Page 110 - analysis-and-interpretation-of-astronomical-sp

Analysis and Interpretation of Astronomical Spectra 110

24 Spectroscopic Parallax

24.1 Spectroscopic Possibilities of Distance Measurement

Distances can spectroscopically be determined either with the spectroscopic parallax or in
the extragalactic range, with help of the Doppler-related redshift, combined with the Hub-
ble’s Law (sect. 15.8). These methods are supplemented by radar and laser reflectance
measurements (solar system), the trigonometric parallax (closer solar neighborhood) and
the photometric parallax (Milky Way and extragalactic area). The latter is based on the
brightness, compared with precisely known, so-called "standard candles" as Cepheids and
supernovae of type Ia.

24.2 Term and Principle of Spectroscopic Parallax

The spectroscopic parallax allows the rough distance-estimation to a star, based solely on
the spectroscopically determined spectral class and photometrically measured, apparent
brightness. Therefore the term "parallax" is here a misnomer. However, it is correct for the
trigonometric parallax. This corresponds to the apparent shift of the observed celestial body
relative to the sky background, caused by the Earth's orbit around the sun. The principle of
spectroscopic parallax works similar to the photometric parallax. The absolute magnitude
of an object is generally defined for the distance of 10 parsecs [pc] or 32.6 light years [ly].
This value is first compared with the actually measured, apparent brightness, enabling the
calculation of the distance. Applying the spectroscopic parallax, the absolute brightness of
a star is determined by its spectral class.

24.3 Spectral Class and Absolute Magnitude

The following table shows the values of the absolute magnitudes for the main sequence
stars (V) from a lecture at the University of Northern Iowa http://www.uni.edu/. Their devia-
tion, in comparison with known literature values, remains, for our purpose, within accept-
able limits. For instance, the table value for the spectral class G2V does 5.0M, compared to
the literature value for the sun of 4.83M. For the giants (III) and supergiants (I), I have col-
lected some literature values of known stars from different sources in order to give an im-
pression of the magnitude and the enormous spread. At these luminosity classes no usable
conjunction with the spectral classes can be recognised. Further supergiants of early spec-
tral classes are often spectroscopic binaries. These facts also drastically demonstrate the
limitations of this method. Therefore the determination of the distance, applying the spec-
troscopic parallax is, at least for amateurs, restricted to main-sequence stars. To find In the
annex to Gray/Corballi [4] is a calibration table of the absolute magnitudes for all spectral-
and luminosity classes of the MK System.

Spectral Main Sequence (V) Giants (III) Supergiants (I)
Class

O5 –4.5

O6 –4.0

O7 –3.9

O8 –3.8 Meissa, λ Ori –4.3

O9 –3.6 Iota Ori –5.3 ζ Ori, Alnitak –5.3

B0 –3.3 Alnilam, ε Ori –6.7

B1 –2.3 Alfirk, β Cep –3.5

B2 –1.9 Bellatrix, γ Ori –2.8