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Analysis and Interpretation of Astronomical Spectra 93

20 Balmer–Decrement

20.1 Introduction

In spectra where the H-Balmer series occurs in emission, the line intensity fades with

decreasing wavelength . This phenomenon is called the Balmer-Decrement D. The inten-

sity loss is reproducible by the laws of physics and is therefore a highly important indicator
for astrophysics. The hydrogen emission lines are formed by the electron transitions, which
end, as well known, in "downward direction" on the second-lowest energy level . The

probability, from which of the higher levels an electron comes, is determined for the indi-
vidual lines by quantum mechanical laws. From this it follows that the intensity is highest

at the line and gets continuously weaker at the shorter wavelength lines, , , ,

, etc. The extent of this decrease (decrement) is additionally, but only moderately, de-

pendent on the density and temperature of the electrons and .

20.2 Qualitative Analysis
For most amateurs probably qualitative applications of this effect are in the focus. On a low-
resolution spectrum of P Cygni (DADOS 200L), the intensity-decrease of the dominant hy-
drogen emission lines, normalised on a unified continuum intensity, is demonstrated.

Balmer – Decrement P Cygni Hα

Hβ

Hδ Hγ

Contrary to this trend Mira (o Ceti) shows only Hδ, and significantly attenuated, Hγ in emis-
sion. These impressive lines indicate what enormous intensities the Hα and Hβ-Balmer
emissions should really show, according to the Balmer-Decrement. But towards the long-
wave region, starting from ca. , these lines get, like almost all other discrete absorptions,
increasingly overprinted by titanium oxide vibration bands (TiO). This effect generates an
unusual, negative Balmer-Decrement, because TiO arises obviously in higher layers of the
stellar atmosphere, as the H emission lines, details see [33].

Balmer – Decrement Mira, o Ceti

Hδ Hγ TiO

TiO TiO TiO TiO
TiO
TiO
TiO