Astronomy 162:
Introduction to Stellar, Galactic, & Extragalactic Astronomy

# Lecture 8: Binary Stars: Stellar Masses & Radii

## Key Ideas:

• Types of Binary Stars:
• Visual
• Spectroscopic
• Eclipsing
• Can only measure masses for Binary Stars
• Radii are measured for very few stars

## Binary Stars

Apparent Binaries:
• 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

Visual Binary:
Can see both stars and follow their orbits over time.
Spectroscopic Binary:
Cannot separate the two stars, but see their orbit motions as Doppler shifts in their spectral lines.
Eclipsing Binary:
Can separate the stars, but see the total brightness drop when they periodically eclipse each other.

## Visual Binaries

Two stars orbiting about their center-of-mass.

### Center of Mass

Two stars orbit about their center of mass.

• Measure semi-major axis, a, from projected orbit & the distance.
• Relative positions about the center give: M1/M2 = a2/a1
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.

## Measuring Masses

Newton's Form of Kepler's Third Law:

Procedure:

1. Measure the period, P, by following the orbit.
2. Measure semi-major axis, a, and the Mass Ratio, M1/M2, from the projected orbit on the sky.
3. Solve the equation above and separate Masses.
Problems
We need to follow the orbits long enough to trace them out in detail:
• Need to work out the projection on the sky
Everything depends on knowing the distance:
• semi-major axis depends on d
• derived mass depends on d3

## Spectroscopic Binaries

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 orbital velocities

Here is a movie showing a spectroscopic binary star.

Problems:
Cannot see the two stars separately:

• Semi-major axis must be guessed from the orbit motions.
• Can't tell how the orbit is tilted on the sky
Everything depends critically on knowing the distance.

## Eclipsing Binaries

Two stars orbiting nearly edge-on to our line-of-sight.
• See a periodic drop in brightness as one star eclipses the other.
• Combine with spectra which measure orbital speeds
With the best data, one can find the masses of the stars without having to know the distance!!!

Here is a movie showing an eclipsing binary star and its light curve.

Problems
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.

## Stellar Masses

From a combination of visual and eclipsing binaries, masses are known for about 150 stars.

Range: ~0.1 to 50 Solar Masses