please see here for earlier discussion on this:

viewtopic.php?f=2&t=13885&st=0&sk=t&sd=a&start=15

I opened a separate development thread about this matter, since there is more to come on these matters from my side.

The requirement for a supplementary Mass-Luminosity relation seems to be rather unavoidable for filling the many empty slots in the binary data base with sensible content!

Here is a general scheme of

**apparent magnitude assignments**for both components of binary star systems that I am currently exploring in an experimental manner:

The formula that 'bdm' already exposed earlier, amounts

**physicswise**to assume that the star luminosities in a multiple system are additive. In astronomy, luminosity is the amount of

**energy**a body radiates per unit time, and

**energies are additive**...

[tex]\frac{L_{AB}}{L_\bigodot} = \frac{L_A}{L_\bigodot} + \frac{L_B}{L_\bigodot}[/tex]

Here I have conveniently introduced our Sun's luminosity [tex]L_\bigodot[/tex] as a reference.

By exploiting, moreover, the approximate equality of distances [tex]d_{AB}\approx d_A\approx d_B[/tex] for far away binary systems, this relation can be simply expressed in terms of apparent magnitudes m that are of interest, here:

[tex]10^{-0.4\,m_{AB}} = 10^{-0.4\,m_A} + 10^{-0.4\,m_B},[/tex]

which is equivalent to the formula bdm used above. For the point of this discussion, let's not worry about how well this formula works in reality. At least, it is based on the sensible assumption that the component luminosities add up to give the system's total luminosity L_AB.

Next I adopt the following strategy:

I compute the apparent magnitude m_A of the A-component from a standard

**Mass-Luminosity relation**that has been extensively tested in case of binary stars with known masses:

[tex]\frac{L_{A}}{L_\bigodot} \approx \left( \frac{mass_A}{mass_\bigodot}\right )^b.[/tex]

The power b ranges between 3.0 and 4.0, depending on the mass range. b=3.5 (cf figure) is usually a good compromise. For practically all of my binaries, the mass ratios [tex]\frac{mass}{mass_\bigodot}[/tex] are known!

The standard relation between luminosity and apparent magnitude for m_A reads:

[tex]m_A = m_\bigodot -2.5\,\log_{10}\left [\frac{d_\bigodot^2}{d_A^2}\,\frac{L_A}{L_\bigodot}\right ][/tex]

hence, by inserting the Mass-Luminosity relation, we get:

[tex]m_A = m_\bigodot -2.5\,\log_{10}\left [\frac{d_\bigodot^2}{d_A^2}\,\left( \frac{mass_A}{mass_\bigodot}\right )^b\right ].[/tex]

To guarantee consistency with the apparent magnitude of the unresolved system m_AB that is always available, I finally compute m_B via the above relation expressing the additivity of luminosities:

[tex]10^{-0.4\,m_B} = 10^{-0.4\,m_{AB}} - 10^{-0.4\,m_A},[/tex]

or equivalently,

[tex]m_B = -2.5\,\log_{10}\left(10^{-0.4\,m_{AB}} - 10^{-0.4\,m_A}\right ).[/tex]

In

**summary**: This outlined scheme will assign apparent magnitudes for each of the components that automatically are consistent with the known apparent magnitude of the entire binary system. What will remain is to assert the degree of accuracy of the used

**Mass-Luminosity relation**for the Celestia binaries...

Any comments?

Fridger