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Analysis and Interpretation of Astronomical Spectra 65

15.6 Radial Velocities of Nearby Stars

The radial velocities of stars in the vicinity of the solar system reach for the most part only
one-or two-digit values in [km/s]. Examples: Aldebaran +54 km/s, Sirius –8.6 km/s, Betel-
geuse +21 km/s, Capella +22 km/s [100].

The corresponding shifts of are therefore very low, usually just a fraction of a 1Å. For
and based on the Hα line (6563 Å), corresponds to ~46 km/s (formula {16}).

Therefore highly-resolved and accurately calibrated spectra are necessary.

15.7 Relative Shift within a Spectrum caused by the Doppler Effect

Textbook examples for this effect are the so-called P Cygni profiles (sect. 5.6). For the de-
termination of the expansion velocity of the stellar envelope neither an absolutely wave-
length calibrated spectrum nor a heliocentric correction [30] is required. The measurement
of the relative shift between the absorption and the emission part of the P Cygni profile is
sufficient. For P Cygni this displacement within the Hα line amounts to some 4.4 Å, corre-
sponding to an expansion velocity of ~200 km/s [33].

15.8 Radial Velocities of Galaxies

In the area between the galaxies, which means outside of strongly gravitational acting sys-
tems, the cosmologically induced expansion of the so-called space-time lattice gets more
and more dominant and the kinematic peculiar motion of the galaxies increasingly negligi-
ble. This effect must always be taken into account by the interpretation of extragalactic
spectra. In the relative "near vicinity" up to some 100 Mega Parsec or 1 bn ly – which also
includes Messier's galaxies-world – it still needs to distinguish between the components of
the kinematic Doppler Effect, due to the peculiar motion, and the relativistic cosmological
redshift, caused by the expansion of the spacetime. This way, six of the 38 Messier-
galaxies tend to move – against the "cosmological trend" – ie with blue-shifted spectra, to-
wards our Milky Way! These include M31 (Andromeda) with about –300 km/s, and M33
(Triangulum) with some –179 km/s [101], see table sect. 15.10.

Georges Lemaître (1894 – 1966, picture Wikimedia) and Edwin Hub-
ble (1889-1953), are considered the discoverer of the expanding uni-
verse. Independent of each other they postulated, based on a statisti-
cally rather small basis of just 18 galaxies [431], in relation to the
photometrically determined distances D, an approximately propor-
tional increase of the redshift , and the associated radial velocity .

Today, the proportionality factor is called Hubble Parameter. Because nowadays it is

known that , considered over the time, doesn't remain a constant, this term has re-

placed the historically used term "Hubble Constant ". The current value for was first

determined in the so-called Key Project with the Hubble Space Telescope HST and

2012 improved with the Spitzer Space Telescope in the mid infrared. As the cause of the
progressive redshift, Hubble, in contrast to Lemaître, firstly still believed to the Doppler ef-
fect, as a result of a purely kinematic expansion. That's why, even today, the term "escape
velocity" is still in use. Today, however, it seems clear that, from a distance, longer than
some 100 mega parsecs, the cosmological spacetime expansion dominates and the phe-
nomenon of redshift has here nothing more to do with the Doppler effect! Due to the ex-
pansion- and curvature of space, in this extreme distance range, the classical notion of dis-
tance, measured in light years [ly] or parsec [pc], gets increasingly problematic and the
Hubble law as about >400 Mpc or , should no more be applied proportionally, ie