For the problem below, the expectation is that you submit a standalone HTML file (any images should be embedded) back to GitHub. Data for the problem is provided in the starting repository in the /data folder. Since this is the first assignment in a new unit, you’ll need to form your new groups when you accept the assignment. The first person to accept the assignment should form an easily identifiable group name (likely using the names of your group members). Others in the group should also accept the assignment, and then they can just join the existing group.
Problem 2: Cepheid Variables
Part A
Henrietta Leavitt first published her findings on Cepheid variables in 19121. In the paper, she lists out the Cepheid variables that she observed in Table 1, which I have transcribed into the CSV file leavitt_cepheids.csv for your use. It includes the Harvard identification number, the maximum and minimum apparent magnitudes, and the observed period in days. A simple plot of the period of the stars vs their average apparent magnitude will show a clear trend, but a log-log plot will show a linear trend (note that because magnitude is already a log value, you only need to take the log (base 10) of the period.) All of these stars were observed in the Large Magellanic Cloud, which is located 49.97 kpc from our Sun. You can use this fact to convert the average apparent magnitude of the stars into an average absolute magnitude. Then fit a line to the trend to extract the fit constants for later. In particular, you’ll need the slope and intercept. These values might not perfectly agree with the modern values, as we are using 120 year-old observational data and estimating that all the stars are all essentially the exact same distance away, but they’ll be fairly close.
Part B
You can find observations of a lightcurve of one particular Cepheid variable star in cepheid_lightcurve.csv. Determine the period of the star’s pulsations, and then use this information and findings from part A to determine the distance to this star in parsecs. HDJ here stands for “Heliocentric Julian Day” and is measured in units of days. V_mag is just the apparent magnitude in the visual band.
Footnotes
Periods of 25 Variable Stars in the Small Magellanic Cloud., Leavitt, H. S. and Pickering, E. C., HarCi.173, 1912.↩︎