High Precision Photometry of Transiting Exoplanets as I currently know it : Part VI

Methodology &

Differential Photometry cont.

A professor at RIT used real data to explain how Differential Photometry is analyzed.  The following plot illustrate the measurements taken after data reduction.

Figure 1: Raw photometry of three stars plotted in this light curve.  "Magnitude" is another unit of measurement for a star's brightness.  The Instrumental magnitude is the magnitude, or flux, measured by a camera on Earth.  This measurement of brightness can differ if the Earth was much closer or much farther away from these stars.    Picture Credit: RIT

First of all, be mindful of the fact that light curves usually have "days" or some familiar unit of time for the x-axis.  "Image number" is, in essence, a unit of time but the analysis would be much more thorough and more information would be gathered if a familiar unit of time was utilized.  With this choice of axis, a variety of questions are left unanswered because of the author's reluctance to simply show the time stamp of each image number.  How do we know that image 20 was taken the same night as image 40?  Does the flux of star IY vary significantly over the course of days, weeks or hours?  Are the time intervals between when each image was taken the same?  (The author actually does show a more descriptive choice of x-axis later at the bottom of his/her web page.)

 Based on the plot, it seems like all three of the stars are variable, i.e. for some reason they change in brightness over time.  The next plot will show how such a conjecture would not be true.

Figure 2: Light curve of photometric measurements after utilizing the two comparison stars A and B.  As described in the legend of the plot, all instrumental magnitudes were subtracted by the corresponding instrumental magnitude of star A at that time.  This is why all of the values for star A are at magnitude 0.  Star A is being used the comparison star.  Star B is another comparison star used to confirm the assumption that both stars A and B are not variable stars.  Picture Credit: RIT

As stated in my previous post, comparison stars are useful for determining when the Earth's atmosphere is interfering with the incoming photons from stars in such a way that makes the star look like it is changing in brightness.  Therefore, it is wrong to trust the raw data in Figure 1 and conclude that all three stars vary in brightness over time.  

In Figure 2, the flux of star B remains nearly constant--relative to star A.  This means that the initial measured flux of stars A and B varied in the same amount at the same times.  Because it is highly improbable that both stars would fluctuate at exactly the same times and with the same amplitude of fluctuation, it is safe to assume that the variability seen in Figure 1 is due to the Earth's atmosphere.  There are a few bumps in the Figure 2 light curve for star B.  However, those bumps are so small that they are insignificant when searching for a variable star.  The flux of star B is certainly consistent enough for this example.  However, if one was skeptical and wanted to more evidence that both stars A and B are good comparison stars (i.e. remain constant in flux during the observation), then more comparison stars should be observed simultaneously with the primary star of interest.  Once more non-variable stars are observed and their flux plotted, one would see how the data points for each comparison star remains sufficiently constant throughout the observation.