5 The A$_\lambda$/A $_\mathsf{V}$ curve

Extinction has normally been analyzed using a two-colour normalization of the form $E(\lambda -V)/E(B-V)$. However, the true nature of the variability of observed extinction may be hidden by the choice of normalization. The quantity $A_\lambda /A_V$ reflects a more fundamental extinction behaviour than the $E(\lambda -V)/E(B-V)$ (cf. Cardelli et al. 1989). The average colour excess ratios given in Table 5 can be used to estimate the quantity $A_\lambda /A_V$ in the following manner,

$$A_\lambda/A_V = [E(\lambda-V)/E(B-V) R_{\rm cluster}] + 1$$ (3)

where $R_{\rm cluster}$ is taken from Table 6. In Fig. 13a the normalized extinction in the form $A_\lambda /A_V$ is plotted against $\lambda ^{-1}$ for the clusters NGC 654, NGC 663, NGC 869 and NGC 884 alongwith the average extinction law for $R_{\rm cluster} = 3.1$ given by Cardelli et al. (1989). Figure 13a indicates that the agreement between observations and the extinction law by Cardelli et al. (1989) is good barring the A_U/A_V values for NGC 869 and NGC 663. In the case of NGC 869 the ratio A_U/A_V is higher than the normal one whereas in the case of NGC 663 it is lower than the normal one. The value of A_U/A_V = 1.46 in the case of NGC 663 supports $R_{\rm cluster} \sim 3.5$. Whereas in the case of NGC 869 the colour excess ratios indicate a perfectly normal reddening law. It seems somewhat strange that in the case of these two clusters the ISM behaves at $\lambda_U$ in a different way.

The extinction law in the direction of two clusters IC 1502 and IC 1805 is found to be anomalous. The normalized extinction $A_\lambda /A_V$ for these two clusters along with the $\rho$ Oph dark cloud (data taken from Martin & Whittet 1990) is plotted in Fig. 13b. The effect of varying $R_{\rm cluster}$ on the shape of the extinction curves is quite apparent at the shorter wavelengths for different environments of the star forming regions.

As we have discussed the extinction in the direction of star clusters arises due to the general ISM in the foreground of the cluster and also due to the cloud associated with the cluster. Various studies using OB type single stars support a value of $R\sim 3.1$ for the general ISM (Wegner 1993; Lida et al. 1995; Winkler 1997). The minimum reddening, $E(B-V)_{\min}$, towards the direction of the cluster is representative of reddening due to the foreground dust. The slopes of the distribution of stars having $E(B-V) \leq E(B-V)_{\min}$ on the TCDs can give information about the foreground reddening law. In the case of IC 1805 (and NGC 654), where $E(B-V)_{\min}$ is 0.65 (0.77), we used stars having $E(B-V) \leq 0.80$ (0.85) to estimate the foreground reddening presuming that star having $0.65 (0.77) \leq E(B-V) \leq 0.80 (0.85)$ are not much affected by the anomalous reddening law in the cluster region. The colour excess ratios E(J-V)/E(B-V), E(H-V)/E(B-V), and E(K-V)/E(B-V) obtained are $-2.00\pm0.32 (-1.98\pm0.28), -2.58\pm0.35 (-2.47\pm0.27)$ and $-2.80\pm0.39 (-2.82\pm0.36)$ respectively, which support a normal reddening law in front of the cluster IC 1805. We further combined data of all the clusters having stars with reddening $E(B-V) \leq 0.50$. We feel that the limit of $E(B-V) \leq 0.50$ safely excludes the reddening due to intra-cluster matter as the smallest E(B-V) for the NGC 869 and NGC 884 is $\approx$0.50 (e.g. Uribe et al. 2002). A least-squares fit to 8 data points having $0.01\leq E(B-V) \leq 0.50$ gives the colour excess ratio $E(J-V)/E(B-V)=-2.23\pm0.32, E(H-V)/E(B-V)=-2.62\pm0.22$, and $E(K-V)/E(B-V)=-2.79\pm0.26$. These colour excess ratios also indicate a normal foreground reddening law towards the direction of the clusters used in the present study.

Several studies have pointed to the apparent concentration of stars with high R-values in the vicinity of star forming regions. This effect has, for example, in the $\eta$ Carina nebula (Forte 1978; Thé & Groot 1983), M 16 (Chini & Wargau 1990) and M 17 (Chini et al. 1980; Chini & Wargau 1998) and it may be presumed to be characterstic of many more HII regions (Winkler 1997). Winkler (1997) compared the value of R obtained for hottest stars in the Galaxy (spectral type O8 or earlier), which can be considered as indicators of regions with recent star formation, and he confirms that in the majority of the cases the stars with large R indeed seems to be in the vicinity of star forming regions.

On the basis of the above discussions we presume that the anomalous extinction law in the direction of cluster IC 1805 is due to the intra-cluster material.

Figure 13: The normalized extinction curves $A_\lambda /A_V$. The values written along the curves represent the value of $R_{\rm cluster}$.