We correct all centroids of target stars and reference stars for differential chromatic refraction (DCR). These corrections are needed to account for the target star and its reference stars not being of identical color, which causes their positions as seen from Earth to shift relative to one another due to atmospheric refraction. The amount of correction needed for each star depends on the filter used and the hour angle of observation, as well as the temperature, pressure, and humidity; however, these environmental factors can be ignored assuming we have stable observing conditions, as discussed in Monet et al. (1992) and Stone (1996). To see at length how DCR correction is performed for our astrometry targets, see Jao et al. (2005).
62 As an example, Figure 5.1 displays the difference in astrometric residuals obtained with and without correction for G 169-029, which was observed in the R filter. The refraction correction to the centroids for G 169-029 led to a change in its final position as large as
∼20 mas in the R.A. axis compared to the frames uncorrected for DCR. Comparatively, the correction for centroids in the Decl. axis leads to a much smaller change in the final positions; the centroid correction for the Decl. axis is almost zero when the star is observed near zero hour angle (Jao et al. 2005). In Figure 5.1, the residual deviations (in later chapters referred to as the series deviations) are the standard deviations of the astrometric measurements and the mean errors (in later chapters referred to as the nightly errors) are the average statistical uncertainties of all the measurements. For the R.A. axes of G 169-029 with DCR correction the series deviation is 2.4 times less than the series deviation without DCR correction.
After correcting for DCR, we measure accurate positions using the SExtractor Centroid- ing algorithm from Bertin & Arnouts (1996) and use the Gaussfit program (Jefferys et al. 1987) to simultaneously solve for the parallax relative to the reference stars and proper motion using all available data (for more details see Jao et al. 2005). The Gaussfit program computes a least-squares fit to the astrometric equations and determines the best answer by minimizing χ2
. If after running our Gaussfit program, reference stars are found to have proper motions greater than 0′′.
05/yr or parallaxes greater than 10 mas based on photometric parallaxes, then those stars are rejected as reference stars. To obtain the absolute parallax of our target star, we must correct for the parallactic motion of the reference stars as these stars are not infinitely far away. We use photometric parallaxes and accurate V, R and I
63
Figure 5.1: DCR correction for G 169-029. The left panels show the astrometric residuals of G 169-029 without DCR correction, while right panels show the residuals with DCR correction. The filled circles indicate nights with multiple exposures (typically 5), whereas the open circles are taken on nights with a single frame of data (typically for photome- try). Examination of the two plots shows a significant improvement in the RA astrometric residuals.
photometry described in §4 to correct our relative parallax to the absolute parallax value (Jao et al. 2005). All of the remaining frames are used to fit the parallactic orbit of the star, including single frames on photometric nights. However, only nights with 2 or more good images are used to search for any residual astrometric signal that remains after correcting for the parallactic motion and proper motion of our target.
During the ∼16 years of astrometric observations, two different VJ filters were used. The first VJ filter was cracked and was replaced in February 2005 with a nearly identical
VJ filter, which we adopted assuming that it possessed a similar enough transmission profile as the original to provide consistent astrometry. After a few years of obtaining data, we noticed a few milli-arcsecond (mas) offset in the astrometric residuals of some stars that
64 were known to be single from other techniques (Subasavage et al. 2009); we determined that the offset first appeared when we replaced theVJ filter. The effect of using the replacement
VJ filter is more clearly seen in the astrometric residuals in the right ascension axis. After a close inspection of the first VJ filter, it was realized that the small crack does not project onto the part of the chip that is regularly used (i.e. the central quarter). Therefore, in July 2009, we replaced the second VJ filter with the original VJ filter (Riedel et al. 2010). All data acquired after July 2009 were with the originalVJ filter. Using data from both filters may increase the parallax error, but does not change the parallax value (Subasavage et al. 2009; Riedel et al. 2010) and the average residual deviation for the stars is still less than 4 mas for 35 stars observed in the VJ filter (see §7.3). Therefore, we choose to use data obtained in both filters to maximize the time coverage.
Parallax errors are determined by adding in quadrature the relative parallax error given by the Gaussfit program (Jefferys et al. 1987) and the absolute parallax correction (for more details see Jao et al. 2005). The errors for the residual astrometric signal are determined empirically based on both the nightly dispersions and the overall dispersions. The parallax errors and the errors for the residual astrometric signal are discussed further in §6.1 and
65
– 6 –
Astrometric Results