Astrometry: The Proper Motion of Barnard's Star

 
Astrometry is the art and science of measuring the postions of celestial objects. AIP4Win has three software tools that make use of astrometry: the Astrometry Tool, the Distance Tool, and the Magnitude Measurement Tool. In the summer of 2009, I began to wonder what the limit of CCD astrometric measurement might be. I began to look for a project that would push the normal "measure an asteroid" type astrometry to its limits.

Proper motion (µ=mu)

RA: -0.79871 arcsec/yr
Dec.: 10.33777 arcsec/yr

Parallax (p=pi)

0.5454 ± 0.0003 arcsec

Distance

5.98 ± 0.003 light-years
The otherwise inconspicuous red dwarf, Barnard's Star, has an annual proper motion of 10.3 arcseconds per year. A change that large is easy to measure with conventional astrometry. The challenge I took was this: what is the shortest time interval that would allow me to detect -- unambiguously -- the proper motion of Barnard's Star. The answer turns out to be somewhere between five and seven days.

Initial Observations

Barnard's Star is located in Ophiuchus a few degrees east of beta Ophiuchi, near the open cluster IC4665. Visually, it is a tenth magnitude star.

I made a first group of observations on four nights in June/July 2009 from Alpaca Meadows Observatory and Pine Mountain Observatory. At Alpaca Meadows, I used an 8-inch f/4 Newtonian reflector plus ParaCorr coma corrector, and on Pine Mountain, a Celestron 11-inch f/10 EdgeHD. At both sites, I used my QSI 532ws CCD camera with a photometric V filter. Observations were reduced using AIP4Win v2.3.11 (beta) in debug mode, since the exercise was to serve the dual purposes of reducing the image data and debugging new features in the AIP4Win software.

2009-06-27/28: This was a trial run. I made a test sequence consisting of 5 repetions of 50-second integrations through B, V, Rc, Ic filters using the 8-inch Newtonian. Preliminary reduction showed a "color term," that is, the measured astrometric coordinates for the star appeared to depend on the filter used.

2009-07-15/16: This was a trial run at Pine Mountain, immediate before the Russ Genet Summer Science Workshop. Danyal Medley of Celestron brought a CGE Pro mount with the 11-inch EdgeHD, Celestron's new flat-field SCT astrograph. I ran the same sequence of 5 repetitions of 50 second integrations through the B, V, Rc, Ic filter sequence. Preliminary reduction showed some dependence of the measured astrometric coordinates on the star's position in the field.

2009-07-17/18: These observations were sequeezed in before beginning a photometric run on the SX Phe star XX Cygni with two students, Jared Green and Nick Rebol, and Professor Rick Watkins of Willamette University, with Danyal again assisting. This effort netted ten further integrations throught the V filter. I didn't look at these images until I was home again.

2009-07-24/25: Back at Alpaca Meadows again, I did run intended to produce 10 repetitions of a sequence of 10, 20, and 50 second exposures all through the V filter. This clock drive was running erratically, so tracking was poor. This effort netted 27 usable exposures.

To make careful astrometric measurements, I selected 11 reference stars from the USNO UCAC2 catalog. Each star is reasonably well isolated from faint background stars and is available on images taken with the reflector and SCT. The astrometric residuals in RA and Dec were both close to 0.1 arcseconds. The reference stars are shown below:

Barnard's Star: 17h 57m 47.98 +04d 43' 15.5 (J2000) 2009.646 epoch of observation

Barnard's Star is the bright object in the center. This image was made by summing a total of 48 images shot through the 11-inch EdgeHD using different color filters during the two nights on Pine Mountain. It shows much fainter stars than any of the individual images used for astrometry.

Finally, using a new feature just added to the Magnitude Measurement Tool, I did astrometry on all of the images from all four nights. I used every image, even those with very poor tracking. The results are summarized in an Excel graph below:

The small diamonds in the graph show every image individually. The large circles show the means for each night. The table below gives the standard deviations in arcseconds for each of the nights of observation. One image in the June 27/28 group was poorly tracked and gave a clearly outlying value. Both groups taken with the 11-inch SCT are tightly grouped. The July 24/25 group shows an approximately uniform distribution of position errors about the mean value. North is up; east is the the left. Each major division on the axes is 0.0001 degrees = 0.36 arcseconds.

Date

StDev in RA [arcsec]

StDev in Dec [arcsec]

June 27/28

0.247

0.229

July 15/16

0.065

0.074

July 17/18

0.067

0.036

July 24/25

0.136

0.103
The motion of Barnard's Star to the north and west is clearly visible in the plot. The northward motion is almost entirely due to proper motion; the westward motion is due to proper motion plus the shift due to trigonometric parallax. This motion should stop and then reverse in the coming months.

Two Nights' More Observations
Two further nights' determination from Alpaca Meadows with the Vixen R200SS telescope extend the proper motion graph below. On August 16/17, I took 20 images of 50 seconds exposure eachwith the V filter; on August 24/24, I took another 20 images with 30 seconds exposure each, again, using the V filter. The August AIP4Win v2.3.15(beta) has new functions in the Magnitude Measurement Tool that simplify measuring coordinates from a series of images.

Here is the new graph:
Date

StDev in RA [arcsec]

StDev in Dec [arcsec]

August 16/17

0.097

0.056

August 23/24

0.054

0.090
In addition, more care in taking the images, especially insuring better focus and getting better tracking seemes to have resulted in considerably smaller standard deviations, as shown by the quantitatively in the table and qualitatively by tight clustering of individual points on the plot for each of the two nights.

Stay tuned for more observations...

--Richard Berry
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