Homework 1: The HR diagram, based on Gaia data

Start: Run a new query to find all stars which lie within 10 pc of the Sun, and which have "g" magnitudes brighter than 15. The results of this query will be used to answer the following questions.

  1. How many stars meeting these conditions are in the Gaia DR3 Archive?

  2. Create an HR diagram showing these stars, with (B-R) color on the horizontal axis, and ABSOLUTE "g" magnitude on the vertical axis. You will have to compute the absolute magnitude for each star yourself.

  3. Using the HR diagram you have created, answer the following questions:
    1. How many stars lie on the main sequence? What percentage of all the stars is this?
            2. 266 = 94 percent
    2. How many stars are white dwarfs? What percentage of all the stars is this?
            3. 18 = 6 percent
    3. How many stars are giants? What percentage of all the stars is this?
            4. 0 = 0 percent

  4. You ought to find that there are no giant stars in this first set of stars. The problem is that giants are relatively rare, and there just happen to be none of them as close to the Sun as 10 pc.
    1. Are there any giants within a sphere of radius 20 pc?
            2. Not really -- just 7 stars starting to leave the main sequence
    2. Roughly how far out must you search to find enough giants to fill out the "giant branch" of the HR diagram?
            3. At 50 pc, the giant branch fills to the red clump.

            At 100 pc, the giant branch starts to reach the supergiant region.

            At 200 pc, the giant branch is completely filled.
    3. Why might it be difficult to measure the properties of these giant stars accurately?
            4. Stars at large distances have very small parallax values, which are really hard to measure accurately. At a distance of 100 pc, for example, a star's parallax is only 0.010 arcseconds. As a general rule, the uncertainty in parallax should be less than one-tenth of the measurement to be reliable. So, in order to compute accurately the luminosities of stars at a distance of 100 pc, we must be able to measure the parallax shift of a star down to 0.001 arcseconds!