Early Radio Positions of Stars

THE ASTRONOMICAL JOURNAL, 117 : 483È491, 1999 January ( 1999. The American Astronomical Society. All rights reserved. Printed in U.S.A. EARLY RADIO POSITIONS OF STARS A. H. ANDREI Observatorio Nacional, CNPq, Rua General Jose Cristino 77, 20921-030 Sa8 o Cristova8 o, RJ, Brazil M. ASSAFIN Observatorio do Valongo, Universidade Federal do Rio de Janeiro, Ladeira Pedro Antoünio 43, 20080-090 Rio de Janeiro, RJ, Brazil AND S. P. PULIAEV,1 R. VIEIRA MARTINS, E. G. JILINSKI,1 AND W. BARTHOLOMEU E SILVA2 Observatorio Nacional, CNPq, Rua General Jose Cristino 77, 20921-030 Sa8 o Cristova8 o, RJ, Brazil Received 1998 June 29 ; accepted 1998 September 14 ABSTRACT Early radio positions for a sample of 100 Hipparcos stars, three Tycho-only stars, and nine radio stars with optical positions referred to the Hipparcos/ICRS frame are analyzed. The optical proper motions are used to compare the optical and radio positions. From an original sample of 247 radio positions for the above 112 stars, a set of 220 shows coincidence between the optical and radio centers of emission closer than 500 mas. This set is analyzed for systematic departures between the optical and radio positions. A smaller subset of 136 early radio positions for 72 stars show radio-minus-optical o†sets smaller than 100 mas and are useful for monitoring of the spin of the Hipparcos frame. Key word : astrometry 1. able information that can be used to calculate the Hipparcos frameÏs spin rate (Feissel & Mignard 1998). In this paper, we use a sample of 247 radio positions for 112 stars, gathered in the literature from di†erent research programs. The optical positions and proper motions were preferentially taken from the Hipparcos and Tycho Catalogues (ESA 1997), ensuring a rigid reference frame and high accuracy. A smaller subset of stars, for which no Hipparcos or Tycho positions exist, has been observed by the authors and placed on the Hipparcos frame. In a complementary fashion, stars from the Flagsta† program (Stone 1994), directly tied to the positions of extragalactic radio sources, were also used. The reliability of the radio positions is probed, and conclusions are drawn from the radio-minusoptical di†erences found. Section 2 presents the methods used to place in the Hipparcos/ICRS frame the non-Hipparcos and non-Tycho stars observed by the authors with the 0.40 m Zeiss astrograph of the Universidade Federal do Rio de Janeiro in Campinas, Sa8 o Paulo, or with the 1.60 m telescope of the Laboratorio Nacional de Astrof• sica with a CCD camera. In ° 3, the complete database is presented. In ° 4 the radiominus-optical o†sets are analyzed, and conclusions are drawn in ° 5. INTRODUCTION The determination of the radio astrometric positions of stars is a powerful tool for tying the optical and radio reference frames together. The radio-based International Celestial Reference Frame (ICRF ; Arias et al. 1995), characterized by hundreds of extragalactic point-source positions, and the optical frame deÐned by the Hipparcos Catalogue (ESA 1997) are realizations of the International Celestial Reference System (ICRS) at these wavelengths. The link between these frames can ideally be determined directly with positions of radio-emitting stars in the Hipparcos Catalogue. Observations at di†erent epochs enable the Hipparcos frameÏs spin rate to be computed relative to the ICRF. Both tasks have been e†ectively carried out for the orientation of the Hipparcos frame (Kovalevsky et al. 1997). However, the possibility of useful radio observation of most stars with high enough radio Ñux depends on their variability, making the astrometric accuracy, or even the detection, hard to predict (Stone 1997). Moreover, the center of radio emission can be displaced from the optical center by large amounts. This makes it