Week 5 Lab: Globular Cluster Analysis with Gaia Data

In this week’s lab, we will use the skills you have learned about numpy and matplotlib to do some real scientific data analysis. For today, please write all your code in a Jupyter Notebook!

Instructions for Starting Your Jupyter Notebook¶

Open a terminal and navigate to the directory you want to work in:
- Run the following commands to activate the environment and start Jupyter Lab:
```
conda activate astro-rps
jupyter lab
```
Create a new Jupyter Notebook:
- In the Jupyter interface, click “New” and select “Python 3” to create a new notebook.
Code Submission:
- Write all your code in the notebook.
- Once completed, upload the notebook file (.ipynb) to the Google submission form

Exercise 1: Plotting a Hertzsprung-Russell Diagram of the Globular Cluster M92 using Data from the Gaia Mission

The Gaia satellite has collected stellar positions, motions, and brightnesses for nearly two billion stars in the Milky Way. The file “GaiaM92.npy” contains example data from Gaia specifically for the globular star cluster Messier 92 (M92). To investigate the data, take the following steps:

Load the .npy file into an array. Each row in this data file represents an individual star. Use np.load() to load the data from the file.
Scatter plot of Color vs. Brightness: Now, create a scatterplot with the column bp_rp (a proxy for color) on the x-axis and phot_g_mean_mag (a proxy for luminosity) on the y-axis. Is the distribution in this plane uniform, or do you see patterns/sequences?
Improve your scatter plot:
- Invert the y-axis so that smaller numbers are at the top (since brighter stars have lower magnitudes).
- Limit the x-range to -0.5 to 2.
- Choose a smaller marker size and change the color.
- Label both axes with meaningful labels, not just the column names.
Compare your diagram to the one shown at this link: Cluster HR Diagram. Do you observe the same features in your plot? Write out some of your observations, either as comments below your code or in a markdown cell in Jupyter (you can change the cell type to “markdown” on the top bar, and markdown allows you to type in plain text).

Exercise 2: Computing the Distance to the Cluster M92

The horizontal branch of the HR diagram (see Q4 of Exercise 1) is comprised of stars at roughly the same luminosity regardless of temperature. Since we have a sense of the instrinsic (absolute) luminosity of these stars, we can compared that to their observed luminosity to get a sense of their distance. For a globular cluster like M92, we can then average over the distance to these special stars to get a distance to the cluster. In this exercise, we’ll do exactly that!

First, isolate the horizontal branch by filtering based on the phot_g_mean_mag column and the bp_rp column. In practice, you need four selections total which select for stars in this feature (e.g, mag > 15 and mag < 16 and similar for bp_rp). I recommend you impose phot_g_mean_mag < 15.5 as one of them to get the best possible results. Recall we can filter using this syntax in numpy: myarray[condition].

The “absolute” G-band luminosity of stars on the horizontal branch is G = 0.3. Create a new variable called DistanceModulus for an array which is phot_g_mean_mag minus this number.
The distance modulus (unitless) is related to the distance (in kiloparsecs) via the formula
$\rm distance \ (kpc) = \frac{1}{1000}\left(10^{((DistanceModulus/5) + 1)}\right)$
(1)
Compute the distance in kiloparsecs using this formula, using the DistanceModulus from Q2.
Now convert your distances to light-years, by multiplying your distance in kpc by 3262.
Lastly, print the average and standard deviation of your computed distances in light-years. What distance is the cluster? If you assume the mean value and the standard deviation as the error, does your value match that shown on the Wikipedia page for M92?

Week 4

Lab 4: Exploring Cosmological Parameters with Functions