Homework 2: Stars in the local neighborhood

This homework must be submitted on paper; you may write out your work on paper, or type it into some word processor and then print it. Either way, staple together all pages and write your name legibly at the top of each page.

This homework is centered on data from the Gaia DR3 Archive, which you can find at

https://gea.esac.esa.int/archive/

The problems below require you to run a query, collect the results, and analyze them. Begin by choosing the "Search" tab at the top of the archive page. As an example, click on the "Advanced (ADQL)" tab, and type the following into the query box (just below the words "Job Name"),


   SELECT *
   FROM gaiadr3.gaia_source
   WHERE parallax >= 200
   AND phot_g_mean_mag <= 15

Then click the "Submit Query" button, and wait a minute or so. When the "Status" icon changes from a rotating gear to a stationary check mark, your results are ready. You can view the results in your browser by clicking on the fifth icon to the right of the "Size" column (the icon will pop up "Display top 2000 results" if you hover over it). As you can see, there are a LOT of columns with information about each star. The columns you need to identify are:

parallax (in units of milli-arcseconds)
phot_g_mean_mag (apparent magnitude in g passband)
bp_rp (color of star, in B-R)

Near the bottom of the screen, in the "Download format" box, select "CSV". Then download the results of your search by clicking the third icon to the right of the "Size" column (the icon will pop up "Download results" if you hover over it). The resulting text file is in comma-separated-value format. It has a LOT of columns, but should contain only 48 rows: the first is a header, describing the contents of each row, and all the others are entries with one star per line.

If you are unable to run this procedure, and can't produce a CSV file with the properties described above, contact me so that we can work on it together. I'll be happy to demonstrate.

So, that's how you can grab data from the Gaia DR3 archive. In order to answer the questions below, you will have to modify the query slightly, run it again, download the results of the new query, and then analyze the contents of those selected columns in the output.

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.

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

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.

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. How many stars are white dwarfs? What percentage of all the stars is this?
3. How many stars are giants? What percentage of all the stars is this?

Are stars uniformly distributed in space around the Sun? If they are, then the number of stars within a sphere of radius R should increase as R³ -- right?
To test this idea, we'll need a larger sample of stars. Run a new query to find all the stars within a distance of 25 pc, and which have apparent "g" magnitude brighter than 17. Once again, download the results and analyze them.
Make a table and/or graph which shows the number of stars as a function of distance from the Sun, and use it to test the hypothesis that stars are uniformly distributed in space.