Bruce L. Gary; Hereford Arizona Observatory

This web page shows the brightness stability of candidate reference stars for the XO-1 star field. During a 4-week period in April/May I observed the region of interest on 20 nights for the purpose of searching for XO-1 fadings. In the process of performing this analysis I was able to study the stability of 4 nearby reference stars. Each reference star appears to exhibit variations of a few mmag with periods of 1 to 2 months. XO-1 appears to be stable at the 4 mmag level.

This is a project suited to a single telescope, using the same telescope configuration, the same analysis software and performed by the same person.  The only thing that was different each observing session was a new flat field (and sometimes dark frames). I placed the autoguider at the same pixel location, and the AO-7 tip/tilt image stabilizer keeps the star field on the main chip at the same pixel location for the entire observing session with an accuracy of ~2 pixels. Ensemble photometry was performed with the same 4 reference stars using the same magnitude assignments, and I used the same photometry aperture pixel settings. Extinction changes were monitored on an image-by-image basis, and those with >1.5% additional extinction (due to clouds) were rejected. I also used the same spreadsheet template and rules for rejecting outlier data (>8 mmag). I claim that this is the kind of project that groups of amateurs could not perform, that it has to be performed by a single person using a dedicated facility, and that is not well-suited for professional observatories due to the large amount of telescope time required.

Finder chart

Figure 1. "Finder chart" for XO-1 showing 4 reference stars and one check star. FOV = 14.2 x 19.0 'arc, north up and east left (crop of original).

Reference star R-mag's are 11.046, 9.261, 10.680 and 10.330. The check star has R-mag = 12.282 and XO-1 has R-mag = 10.806. These R-mag's are based on all-sky photometry observations in February and March, 2006.

Under the assumption that none of the reference stars is variable the XO-1 R-magnitude was derived versus date, as shown below.

XO1 Nightly LC uncorrected

Figure 2. XO-1 R-magnitude for dates 2006.04.16 to 2006.05.14 under the assumption that none of the reference stars was variable.

Throughout this 29-day observing period the star of interest appears to be stable at about the 4 mmag level. As the following graph shows there are no obvious variations of the nearby check star.

Check star - uncorrected

Figure 3. Check star R-band brightness versus date. No discernible periodicity is present. (Twice the R-mag range as in Fig. 1.)

Part of the explanation for the check star's larger scatter is due to its being 1/4th as bright as XO-1.  

Before showing the graphs of apparent R-mag for the 4 reference stars let's consider what happens during an ensemble photometry analysis. The user assigns magnitudes to each star and the photometry tool adjusts an offset that's applied to all of them so that the average difference with the user-assigned magnitudes is zero. The solution text file that's created includes the apparent magnitude for the unknown object, the magnitude for check stars, and the apparent magnitudes for all reference stars. Therefore, if one reference star is a variable the text file will show magnitudes for the reference stars that are affected by the one variable. For example, if Ref#4 is variable with amplitude Y then Ref#1, 2 and 3 will vary in the opposite direction with an amplitude 1/4 of Ref#4's amplitude.

If only one of the 4 references stars is a variable the expected pattern of their ensemble photometry variations is easy to identify and interpret. When two or more of the reference stars is variable the solution is not straight forward (for me). In the present case it appears that all four reference stars are variable at a low level. The following plots show the apparent ensemble R-magnitudes for a 4-week period and the model predicted variations using one of many possible solutions.

Ref star uncorrected LCs

Figure 4. Reference stars R-band brightness versus date that results from an ensemble photometry solution that forces the average for each date to be the same. The traces are based on a model in which periodic variations are assigned to each star in a subjective manner.

Figure 5. Modeled true variations of reference stars after adopting one of many possible models for their variability. Typical RMS deviations from the model are 3 mmag (with an occasional much larger "outlier" such as for DOY = 116).

All apparent variations exhibit a reasonably good fit with the model. This model of true brightness variation for each reference star can be used to produce a correction for any stars in the FOV. The following is a graph of the model-based correction that should be applied to XO-1 and the check star.

Figure 6. Model-based correction required by the fact that the reference stars are variable.

Figure 7. XO-1 and check star nightly light curve after applying corrections based on the model in which all reference stars are variable. (Same R -mag scale as in previous figure.)

After applying the R-magnitude corrections of Fig. 6 to XO-1 and the check star there is only a small variation for XO-1 and no obvious variation for the check star. The modeled 1 mmag sinusoid fit to the XO-1 brightnesses is uncertain due to the way subjective assumptions for the reference star variations change the correction model (Fig. 6).

Figure 8. Expanded version of the 4-week light curve for XO-1. The RMS deviation from the average is 2.2 mmag.

Based on this graph I take the position that the star of interest does not vary more than ~ 5 mmag.

Many uncertainties are present due to the subjective nature of modeling reference star variability. This is a "work in progress."


This site opened:  April 30, 2006 Last Update:  May 15, 2006