KIC 8462852 Reference Star Analysis, Hereford Arizona Observatory Observations
Bruce L. Gary, 2017.09.010, 01 UT

In 2015 I performed all-sky photometry calibrations of 25 nearby stars for later use as reference stars for Tabby Star calibration. Since then I have excluded use of 10 of them due to either extreme redness, variability or a high 4-month trend. The remaining 15 stars are stable at the level of ~ 3 mmag over the 4-month interval 2017 May to Sep.

It is obvious that the fraction of stars that are suitable for use as reference will depend on the goal for the target star's amount of variation. For example, a star that undergoes 1.0 mag variations during the course of a few hours (e.g., a
cataclysmic variable) can be monitored adequately by using a reference star that undergoes much smaller variations on the same time scale, such as 0.010 variability (1 %) with day or longer periods. AAVSO observers typically use one reference star and one check star, and when the check star (also calibrated using the same reference star) appears constant the target star's variations are accepted as valid. Tabby's Star has significantly different requirements because our goal is to avoid systematic errors of 0.001 magnitude during several months of observations! Note that 0.001 mag equates to 0.1%, and our goal is to characterize the shape of fades that are only 0.010 mag deep (normalized flux depth of 1.0 %).

We must confront the rare question: How many stars are well-behaved at the 1 mmag level over timescales of several months?

My tentative answer is that ~ 60 % of stars are well-behaved at the 3 mmag level over several month timescales. In other words, the common practice of using one reference star and one check star (used by most AAVSO observers) will produce spurious results 40 % of the time unless a careful process is used in choosing the reference star. Ensemble photometry makes use of several reference stars, so if one of them is variable its effect on the ensemble calibration is reduced. For this reason, I initially began with 25 stars for ensemble photometry, but quickly reduced the number to to 23 because of two that were very red. After a few months I recognized that a few stars were simply too "noisy," for an unknown reason, so they were rejected from use. After acquiring several months of measurements it became possible to identify three stars that trended (linearly) by an amount exceeding 30 millionths of a magnitude per day, so these were rejected from use. I'm now down to just 15 that are well-behaved. The ensemble photometry of 15 well-behaved reference stars is therefore used for deriving both multi-month long-term variations and also multi-day dips with respect to the long-term variation.

Figure 1. Final plot of long-term variation of TS OOT V-mags based on the 10 best-behaved reference stars. The model is a  fit for only the 4-months of data from 2107 May to Sep.

Figure 2. Average of all TS V-mags (OOT and dips) vs date for 2017 May to Sep.

Reference Star List

The following 25 stars were included in my all-sky photometry measurements, and subsets of these have been adopted for calibration since 2015, when my long-term monitoring observations began. Four of them were found to be unusable either due to their extreme redness or "noisiness" (5, 13, 19 & 22). Three more have been deemed undesirable based on their slow, long-term (linear) drift (6, 14 & 20). I have discontinued using them.   

Figure 3. Finder image, with reference stars numbered. North up, east left. FOV = 14.0x9.4 'arc. Table on right summarizes the properties of each star used for either accepting or rejecting a candidate reference star for use. [Choose a wide screen view to see the table next to the image.]

The "score" values in the above table are based on redness, variability and trend. There are 10 stars with a "Good" score. The variability properties are shown in the next graph.

Figure 4. RMS scatter vs. V-mag for all candidate reference stars. The 5 stars rejected for their variability are labeled in the right panel.

I want to thank Tabby for pointing out to me (2016 December 11) that Star#24 appears in Kepler data to be a periodic (rotational) variable (with a 16.3-day period, full amplitude of 8.4 mmag). I also want to thank Rafik Bourne for independently notifying me (2017 September 09) that Star#24 is variable in Kepler data at about the 1% level (actually, 0.77 % peak-to-peak variation). I had neglected to reject Star#24 from use last year based on Tabby's warning - no excuses.

The trend properties are shown in the following graphs.

Figure 5. Panels A through F show V-mag vs. date for selections of candidate reference stars. Arbitrary offsets have been added to each star's V-mag. 

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