# Visual Binary Stars

We are starting to build up our description of stars. We can get
• Distance (from parallax)
• Temperature (from colors)
• Chemical composition (from spectra)
• Luminosity (from distance and apparent brightness)
• Size (crudely, from Stefan-Boltzmann law)
• Velocity (from doppler shift and proper motion)
What's left? A biggie - Mass!

How can we get mass? Well, how did we determine the mass of the Sun? Or for Jupiter?

And how can we do this for other stars?

Binary stars -- stars in orbit around a common mass. At least half of all stars are binaries (in this sense, we may be a minority). Triples, quadruples can even exist!

A visual binary is a star system whose members are far enough apart, and close enough, that we can see both stars (ie the stars are > 1" apart). Be careful though -- many optical doubles exist, stars which appear close to each other on the sky but which have very different distances (Alcor and Mizar, for example, in the Big Dipper -- although they themselves are binaries!).

If we watch the positions of binary stars over many years, we can plot their relative orbit.

Now what? Use Kepler's 3rd law to determine the total mass of the binary pair. Remember Kepler's 3rd law?

• We can measure P directly.
• We can measure the apparent semimajor axis of the orbit (in arcsec, for example) directly.
• If we know the distance, we can then calculate the true semimajor axis (in cm, or AU, or whatever).
• Then we can solve for the combined mass M1+M2
Question: Most visual binaries have long period (many years). Why?

Easy, right? Not as simple as that -- there is no reason why we should be looking directly onto the orbital plane. In other words, the apparent orbit is almost never the true orbit (which is what we need to do the calculation). We can do a geometric correction for this, though.

What if we don't know the distance? Are we stuck? Not necessarily. If we have spectra of the stars, so that we can use the doppler shift to get the velocities of the stars, we can use that information along with the projected separation and orbital period to get the combined mass.