Figure 3 (click here) and 4 (click here) show the proper motion differences H37cr-absolute for all 360 selected Hipparcos stars before the determination of the spin parameters. The data were binned in five intervals, with 27, 77, 145, 84 and 26 (from bright to faint) stars, respectively.
Figure 3: Proper motion differences
H37cr-absolute in over the B
magnitude. All 360 stars with reliable measurements are plotted.
Filled squares with error bars show the mean differences and
their dispersions in five intervals:
and
.
Only the stars on the right side of the dashed
line (
) were used in the final solution
Figure 4: Same as Fig. 3, but for proper motion differences
. Filled rhombs and error bars show the
mean proper motion differences and their dispersions
over the B magnitude
Figure 5: Change of the dispersion of the proper motion differences
H37cr-absolute in (filled squares)
and
(filled rhombs) over the B magnitude.
The 360 stars with reliable measurements were binned in five
intervals:
and
. Only the stars on the right side of the dashed
line (
) were used in the final solution
Figure 6: Values of computed from all stars with
.
The lower diagrams show for the star solution the number of stars
included and for the field solution the range of the number of
stars per field and as crosses the mean number over all fields
Figure 5 (click here) shows the dispersion of the proper motion differences H37cr-absolute for the same magnitude intervals. A clear trend towards smaller dispersions with fainter stars can be seen. The larger dispersions of the proper motion differences H37cr-absolute of bright stars in Fig. 5 (click here) are caused by larger errors in our proper motion determination for these stars. There is a deviation of the mean differences H37cr-absolute from zero seen in Fig. 3 (click here), and especially in Fig. 4 (click here) for the bright stars. This possible systematic error in the obtained absolute proper motions of bright stars makes an exclusion of these stars from the final link plausible. A further argument for their exclusion is their nonuniform distribution over the link fields (compare the last two columns in Table 1 (click here)) which may lead to systematic effect in the determination of the spin parameters.
A simple test of the magnitude dependence of the link coefficients was made:
The whole set was subdivided into 2 subsets of 180 bright ()
and 180 faint (B > 9.5) stars. The computation of the rotation
parameters
,
,
yielded significantly different
results for these subsets.
To study this magnitude dependent effect in more detail, the bright stars were
successively omitted from the solution in steps of 0.1 mag (see
Fig. 6 (click here)). Due to the
relatively small number of bright stars (only 27 stars with B < 8)
there are almost no changes in the left part of the diagrams in
Fig. 6 (click here). But from
to
a trend can be seen,
i.e. the bright stars increase the values of
and
systematically. The number of stars per field (see lower right
diagram of Fig. 6 (click here)) decreases rapidly for
. From
there are only one or no stars in some of the link
fields, i.e. the solution becomes unstable. Therefore,
the selected value
represents a compromise between a
sufficient number of stars (per link field) and a minimum influence of
bright stars affected by larger (and possible systematic) proper motion errors.
Final solution with 256 stars in 24 fields | |
referred to the final Hipparcos system (see Sect. 6 (click here)) | |
star solution | field solution |
residual spin parameters [mas/yr] | |
![]() | ![]() |
![]() | ![]() |
![]() | ![]() |
rms of solution | |
6.5 mas/yr | 3.1 mas/yr |
correlation coefficients | |
rxy = +0.20 | rxy = +0.21 |
rxz = -0.04 | rxz = -0.04 |
ryz = -0.04 | ryz = -0.01. |
The final solution for the spin parameters was obtained with 256 stars
with distributed over 24 link fields. The minimum number of
stars per field was 4.
The star solution and the field solution show the same behaviour in Fig. 6 (click here) although the errors of the spin parameters from the field solution are larger. In every case, the star solution and the field solution agree within their errors.