3 Extinction

One of the main characterstics of the diffuse interstellar matter in the Galaxy is its irregular structure. This makes it difficult to map the extinction as a function of galactic longitude and distance. Young open clusters also show differential reddening due to the remains of the associated parental clouds. The differential reddening decreases with the age of the clusters (cf. Pandey et al. 1990). However, it does not show any correlation with the location of the cluster in the galactic disk.

Thus the extinction in star clusters arises due to two distinct sources; (i) the general interstellar medium (ISM) in the foreground of the cluster, and (ii) the localized cloud associated with the cluster. While for the former component a value of R = 3.1 is well accepted (Wegner 1993; Lida et al. 1995; Winkler 1997), for the intra-cluster regions the value of R varies from 2.42 (Tapia et al. 1991) to 4.9 (Pandey et al. 2000 and references therein) or even higher depending upon the conditions occurring in the region.

3.1 Extinction curve

Extinction has often been analyzed using a two-colour normalizations of the form $E(\lambda -V)/E(B-V)$. In the present work the following methods are used to derive the ratio of $E(\lambda -V)/E(B-V)$.

a) Colour excess diagrams (CEDs); method "A''

The colour excesses of the stars in the cluster region can be obtained by comparing the observed colours of the stars with their intrinsic colours derived from the MKK bi-dimensional spectral classification. For this purpose we used the data available in the online catalogue by Mermilliod (1995). When multiple data points are available for a star, we used those selected by Mermilliod and given as MKS in the online catalogue. The colour excess in a colour index ( $\lambda - V)$ is obtained from the relation $E(\lambda - V) = (\lambda - V) - (\lambda - V)_0$, where $(\lambda - V)_0$ is the intrinsic colour index and $\lambda$ represents the magnitude in the UBVRIJHK pass bands. Intrinsic colours are obtained from the MKK spectral type-luminosity class relation given by Schmidt-Kaler (1982) for UBV, by Johnson (1966) for VRI converted to the Cousin's system using the relation given by Bessel (1979), and by Koornneef (1983) for VJHK.

Figure 1: E(U-V) vs. E(B-V) colour-excess diagrams. Straight line shows a least-square fit to the data.

The colour excesses E(U-V), E(I-V), E(J-V), E(H-V) and E(K-V) are shown as a function of E(B-V) in Figs. 1, 2, 3 and 4. The stars having H$_{\alpha}$emission features and stars apparently lying away from the general distribution are not included in the analysis. A least-squares fit to the data is shown by a straight line which gives the ratio of $E(\lambda -V)/E(B-V)$ for the stars in the cluster region. The slope of the line representing the ratio $E(\lambda -V)/E(B-V)$ along with the error is given in Table 2. In general, the least-square errors are quite large. The reason for the large errors is mainly the small sample and the small range in the E(B-V). For comparison the colour excess ratios for the normal reddening law (cf. Johnson 1968; Dean et al. 1978) are also given in Table 2.

Figure 2: E(I-V) vs. E(B-V) colour-excess diagrams.

 

Table 2: The colour excess ratios $E(\lambda -V)/E(B-V)$ obtained from the CEDs.

Cluster	$\frac{E(U-V)}{E(B-V)}$	$\frac{E(I-V)}{E(B-V)}$	$\frac{E(J-V)}{E(B-V)}$	$\frac{E(H-V)}{E(B-V)}$	$\frac{E(K-V)}{E(B-V)}$
NGC 654			$-2.20\pm0.26$	$-2.47\pm0.26$	$-2.71\pm0.27$
NGC 663	$2.12\pm0.32$		$-2.28\pm0.25$	$-2.79\pm0.30$	$-2.99\pm0.30$
NGC 869	$1.90\pm0.13$		$-1.20\pm0.46$	$-1.75\pm0.48$	$-1.59\pm0.50$
NGC 1502	$1.74\pm0.18$		$-1.87\pm0.16$	$-2.04\pm0.23$	$-2.17\pm0.22$
IC 1805	$1.76\pm0.08$	$-1.34\pm0.04$	$-2.74\pm0.30$	$-3.30\pm0.37$	$-3.66\pm0.38$
IC 1590	$1.56\pm0.30$	$-1.33\pm0.17$
Normal	1.72	-1.25	-2.30	-2.58	-2.78

Figure 3: E(J-V), E(H-V), E(K-V) vs. E(B-V) colour-excess diagrams for the clusters IC 1805, NGC 1502 and NGC 663.

