5 Non-standard reddening laws

The reddening determination method presented in the previous section does not take into account the possibility of a non-standard reddening law. We will now address the following question: can we determine whether or not the reddening of a star observed with the XMM-OM is anomalous? To answer this, we integrated the same spectra with alternative values of R_V. Instead of R_V=3.1, --the standard value for diffuse interstellar medium and average value for the LMC--, we used R_V=2.6 and R_V=5.5 (observed by Cardelli et al. 1989, in the direction of HD204827 and HD37022 respectively). We also considered the peculiar UV absorption law established by Prévot et al. (1984) for the SMC. This reddening law does not show any absorption bump around 2175 Å. It is specific to the ultraviolet and was thus only applied to the UV filters.

Figures 6a and 6b show the resulting (u-b) vs. (b-v) and (u-uvw1) vs. (b-v) colour diagrams in the R_V=5.5 case. Let us consider a 15000 K star affected by 2 magnitudes of absorption (in V) with a reddening law characterized by such a high value of R_V and let us see what will happen if we try to interpret the observed colours assuming a classical reddening law with R_V=3.1. In the (u-b) vs. (b-v) diagram, the colours mimic those of a slightly hotter star, affected by hardly more than one magnitude of absorption but in (u-uvw1) vs. (b-v), the star falls out of the "authorized'' range of colours. This discrepancy will clearly reveal that the assumption was wrong and that the star suffers from a peculiar absorption law. Figure 6 thus reveals that (u-uvw1), (b-v) and (u-b) can be used to determine $T_{\rm eff}$, A_V and R_V just as Fig. 4 shows that (u-uvw1) vs. (b-v) can be used to determine $T_{\rm eff}$ and A_V once R_V is known.

Of course, peculiar absorption laws also influence $ic_{\rm0}$ and $ic_{\rm red}$. As expected from Fig. 6, the colour excess ratios are reddening law dependent. Considering $0 \leq A_V \leq 4.$, we found the mean value of E(uvw2-uvw1) /E(u-uvw1) to vary between -2.83 and -3.68 for $R_V \in[2.6;5.5]$ (the value for the Prévot et al. 1984 reddening law is -3.04). Consequently, the appropriate ($ic_{\rm0}$,  $ic_{\rm red}$) has to be used once R_V has been determined. Figure 5b shows the influence of the reddening law variations on the ($ic_{\rm0}$,  $ic_{\rm red}$) diagram through comparison between $ic_{\rm0}=0.6$ sections performed in the various realizations of that diagram.

As a conclusion, regarding the reddening determination, the main advantages of the XMM-OM UV filters are that

• at equivalent photometric accuracy, they allow a better determination of the amount of interstellar extinction than what is achievable with the optical filters only;
• they allow discrimination between standard and non-standard extinction laws; this is of primary importance since interpretation of X-ray data requires knowledge of the column density along the line of sight, what is often estimated through reddening measurements (e.g. Bohlin et al. 1978).