Extinction by cosmic dust is highly wavelength dependent and hence can change observed line flux ratios significantly away from the intrinsic (i.e. emitted) values. This provides a classic method for determining the amount of dust extinction along the line of sight to a particular emission line region. The relative ratios of the Balmer lines of hydrogen are often used as extinction indicators due to the fact that they are observationally convenient (being in the optical band), strong and their intrinsic relative flux ratios are fairly well determined from atomic theory.
In the case of Balmer lines from AGN, one would ideally deblend the lines into kinematically distinct components, e.g. a broad component (from the BLR) and a narrow component (from the NLR). One could then obtain information about the extinction through to each component. However, high-resolution data is required to facilitate the deblending. To avoid introducing uncertainties due to the deblending procedure we choose to use the total Balmer decrements: thus, the extinction estimates below should be considered as average values over all of the emission line regions.
Table 2: Balmer decrements and inferred extinction for MCG-6-30-15. See
text for a discussion of the significance and possible causes of
differences between E(B-V) as calculated from difference Balmer
decrements. The figures in brackets are the allowed range of the parameter
given the various systematic effects discussed in the text.
Table 2 gives the observed Balmer decrements and the expected intrinsic value based upon the assumption of case-B recombination. These decrements have been converted into the reddening, E(B-V), using the standard interstellar extinction curve of Osterbrock (1989). This interstellar extinction curve leads to the expression
where 
is the observed Balmer decrement, 
is
the intrinsic Balmer decrement and a is a constant which is given in
Table 2 for the three Balmer decrements quoted. Table 2 also associates a
hydrogen column density, 
, with this reddening. This is given
by (Heiles, Kulkani & Stark 1981)
and is the column density of cold gas that would be present under the assumption that the nature of the dust and the cold-gas/dust ratio is the same as is found locally in our Galaxy.
The calculation of the uncertainties in E(B-V) deserves discussion. We must critically consider both the observational uncertainties and the intrinsic nature of the source.
First, we consider observational uncertainties. The H 
line and
H 
line were measured in different spectrographs, the data from which
have undergone independent reduction and calibration. This will introduce
some uncertainty into the H /H Balmer decrement: in Section
2.1 we estimated that both the red and blue spectra have absolute
normalizations which are uncertain to 
per cent (with these two
uncertainties being independent). This leads to a 4-5 per cent in the
H /H Balmer decrement, corresponding to an error on the
reddening of 
. The H ,
H 
and H 
lines all appear in the data from the same spectrograph
and so the two independent Balmer decrements that can be formed from these
three lines are not sensitive to uncertainties in the overall
normalization. However, H and H do suffer from potentially
significant observationally-related uncertainties. The H line is
blended with the [OIII] 
line and so an unambiguous
determination of the H flux, 
, is difficult without
higher resolution data. By examining extreme cases, we can conservatively
bracket to the range 
.
The corresponding range of inferred reddening is
0.56-1.72. The H flux, 
, is
uncertain due to the fact that it is weak compared with the local continuum
and so is sensitive to the modeling of that continuum. By examining
extreme cases, we can conservatively bracket to 
. The corresponding range of inferred extinctions is
0-1.47.
Secondly, we must consider the possibility that the intrinsic Balmer
decrements are not well represented by their case-B recombination limits.
Deviations from case-B values can occur due to collisional effects and
radiative transfer effects which are especially important in the
high-density gas found within the BLR. Theoretically, these processes can
increase the H /H decrement from the case-B value to 10 (Kwan
& Krolik 1981) or more (Canfield & Puetter 1981). In these extreme
cases, we would not have to postulate any dust reddening towards the
emission line regions of MCG-6-30-15 at all. However, observations of
other Seyfert 1 nuclei which are thought to be unreddened suggest that
intrinsic H /H decrements do not exceed 4 (e.g. Malkan 1983;
Wu, Boggess & Gull 1983). Using this value of the H /H
ratio instead of the case-B value decreases the inferred reddening from
E(B-V)=1.02 to E(B-V)=0.67. Including the uncertainty in the measured
H /H ratio, the lower limit to the reddening is
E(B-V)=0.61. The effect of deviations from case-B recombination on the
intrinsic H /H and H /H have not been
investigated in as much theoretical detail as for H /H .
However, the corresponding uncertainties on the reddening are likely to be
insignificant compared with the observational uncertainties discussed
above.
To summarize these Balmer decrement studies, the large H /H
ratio suggests a reddening in the range E(B-V)=0.61-1.09. This is
compatible with the reddening inferred from H /H and
H /H although these two Balmer decrements have large
uncertainties due to line blending and the modeling of the
continuum. Assuming that the cold-dust/gas ratio is similar to that
observed locally in our Galaxy, the column density of gas associated with
this reddening is in the range 
.