Homework 6

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 second homework in this unit, groups have already been created, so just join with your group when you accept the assignment.

Accept Assignment


Problem: A Massive Undertaking

In this problem you have doppler data for a distance star. Your task is to investigate the periodicity of the radial velocity of the star to search for evidence of exoplanets. You can assume for this problem that you are looking at the system perfectly “edge-on”. Supplementary observations of the star have established its mass at 1.9885\times10^{30} kilograms. Using these data, your task is to determine:

  • How many planets are orbiting around the candidate star?
  • What is the mass of each planet?

Clearly describe your logic and reasoning as you go, and provide supporting visuals as necessary.

Tip

It can always be confusing when working with periodograms with aliases. Some tips that might help:

  • Usually you want to work from left from right, but be aware that higher-order aliases can appear to the left of a real signal. But since aliases usually drop in amplitude with each “reflection”, those peaks would probably be smaller than the dominant real peak, which might help.
  • If you think you have identified a real peak, visualize all the possible aliases of that peak. If they nicely align with a bunch of the other peaks you see, that is probably a good sign that you have chosen wisely (or luckily).
  • If you are confident that the dominant peak must lie in a smaller range, don’t hesitate to rerun your Lomb-Scargle analysis using that narrower frequency range. This will usually greatly boost your resolution in that region, and can lead to a much clearer picture in some cases.
  • Once you find a true peak and corresponding components, subtract them from original signal and then run Lomb-Scargle on the result. This can ensure you don’t miss smaller true peaks that were overwhelmed by a dominant peak and its aliases.