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Binary Stars
Astronomy 315
Professor Lee Carkner
Lecture 9
Masses of Stars
While we can find the radius of a star
from the Stefan-Boltzmann Law, we
still do not know the mass
How do you find mass?
On Earth we weigh things
Weighing means measuring how
gravity affects the object
How can we weigh things in space?
Watch how the star moves under the
influence of the gravity of another star
Binary Stars
Most stars are in multiple systems
Our own sun is an exception
How do we find binary stars?
Some stars appear to be very close
together on the sky
Called optical doubles
May just be a projection effect
We want stars that are gravitationally
bound
In orbit around each other
Visual Binaries
The simplest type to observe are visual
binaries
You can see one star orbit around another
The periods of such stars are often very
long
Have to observe for decades to plot the
orbit
Most visual binaries have a relatively
stationary bright star and a moving
fainter star
Binary Motion of Castor
Problems with Binaries
Period and Separation
In order to resolve the stars they have to
have a large separation, but his also means
a long period
Inclination
The orbit is not exactly face on to you, so
you see its projection onto the plane of the
sky
Inclination Effects
Using Binary Stars
What can we measure?
Orbital period
The time for one complete orbit
Orbital radius
The distance from each star to the center of
mass
Need the distance to the binary from parallax
first
What do we do with this information?
Need to understand gravity
Kepler’s Laws
In the early 1600’s Johannes Kepler published
his laws of planetary motion
His first laws states that planetary orbits are
elliptical
The longest axis of the ellipse is called the major
axis (1/2 of it is called the semi-major axis a)
His third law states that the period (P) of the
planet’s orbit (in years) squared is equal to
the semi-major axis in astronomical units
(AU) cubed (1 AU is the Earth-Sun distance)
P2 = a3
Kepler’s Laws
Kepler and Newton
Kepler did not know why his laws
worked
In the late 1600’s Isaac Newton used
Kepler’s laws to develop his theory of
gravity
The orbits of planets obey the Law of
Universal gravitation
Gravitational force depends on mass
We can use Newton and Kepler’s laws
together to find the mass of binary stars
Finding Masses
We can write a version of Kepler’s third
law for binary stars:
MA + MB = a3/P2
where:
MA + MB is the combined mass of both
stars in solar masses (Msun)
a is the semi-major axis of the orbit in
astronomical units (AU)
P is the period of the orbit in years (yr)
Problems with Mass Determination
Our formula only gives us the sum of the
masses
However, we can find the ratio of the
masses by finding the distance to the center
of mass for each star
Examples:
If one star is basically stationary, it has all the
mass (like the sun and earth)
If both stars are equally distant from the center
of mass they have the same mass
Ratio of mass is inverse ratio of distance to
center of mass
Center of Mass Distances
Spectroscopic Binaries
There are very few visible binaries in
the sky, so we have very few mass
measurements
We have to try and find binaries in
other ways
Easier to find double line spectroscopic
binaries
We can’t resolve two individual stars
(they are too close together)
however, we see two sets of spectral lines
Spectroscopic Binary Motion
What information can we get about the
orbit if we can’t see it?
Can get the velocity of the orbit from
the Doppler shift
More shifted the lines the faster the star is
moving in its orbit
Can also get the period of the star from
the Doppler shift
Time for Doppler shift to go from zero to
max away to zero to max towards to zero
Spectroscopic Binary in Action
Velocities of Binary Components
Spectroscopic Binary Masses
The big problem with spectroscopic
binaries is we do not know the
inclination
Velocities highest in edge-on system and
go to zero in face-on system
We only see component of Doppler shift
for motion towards and away from us
We can get masses of stars statistically
Assume a random distribution of
inclinations
Masses of Stars
Compare mass to position on HR diagram
Main sequence:
Cool, dim stars (red dwarfs) have low mass (M ~
0.3-0.8 Msun)
Medium-bright yellow stars have solar masses
(M ~ 0.8-2 Msun)
Hot, bright stars have high mass (M ~ 2-40 Msun)
White dwarfs
Mass about equal to sun
Giants
Large range of masses
Masses on the HR Diagram
Mass Distribution
There is a relationship between mass
and luminosity for main sequence stars:
L = M3.5
Large mass. Large luminosity
White dwarfs are very dense
Solar mass in object the size of the Earth
Giants have low density
Generally much larger than main sequence
stars of the same mass
Next Time
No homework Monday
First quiz on Monday
Covers all material since start of course through
today
Multiple choice and short essay
Short essay include both written and problems
Be able to solve problems like the exercises and be able
to write a paragraph explanation of key concepts
Study notes, exercises and readings
Study hard