|Annu. Rev. Astron. Astrophys. 1992. 30:
Copyright © 1992 by Annual Reviews. All rights reserved
2.5 Reddening and Extinction
In principle the determination of R = A / EB-V requires the knowledge of the extinction and the color excess. Using cluster galaxies Sandage (1976) has illustrated how standard candles can be used to determine R. Depending on the dust properties the value of R can change arbitrarily, but within the Galaxy variations of R appear to be marginal. Because of the width of the B and V passbands, R changes somewhat with spectral type. For example, if RB = 4.2 for an O-type star, then RB = 4.9 for an M-type star (Buser 1978). R. Buser (private communication) has calculated RB from the well observed maximum-light spectrum of the type Ia SN 1981B (Branch et al 1983) on the assumption of a 1/ extinction law and has found that RB would be nearly the same as for a late O-type star.
In spite of this expectation there are clear indications that R is surprisingly small for SNe Ia (Joeever 1982; Tammann 1982, 1987; Capaccioli et al 1990). For instance, the observed color range of SNe Ia at maximum is at least 0.8 mag, which with RB = 4 corresponds to a range in AB of 3.2 mag, which is clearly not the case. The generally small effect of extinction can also be seen by comparing Equations 1 and 2 below.
As an illustration one may use the SNe Ia in the Virgo cluster (Table 2), two of which are in elliptical galaxies and four in spirals. The latter are on average 0.18 mag redder and 0.35 mag fainter. These admittedly incomplete data thus suggest RB = 2. The three galaxies with two SNe Ia (Table 1) are all of spiral type. The fainter supernova in each galaxy is 0.35 mag redder and only 0.43 mag fainter on average than its bright counterpart. This suggests RB = 1.2.
A more solid test for R is provided by the Hubble diagram for SNe Ia. A value of RB = 4 would drastically increase the scatter about the Hubble line. Using 14 field SNe Ia with color information, LT92 have found from a least-squares solution R = 0.7 ± 0.1 (which is unphysical), whereas the 17 SNe Ia with colors from the sample of MB90 give R = 1.3 ± 0.2.
A powerful test for R is in principle provided by a plot of (B - V) versus (B - H) (LT92). While (B - V) measures the color excess, (B - H) measures essentially the extinction AB, because AH is small (AH = 0.11 AB (Elias et al 1985). So far only four SNe Ia have measured values of (B - H) at tB = 0 (L88), but they already require a low value of R. While these objects have a range in (B - V) of 0.35 mag, the range in (B - H) is only 0.16 mag, implying a range in AB of 0.18 and R = 0.5.
The large extinction corrections one would obtain with RB = 4 could be avoided by assuming a redder color (B - V) for SNe Ia at maximum, i.e. (B - V) = 0.0 or 0.1 instead of -0.15. There are, however, too many SNe Ia observed with negative (B - V) for this solution to be acceptable. The available observations strongly indicate a low value of R for SNe Ia. As a compromise value we adopt throughout this paper RB = 1.5 and RV = 0.5.
Why is R for SNe Ia so small? One might think of the following possibilities.
The very small value of R required by the available SN Ia data remains a mystery awaiting future resolution.
van den Bergh & Pazder (1992), Della Valle & Panagia (1992), and van den Bergh & Pierce (1992) recently have investigated the dispersion in the SN Ia absolute magnitudes on the assumptions of 1. a unique SN Ia color at maximum, 2. error-free observed colors, and 3. a unique value of R. The large extinction corrections applied by these authors produce a larger dispersion in absolute magnitude than we have found here. However, the large extinction corrections also have the dubious property of producing superluminous SNe Ia, while none were present before extinction corrections were applied. Rather than putting all of the ``blame'' on the absolute-magnitude dispersion, one should consider simultaneously the possibilities of a range in intrinsic color, errors in the colors, and a range in the value of R.