Figure 4: Same as Fig. 3 but for the clusters NGC 869, NGC 884 and NGC 654.

b) Two colour diagrams (TCDs); method "B''

In most of the cases the MKK spectral classification is available only for a few stars of the cluster, which make the CEDs quite noisy (see e.g. the CEDs of NGC 654, NGC 663, NGC 869 and NGC 884). The TCDs of the form of $(\lambda-V)$ vs. (B-V), where $\lambda$ is one of the wavelength of the broad band filters ( R,I,J,H,K,L), provide an effective method for separating the influence of the normal extinction produced by the diffuse interstellar medium from that of the abnormal extinction arising within regions having a peculiar distribution of dust sizes (cf. Chini & Wargau 1990; Pandey et al. 2000). On these diagrams the unreddened MS and the normal reddening vector are practically parallel. This makes these diagrams useless for determining the amount of reddening, but instead, very useful for detecting anomalies in the reddening law. Chini & Wargau (1990) and Pandey et al. (2000) used TCDs to study the anomalous extinction law in the clusters M 16 and NGC 3603 respectively. Figures 5, 6, 7 and 8 show TCDs for the central region of the clusters. We used the data of the central region of the clusters to reduce the contamination due to field stars. The stars apparently lying away from the general distribution are not included in the analysis. The slopes of the distribution, $m_{\rm cluster}$, are given in Table 3. The slopes of the theoretical MS, $m_{\rm normal}$, on the TCDs, obtained for the stellar models by Bertelli et al. (1994) are also given in Table 3. The errors associated with the slopes are significantly smaller than the errors obtained in the CEDs. The values of the $(\lambda -V)/(B-V)$ can be converted to the ratio $E(\lambda -V)/E(B-V)$ using the following approximate relation;

$$\frac{E(\lambda-V)}{E(B-V)}=\frac{m_{\rm cluster}}{m_{\rm nor... ...imes\left[\frac{E(\lambda-V)}{E(B-V)}\right]_{\rm normal}\cdot$$

Figure 5: (R-V) vs. (B-V) two-colour diagram. The data point shown by open circles is not included in the least-squares fit (see text).

Figure 6: (I-V) vs. (B-V) two-colour diagram.

Figure 7: (J-V), (H-V), (K-V) vs. (B-V) two-colour diagrams for the clusters IC 1805, NGC 1502 and NGC 663. The data point shown by open circles are not included in the least-squares fit (see text).

Figure 8: Same as Fig. 7 but for the clusters NGC 869, NGC 884 and NGC 654.

Figure 9: (U-B)/(B-V) two-colour diagram for the cluster NGC 663. The continuous curve represents the MS shifted along E(U-B)/E(B-V)=0.60, whereas dashed curve shows the MS shifted along a normal reddening vector. Star having $V\leq 16.0$are shown by filled circles.

 

Table 3: The slopes of the distribution of stars obtained from the $(\lambda -V)/(B-V)$ TCDs.

Cluster	$\frac{(R-V)}{(B-V)}$	$\frac{(I-V)}{(B-V)}$	$\frac{(J-V)}{(B-V)}$	$\frac{(H-V)}{(B-V)}$	$\frac{(K-V)}{(B-V)}$
NGC 654	$-0.61\pm0.02$	$-1.20\pm0.04$	$-2.16\pm0.25$	$-2.39\pm0.23$	$-2.50\pm0.25$
NGC 663	$-0.50\pm0.02$	$-1.13\pm0.03$	$-2.33\pm0.30$	$-2.73\pm0.35$	$-3.07\pm0.43$
NGC 869	$-0.60\pm0.02$	$-1.12\pm0.02$	$-1.90\pm0.10$	$-2.41\pm0.10$	$-2.53\pm0.11$
NGC 884	$-0.62\pm0.02$	$-1.06\pm0.02$	$-1.96\pm0.08$	$-2.44\pm0.08$	$-2.59\pm0.10$
NGC 1502			$-1.92\pm0.24$	$-2.04\pm0.24$	$-2.08\pm0.24$
IC 1590		$-1.36\pm0.09$
IC 1805		$-0.98\pm0.04$	$-2.12\pm0.15$	$-2.58\pm0.17$	$-2.73\pm0.18$
Normal	-0.55	-1.1	-1.96	-2.42	-2.60

c) (U-B)/(B-V) two-colour diagram and colour-magnitude diagrams; method "C''

In absence of spectroscopic observations, the (U-B)/(B-V) TCD and colour-magnitude diagrams (CMDs) are important tools to study the interstellar reddening towards the cluster as well as intra-cluster reddening.

