UT Sep 03, 2022: Astrometry of Ross 248 and GX And, notes on astrometry network

Michael Richmond
Sep 05, 2022

On the night of Sep 02/03, 2022, under good conditions, I acquired images of

These are the second measurements of these stars that I have made in over a year. In the course of analyzing the results, I discovered a potentially important effect of the number of stars used as astrometric references. I'll place those notes at the end of this document.

These measurements are made in the "traditional" manner, similar to that used for the many measurements in previous years:


Ross 248

This is one of the stars that a capstone student may study over the next year in a project involving parallax. Ross 248 is a relatively faint red star surrounded by many other stars of similar brightness, so it's a good candidate for high-precision parallax measurements.

These observations involved:

The object is (currently) near position



  RA = 23:41:55.27     Dec = +44:10:06.38    (J2000)

A chart of the field is shown below. The size of the chart is about 41 x 27 arcminutes. The noisy area at right (West) is the shadow of the guider's pickoff mirror.

I've marked the location of several comparison stars.



  star       UCAC4               B          V         r       
-------------------------------------------------------------------------

   A     UCAC4 671-120730      12.617     10.689                        

   B     UCAC4 671-120688                                            

   C     UCAC4 671-120749      10.987     10.663         


   P     kappa And              4.06       4.14

--------------------------------------------------------------------------

 

I took a photo of the finder TV's screen when pointing to Ross 248; this could be a useful reference for the future:

Here are the positions I've measured so far. The most recent measurements are at bottom right.


GX And

Like Ross 248, GX And is a nearby (binary) star which will be the target of a parallax project in the coming year. One of the two components is bright -- about mag V = 8 -- so one must use short exposures to prevent it from saturating the detector. That may mean that this system isn't as easy to measure as Ross 248 or some others.

On this night, for GX And,

The object is currently close to this position:



  RA = 00:18:28.4  	  Dec = +44:01:31     (J2000)

but it does have a very high proper motion.

A chart of the field is shown below. The size of the chart is about 41 x 27 arcminutes. The noisy area at right (West) is the shadow of the guider's pickoff mirror.

The two components of the GX And binary sit inside the box. I've marked the location of several comparison stars as well.



  star       UCAC4               B          V          r
-----------------------------------------------------------

   A        671-001473          9.939      9.790        

   B        670-001639          9.413      8.472        

   C        671-001509         12.712     11.421     11.001

-----------------------------------------------------------

 

I took a photo of the finder TV's screen when pointing to GX And; this could be a useful reference for the future:

Using the same techniques as described for earlier nights, I matched detected stellar positions to the Gaia DR2 catalog.

The target is moving to the upper-right with time, and clearly shows the back-and-forth motion due to parallax.


Notes on astrometry and reference stars

When I analyzed the data for Ross 248 in the usual manner -- as I have done for all the other nights of measurements of this star -- I was surprised in an unpleasant way by one aspect of the results: the star's RA position was far from its expected position. Look at the rightmost symbol in the top panel of this graph:

The measured RA position is a full 400 milli-arcseconds or so away from the expected position. That is much, much larger than the estimated uncertainty in the measured position, which was only 50 or milli-arcseconds.

What was going on?

After some investigation, I think I've found the answer. The choice of astrometric reference stars can cause the derived position of the target to change by hundreds of milli-arcseconds. Now, in the analysis that follows, I've chosen reference stars from the Gaia EDR3 catalog. The big question is -- WHICH catalog stars are used to match against stars detected in the field?

My default has been to use all the stars detected in each image to act as possible astrometric references. However, after some noodling around with different choices, I don't think that's the best idea. Consider the following four choices for reference stars:

  1. "small" net: stars within 300 pixels = 7 arcmin
  2. "intermediate" net: stars within 500 pixels = 10.5 arcmin
  3. "largeish" net: stars within 700 pixels = 14.7 arcmin
  4. "full" net: all stars in the field = ≤ 19 arcmin

In all cases, there are plenty of stars to derive a good astrometric transformation; the linear model I've adopted requires a minimum of three stars, and the networks listed above have about 10, 34, 56, and 81 stars, respectively. I acquired about 98 images of the field, and processed all of them independently. The graph below shows the derived positions for Ross 248 in each image, for each of the four possible networks.

First, note that there is quite a scatter between positions derived within each set of images, so that each clump of symbols has a dispersion of ±0.15 arcsec or so. That scatter does NOT change with the choice of reference star network, so it is presumably a function of the atmosphere or instrumental factors.

But second, note that while the Dec position is roughly the same for all four choices, the RA position is not. The RA position drifts systematically to the West (negative RA) as more astrometric stars are added to the solution. This drift is much larger in size than the typical scatter from one image to another image.

That's not the only consequence of including more stars in the solution. The table below lists the typical residual in each reference star's postion relative to its catalog position.



reference network           RA residual (arcsec)        Dec residual (arcsec)
------------------------------------------------------------------------------
   small                              0.077                    0.047

   intermediate                       0.166                    0.127
 
   largeish                           0.220                    0.166

   full                               0.343                    0.244
------------------------------------------------------------------------------

If I adopt the "small" network of astrometric reference stars, then the position we derive for Ross 248 on the night does agree very well with the position predicted on the basis of its Gaia distance and proper motion:

However, this change in reference network does not help the measurement made on UT 2022 July 31; in fact, it pushes the RA value slightly farther away from the predicted position. Then again, that measurement was made without a filter, so we might expect some shift due to differential refraction.

In any case, I will keep a close eye on this effect of the reference network in the future.