# The Solar Motion

How do we define the motion of the Sun?
How would we know the Sun is moving at all?

Look at the velocities of stars around us.

• Most stars have a small velocity relative to us, < ~ 30 km/s
• Metal poor halo stars have a high relative velocity, ~ 200 - 250 km/s
What does this mean?

## The Local Standard of Rest

Let's define a coordinate system:

 Position Velocity R = Radius (cylindrical) theta = Angular coordinate z = Distance from plane Pi = velocity in/out from centerTheta = tangential velocityZ = up/down velocity

Define a point in space that is moving on a perfectly circular orbit around the center of the galaxy at the Sun's galactocentric distance. We measure all velocities of stars relative to this point, which is known as the Local Standard of Rest.

The velocity of the Local Standard of Rest (LSR) is then given by

(Pi, Theta, Z)LSR = (0, Vcirc, 0)

Now we define the velocity of stars relative to the LSR.

(u,v,w) = (Pi, Theta-Vcirc, Z)

For example, look at three hypothetical orbits:

• Star A lags the LSR -- negative tangential velocity (v < 0)
• Star B leads the LSR -- positive tangential velocity (v > 0)
• Star C orbits with the LSR -- circular orbit (v=0)
Note: The LSR is not the orbit of the Sun!!!

## What is the Sun's motion relative to the LSR?

 Look at all the disk stars around us, and measure their radial velocities (vr) and proper motions (mu). Do this for lots of stars, and take the average along different lines of sight. If the sun wasn't moving, what would you expect to see? In fact,  you should see that, on average, star move towards us in one direction and away from us in the opposite direction, due to the Sun's motion relative to these nearby stars.  The residual non-zero averages give us the Sun's peculiar motion: (u,v,w) = (-10, 5, 7) km/s The Sun is moving a bit towards the galactic center faster than the LSR northward out of the galactic plane (Remember this is after we've factored out the general rotation velocity of the disk!)