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4. Determination of the spin parameters

The systematic part of the difference between the Hipparcos positions and positions in an inertial reference system can be described by a rotation. Whereas, the differences in proper motions are represented by the spin, the time derivative of the rotation. For the determination of the spin vector tex2html_wrap_inline1082 we used the basic equations
 displaymath1080

tex2html_wrap_inline1084 and tex2html_wrap_inline1086 are the proper motion differences in the sense Hipparcos minus absolute, tex2html_wrap_inline1088 and tex2html_wrap_inline1090 are the equatorial coordinates of the link stars. The indices x to z refer to a right-handed triad with the x-axis pointing towards the vernal equinox and the z-axis towards the north equatorial pole.

The tex2html_wrap_inline1100 were computed from both components of the proper motion differences, i.e. from the least squares solution of 2n equations, where n is the number of link stars. This is called the "star solution''. For three out of 360 stars used in the solution, proper motions were determined in two fields (M3-Z and M3-IV). In the star solution we used the average of both proper motion determinations for these stars.

The proper motion differences tex2html_wrap_inline1106 in a given field may be correlated due to a systematic error of the extragalactic link in each field. Therefore, we used the average proper motion differences for each field in a second least squares solution of 2m equations, where m is the number of link fields. This is called the "field solution''.

Both, star and field solution should be identical if the stars are homogeneously distributed in the fields with the same weights and if the fields are homogeneously distributed over the sky. This is not the case, therefore the solutions will differ. Formally, the rms error of the star solution is smaller than that of the field solution because of the greater number of equations.

Using H37cr data and the absolute proper motions of all 360 stars in the whole magnitude interval 6 < B < 13 the following results were obtained, for the star solution and the field solution, respectively:

preliminary solution with 360 stars in 24 fields
referred to the final Hipparcos system (see Sect. 6 (click here))
star solution field solution
residual spin parameters [mas/yr]
tex2html_wrap_inline1114 tex2html_wrap_inline1116
tex2html_wrap_inline1118 tex2html_wrap_inline1120
tex2html_wrap_inline1122 tex2html_wrap_inline1124
rms of solution
6.9 mas/yr 3.1 mas/yr
correlation coefficients
rxy = +0.20 rxy = +0.21
rxz = +0.04 rxz = -0.04
ryz = +0.02 ryz = -0.01.


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