AAO Newsletter October 1996 - Page 7
Requirements for 2dF
The 2dF manual suggests that target coordinates should be accurate
to 0.5 arcsec. However in order to position the telescope accurately onto
these targets, the positions of the 4 reference stars must also be measured
to the same precision and with no systematic offset from the target
coordinate frame. This condition requires that the stars be fainter
than about BJ = 11 mag (see Drinkwater,
Barnes, & Ellison, 1995, PASA, 12, 248). There will be additional errors
in the reference star positions if any of them have proper motions and
have moved significantly between the epoch of the original target data
and the 2dF observation. In this article we describe measurements we have
made of the mean proper motions of stars that might be used for 2dF.
2dF uses four reference stars so there is a degree of redundancy built-in:
if one star has moved, the others still define the correct position. However
if two stars have moved the redundancy is not enough because the motions
can be in the same direction in which case it would not be possible
to tell which pair was correct. We therefore adopt a conservative requirement
for the reference stars that no more than one move more than 0.45
arcsec between epochs. This limit corresponds to three different domains
of proper motion corresponding to the different plate material used for
the target positions. If recent Second Epoch Survey (SES) plates about
3 years old are used the limit is 150 milliarcsec per year (mas/y); for
5 year old SES plates the limit is 90 mas/y. If the targets are measured
from the original blue survey (SRC J/EJ) plates, about 15 years old, proper
motion is more likely to be a problem and the limit is 30 mas/y.
What we measure below is the probability p that a single star
moves too far. We use the binomial theorem to calculate the probability
of our desired result (that only 0 or 1 stars out of 4 move) in terms of
p. This is P(< 2; p, 4) = (1 - p)4 + 4p(1
- p)3. For p = 0.10, P = 0.948 and for
p = 0.05, P = 0.986. So if the probability of a single star moving
is 10% we are 95% confident of getting the right position. To be sure of
the correct position at the 99% level, we require that the probability
a single star moves be 5% or less.
Method: Analysis of Sky Survey Plates
The APM Sky Catalogues (available at http://www.aao.gov.au/local/www/apmcatbin/
at AAO or http://www.ast.cam.ac.uk/~apmcat/ at RGO) include data from both
the POSS-I and UKST ER red surveys which overlap in the equatorial region
(dec. = 0°) with a typical epoch difference of 40 years. We used these
to measure accurate proper motions from the overlapping regions of four
POSS-I/UKST plate pairs. We used a simple matching algorithm to find the
stars with significant proper motions: we assumed that the majority of
stars were not moving and used these to define a transformation between
the coordinates on the two plates with an uncertainty of 0.5 arcsec. We
then selected all stars with position "errors" of 1.2- 7.5 arcsec
corresponding to proper motions of 30-180 mas/y. This gave a set of moving
stars detected at the 3 sigma level. Several additional tests based on
the image parameters from both plates were imposed to minimise the number
of false detections in conjunction with visual inspection of the objects
on the plates. We also limited the search to the magnitude range 11 <
mR < 16 of interest for 2dF.
Results
We first considered the percentage of stars with proper motions of µ
> 30 mas/y in one field as a function of magnitude. The results, given
in Figure 5 show that the fraction of moving stars drops as the stars get
fainter. The values (around 9%) for the fainter stars are still somewhat
too high for 2dF use. At higher limits of proper motion the fractions of
moving stars are much lower. At the
