Astronomical Applications Department, U.S. Naval Observatory pm AAS poster Page 15
Deriving External Errors for the Catalogs
Suppose
x
and
y
represent the mean external errors in the proper motions,
µ
, in two indepen-
dent star catalogs, x and y. Then a star-by-star comparison of the proper motions should yield a
difference distribution with an RMS,
yx
, given by
yx
2
=
x
2
+
y
2
. The same relation holds if
the relative proper motions,
µ
, of stars in double systems are being compared, as is the case
here. For the three difference distributions shown above, then, we should have:
(measured RMS of
µ
TYC
µ
HIP
distribution)
2
=
2
TYCHIP
=
2
TYC
+
2
HIP
(measured RMS of
µ
WDS
µ
HIP
distribution)
2
=
2
WDSHIP
=
2
WDS
+
2
HIP
(measured RMS of
µ
WDS
µ
TYC
distribution)
2
=
2
WDSTYC
=
2
WDS
+
2
TYC
We have three equations in three unknowns, which can be solved for
2
HIP
,
2
TYC
, and
2
WDS,
the
squares of the estimated external mean errors of the relative proper motions from our three data
sources. It is only because of the three-way catalog comparison that such estimates of the mean
errors in the individual catalogs can be obtained.
Solving, we obtain:
µ
(RA):
WDS
= 2.44
TYC
= 3.53
HIP
= 4.88
µ
(Dec):
WDS
= 1.35
TYC
= 3.39
HIP
= 5.11
(units are mas/yr)
