Two different extinction curves are used: the Milky Way extinction law (MW) given by Seaton (1979) and Howarth (1983) and the Large Magellanic Cloud one (LMC) given by Howarth (1983). The main parameters of both laws are given in Table A1.
k(H)-k(H) | k(H)-k(H) | R=k(5464Å) | k([OII]3727) | k(1700Å) | |
MW | - 1.25 | 0.45 | 3.2 | 4.67 | 7.80 |
LMC | - 1.18 | 0.48 | 3.2 | 4.86 | 9.54 |
Calzetti | - 0.58 | 0.23 | 2.7 | 3.46 | 5.10 |
A1. Dust Extinction Corrections to the Continuum Fluxes
Calzetti and collaborators developed an empirical method to estimate the UV extinction (Calzetti, Kinney and Storchi-Bergmann, 1994). They found that the power-law index in the ultraviolet defined as F_{} ^{} is well correlated with the difference in optical depth between H and H defined as _{B}^{l} = ln{[F(H) / F(H)] / 2.86} where F(H) and F(H) are the intensities of the H and H emission lines respectively. This correlation, which is linear and independent of the adopted extinction law is given by,
(A1) |
The parameter is obtained by fitting the power law to the IUE ultraviolet spectra. Calzetti et al. (1994) and Meurer, Heckman and Calzetti (1999) values of are presented in Table 2 as well as our estimate for CAM0840, CAM1543, TOL1247, ESO572 and MRK309.
The effect of reddening using different dust spatial distributions can be estimated from Equation A1 by comparing ultraviolet with optical spectra. Calzetti et al. (1994) estimate the optical depth _{} by solving the transfer equation for five different geometries, uniform or clumpy dust screen, uniform or clumpy scattering slab and internal dust. The uniform dust screen constitutes the easiest case where the optical depth is related to the visual extinction by
where E(B - V) is the colour excess and k() is the extinction law. For the other geometries, apart from the assumed extinction law, the optical depth is a function of dust parameters such as the albedo, the phase parameter or the number of clumps. After comparing synthetic extinction corrected spectra with observations of emission line galaxies Calzetti et al. (1994) conclude that none of the adopted geometries combined with the standard MW and LMC extinction laws could explain the observed tight relation between _{B}^{l} and and proposed an empirical extinction law obtained from IUE spectra of a sample of nearby starburst galaxies.
Calzetti et al. (1994) created 6 different templates averaging galaxies with the same amount of dust (judging by their Balmer decrements). The template with _{B}^{l} = 0.05 is taken as the reference one (free of dust). An optical depth, _{n}(), is calculated for each template by comparing the observed fluxes, F_{n}() and F_{1}(),
(A2) |
where the subindex 1 corresponds to the dusty free template and the subindex n corresponds to the n template. For each template a rescaled optical depth can be defined
(A3) |
Averaging this quantity, Calzetti et al. (1994) found an extinction curve, Q() which can be transformed to k() (e.g. Seaton, 1979) by,
(A4) |
where the difference k(H) - k(H) is given by the Seaton (1979) extinction curve. The observed ultraviolet flux is related to the emitted one by,
(A5) |
where k() is given by [Calzetti 1999]
(A6) |
valid for the range 0.12 µm < < 0.63 µm.
The obtained extinction curve can be considered as an average of the different dust distributions described by Calzetti et al. (1994).
In order to correct the ultraviolet flux using this procedure it is necessary to estimate Av from the observed H / H ratios and then apply Equation A6 to the observed ultraviolet fluxes. Physically this correction is understood assuming that the ionized gas is more affected by extinction than the stars which are producing the observed UV flux [Calzetti et al. 1994].
No corrections were applied to the IR data.
The different extinction curves are plotted in Figure A1.
Figure A1. Adopted extinction curves. The solid line is the empirical relation given by Calzetti (1999). The dashed line is the curve for the MW (Seaton 1979 and Howarth 1983) and the dot-dashed line is the curve for the LMC [Howarth 1983]. |
A2. Dust extinction corrections to the Emission Line Fluxes
Extinction affects the emission lines in different degrees depending on wavelength. Corrections are usually obtained from the observed ratio of Balmer lines, the intrinsic ratio, and an adopted interstellar extinction curve.
The ratio between the intensity of a given line F() and the intensity of H, F(H) can be expressed by:
(A7) |
where the difference k() - k(H) is tabulated for different extinction laws (Table A1). The total visual extinction Av, depends on the observed object (see Table 2). The subindex o indicates the unreddened values. We use as reference the theoretical ratio for Case B recombination F_{o}(H) / F_{o}(H) = 2.86 and F_{o}(H) / F_{o}(H) = 0.47 [Osterbrock 1989]. The observed flux ratios can be expressed as a function of the theoretical ratios and the visual extinction,
(A8) |
This Equation was used to analyze the presence of an underlying stellar population in Section 5.1.