Equivalent Width Activity for EXES

Searching for Europium using Stellar Spectroscopy

The complete activity is meant to take a full class and maybe even two.

The visible spectrum of the sun. Credit: OpenStax Astronomy. Fraknoi, Morrison, and Wolf

We are going to compare the relative amount of the elements nickel and europium in a couple of stars.

Plotting A Stellar Spectrum

Watch the “HOW TO” video: https://www.youtube.com/watch?v=XkOUVOJrtrQ

  1. If you haven’t already, copy the data to your Google Drive (use your initials in the file name).
  2. Highlight the 2 columns of data. Most spreadsheets will assume the left column goes on the x-axis and the right column goes on the y-axis. This data is ready to go since column A is the wavelength in Angstroms and column B is the relative flux or amount of starlight. You can think of this as the brightness of a particular wavelength.
  3. The easiest way to measure with the plot is if the chart type is set to ‘smooth line’.
  4. Change the title of the graph to “Star name Spectrum” but use the real star name. 🙂
  5. Change the y-axis title to Relative Flux or something similar.
  6. Change the limits on the x-axis and y-axis so just the region with the absorption feature is visible.
  7. Change the tick marks on the x-axis and y-axis so you can easily read off the plot. I used 0.05 on the y-axis with 4 minor marks and 0.1 on the x-axis with 4 minor marks. I also turned on all the various tick marks.

Determining atomic abundance: Equivalent Width

Example plot for determining the equivalent width for absorption feature.

How to measure equivalent width

  1. First, count how far down from 1on the y-axis the “bell curve” bit goes and write that in a cell labeled Max Abs or something similar. This is the maximum absorption for this feature.
  2. Next, in an adjacent cell, hit = to enter a formula and click on the cell where you typed the value for the max absorption and divide that by 2. This is the half-max value.
  3. We will use the half-max value to count down from 1 on the y-axis to where the curve meets that y-value on both the right and the left. Write down in an empty cell the left wavelength where the curve meets that half-max value and then write down in another empty cell the similar value on the right side of the curve.
  4. Next, click an empty cell and click = to enter a formula. Be sure to put the difference between the right and left values in parentheses before you multiply by the max absorption.
  5. This value represents the equivalent width for this spectral feature. This is a numerical way to describe the relative abundance of a particular atom for a star. (Note: this is not the actual number of a particular atom.)
  6. Repeat for the other stars!

Plotting Spectra with Python and Google Colab

You can also try out some Python coding to plot the stellar spectra using Google Colab Notebook. Give it a try!

Google Colab Notebook Python Plot of Spectra

CT and Kepler’s 3rd Law

The Kepler spacecraft made some incredible discoveries over the years. The planetary system Kepler-11 is very interesting. It is a very compact solar system with 6 planets. Of course, the spacecraft is named for Johannes Kepler who first empirically determined the now famous three laws of planetary motion.

Kepler-11 System from NASA Exoplanet Catalog

I felt like this small dataset would make a great computational thinking (CT) activity. CT can mean writing programming code or working with a spreadsheet to do some data science or creating or using a model or simulation. The goal is to explore Kepler’s 3rd law of planetary motion.

Kepler’s 3rd Law

In the original activity, students linear the data set using Kepler’s 3rd law of planetary motion to determine the mass of the star Kepler-11. Check out the spreadsheet version here. This is meant to be an introductory exercise is working with data in a spreadsheet. Students create a plot and answer questions using some basic skills.

Spreadsheet Version of Kepler’s 3rd Law Lab

Although the spreadsheet version of the lab worked out pretty well, I decided to make a Desmos calculator version. Students can work with the whole list of planetary data all at once. This is more like a students creating a numerical model to find the mass of the star. Check out the Desmos version here.

Desmos Version of Kepler’s 3rd Law Lab

Finally I decided to create a version of the Kepler’s 3rd law lab using some Python code in Google Colab. This version uses some standard data science techniques to determine the mass of the central star in the Kepler-11 system. Check out the Google Colab version on my GitHub repository.

Google Colab Python version of Kepler’s 3rd Law

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CAST 2021

Come see either of my CAST 2021 sessions.

Thursday, Nov 11, 2021 2:30 PM – 3:30 PM CST
Location: Sundance 6, Omni Hotel
Session Code: 20068

Check out our CAST 2021 presentation and equivalent-width spectroscopy lab activity. Also visit the project webpage for a lot more info. There is also a coding version of the lab as well.

Friday, Nov 12, 2021 11:00 AM – 12:00 PM CST
Location: 200, Fort Worth Convention Center
Session Code: 5067

Check out my solo CAST 2021 presentation and visit the project webpage for a lot more info including activities and code.