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4 Horizontal branch

4.1 The sample of horizontal-branch stars

To study the horizontal branch (HB), we first had to identify the stars belonging to this evolutionary sequence. We note that in the I-(B-I) diagram (Fig. 3b) the HB is indeed more or less horizontal. We judge that the luminosity limits of the HB, from this CMD, are I=17.8 and I=18.3. Using the advantages of multicolor photometry, we can separate HB stars from the stars of the giant branch more reliably. On one hand, HB stars show the largest difference in color from giant-branch stars in both B-I and B-R. The color-magnitude diagrams with these color indices show no significant overlap of these sequences. On the other hand, we selected only those stars which are located within the HB range, adopted from visual inspection of the CMDs, simultaneously for B-R, B-I, and V-I colors [1.250<B-R<1.500, 1.760<B-I<2.028, 0.914<V-I<1.070]. A total of 319 stars satisfy these color criteria as well as the I luminosity criterion.

To determine the mean V and I magnitudes of the horizontal branch, we used a still smaller sample of 201 most probable cluster members, within the ellipse with $a=1\hbox{$.\mkern-4mu^\prime$}9$.The mean $V_{\rm HB}$ value, from this sample, is $19.057\pm0.008$ (the error quoted is the rms error of the average). The mean $I_{\rm HB}$value is $18.056\pm0.007$.

Because NGC 1978 is decidedly elliptical in shape, our subsequent analysis of HB subsamples refers either to elliptical zones or to zones limited, in the radial direction, by similar ellipses of different sizes. We adopt the ellipticity parameter value e=(a-b)/a, where a and b are the semi-major and semi-minor axes of the ellipse, equal to 0.3 for NGC 1978 (Fischer et al. 1992). We also adopt the position angle of the major axis $\rm PA=145^\circ$,which lies within the range of this parameter in Fischer et al. and close to the value they find for the peripheral zone of the cluster. We adopt the position of the cluster center based upon the brighter (I<17.8) giants which clearly show concentration towards the cluster center.

From luminosity profiles, Fischer et al. (1992) found that the semimajor axis of NGC 1978 is at least 55 pc in V light and 65 pc, in B light (i.e. $\sim 4\hbox{$.\mkern-4mu^\prime$}5$ at the LMC distance of 50 kpc). We have adopted the B-light value as the cluster size. Thus, the field studied by us is almost completely within the body of the cluster.

4.2 Horizontal branches of two parts of the cluster

One of the possible explanations of the significant ellipticity of the cluster is the formation of NGC 1978 as a merger of two clusters (see, for instance, Fischer et al. 1992). Having a rather large sample of HB stars, we can compare stellar populations in two parts of the cluster. A natural separation line between the two parts of the cluster is its minor axis. In the following, we will compare the color distributions of HB stars in two fields (quadrants) of NGC 1978, both situated to the northeast of the cluster's major axis and separated by the semi-minor axis. We shall subsequently call the zone to the north of the cluster center "quadrant A'', and the zone to the east of the cluster center, "quadrant B''.

To make the two quadrants approximately equal in area and the field of the cluster more or less symmetrical relative to its minor axis, we artificially imposed a western border at x=150, an eastern border at x=850, and a northern border at y=700 (200 pixels correspond to approximately $1\hbox{$.\mkern-4mu^\prime$}1$). Outer border is imposed at $a_{\rm ext}\approx3\hbox{$.\mkern-4mu^\prime$}3$ from the cluster center. We excluded the densest part of the cluster inside $a_{\rm int}\approx0\hbox{$.\mkern-4mu^\prime$}8$.

The subsamples contain 78 stars for quadrant A and 77, for quadrant B. Their color (B-V, B-R, B-I) distributions are shown in Figs. 4a,b,c. The dashed line is the distribution of stars from quadrant A; the dotted line, that of stars from quadrant B. The distribution of 319 HB stars from the whole cluster field is presented by the solid line. For each of the three color indices, we reveal systematic differences among distributions of stars in the two parts of the cluster. The distribution for quadrant B seems to be more symmetrical, with a maximum near the distribution center, whereas the distribution for quadrant A shows a deficiency of stars in the center of distribution compared to quadrant B, with maybe a slight excess at the red end compared to B. As can be seen from Figs. 4a,b,c, these differences are characteristic not only of the two restricted fields (quadrants) but they are traced in corresponding color distributions (solid line) of the whole sample of the HB stars. These differences are apparent for colors formed using B magnitudes, but are practically absent for V-I.

\includegraphics [angle=-90,width=12cm,clip=]{ds7575f4.eps}
\end{figure} Figure 4: The color [B-V - a); B-R - b); B-I - c)] distributions of the horizontal branch in different zones of NGC 1978: the dashed line, for quadrant A (see text); the dotted line, for quadrant B; the solid line, for the complete sample of HB stars. See text for details

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