In order to determine the turn-off (TO) for clusters and field, we employed the same technique. We adapted the Sobel Kernel technique explained in Sect. 5.2.2 to find the edge in the color distribution. The methodology for the field is the same as described in Chap. 5 but using this time colors instead of temperatures. Clusters stars having the same metallicity and TO color can be simply found from histograms of the color distribution. The value of the turn-off (g−r) color is indicated in the forth column of Table 7.1 (the value listed in the table is not corrected by reddening). The numbers in parenthesis in Table 7.1 represent the turn-off point of the cluster fiducial sequence taken from the Tables 9-28 of An08. A cluster fiducial sequence is defined as the locus of the density peaks in the color-magnitude diagram. We decided to consider the fiducial TO-point3 for these clusters
because we were not able to detect properly the TO with the Sobel Kernel technique. The rather narrow sequence of M92 and M5 (see top panels of Fig. 7.1) produced an abrupt drop in the color distribution. As an example, we have plotted in Fig. 7.2 the CMD of M5 in the upper panel and its color distribution in the lower panel. The edge-detection filter gave its maximum response in the blue side of the drop, which is illustrated with the blue line in Fig. 7.2. This yielded a TO located in a color region where there were very few stars in the CMD. The TO given by the fiducial sequence, however, is located at the red side of the drop. It is instructive to remark that the turn-off given by the fiducial
3
7.3 Observational evidence 109 sequence does not represent the bluest point. The mean in the CMD at the region close to the TO will yield redder value than that obtained from the Sobel Kernel filter. For the narrow sequence of M92 and M5 we accept the bluest point of the fiducial sequence as a good approximation of the main sequence turn-off. The sparsely populated clusters NGC4147 and Pal5, on the other hand, did not show a clear TO in the color distribution. It produced unrealistic edge-detection with the Sobel Kernel, driving us to use for these cases the fiducial TO of An08 as well. We are aware that this value is not as good approximation for the bluest point as for the other two cases discussed above, but it is still better to use TO-point given by the fiducial sequence than by the Sobel Kernel filter.
Using theE(B−V) reddening value indicated in Table 7.1 and the de-reddening correc- tion formula of Eq. (7.3), we corrected the turn-off color for each cluster and plotted them against their metallicity, as seen with the red asterisks in Fig. 7.3. The blue line indicates the MSTO color of the field stars, with the dashed line representing the bootstrapping error obtained with the Sobel Kernel technique. In Fig. 7.3 we observe how the MSTO color as a function of metallicity of the field stars agrees well with that of the globular clusters. We see that metal-poor stars have a bluer turn-off color than metal-rich ones at the same evolutionary stage.
Figure 7.2: Upper panel: M5 color-magnitude diagram. Lower panel: color distribution, smoothed with the probability function given by Eq. 5.1. The red line corresponds to the turn-off from the fiducial sequence while the blue line to that obtained from the Sobel Kernel technique.
The trend of the MSTO color plotted in Fig. 7.3 with the blue line corresponds to the quadratic polynomial
(g−r)TO,field = 0.467 + 0.217·[Fe/H] + 0.039·[Fe/H]2. (7.4)
It is very similar to the trend of the MSTO color of the globular clusters, plotted with the red dotted line, which is
(g−r)TO,GC = 0.471 + 0.217·[Fe/H] + 0.035·[Fe/H]2. (7.5)
The coefficients of the parabola are very similar and have an offset of 0.04 mag at the zero-point, which is smaller than the bootstrapping errors obtained for the TO-detection of the field stars. In Fig. 7.3 we can see how the TO-color of the GC lie within the TO-color of the field, with the globulars being slightly bluer than the field stars. In general terms, the TO-color of field and clusters agree, suggesting that the age trend of the MSTO field stars should also agree with that of the clusters. We will come to this point in Sect. 7.4.
Figure 7.3: De-reddened (g−r) color of 10,000 randomly selected field stars as a function of metallicity. The blue line correspond to the turn-off and the dashed line its error. Red asterisks indicate the turn-off de-reddened (g −r) color and metallicity of 11 clusters of An et al. (2008). Their names are indicated at the top of the diagram.
7.3 Observational evidence 111
Figure 7.4: Color distribution of the globular clusters of Table 7.1 with dashed line. The distribution for the field stars with the same metallicity as the cluster is plotted with solid line.