Three types of binary stars.

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 redward
(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
• 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. 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.