A spatially resolved study of ionized regions in galaxies at different ...

160 Appendix A
where c=0.434C. This value is the reddening constant, and is found in the literature as
c(Hβ), the logarithmic extinction at Hβ (F Hβ = F Hβ0 10 −c ). We can rearrange equation A.2
as
F λ = F λ0 10 −c(λ) = F λ0 10 −c(Hβ)(1+g(λ))
(A.3)
where g(λ) = f(λ) - f(Hβ) and c(Hβ) the logarithmic extinction at Hβ, which can be written
as c(Hβ) = 0.4A Hβ . Comparing equation A.3 with A.1 and taking into account the reddening
curve ζ(λ),
g(λ) = A λ
A β
− 1 =
ζ(λ)
ζ(λ Hβ ) − 1
(A.4)
Finally, we can write the logarithmic extinction at any wavelength c(λ) as a function of
the reddening curve
c(λ) = c(Hβ)(1 + g(λ)) = c(Hβ) ζ(λ)
ζ(λ Hβ )
(A.5)
We can also write the constant of reddening in terms of the color excess
c(Hβ) = 0.4A Hβ = 0.4ζ(λ Hβ )R V E(B − V )
(A.6)
Taking into account the reddening law of Cardelli et al. (1989) and a value of R V = 3.1,
we obtain A Hβ /A V = ζ(λ Hβ ) = 1.164, which allows to write the reddening constant as a
function of the color excess as c(Hβ) = 1.443 E(B-V).
Another way of estimating the extinction is by relating the visual extinction to the
observed ratio of two lines. This method is useful when only Hα and Hβ are available. The
relation is given by:
and re-arranging it gives
F Hα
F Hβ
= F Hα0 · 10 −0.4A Hα
F Hβ0 · 10 −0.4A Hβ
= F Hα0
F Hβ0
· 10 0.4 A Hβ −A Hα
A V
·A V
(A.7)
A V = 2.5 ·
( )
FHα /F
log Hβ
10 F Hα0 /F Hβ0
A Hβ −A Hα
A V
(A.8)