Introduction to Stellar, Galactic, & Extragalactic Astronomy
Lecture 8: Binary Stars: Stellar Masses & Radii
- Types of Binary Stars:
- Can only measure masses for Binary Stars
- Radii are measured for very few stars
- Chance projection of two distinct stars along the line of sight.
- Often at very different distances.
True Binary Stars:
- A pair of stars bound together by gravity.
- Orbit each other about their center of mass.
- Between 20% and 80% of all stars are binaries
Types of Binaries
- Can see both stars and follow their orbits over time.
- Cannot separate the two stars, but see their orbit motions
as Doppler shifts in their spectral lines.
- Can separate the stars, but see the total brightness drop when
they periodically eclipse each other.
Two stars orbiting about their center-of-mass.
Center of Mass
Two stars orbit about their center of mass.
Here are two movies showing
visual binary stars, one with a circular orbit, the other with an elliptical
orbit, emphasizing the point about their orbits around their common center
of mass in all cases.
- Measure semi-major axis, a, from projected orbit & the
- Relative positions about the center give:
M1/M2 = a2/a1
Newton's Form of Kepler's Third Law:
- Measure the period, P, by following the orbit.
- Measure semi-major axis, a, and the Mass Ratio,
M1/M2, from the projected orbit on the sky.
- Solve the equation above and separate Masses.
We need to follow the orbits long enough to trace them out in detail:
Everything depends on knowing the distance:
- This can take decades
- Need to work out the projection on the sky
Small errors add up quickly.
- semi-major axis depends on d
- derived mass depends on d3
Most binaries are too far away to be able to see both stars separately.
But, you can detect their orbital motions by the periodic
Doppler shifts of the spectral lines:
- Determine the orbit period & size from the pattern of
Here is a movie showing
a spectroscopic binary star.
Cannot see the two stars separately:
Everything depends critically on knowing the distance.
- Semi-major axis must be guessed from the orbit motions.
- Can't tell how the orbit is tilted on the sky
Two stars orbiting nearly edge-on to our line-of-sight.
With the best data, one can find the masses of the stars without
having to know the distance!!!
- See a periodic drop in brightness as one star eclipses the other.
- Combine with spectra which measure orbital speeds
Here is a movie showing
an eclipsing binary star and its light curve.
Eclipsing Binary stars are very rare.
Measurement of the light curves is complicated by details:
- Partial eclipses yield less accurate numbers.
- The atmospheres of the stars soften the edges.
- Close binaries can be tidally distorted.
From a combination of visual and eclipsing binaries, masses are
known for about 150 stars.
Range: ~0.1 to 50 Solar Masses
Radii are very difficult to measure because stars are so far away.
Radii have only been measured for about 25 stars.
- Eclipsing binaries (need distance)
- Interferometry (single stars)
- Lunar Occultation (single stars)
Advances in optical interferometry should greatly increase that number in the