Determining Mass Ratio of Double Star Systems with Spectroscopy

[JeffOCA]

Hi everybody

When you have observed the complete revolution of a star around an other one, you can derive the mass of the double star system (the sum of the masses) by using the Kepler's third law. That's OK.

I have heard that you can find the mass ratio of the system by using spectroscopy. Then, with the sum and the ratio, you can derive each mass separately.

My question is : how can we determine the mass ratio with spectroscopy ?

Kind regards
Jeff

 

[Drakkith]

A more massive star will produce, in general, more light at a higher frequency than a lower mass star. The Sun for example puts out the majority of it's EM radiation in the visible wavelength I believe and so looks white. (Not yellow like most people think. That is due to atmospheric effects) In contrast, very high mass stars typically spend their lives as Blue Supergiants and put out an enormous amount of EM radiation in the UV range of the spectrum. On the other end of the scale, red dwarf's are less massive than the sun, put out less light at lower frequencies. Typically in the infrared range with the lowest mass stars. By measuring the specific output of EM radiation from a star we can make predictions about their mass.

 

[phyzguy]

I don't think this is the full answer to the OP's question. A more accurate measure of the mass ratio can be determined by measuring the Doppler shift of the two stars as they rotate around each other. The ratio of the maximum Doppler shift of the two stars will be proportional to the inverse of the mass ratio of the two stars, since the heavier star will move more slowly and the lighter star will move faster. Try this site:

http://csep10.phys.utk.edu/astr162/lect/binaries/spectroscopic.html

 

[Drakkith]

Ah, ok I see now. Once you determine the combined mass you can determine the orbits of each one using doppler shift measurements and hence the ratio.

 

[JeffOCA]

Thanks for all the answers.

Someone told me it is possible to derive the mass ratio by writing the orbital equations (or Kepler's laws i don't remember) for the two rotating stars.

What are the equations if we want to calculate the mass ratio by considering the Doppler shift ? Any source or references on the web ?

Kind regards
Jeff

 

[Drakkith]

No idea. All I can suggest is a google search.

 

[Janus]

Thanks for all the answers.

Someone told me it is possible to derive the mass ratio by writing the orbital equations (or Kepler's laws i don't remember) for the two rotating stars.

What are the equations if we want to calculate the mass ratio by considering the Doppler shift ? Any source or references on the web ?

Kind regards
Jeff

In such a case, orbital velocity for either body is found by

$$V_o = \sqrt{\frac{GM^2}{r(M+m)}}$$

where m is the body for which you finding Vo.

 

[JeffOCA]

In such a case, orbital velocity for either body is found by

$$V_o = \sqrt{\frac{GM^2}{r(M+m)}}$$

where m is the body for which you finding Vo.

Ok, but by doing this, you don't use spectroscopy at all (look first post of the thread...) ?

 

[phyzguy]

Spectroscopy is how you measure the orbital velocities. How else will you come up with V?

 

[JeffOCA]

Ok, thanks everybody !