Page 89 - analysis-and-interpretation-of-astronomical-sp

Analysis and Interpretation of Astronomical Spectra 89

The above introduced formulas for the Doppler shift allow, after a simple change, to cal-
culate the sum of the radial velocities with the line splitting . For the general

case:

The Calculation of the Individual Radial Velocities and

If the mass difference is large enough, the splitting of the ∆λ1 ∆λ2
spectral line occurs asymmetrically with respect to the neu-
tral wavelength . With these uneven distances and

and by analogy to {39} the individual radial velocities
can be calculated separately [172].

As a result of the heliocentric radial movement of the entire λ1 λr0 λ2

star system [100], the wavelength of the "neutral",

unsplitted spectral line is shifted by the Doppler Effect from the stationary laboratory wave-
length to [170].

This is now the adjusted reference point for the measurement of the two distances , .
But first the , values must be heliocentrically corrected to , according to [30], sect.
10.3, step 7. Then it follows:

,,

If no asymmetry occurs of the splitted line with respect to , and are approximately
equal and the sum of the two radial velocities just needs to be halved.

2. Double stars with only one component in the spectrum – SB1–systems

In most cases the apparent brightness difference between the two components is signifi-
cantly . Here with amateur equipment, only the spectrum of the brighter star can be

recorded. Extreme cases are entirely invisible black holes as double star components, or
extrasolar planets, which shift the spectrum of the orbited star by just a few dozen me-
ters/sec! In such cases, a splitting of the line isn’t recognisable, but only the shift of to

the right or left in respect of the neutral position .

The following example, recorded with λr0 Adjusted reference point
DADOS 900L/mm shows this effect,
using the spectroscopic A components
within the quintuple system β Scorpii. 08.18.2009 22‘00 UTC 08.15.2009 22‘00 UTC
Impressively visible is here the Hα-shift ∆λ = –1.37Å = –63 km/s ∆λ = +1.71Å = +78 km/s

of the brighter component, within three
days. With this Vspec plot just this ef-
fect shall be demonstrated. A serious
investigation of the orbital parameters
would require the recording of multiple
orbits at least at daily intervals! The line
shifts are plotted here with respect to
. The X-axis is scaled here in Doppler

velocity, according to [30], sect. 19,
and allows a rough reading of the radial
velocity. The values , have been determined by Gaussian fit on the heliocentrically cor-
rected profiles. Detailed procedure see [30] sect. 24.2.