Page 90 - analysis-and-interpretation-of-astronomical-sp

Analysis and Interpretation of Astronomical Spectra 90

Here are some orbital parameters of β Scorpii according to an earlier study by Peterson et
al. [177]. These values are based on the measured, maximum radial velocities und ,

obtained from the spectra of both components. The terms in the data list, and

for the masses, demonstrate that the inclination is unknown and therefore the

values are uncertain by this factor (for details see sect. 19.3 and 19.4).

- Spectral class of the brighter component: B0.5V, of the weaker component: unknown
- Orbital period:

- Stellar masses: , ss

- Mass Ratio:

- Max. recorded radial velocities: ,

- Major semi axes of the orbital ellipse: s s

These figures show that the mass and brightness difference is substantial. With the large
telescopes, involved in this study [177], the spectrum of the weaker component could still
be recognised, but analysed just with substantial difficulties.

19.3 The Perspectivic Influence from the Spatial Orientation of the Orbit

The orientation of the binary star orbital planes, with respect to our line of sight, shows a
random distribution. The angle between the axis, perpendicularly standing on the orbital
plane (normal vector), and our line of sight is called inclination [175]. Thus the definition

for the inclination of stellar and binary system rotation axes (sect. 16) is the same. Analogi-
cal, s is here the spectroscopically direct measurable share of the radial velocity ,
which is projected into the sight line to Earth. For we see the orbital ellipse exactly

"edge on" i.e. s .

– This elliptical orbit, with a given and fixed inclination , may be rotated freely around the
axis of the sight line, without any consequences for their apparent form.

– Thus for circular binary orbits the inclination fixes the only degree of freedom, which
affects the apparent shape of the orbit.

– For elliptical binary star orbits, the situation is more complex. In contrast to the circle,
the orientation of the ellipse axes in a given orbital plane forms an additional degree of
freedom, determining the apparent ellipse form.

vr

vr sin i i
vr sin i
Sight Line to Earth

vr

If remains unknown, the results can statistically only be evaluated, similar to the
s values of the stellar rotation (sect. 16.6).

Caveat:

There are also reputable sources that define as the angle between the line of sight and the

orbital plane, similar to the inclination angle convention between planetary orbits and the
ecliptic. Consequence: There must always be clarified which definition is used. The two
conventions can easily convert to each other as complementary angle .