worthwhile to recover and analyze earlier astrometric radio positions of stars for which there exist optical positions in the Hipparcos frame. Prior to the large and coherent set of proper motions furnished by the Hipparcos frame, the task of analyzing early radio positions had a limited scope, since it was difficult to sort out true stellar motion from the centroid noncoincidence e†ect (Andrei, Jilinski, & Puliaev 1995). Naturally, this is still true when the starÏs proper motion is a†ected by large orbital motion. Yet, with the Hipparcos set of proper motions, the coincidence between early radio positions and the optical positions on the Hipparcos frame can be studied for a signiÐcant number of stars. These early radio positions provide valu- 2. THE NON-HIPPARCOS STARS In the period 1992È1994, a program to determine astrographic positions for 50 radio stars with published astrometric radio positions was pursued with the 0.40 m Zeiss astrograph (focal distance 2 m, or 103A mm~1 plate scale) of the Universidade Federal do Rio de Janeiro, in Campinas, Sa8 o Paulo (/ \ [22¡53@59@@, L \ 3h7m19s) (AssaÐn et al. w 1996). The range of declinations extended basically from ]40¡ to [30¡ ; the plates used were of unsensitized Kodak IIa-O type, and each plate covered a 4¡ ] 4¡ region of the sky. Two exposures per plate were taken, with di†erent durations to provide for better overall imaging of the catalog and radio stars. Besides the Hipparcos stars, about 80 reference stars from the PPM (RoŽser & Bastian 1993), ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 1 Also Pulkovo Observatory, 196140 St. Petersburg, Russia. 2 Also Universidade Federal Fluminense, Brazil. 483 484 ANDREI ET AL. Vol. 117 TABLE 1 AVERAGE DIFFERENCES : PLATE REDUCTIONS MINUS CATALOG POSITIONS Parameter *a(Ph [ Ch) *d(Ph [ Ch) *a(Pt [ Ch) *d(Pt [ Ch) *a(Pa [ Ch) *d(Pa [ Ch) Average (mas) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard deviation of the mean (mas) . . . . . . Standard deviation (mas) . . . . . . . . . . . . . . . . . . . . ]5 26 154 [13 23 133 ]3 21 122 ]16 21 123 ]34 19 109 ]28 17 97 NOTES.ÈIn the column headings, ““ P ÏÏ refers to the plate reduction, while ““ C ÏÏ refers to catalog ; the letters ““ h,ÏÏ ““ c, ÏÏ and ““ a ÏÏ refer to the Hipparcos, Tycho, and ACT catalogs, respectively. ACRS (Corbin & Urban 1991), CMC (Carlsberg Consortium 1989), and IRS (Corbin 1991) catalogs were measured on each plate. Most of these stars were in the Tycho Catalogue, thereby enabling reductions also to be made using Tycho and ACT reference stars. For the present study, all these radio stars have been rereduced relative to the Hipparcos, Tycho, and ACT (Urban, Corbin, & Wyco† 1998) catalogs, following the same steps as in the previous work. All the plates were digitized with a PDS microdensitometer. The plates were scanned in the direct and reverse directions to correct for possible systematic errors caused by the x and y glass encoders, if any. Three successive scans were made for the radio stars in order to minimize accidental errors. Gaussian adjustments were performed to derive the (x, y) sets of measurements. A second-degree polynomial model plus a thirddegree radial distortion term were used to relate measured and standard coordinates of the catalog reference stars (Vieira, AssaÐn, & Vieira Martins 1992). An empirically obtained correction for magnitude radial distortion was also applied to yield the Ðnal positions. Typically, 25 Hipparcos stars, 66 Tycho stars, and 61 ACT stars were used per plate. Furthermore, two fainter stars were observed at the long focus (16 m) of the 1.60 m telescope of the Laboratorio Nacional de Astrof • sica (LNA) (/ \ [22¡23@55@@, L \ 3h2m20s) with a CCD camera and w TABLE 2A OPTICAL POSITIONS ON THE ACT REFERENCE FRAME Name Magnitude Epoch (1900]) HBC 362 . . . . . . . . . DG Tau . . . . . . . . . . LkHa 101 . . . . . . . . V826 Tau . . . . . . . . GG Tau/N . . . . . . HP Tau/G2 . . . . . . Wolf 424 . . . . . . . . . LS 3299 . . . . . . . . . . Oph 1 . . . . . . . . . . . . Oph 2 . . . . . . . . . . . . Oph 3 . . . . . . . . . . . . UX Cyg . . . . . . . . . . 