Page 92 - analysis-and-interpretation-of-astronomical-sp

Analysis and Interpretation of Astronomical Spectra 92

s

If both lines can be analysed, then with the obtained und the corresponding radii
and can be calculated separately.

Calculation of the Stellar Masses in SB2 Systems

If both lines can be analysed, then with the following formula the total mass of the system
, can be determined. This is obtained if {44}, changed as a sum of radii , is

used in the formula of the third Kepler's law, instead of the semi-major axis .

. with the partial radii

The partial masses can then be calculated by their total mass
and

For binary star systems is often expressed in solar masses and the distance in AU.
To convert:

Calculation of the Stellar Masses in SB1 Systems

The analysis of only one line has logically consequences on the information content and ac-
curacy of the system parameters to be determined. For SB1–systems in the spectrum, only
the radial velocity curve of the brighter component can be analysed, and therefore just

the amplitude can be determined. So with formula {44}, only the corresponding orbital

radius can be calculated. Unfortunately, neither their total mass nor their partial masses

, are directly determinable. Just the so called mass function , can be deter-

mined [51 sect. VI], [179]. This expression is not really demonstrative and means the cube
of the invisible partial mass in relation to the square of the total mass . For

a calculated example, see [171].

s
,

It can be roughly determined eg by estimation of the visible mass by the spectral type.
For a rough guide refer to the table in sect. 14.5. Such results still remain loaded with the
"uncertainty" of s .