NanoKepler -- Hunting for Planets with Kepler
Based on materials originally developed by Kaspar von Braun (NExScI/IPAC/Caltech) for the 2010 Sagan Exoplanet Workshop. This group project was entitled "Hunting for Planets with Kepler."
The basic scenario here is that we have a very small Kepler mission analog -- a "nanoKepler", if you will. You have photometric light curves of 50-100 Kepler targets.
Find and characterize the transiting exoplanets within them. Are there any 'false positives'? (hint: yes) What are they, or could they be? What other kinds of variable sources can you find and identify? What can you say about the variability characteristics of the dataset as a whole?
Questions to consider
- Are there planet transits in the dataset? What can you say about them? What can you say about the planets?
- What other kind of variable stars are there? What are they?
- Are there signals that look like planet transits, but are not (false positives)? What could cause them?
- What kind of statistical properties (e.g., chi‐squared, RMS, etc) are typical for the different kinds of variable stars (i.e., how would you search for a certain kind of variable in a large dataset)?
- What are statistical properties of the dataset (e.g., RMS as a function of brightness, how many variable stars, how many planet transits, how many non‐variable stars, etc)?
- Are there periodic signals present in all light curves (“red noise”)? What could typical sources of red noise be in space‐based data such as these?
- Which algorithm or method is preferable for which goal (e.g., for period‐phasing or for transit finding)?
- Isn’t NASA Exoplanet Archive the coolest thing ever?
Analyze a space-based dataset of photometric light curves with the primary aim of finding and characterizing transiting extrasolar planets.
Questions to Answer (suggestions)
The basic idea here is to present anything that would be publishable if you had been given the money to conduct such a survey. Since the principal aim of this survey is to find planets, they have highest priority, but there are other publishable (and published!) results from similar spaced-based and ground-based surveys. Also keep in mind that it is more important to think about these and other questions than to get them perfectly right. Suggestions for questions are the following, but they are not meant to be exhaustive:
- Are the planet transits present in the data set (hint: yes, there are, I put them in). What can you say about the transiting planets?
- Can you find and identify other kinds of variable stars?
- Are there any signals that look like transiting planets, but are not (false positives)? If so (and even if not), what could cause a photometric signal to look like a planet transit, and how would you confirm or reject its planetary nature?
- If you wanted to look for planets or other variable stars in MUCH larger datasets (for which it would be impractical to look through the light curves by eye), then how would you go on about that? Are there certain statistical "markers" for certain types of variables, like combinations of quantities like RMS, chi-square statistics, etc?
- What overall statistical properties does this small dataset have? What is the frequency of detected transiting planets? How about other variable stars? At what level does every star vary?
- Can you detect red noise in the data set? That would manifest itself in the form of the same or very similar periodic signal inherent in all or a large fraction of the light curves. In ground based data sets, red noise is typically produced by changes in focus, seeing, airmass, etc. What could cause red noise in space-based data?
- If you played around with the various algorithms for phasing different kinds of periodic signals, what are your insights on which ones work better for different kinds of signals? Similarly, if you have a chance to try out multiple different ways of fitting the transit light curves to models or otherwise characterizing the transit signals, which methods worked best for you? Any idea why?
1) Go to NASA Exoplanet Archive Website ( http://exoplanetarchive.ipac.caltech.edu/ )and access the Kepler Public Data ( http://exoplanetarchive.ipac.caltech.edu/applications/ETSS/Kepler_index.html ).
2) This textfile contains the numbers of Kepler IDs that comprise this dataset.
3) Typing in the respective ID number from the textfile into the Kepler ID box will take you to the page(s) of the star. If there are two time series of the star, it means that it was observed during two Kepler observing campaigns. You can work with one, the other, or both (to increase your signal to noise ratio, it is probably advisable to work with the longer one).
4) You can use NASA Exoplanet Archive tools to view and download the time-series data, as well as trying to find the best periods for variable signals using various algorithms. You may also download the phased light curves.
5) Try to identify and characterize the planet transits in the data. You may use the tools suggested below or your own.
6) Try to answer some of the questions above (see notes on the questions).
Documents / Links
NASA Exoplanet Archive Website http://exoplanetarchive.ipac.caltech.edu/
Text file with Kepler ID numbers that comprise this dataset
Transit Analysis Package http://www.ifa.hawaii.edu/users/zgazak/TAP/ Software by J. Z. Gazak (U. of Hawaii) -- IDL required
JKTEBOP page http://www.astro.keele.ac.uk/~jkt/codes/jktebop.html (J. Southworth, Keele University), and the modified version (optimized for transit fitting, courtesy of J. Carlos and I. Ribas)
Paper on geometrical transit fitting (aka Unique Solution) by S. Seager & G. Mallen-Ornelas (2003) http://adsabs.harvard.edu/abs/2003ApJ...585.1038S
Link to my excel worksheet incorporating the equations in Seager & Mallen-Ornelas (2003)
This dataset is hand-picked. Therefore it contains transiting planets. It would obviously be easy to find out which planets are in the dataset and get their characterization from the publications, but it is much more educational to do any detection and characterization with an unbiased attitude (you can compare the results to the published Kepler planets later). The point is more to do it than to get it right.
This dataset is hand-picked. Therefore any planet or other variability statistic is, by definition, skewed. For the purpose of this exercise, it is nevertheless a decent experience to say something about variability statistics, what other sources of variability (if classifiable) there are, etc.
There are several different approaches mentioned above with which to fit transit light curves to the data. Note that this is never trivial and will require some learning and trying. The first method (Transit Analysis Package) relies on creating families of transit light curves based on astrophysical parameters (pioneered in part by Mandel & Agol 2002), and then fitting these families of light curves to the data. The second method uses a well-known eclipsing binary stars code modified for the use of transit fitting (JKTEBOP by J. Southworth). The third method (Unique Solution) relies on geometrical fitting of elements of the observed light curves and correlating them analytically to astrophysical parameters Seager & Mallen-Ornelas (2003).