Speedup, Slowdown, or Steady As She Goes?

We now have enough data to make a plot showing how the period of KIC 9832227 has (or has not) been changing since we started observing at the end of November. And that plot looks like this:

In this graph, the horizontal x-axis is time (the date), and the vertical axis is the orbital period of the binary. Two scales are shown for the vertical axis. On the left is period in hours, and on the right is the period in seconds relative to 11 hours exactly. (So, on the right, a period of 11h00m05s will plot as +5 and a period of 10h59m55s will plot as -5.)

Each measurement of the period has a red dot and a vertical bar that shows the uncertainty of the measurement. A short vertical bar means that this particular measurement is more certain (less fuzzy) than a point with a long vertical bar. (There’s one vertical bar without a red dot. That’s because the red dot falls below the bottom of the plot.)

Measurements come from pairs of observing sessions. Whenever two observing sessions include data from the same part of the binary’s orbit, we can estimate the average period of the binary in between those two observing sessions by finding the value of the period that gives the best (smoothest) overlap when that overlap data is plotted in the phase plot. The time of that measurement is taken to be the time halfway between the two observing sessions.

Measurement uncertainty is driven by several things. First, if the data is noisy (lots of data scatter in the brightness measurements), then the timing uncertainty tends to be bigger. Second, if the number of days between the two observing sessions is big, then the uncertainty tends to be smaller, since the timing uncertainty is divided by the number of orbits that have been completed. If the overlapped data covers multiple hours, the uncertainty will be smaller than if the overlap only lasts a few minutes. Finally, if the brightness doesn’t change very quickly during the overlap period, then the uncertainty can be high. (There’s one overlap period where the brightness is essentially constant. I had to throw out this measurement.)

And the green line is the weighted straight line best fit to the data (a so-called weighted linear regression). (“Weighted” means that measurement uncertainty (the vertical uncertainty bars) have been taken into account in finding the best fit — points with small uncertainty have a bigger influence on the green line than points with large uncertainty.) If that line has a positive slope, then the period is getting longer (and the stars are spiraling outward from each other); a negative slope means that the two stars are spiraling inward. The current green line has a slope of +0.007 seconds/orbit, but has an uncertainty several times bigger than that. Our data so far rules out nothing, and is consistent with the orbit being stable, with them spiraling inward, and with them spiraling outward.

So, we just don’t know yet! We need more data, more images of KIC 9832227. (We currently have 1,934 brightness measurements, one per image.)