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Astron. Astrophys. 339, 61-69 (1998)

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5. Structural parameters

We have derived the density profile of Pal 12 making radial star counts in equal number-of-stars steps. Stars with high membership probability were selected as explained in Sect. 3. The cluster center was determined in an iterative manner, by first computing a median of the x and y coordinates of the stars within an arbitrarily located circle of radius [FORMULA]. Next, a new circle was considered with its center corresponding to the just obtained median point. The process was repeated until two subsequently computed centers were coincident. The offset between our center and that given by HC80 is just [FORMULA] in RA and [FORMULA] in DEC. The background level was estimated outside a suitably large distance from the cluster center, chosen with the following procedure. First, a King law was fitted to the observed profile, and a set of structural parameters was derived. Then the procedure was repeated until the computed tidal radius was smaller than the radius used for the foreground estimate.

The final result is shown in Fig. 7, where the filled circles represent the observed star counts and the solid line the best-fitting King law. The adopted morphological parameters are [FORMULA] and [FORMULA], where the errors were estimated following the methods adopted by Saviane et al. (1996), and represent the formal uncertainties of the fit.

[FIGURE] Fig. 7. Profile determination for Palomar 12; filled circles represent the observed star counts and the solid line the best-fitting King law. The adopted morphological parameters are [FORMULA] and [FORMULA].

A more reliable estimate of the errors was computed by keeping the central density fixed and varying the other 2 parameters in a grid of values. The 90% confidence ranges of the fit for the tidal radius and concentration are [FORMULA] and [FORMULA]. An alternative estimate of the uncertainties of the parameters was obtained by changing the sky level by [FORMULA]. The effect is to lower [FORMULA] by [FORMULA] and to change c by [FORMULA].

Our structural parameters are significantly different from those published in Trager et al. (1995); the authors quote [FORMULA] and [FORMULA], which imply a tidal radius [FORMULA]. Since stars belonging to Pal 12 are clearly seen beyond this radial limit (cf. Fig. 3), it is clear that the Trager's et al. tidal radius is too small. On the other hand, the same authors had previously listed values closer to ours (Trager et al. 1993), analyzing the same data used by Trager et al. (1995). It is therefore possible that the inconsistency comes from some typo in Trager et al. (1995) table.

As a final remark, we notice that a dip in the profile is observed in the very central region. This could be due to a slightly lower completeness as discussed in Sect. 3. We fitted the profile also removing the central 3 points, obtaining almost identical structural parameters.

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998
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