In the case of (U-B)/(B-V) TCD a MS curve (e.g. given by Schmidt-Kaler 1982) is shifted along a reddening vector given by the ratio of $E(U-B)/E(B-V) \equiv X$ until a match between the MS and stellar distribution is found. In this method the reddening vector X plays an important role. Over the years the observational as well as theoretical studies have used (or "misused'', according to Turner 1994) a universal form for the mean galactic reddening law. However, theoretical as well as observational estimates for the reddening vector X show a range from 0.62 to 0.80 (cf. Turner 1994). Recently DeGioia Eastwood et al. (2001) also preferred a value of X=0.64 in the case of Tr 14. The variability of X indicates the variations in the properties of the dust grains responsible for the extinction. High values of X imply a dominance by dust grains of small cross sections while the small values of X indicate a dominance of dust grains of larger cross section (cf. Turner 1994). Turner (1994) raised a question about the so called reddening-free parameter Q  [=(U-B) - 0.72 (B-V)]; how can Q be reddening-free when the reddening vector X is different from 0.72?

As we have mentioned earlier, the distribution of stars in the V/(U-B)CMD of NGC 663 cannot be explained by a normal value of X (i.e. 0.72). The (U-B)/(B-V) TCD and the V/(B-V), V/(U-B) CMDs for the central region of the cluster NGC 663 are shown in Figs. 9 and 10 respectively. The data have been taken using the 105 cm Schmidt telescope of the Kiso Observatory, Japan (for details see Pandey et al. 2002). In Fig. 9, where the dashed curve shows the intrinsic MS by Schmidt-Kaler (1982) shifted along X=0.72, we find a disagreement between the observations and the MS at $(B-V)\sim 0.90$. PJ94 explained the disagreement due to the presence of pre-main-sequence (PMS) stars having UV excess. In Fig. 9 stars with $V\leq16$ are shown by filled circles. The apparent distance modulus for NGC 663 is (m-M_V)=14.4 (cf. Pandey et al. 2002); the stars with V=16 (i.e. M_V=1.6) will have mass $\sim$ $2.5 ~M_{\odot}$. Since the cluster has an age of $\sim$10⁷ yr, the stars of $\sim$ $2.5 ~M_{\odot}$should have reached the MS and no longer be PMS stars. The TCD for these stars also does not support a normal value of X. We find that the MS shifted along a reddening vector of 0.60 and E(B-V)=0.68 explains the observations satisfactorily.

The value of X in the NGC 663 cluster region can further be checked by comparing the theoretical zero-age-main-sequence (ZAMS) with the observed stellar distribution in the V/(B-V) and V/(U-B) CMDs. Once the reddening is known from the (U-B)/(B-V) CCD, the ZAMS is shifted to match the blue envelope of the observed stellar distribution in the V/(B-V) and V/(U-B) CMDs. The ZAMS fitting for E(B-V)=0.68 and apparent distance modulus (m-M_V)=14.4 is shown in Fig. 10a. Figure 10b shows V/(U-B) CMD where ZAMS, shifted for E(U-B)=0.49 (corresponding to the normal reddening vector X=0.72) and (m-M_V)=14.4, is shown by a dashed line, which clearly shows disagreement with the distribution of the stars. The ZAMS for E(U-B)=0.40 (corresponding to X=0.60 and E(B-V)=0.68) nicely fits the blue envelope of the distribution. This supports an anomalous value X=0.60 for the slope in the NGC 663 cluster region.

Figure 10: V/B-V (the left panel), V/U-B (the right panel) CMDs for the cluster NGC 663. Star having $V\leq 16.0$ are shown by filled circles. The continuous curve in left panel represents the ZAMS fitting for E(B-V)=0.68 and apparent distance modulus (m-MV)=14.4. The continuous and dashed curves in right panel shows ZAMS shifted for E(U-B)=0.40 and E(U-B)=0.49 respectively. For details see text.

(U-B)/(B-V) TCDs and V/(B-V) CMDs were used to find out the value of X in all of the 14 clusters examined in the present study. The (U-B)/(B-V)TCD for 3 clusters namely Be 62, NGC 436 and NGC 637 is shown in Fig. 11. The values of the reddening vector Xobtained from the TCD/CMDs are given in Table 4. The uncertainty in the estimated value of X arises due to uncertainties in the intrinsic colours (i.e. ZAMS), uncertainties associated with the observations and also uncertainties associated with the visual fit of the ZAMS to the observations. The typical total uncertainty in the reported values of X is estimated to be $\sim$0.05.

 

Table 4: The value of the reddening vector X=E(U-B)/E(B-V) obtained from the TCD/CMDs.

Cluster	X
IC 1590	0.72
Be 62	0.60
NGC 436	0.84
NGC 457	0.72
NGC 581	0.72
Tr 1	0.72
NGC 637	0.53
NGC 654	0.72
NGC 663	0.60
Be 7	0.72
NGC 869	0.95
IC 1805	0.72
NGC 884	0.72
NGC 1502	0.76