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/λo

where v is the velocity, c is the speed of light, λo is the rest wavelength and Δλ is the doppler shift. Δλ = (λobserved – λo)

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

http://astro.ph.unimelb.edu.au/software/binary/binary.htm

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. M1 = 3M2

2. M1 = M2/3

3. M1 = M2

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 M1 = 3M2 then star #2 will orbit 3 times faster than star #1

Let’s look at Kepler’s Law

(M1 + M2)P2 = (4π2/G)a3

So we have the relative masses

We have the period.

We just need a3.

But vorbital = 2πa/P or a = vorbital*P/2π

So how do we find vorbital ?

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 vorbital

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

(M1 + M2)P2 = (4π2/G)a3

If M1 = 3M2 then we can write:

(3M2 + M2)P2 = (4π2/G)a3

(4M2) = (4π2/G)(a3/P2)

Once we find M2 we know that M1 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.