Question

Although spiral arms are not physical structures, they rotate as if they are solid bodies (i.e., they rotate with a constant angular velocity). Their rotation speed is not always equal to the rotation velocity of the stars in a galaxy. However, the "co-rotation radius" in a disk galaxy is the radius where the rotation velocity of stars equals the rotation velocity of its spiral arms. For the Milky Way, this radius is roughly 10 kpc from the Galactic center.

Estimate the speed at which stars at the radius of the Sun approach the spiral arms, given that the co-rotation radius is 10 kpc. Recall that the Sun is located roughly 8 kpc from the galactic center and its orbital velocity is 220 km/s.?

Answer 1

The question is about estimating the speed at which stars at the Sun's radius approach the Milky Way's spiral arms. The co-rotation radius is at 10 kpc where stars move at the same speed as the spiral arms. Without the rotational velocity of the spiral arms at 8 kpc, we cannot calculate the exact speed, but we know that stars inside the co-rotation radius (such as the Sun) move faster than the spiral arms.

Step-by-step explanation:

A student has inquired about estimating the speed at which stars at the radius of the Sun approach the spiral arms of the Milky Way, given that the co-rotation radius is 10 kpc and the Sun is approximately 8 kpc from the galactic center, with an orbital velocity of 220 km/s. To solve this, we need to understand the concept of differential galactic rotation. In the Milky Way, the stars' rotational velocity varies with their distance from the galactic center.

At the co-rotation radius (10 kpc), the stars' rotation velocity matches the spiral arms' rotation velocity. Since the Sun is at 8 kpc, it orbits faster than the spiral arms because proportions closer to the galactic center have higher rotational speeds. The absolute difference in rotation velocity between the stars at the radius of the Sun and the spiral arms can be estimated by factoring in the difference in orbital radius and the galactic rotation curve.

However, without a specific value for the spiral arms' rotation speed at 8 kpc, we cannot determine the exact speed at which stars approach or recede from the spiral arms. Typically, stars outside the co-rotation radius would move slower than the spiral arms, while those inside would move faster. Therefore, since the Sun is inside the co-rotation radius, it is rotating faster than the spiral arms, and the speed at which the Sun approaches the spiral arms is the difference between its orbital velocity and the spiral arms' rotational speed at Sun's location.