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UPDATING OF B1950 RADIO STAR POSITIONS BY MEANS OF J2000 CALIBRATORS

R.Hering and H.G.Walter
Astronomisches Rechen-Institut, Mönchhofstrasse 12 -14, D-69120 Heidelberg, Germany

 

Starting Basis

Radio star observations make use of extragalactic calibrators. The International Celestial Reference Frame (ICRF) provides updated calibrator positions referring to the coordinate frame of J2000.0. This fact stimulates the demand for a procedure that allows the relative observations of radio stars, originally reduced to B1950.0, to profit from the revised positions of the calibrators. Given are the radio star positions at some observation epoch with reference to the equator and equinox of B1950, and the positions formally transformed from B1950 to J2000 (Aoki et al. 1983). The radio star positions are derived from differential radio observations of the star with respect to a close by extragalactic object, the calibrator, with coordinates referred to B1950. These arc measurements may be assumed to be accurate to 20 - 30 mas.

The Problem

When the revised J2000 position of the calibrator is given with reference to the ICRF, the problem is to determine the respective radio star position. Note that the corrected radio star position cannot be found from comparing the revised J2000 position of the calibrator with the calibrator position which results from the formal transformation of the B1950 position to J2000 since, in general, the observation epoch of the B1950 position is missing.

The Procedure

Starting from the position vectors of the radio star (R) and the calibrator (C), which usually is a quasar, the difference vector in the sense R-C is determined with reference to the J2000 coordinate frame. For this purpose the difference vector is formed at the observation epoch of the radio star (Fig. 1). The length of the vector is independent of the actual position of the calibrator and is invariant to rigid rotations of the coordinate frame.

Let   rR  and  rC   be the position vectors of the radio star and the calibrator, respectively, referred to B1950, the following steps are performed :

Step 1. Using Newcomb's precession for precessing   rR  and rC   to the equator and equinox at   t0 , where  t0   is the observation epoch of the radio star.

Step 2. Eliminating the terms of elliptic aberration from   rR  and  rC ,  yielding   rR1  and  rC1 .

Step 3. Forming the difference vector   Delta(r) = rR1 - rC1 ,  which still refers to the equator and equinox at  t0 . Normalization by forming   Delta(r*) = Delta(r) / |Delta(r)| .

Step 4. Transformation of the direction defined by   Delta(r*)   to the equator and equinox J2000 taking account of the equinox motion and the IAU1976 precession. One gets   Delta(r*J) .

Step 5. The unit vector resulting from Step 4 provides the direction of   Delta(r)   referred to J2000 . Because of the invariant length of   Delta(r) , the difference vector between radio star and calibrator is   Delta(rJ) = |Delta(r)| · Delta(r*J) .

Step 6. The right ascension and declination of the radio star referred to J2000 and with respect to the new calibrator position,   rC(ICRF) , are obtained from   rR = Delta(rJ) + rC(ICRF)   after normalization.

Example

Calibrator :   1404+286 (FK4) RAC(B1950) = 14h04m45.s613 DECC(B1950) = 28°41'29."22 ,
  1404+286 (ICRF) RAC(J2000) = 14h07m00.s3944 DECC(J2000) = 28°27'14."690
  (Ma et al. 1997) .  
 
 
Radio star : HIP 66257=HR 5110 ,      Julian epoch of observation :   t0 = 1982.3619 ,
  RAR(B1950) = 13h32m32.s145    DECR(B1950) = 37°26'16."18     (Florkowski et al. 1985) .
 
  Updated radio star position with respect to the calibrator given in the ICRF :
  RAR(J2000) = 13h34m47.s6817 DECR(J2000) = 37°10'56."854 .
 

Difference between the updated radio star position and that one obtained by formal transformation from B1950 to J2000 :
  Delta(RA) · cos(DEC) = 0."020 Delta(DEC) = 0."007 .

 

Gth-Abb

Figure 1 :  Rotation of the difference vector Delta(r) from B1950 to J2000 .

 

References

Aoki S., Sóma M., Kinoshita H., Inoue K., 1983, A&A 128, 263
Florkowski D.R., Johnston K.J., Wade C.M., de Vegt C., 1985, AJ 90, 2381
Ma C., Arias E.F., Eubanks T.M., Fey A.L., Gontier A.-M., Jacobs C.S., Sovers O.J., Archinal B.A., Charlot P., 1997, The International Celestial Reference Frame realized by VLBI, IERS Technical Note 23, Part II, C. Ma and M. Feissel (eds.), Observatoire de Paris

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Created: 12 Feb 1999

e-mail :  R.Hering,  ARI