Three types of binary stars. Visual binaries – Stars that are far enough apart that they can be seen as separate stars through a telescope. They typically have orbital periods that are hundreds of years long.

Stars orbit a common center of mass. More massive star has smaller orbit.

Spectroscopic Binaries – Much shorter orbital periods because stars are so close to each other that they aren’t separable. But the spectral lines show that there are two stars.

A Dilemma Spectroscopic binaries often show double the absorption lines of a regular spectrum. But the wavelength at which a line forms does not depend on the type of star. It is set by the element that is giving off the light. Why don’t the two absorption lines fall right on top of each other?

A Dilemma Spectroscopic binaries often show double the absorption lines of a regular spectrum. But the wavelength at which a line forms does not depend on the type of star. It is set by the element that is giving off the light. Why don’t the two absorption lines fall right on top of each other? The reason is the Doppler Shift.

The Doppler shift is a wave phenomenon When an object emits a wave, the wave moves out in all directions with its center at the source. This is true of water waves, sound waves, and light waves.

What if the source is moving? If a source of the wave is moving, then as the source emits the wave, the center is continuously moving.

Here is a real picture of Doppler shift

When a star is moving toward or away from us Doppler shift is blue-ward (toward) or red- ward (away) of what it would be if the star was not moving.

We can see this as a shift in the absorption or emission lines in a spectrum. The wavelength that absorption occurs at depends only on the type of atom. But the shift depends on the motion

Using the Doppler shift of light from a star we can not only tell if the star is coming toward us or going away from us, but we can also measure the speed at which it is moving toward or away.

How is the velocity related to the amount of Doppler shift? 1. The faster the object is moving toward or away from us the bigger the shift should be. 2. The faster the object moves toward or away from us the smaller the shift will be. 3. If an object is moving rapidly towards us we get a large speed, but if it is moving rapidly away we get a small speed.

Relation of velocity to Doppler shift The bigger the shift the fast the velocity because the center of the wave is moving rapidly causing greater compression or expansion. v/c = Δλ/λ o where v is the velocity, c is the speed of light, λ o is the rest wavelength and Δλ is the doppler shift. Δλ = (λ observed – λ o )

What about stars orbiting each other? The result is two absorption lines that have slightly different wavelengths from what they have in the lab.

Binary star simulator

What will happen if I put the two stars closer together? 1. They will speed up 2. They will slow down 3. They will remain at the same speed

What did we find out? When the stars are farther apart (a is increased) they move more slowly in their orbit.

How can we find the orbital period for spectroscopic binaries? 1. Watch the stars orbit each other and see how long it takes 2. Watch for the absorption lines to return to their original wavelength 3. Measure the masses and compute the period

What did we find out? When the stars are farther apart (a is increased) they move more slowly in their orbit. Measuring the time it takes for the spectral lines to return to their starting wavelength gives us the orbital period

What will happen I make Star #1 mass three times Star #2 mass? 1. Star #2 will have a bigger orbit than Star #1 2. Star #2 will a smaller orbit than Star #1 3. The orbits will not change

What did we find out? When the stars are farther apart (a is increased) they move more slowly in their orbit. Measuring the time it takes for the spectral lines to return to their starting wavelength gives us the orbital period When the mass of one star is increased the other star orbits at a greater distance.

If Star #2 is orbiting 3 times faster than Star #1, what does that tell you about their masses? 1. M 1 = 3M 2 2. M 1 = M 2 /3 3. M 1 = M 2

What did we find out? When the stars are farther apart (a is increased) they move more slowly in their orbit. Measuring the time it takes for the spectral lines to return to their starting wavelength gives us the orbital period When the mass of one star is increased the other star orbits at a greater distance. If M 1 = 3M 2 then star #2 will orbit 3 times faster than star #1

Let’s look at Kepler’s Law (M 1 + M 2 )P 2 = (4π 2 /G)a 3 So we have the relative masses We have the period. We just need a 3. But v orbital = 2πa/P or a = v orbital *P/2π So how do we find v orbital ?

How can we get the orbital velocity of the stars? 1. Measure the Doppler shift for any spectroscopic binary pair 2. Use the peak radial velocity from the velocity plot to get the orbital velocity. 3. Find binaries which are eclipsing, because we are then in the orbital plane and can determine v orbital

Eclipsing Binaries

If the binary stars are eclipsing, then it is guaranteed that we are in the orbital plane. This means that the maximum radial velocity on the velocity plot gives us the orbital velocity. Now we have “a” and we have “P”. We can get rid of one of the “M”s because we know how they are related.

Example (M 1 + M 2 )P 2 = (4π 2 /G)a 3 If M 1 = 3M 2 then we can write: (3M 2 + M 2 )P 2 = (4π 2 /G)a 3 (4M 2 ) = (4π 2 /G)(a 3 /P 2 ) Once we find M 2 we know that M 1 is three times the mass

Masses of Stars Many such measurements show us that mass increases on the Main Sequence as the temperature and luminosity increase. As theory predicts. Furthermore, Mass does not correlate with luminosity for giant, evolved stars. Giants might have a large mass, or they might have a small mass, but still they are very luminous. Also the mass of a white dwarf is not correlated to its luminosity. Something different is happening for these guys.