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5. The horizontal branch and the distance modulus

Figure 5 (click here) presents the V-(B-V) diagram specially for HB stars with tex2html_wrap_inline1514. Dots are stars in the central cluster region (tex2html_wrap_inline1516); crosses are stars in the more peripheral regions. Some stars are plotted as circled dots, they are discussed below. The CMD shows no significant difference between the color of the reddest stars in the cluster center and in its outer regions. If we identify these stars (at tex2html_wrap_inline1518) with the blue boundary of the instability strip, we find tex2html_wrap_inline1458 as a reasonable estimate of the HB level.

  figure337
Figure 5: The V-(B-V) diagram for the horizontal branch of M 79. The designations are explained in the text

To determine the apparent distance modulus of M 79, we used the relation between the absolute magnitude of the HB and metallicity presented in the catalog by Harris (1994):
displaymath1510

For [Fe/H] = -1.76, we get tex2html_wrap_inline1526 Therefore m-M=15.60.

Our CMDs show that there are a number of stars to both sides of the principal sequence; it is difficult to consider all these stars to be field objects. Similar stars are present in the CMD by Ferraro et al. The stars to the left of the HB are usually called UV-bright stars, they are brighter in the ultraviolet range than the majority of HB stars, and they are situated above the HB in the U-(U-B) diagram. Such a diagram is shown in Fig. 6 (click here); the circled dots designate stars above the upper envelope of the main body of HB stars. The same stars are plotted as circled dots also in Fig. 5 (click here). Comparing the two diagrams, we see that all the stars above the HB in the U-(U-B) diagram (with a single exception) are also outside the principle sequence in the V-(B-V) diagram. The star with the lowest U-B index coincides with the lowest data point in Fig. 5 (click here). The two only data points situated below the HB in Fig. 6 (click here) are the two most red-displaced points in Fig. 5 (click here) for the range of V between tex2html_wrap_inline1540 and tex2html_wrap_inline1542. They might be blue stragglers. The nature of stars below the HB in the V-(B-V) diagram is not clear, if not all of them are field stars. Note that similar stars are present in the CMD of the globular cluster NGC 1841 (Alcaíno et al. 1996).

  figure354
Figure 6: The U-(U-B) diagram for the horizontal branch of M 79. The designations are explained in the text

Interesting enough, the U-(U-B) diagram stresses some morphological details of the HB, namely, its fragmentary structure. The most obvious are the gaps at tex2html_wrap_inline1550, tex2html_wrap_inline1552, and, possibly, at tex2html_wrap_inline1554. The depressions in the HB LF corresponding to these gaps are marked with arrows in Fig. 7 (click here), presenting the luminosity function for the horizontal branch. This figure is discussed in more detail below.

  figure360
Figure 7: The luminosity function for the horizontal-branch stars of M 79. Arrows: the positions of suspected depressions. The letters A, B, C, D designate the HB fragments discussed in the text

Here we encounter a serious problem which has been an object of numerous studies during the recent 25 years (e.g., Simoda & Tanikawa 1972; Newell 1973; Buonanno et al. 1985, 1986): the problem of the existence of any real features (gaps?) in the distribution of stars along the HB, especially along the blue HB. Many factors make it difficult to come to definite conclusions on the presence (or absence) of such details and on their persistence for different clusters. Besides difficulties connected with observations and insufficient statistics, the features may be more prominent or less prominent in different clusters, and the length of the HB (along the axis of magnitudes) may also differ.

The following considerations are also only a preliminary discussion, to be tested by further studies. We concentrate upon details (depressions) repeating themselves in several clusters.

Kravtsov et al. (1997) compare the HB LFs for the clusters NGC 5986 and NGC 6139 (from photographic studies) and for M 79 (from the present study). In particular, they find that, at the level corresponding to that with V=16.9-17.0 in Fig. 7 (click here), the HB LFs (reduced to the same HB level) have either their faint end or a depression. A similar depression occurs for NGC 1841 (Alcaíno et al. 1996) in the V range between 20.0 and 20.1 (the HB levels of NGC 1841 and M 79 differ by tex2html_wrap_inline1560). A significant gap in the HB of M 15 (Buonanno et al. 1985) is observed for 16.1<V<16.5 (here tex2html_wrap_inline1564). We call the part of the blue HB above this depression "fragment A''. In NGC 5986, there is an indication that this fragment consists of two subfragments (let us call them "Aa'' and "Ab''), and the ratio of the star numbers in these subfragments may vary with the distance from the cluster center. Similar radial changes in the structure of the fragment A may be suspected for NGC 1841. Note that the blue HB in NGC 5466 (Buonanno et al. 1985) consists only of the subfragment Aa. It is also stronger populated than Ab for M 79 (Fig. 7 (click here)). For M 15, the subfragment Ab is absent or greatly depressed (though the blue HB does have still fainter stars), and the above-mentioned gap seems significant.

The faint boundary of the next HB fragment ("B'') is separated from that of the fragment A by tex2html_wrap_inline1566 (it is located at tex2html_wrap_inline1568 in Fig. 7 (click here)). A similar depression in M 15 may be suspected at tex2html_wrap_inline1570. According to Buonanno et al. (1986, Fig. 17), the level of this depression shows an abrupt change of the HB population density in NGC 6752 and corresponds to the faint end of the HB in NGC 288.

The next fragment, "C'', is terminated in M 79 at tex2html_wrap_inline1572, where the HB becomes much poorer populated, as it was also noted by Ferraro et al. (1992). This corresponds to the level of the faint end of the HB in M 15 found by Buonanno et al. (1985) and to a low minimum (tex2html_wrap_inline1574) in the HB LF of NGC 6752 (Buonanno et al. 1986).

In some clusters (NGC 6752, M 13, M 79, etc.), a still fainter HB fragment ("D'') is present or may be suspected. It is represented only by several stars in M 79.

We conclude that, apparently, the blue HBs of globular clusters possess a fragmentary structure. Dependent upong the length of the cluster's HB, the luminosity levels marked with arrows in Fig. 7 (click here) correspond either to the HB's faint end or to a feature in the distribution of HB stars: a gap, a depression, or an abrupt change of the HB population density. The clusters with the longest HB (like NGC 6752) may have even four macrofragments (A, B, C, D). Number ratios of stars forming different fragments (or entering different subfragments, like the above-discussed subfragments Aa and Ab) may change with the distance from the cluster center (cf., for instance, Buonanno et al. 1986; Ferraro et al. 1992; Alcaíno et al. 1996; Kravtsov et al. 1997). To confirm these results, it is necessary to observe larger samples of HB stars for each cluster.


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