Studies on the Coma cluster. I. Determination and discussion of membership

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Scientific paper

We propose a statistical method of determining the membership of a galaxy cluster based on the maximum likelihood principle using radial velocities. The mathematical model assumes that the radial velocity of a cluster galaxy follows a one-dimensioanl normal distribution and that of a field galaxy follows k one-dimensional normal distributions superposed on one another. Application to the Coma cluster shows the reasonableness of this model; it determines well the distributional parameters of the cluster and the membership probability of individual galaxies and the criterion for membership is effective. The best result is obtained with K= 2, that is, by separating the field galaxies into a foreground and a background distribution. We point out that, at least in the case of not too large samples, it is not advisable to take K greater than 2.

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