad. Sci., 48 Pyatnitskaya Str., 109017 Moscow, Russia e-mail: piskunov@inasan.rssi.ru
³ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany e-mail: [apiskunov;nkharchenko;rdscholz]@aip.de
⁴ Main Astronomical Observatory, 27 Academica Zabolotnogo Str., 03680 Kiev, Ukraine e-mail: nkhar@mao.kiev.ua

Received: 22 August 2007
Accepted: 9 October 2007

Abstract

Context.In a previous paper we obtained King's parameters for 236 of 650 Galactic open clusters identified in the ASCC-2.5.

Aims.Estimating tidal radii by use of observable parameters available for all clusters. Bias-free results are required.

Methods.We use methods of stellar statistics and develop a semi-empirical model of open clusters.

Results.We check two effects impacting the determination of tidal radii from a fitting of King's profiles to the observed density distribution, i.e., ellipticity of open clusters and a bias depending on distances. Though a typical cluster has an elliptical form, the effect is rather weak to produce a prominent bias in the resulting tidal radii. In contrast, a distance dependent bias is not negligible and can cause a systematic underestimation of tidal radii computed with ASCC-2.5 data by a factor of two for the most distant clusters of our sample. This finding is used to correct the original results for 236 clusters and to extend the system of tidal radii and masses to all 650 clusters. We found that the semi-major axis of the projected distribution of cluster members on the sky is a parameter suited to estimate tidal radii of open clusters of our sample. No systematic differences are found between measured and calibrated tidal radii. From the comparison with mass estimates based on star counts and on the assumption of the Salpeter IMF, empirical evidence is obtained for an evolution of cluster mass functions starting in young clusters.

Conclusions.The set of homogeneous parameters available for all clusters of our sample is extended by tidal radius and mass. Within 850 pc where our sample is complete, the distributions of tidal radii and masses peak at  pc and , respectively. In young open clusters, the mass distributions show differences to the Salpeter IMF, and this discrepancy increases with cluster age.