Appendix A: The interstellar extinction for nearby stars

The distribution of interstellar material in the solar neighborhood is quite complex (Frisch 1994). Studies based on the colour excesses of early type stars (e.g. Lucke 1978) showed that there is a relatively clear region within 100 pc of the Sun. The accuracy of the E(B-V)  determined from the intrinsic colours of hot stars is limited by the intrinsic spread in the colours of these stars (e.g., the dependence of colour on rotational velocity, Gray & Garrison 1987).

Figure A.1: Colour excesses E(B-V) derived from their polarizations for stars within 50 pc (filled circles) as a function of distance. The open circle is the mean value derived from the polarizations of 92 stars at distances between 45 and 55 pc.

Figure A.2: Equivalent widths of Ca  II  K-line (mÅ) vs. a) distance in parsecs and b) E(B-V). The numbered stars in a) are (1) $\alpha$ Oph, (2) 2 And and (3) $\iota$ Oph. See text for reference to sources.

Interstellar dust can also be detected by the polarization that it produces. The precise polarization measurements of Tinbergen (1982) of 180 stars within 35 pc showed that in general the visual extinction (A_v) is 0.002 mag or less within this region. He did find relatively strong polarization (indicating A_v $\approx$ 0.01 mag), however, in stars in a region out to 20 pc in the direction bounded by galactic coordinates l = 350 ${\hbox{$^\circ$ }}$ to 20 ${\hbox{$^\circ$ }}$  and b = -40 ${\hbox{$^\circ$ }}$  to -5 ${\hbox{$^\circ$ }}$  and a few other isolated directions. This generally low extinction has been confirmed by Leroy (1993b) whose catalogue (Leroy 1993a) gives the polarizations of stars within about 50 pc. The 92 stars in this catalogue with distances between 45 and 55 pc have a mean percentage polarization of $23\pm2$ $\times$10^-5. Using Tinbergen's conversion factor, this corresponds to a E(B-V) of $0.0025\pm0.0002$ mag.

In Sect. 3.3, we consider ten F dwarfs that lie within 52 pc. Polarizations are given for two of these stars (HD 3268 and HD 182807) in Leroy (1993a). For the remainder, the polarizations were assumed to be similar to stars at a comparable distance and as closely as possible the same part of the sky. These polarizations were converted to E(B-V)  and are shown plotted against distance in Fig. A.1. These E(B-V)  are comparable with the mean value at 50 pc (discussed above) which is shown by the open circle. We conclude that none of these F dwarfs are in regions of unusually high extinction and that it is reasonable to derive their extinctions (Col. 8 in Table 5) from their polarizations. These E(B-V) are significantly less than those adopted by Di B98 (Col. 7, Table 5).

The interstellar Ca  II K-line is also an indicator of interstellar material, but its equivalent width correlates only weakly with E(B-V)  as is shown in Fig. A.2b where the data is taken from Welty et al. (1996). Some of the scatter may well be caused from errors in the E(B-V)  which were calculated assuming intrinsic colors. The scale height of the Ca  II K-line equivalent widths is of the order of 1 kpc (Beers 1990) which is significantly greater than that of the optical extinction and so a tight correlation is not expected. The plot of the Ca  II K-line equivalent width against distance shown in Fig. A.2a (using data from Welty et al. 1996 and Vallerga et al. 1993) shows that the line only appears in strength for stars at distances greater than 50 kpc. The only exceptions to this are stars in Ophiuchus and 2 And for which Tinbergen found significant polarization; presumably these are behind isolated local clouds. Thus the evidence from the Ca  II K-line also suggests that the region out to 50 pc is relatively clear.

Far UV lines such as those of Mg  II are also observable in such nearby stars as Sirius and Procyon in which the Ca  II K-line is not observed. Frisch (loc. cit.) uses this Mg  II strength to show that the N(H  I + H  II) column densities in front of Sirius and Procyon are 3.0 $\times$ 10¹⁷ and 1.1 $\times$ 10¹⁸ cm^-2 respectively. This assumes the same N(Mg  II)/ N(H  I + H  II) ratio as for $\eta$ UMa (42 pc) for which the hydrogen column density is known. If we assume that N(H  I + H  II)/E(B-V)= 4.9 $\times$ 10²¹cm^-2 mag^-1 (Diplas & Savage 1994), then the E(B-V)  for Sirius and Procyon are 0.00006 and 0.00022 respectively. Frisch notes that data on the EUV spectrum of the white dwarf companion to Sirius give a hydrogen column density that is an order of magnitude greater than that derived above. Even so, the E(B-V) of Sirius would be $\approx$0.001. The E(B-V) of Sirius and Procyon that are derived from their polarization are $0.0018\pm0.0013$ and $0.0005\pm0.0009$ respectively which are consistent with the low extinctions derived from the Mg  II line estimate. It has therefore seemed reasonable to use the E(B-V) derived from their polarizations for the bright stars (Sirius, Procyon etc.) described in Table 2.