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Analysis and Interpretation of Astronomical Spectra 95

20.4 Quantitative Definition of the Balmer-Decrement is

For most astrophysical analysis the measured intensity ratio of the Hα and Hβ lines
required. This corresponds to the quantitative definition of the Balmer-Decrement:

{50}

20.5 Experiments with the Balmer-Decrement

The following graph shows the Balmer-Decrement of P Cygni, recorded with the DADOS
spectrograph. Once the decrements are referred to a radiometrically corrected profile (red),
which corresponds to the intensity profile of a B2 II star from the Vspec library, and once
based on a continuum with a normalised energy flow (blue). Due to the low spectral resolu-
tion the labelled decrements are intensity values , directly measured in the strongly
reddened P Cygni profile and subsequently divided by the corresponding Hβ intensities

.

Irel Hβ Hα

Hγ 1 1.8
Hε 5

0.5

1 λ
0.3

Flux normalised continuum

Within the intensity-normalised, blue profile, the roughly determined decrements match
pretty well to the spread of the accepted values –> for (Hα)/ (Hβ) between 4.3 – 5. The

red profile, represents approximately the intensity course of the original- and unattenuated
spectrum. It shows however drastically different and physically even impossible decrement
values. The defined Balmer-Decrement is here only 1.8, ie substantially

lower than !

The theoretical Balmer-Decrement is based on the probabilities for certain electron

transitions, determined by the laws of quantum physics. This statistical regularity (sect.
20.3) is overprinted here in the red-, radiometrically corrected profile by the blackbody-like

distributed and wavelength-dependent radiation intensity of the star, i.e. The

intensity of the individual emission lines depends in stellar atmospheres, inter alia on the
number of the occurring direct- or resonance absorptions and thus also on the photon den-

sity at the corresponding wavelength . In this respect, the blue, intensity-normalised pro-

file behaves here neutrally, due to

If a continuum is present, also in the professional sector, the Balmer-Decrement is deter-
mined by the EW-values and therefore also based on an intensity-normalised profile. At the
example of extra-galactic spectra this is demonstrated in The Balmer-Decrement of SDSS
Galaxies, by Brent Groves et al. [210].