For the problem below, the expectation is that you submit a standalone HTML file (any images should be embedded) back to GitHub. The first person to accept the assignment below 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.
Accept AssignmentProblem: Hot Star Speeds
In the data folder in the repository is a file called star.csv, which contains brightness measurements of a particular star at a range of wavelengths. The brightness measurements are given as a unitless “flux” value, representing some arbitrary instrument units. The important idea is that they just represent a scaling of the actual brightness by some equipment calibration constant. The wavelengths are given in units of nanometers (10^{-9} meters). Your task in this problem is to determine as much information about the star as possible from this spectrum.
Part A
Determine the surface temperature of the star, in degrees kelvin, using both Wien’s Law and Planck’s Law methods. Describe how you went about doing so and provide graphical evidence of your work in your essay. Compare the temperatures you got from each method and comment on which you’d trust more in this particular case. If one of the methods was not possible, explain why.
Part B
You can get information about the star’s radial speed from the absorption peak locations. Your task is to determine the exact location of at least 4 spectral peaks and to plot the rest wavelengths vs the observed wavelengths. You can fit a line to this data and compare to the known Doppler relation to determine the speed of the star with respect to Earth. To help with identifying common spectral lines and their rest wavelengths, I’m including the table below, where the shown wavelength is that transition’s rest wavelength:
| Wavelength (nm) | Element |
|---|---|
| 410.175 | H_\delta |
| 434.047 | H_\gamma |
| 438.355 | Fe |
| 486.270 | H_\beta |
| 518.362 | Mg |
| 527.039 | Fe |
| 588.995 | Na |
| 589.592 | Na |
| 656.464 | H_\alpha |
| 759.370 | O_2 |
| 849.8 | Ca II |
| 854.2 | Ca II |
| 866.2 | Ca II |
Students often want to apply the Doppler relation to individual peaks, getting a speed for each. Do not do this! It is highly sensitive to noise. Instead, make the plot of rest wavelengths vs observed wavelengths (which should have 4 points on it, one for each measured peak), and then fit a line to it. You can then get the speed by relating the Doppler relation to the slope of the line.