7 The CM diagram and identification of non-members

Figure 8: Dereddened $R_{\rm C,0}$ vs.  $(R-I)_{\rm C,0}$ CM diagram for NGC663 shifted in magnitude by the value of the distance modulus, 11.6 mag. Be stars and stars identified as non-members in Sect. 7 are not shown here. The isochrones from Bertelli et al. (1994) for Y = 0.28 and Z = 0.02 are plotted for comparison. The numbers to the right of isochrones are the logarithms of age in years.

The members of NGC663 form a well-defined main sequence in the CM diagram (Fig. 7). The main sequence is slightly widened by a differential reddening. Some non-members can be seen redward of the cluster main sequence. Non-members also contaminate the lower part of the main sequence, because with the mean reddening of NGC663 (0.8 mag in terms of the E(B-V) colour excess according to Phelps & Janes 1994), foreground late-type dwarfs and the reddened cluster B- and A-type stars coincide in the CM diagram.

Since the late-type non-members also affect Fig. 4, we would like to distinguish them from the cluster members. Although not unambiguous, the only selection we can practically perform is the selection that uses two-colour photometry. For instance, the non-members can be roughly selected by a dereddening procedure which takes into account the information on the spatial distribution of stars. Assuming that there is no reddening within the cluster and adopting a certain value of the spatial scale of reddening variation, characterized by a parameter  $\varepsilon$ (see below), a reddening map can be derived and then used to correct the colours for differential reddening and magnitudes for differential extinction.

We made an attempt to calculate the variable part of the reddening with the procedure applied by Pigulski & Koaczkowski (1998) to the Cygnus OB2 association. We refer the reader to that paper for details of the calculations. Unlike that case, however, for NGC663 we did not assume a priori the shape of the unreddened main sequence. Instead, the sequence was fitted by a third degree polynomial. The procedure was done iteratively in the following steps: (i) fitting the cluster main-sequence with a polynomial, (ii) calculating the differences between the observed position of a star and the intersection of the reddening line passing through that point with the main sequence (the difference was measured along the reddening line), (iii) calculating the reddening map with the use of the above differences transformed into reddenings and then deriving the residuals from this map for each star, (iv) selecting of non-members. In the last step, a star was identified as a non-member if its residual from the reddening map was larger than an assumed threshold. The rejected stars were not used in fitting the cluster main sequence in the next iteration. The iterations were terminated when no change in residuals occured.

The appearance of the reddening map depends on the assumed value of  $\varepsilon$ (see Pigulski & Koaczkowski 1998 for the definition of this parameter) which, generally, is not known. The lower value of  $\varepsilon$ results in a more detailed extinction map and narrower dereddened main sequence, a larger value gives the opposite effect. Fortunately, the selection of non-members is almost independent of the choice of  $\varepsilon$. The main parameter which determines how many stars will be selected as non-members is the threshold adopted in step (iv) of the dereddening procedure. We have assumed the threshold to be equal to 0.1 mag. Despite some subjectivity in the method of selecting non-members, we think it is reasonable to use it, because it helps to find new Be stars. In Fig. 4 we see that some late-type non-members and Be stars with weak emission have similar values of $\alpha$. The selection we made allows us to distinguish fairly well between these two groups of stars.