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Analysis and Interpretation of Astronomical Spectra 85

18.4 Temperature Determination Based on Individual Lines

Generally these methods are based on the temperature dependency of the line intensity
. However, according to sect. 6.2, the intensity and shape of the spectral lines are

determined by many other variables, such as element-abundance, pressure, turbulence,

metallicity Fe/H and the rotation speed of the star. Similar to the determination of the rota-
tion velocity (sect. 16), all such methods must therefore be able to significantly hide such
interfering side influences or analyse lines, which are specifically sensitive to temperature
[11]. If the temperature should not only be "estimated" but rather accurately "determined",
therefore relatively sophisticated methods remain, based on high-resolution spectroscopy
and detailed analysis of especially temperature-sensitive, non ionised metal lines of the late
spectral classes K – M. A representative impression provides [190], [191], [191b]. Here,
ratios are calculated with the relative line depths of differently temperature-

sensitive metal absorptions [11]. These are subsequently calibrated in respect of known
values (LDR Line Depth Ratio). This way an accuracy of a few Kelvin can be achieved.

With a longer lasting temperature monitoring, eg the detection and even measurement of
giant dark sun spots is possible, typically observed at the late spectral type K [191b].

18.5 The “Balmer-Thermometer“ Hβ 4861
The temperature determination, based on Hβ 4861
the intensity of the H-Balmer lines, is often
called "Balmer-Thermometer". This method O9
is rather rudimentary, but it provides an in-
teresting experimental field. The H-lines are 25‘000 K
well suited, because the stellar photo-
spheres of most spectral classes consist to B1
>90% of hydrogen atoms. Only this element
can exclusively be detected and evaluated 22‘000 K
over almost the entire temperature se-
quence (classes O – M). B7
In contrast, ionised calcium Ca II appears
only within the spectral classes A – M. The 15‘000 K
often proposed sodium double line D1,2 is
analysable just at type ~F – M because Na I A1
becomes ionised at higher temperatures and
Na II absorptions appear exclusively in the 10‘000 K
UV range of the spectrum. In the earlier
spectral classes, Na I is therefore always of A7
interstellar origin and hence useless for this
purpose. 7‘550 K
The graphic on the right shows the intensity
profile of the Hβ line – a cutout of the over- F0
view to the spectral sequence in sect. 13.8
and [33]. From all Balmer lines, this absorp- 7‘030 K
tion can be observed within the largest
wavelength range. At this low resolution, it F5
remains analysable, even in the long wave-
length region, down to about K5. The maxi- 6‘330 K
mum intensity is reached at the spectral
class A1. The quantum-mechanical reasons G2
for this effect are discussed in sect. 9.2.
5‘700 K

G8

4‘990 K

K2

4‘290 K

K5

3‘950 K