Binary Stars

Astronomy 315Professor Lee

CarknerLecture 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