Color-Magnitude Diagrams

Figure 3 shows the color-magnitude plots (J-K vs. M$_{K_{s}}$) of IC348 and the control field. The dotted lines represent the theoretical main sequence plotted from values taken from Table 4 of the lab handout after transforming from the visual absolute magnitudes to the apparent magnitudes in the K$_{s}$-band with different extinction values at a distance of 320pc (the distance to our cluster) using Equation 4.

$$m_{\lambda} = M_{\lambda} + 5\log_{10}\left(\frac{D}{10\mbox{pc}}\right) + A_{\lambda}$$ (4)

In the plot for the cluster, all of the stars lie to the right of the main sequence line in the figure. This shows that there is a significant amount of reddening within the cluster. We know this is true since a positive J-K value corresponds to a star that is redder than Vega (the standard star chosen to have a magnitude of 0 in all bands), thus a J-K value that is larger than the main sequence colors would correspond to stars that are redder than the stars on the main sequence. The different extinction values are drawn in order to show (assuming that all the stars in the cluster are main sequence stars) where the main sequence falls as we increase the extinction value. The lines are plotted by following the shift in the apparent magnitudes of the main sequence stars as we increase the extinction. The K-magnitude will be shifted by an amount equal to the extinction that we add to the cluster. The J-K color will also be shifted since the extinction values are dependent on wavelengths (Equation 4). The relative shifts of the extinction in J and K can be read off of Table 3 in the lab handout. Equation 5 shows the scaling factor associated with the difference in extinction between J and H.

$$A_{J} - A_{K} = A_{K}\left(\frac{A_{J}-A_{K}}{A_{K}}\right)$$

$$= A_{K}\left(\frac{A_{J}/A_{V}}{A_{K}/A_{V}} - 1\right)$$

$$A_{J} - A_{K} = 1.52A_{K}$$ (5)

We can estimate the amount of extinction in our cluster from Figure 3(a) by examining the plotted main sequence curves with different amounts of extinction. We find that a good estimate for the average reddening amount based on the plot is about 0.5 magnitudes of extinction in the K-band. The maximum amount of reddening is about 2.5 magnitudes.

$$A_{V, avg} = \frac{A_{K, avg}}{.112} = 8.929$$ (6)

Figure 3: The two above figures are the color-magnitude plots for IC348 and the control field. The dashed lines are plots of the main sequence stars at three different extinctions (A$_{K_{s}}$) using the theoretical absolute colors of the main sequence stars given in Table 4 of the lab handout after being shifted to represent the apparent magnitudes of these stars at 320 pc (the distance of our cluster). The dotted line in (b) shows the main sequence after being shifted to a distance of 1200pc. Both the lines in (b) are with no extinction.

Looking at the control plot with the same main sequences plotted, we can see that there are many stars that are located to the left of the main sequence. Since it cannot be the case that these stars are bluer than the main sequence stars, these stars must be located at an even further distance away from us than the cluster is. This can be visualized if we shift the main sequence to a higher magnitude by increasing the input distance to calculate the apparent magnitude. Looking at Equation 4, you can see that as you increase the distance D, the apparent magnitude becomes larger. Looking at Figure 3(b) we can see that if the main sequence is shifted to a distance of 1200pc, all of the stars lie on or to the right of the main sequence. Thus, 1200pc is an upper limit for the distance for the farthest star that is detected in our control field. ³