Reproducing the plots put forth by Petigura et al. (2013) in terms of incident flux values allowed us to investigate alternate definitions of what may be considered habitable. According to multiple HZ calculations, especially those suggested by Kopparapu et al. (2013), the bulk of the HZ lies within a zone of 0.25-1 \({F_\oplus}\). Since Petigura et al. (2013) use eKOIs with \(F_P\) extending all the way to 4 \({F_\oplus}\), they had to make extrapolations in terms of period due to a drastic drop in completeness. We performed a series of new extrapolations using results from Groups 1 and 2 in order to produce a more useful and meaningful representation of the data. Using incident flux, which is provided for each eKOI as a ratio of planet flux \(F_P\) to earth flux \({F_\oplus}\), we recreated Figure 5 from Petigura et al. (2013) to show a more useful relation. We then extrapolated to lower fluxes to achieve a more accurate view of what we consider the inner HZ. We also created an entirely new plot where we extrapolated to lower radii in order to show the relationship between occurrence rate and planet size.
We worked first to extrapolate the planet occurrence rate to planets with fluxes lower than that of Earth in order to create an analogous version of Figure 5 from Petigura et al. (2013). To do this, we completely recreated the figure by converting the x-axis to incident flux (\(F_P\) /\({F_\oplus}\)) and the y-axis to cumulative occurrence rate. We imported the occurrence rates for each planet by converting a pickle file provided by Group 1 and extracted the flux ratios from the Petigura et al. (2013) data table (S2), also provided by Group 1. The data for all 836 eKOIs were analyzed and binned using Microsoft Excel 2013. The cumulative values from this data processing were then plotted using SigmaPlot v. 12.5. Petigura et al. (2013) uses flux values extending to 4 \({F_\oplus}\), which seems to be a highly unreasonable flux value for a planet within the HZ. Because of this, their extrapolation to lower flux values may have been skewed due to a drop in completeness. Using our new plot, we performed our own extrapolation to lower fluxes (0.25-1 \({F_\oplus}\)) using a logarithmic regression. We further separated all the flux data into three different sets based on planet size in order to make individual plots for each group. The groups are defined by their radii in terms of \({R_\oplus}\) as follows: 1-1.49 \({R_\oplus}\) (black circles), 1.5-2.24 \({R_\oplus}\) (red inverted triangles), and 2.25-3.375 \({R_\oplus}\) (green squares). These three radius bins correspond to the bins agreed upon by Group 2, which will then be used further by Group 4. A fourth experimental radius bin which spans 1-2 \({R_\oplus}\) (blue diamonds) was added without performing an extrapolation just to emphasize the cumulative occurrence rate for the range of planet sizes Petigura et al. (2013) refers to as “Earth-like.” These four sets of planet sizes show the relation between incident flux and planet occurrence rate. Each extrapolation was chosen by eye to begin at the first plotted point where the slope changes significantly. The plot shows the percentage of stars that possess planets receiving a flux greater than F \({F_\oplus}\) within one of three size bins. This allows us to make a better judgment about how many planets may actually lie in the HZ according to their incident flux.
In parallel with the Excel plotting of this data, a Python script was written to recreate these same graphs and perform the extrapolation. This script uses Matplotlib, Numpy, and a CSV module to read the CSV file created with the pickle file from Group 1 and plot cumulative occurrence rate against flux for planets of a given radius range. The effect of this was to create the same graphs as the Excel and SigmaPlot analysis, but it requires much less manual calculation. This Python script can then be placed into a pipeline, so if the data output from Group 1 and Group 2 changes, minimal effort will be needed to reproduce the results from this section of the project. The relevant output of this Python script that will be used to determine the final occurrence rate is the result of the extrapolation. The source code for this Python script is attached.