14.7 11.6 16.5 11.8 13.7 10.4 13.1 10.4 12.5 11.7 12.3 10.2 94.80 92.73 95.04 93.87 92.73 92.66 93.30 92.65 93.56 93.49 93.56 94.70 a Error (mas) a (ACT) 04 04 04 04 04 04 12 14 16 16 16 20 05 27 30 32 32 35 33 59 11 11 12 55 30.875 04.698 14.440 15.833 30.329 54.149 18.029 53.507 08.920 59.263 40.533 05.490 41 90 75 110 70 40 70 140 180 70 70 90 d (ACT) ]21 ]26 ]35 ]18 ]17 ]22 ]09 [54 [19 [19 [18 ]30 51 06 16 01 31 54 01 18 04 06 59 24 10.79 15.99 24.51 38.78 40.71 13.48 14.49 07.49 46.83 53.32 28.08 52.01 d Error (mas) k a cos d (mas yr~1) k d (mas yr~1) 38 90 57 40 220 60 50 130 150 30 120 80 ... ]6.6 ... ]10.2 ]7.2 ]6.4 [1796.0 ... [27.8 [25.7 ]27.4 [7.8 ... [15.7 ... [22.8 [21.0 [14.0 ]233.0 ... [23.3 [1.7 [39.9 [19.6 NOTES.ÈStars not belonging to the Hipparcos or the Tycho Catalogue. The positions were measured by the authors at the indicated epoch. The reference catalog for reduction was the ACT. The right ascension errors are multiplied by cos d. See text for origin of the proper motions. Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. TABLE 2B SUPPLEMENTARY OPTICAL POSITIONS ON THE TYCHO AND Hipparcos REFERENCE FRAMES TYCHO NAME HBC 362 . . . . . . . . . DG Tau . . . . . . . . . . LkHa 101 . . . . . . . . V826 Tau . . . . . . . . GG Tau/N . . . . . . HP Tau/G2 . . . . . . Wolf 424 . . . . . . . . . LS 3299 . . . . . . . . . . Oph 1 . . . . . . . . . . . . Oph 2 . . . . . . . . . . . . Oph 3 . . . . . . . . . . . . UX Cyg . . . . . . . . . . 04 04 04 04 04 04 12 14 16 16 16 20 05 27 30 32 32 35 33 59 11 11 12 55 a a Error (mas) 30.891 04.693 14.428 15.829 30.328 54.148 18.027 53.510 08.917 59.265 40.532 05.491 43 94.29 77 142.64 85.82 41.45 88.89 140.04 226.82 70.86 70.92 103.49 Hipparcos d ]21 ]26 ]35 ]18 ]17 ]22 ]09 [54 [19 [19 [18 ]30 51 06 16 01 31 54 01 18 04 06 59 24 10.75 16.00 24.50 38.80 40.74 13.44 14.48 07.49 46.87 53.11 28.07 52.02 d Error (mas) a a Error (mas) d d Error (mas) 40 80 60 60 240 50 60 130 130 30 120 70 30.874 4.702 14.434 15.832 30.323 54.151 18.037 53.527 8.916 ... 40.528 5.498 48 107.76 83 128.37 85.82 96.72 74.07 210.06 240.99 ... 56.73 181.10 10.80 16.00 24.33 38.86 40.80 13.49 14.44 7.46 46.83 ... 28.14 52.00 45 70 67 90 240 30 60 130 260 ... 100 90 NOTES.ÈPositions for the same observations of 12 non-Hipparcos stars as in Table 2A. Here the reference catalogs used are Tycho and Hipparcos. For Oph 2, no convergence was reached in the Hipparcos-referred plate solution. No. 1, 1999 EARLY RADIO POSITIONS OF STARS TABLE 3 DISTRIBUTION OF THE RADIO POSITIONS Type of Observation Number Average Error (mas) Median Error (mas) All . . . . . . . . . . . . . . . . . . . . 247 56 25 Continuum . . . . . . . . . . VLA . . . . . . . . . . . . . . . . . . VLBI . . . . . . . . . . . . . . . . . 192 169 23 35 35 36 25 25 5 Line . . . . . . . . . . . . . . . . . . 55 128 130 SiO . . . . . . . . . . . . . . . . . . . 20 162 150 H O .................. 24 64 75 2 NOTE.ÈLine observations are from maser stars observed at the VLA, Hat Creek, and IRAM interferometers. The VLA entry refers only to continuum observations. reduced through a mosaicking technique (AssaÐn, Vieira Martins, & Andrei 1997), to precisions similar to those of the main program stars. From the complete program, 12 stars were not in either the Hipparcos or the Tycho Catalogue. The 40 remaining stars, belonging to the Hipparcos Catalogue, were also rereduced and their positions compared with their corresponding Hipparcos Catalogue positions, after being reduced to a common epoch with the catalog proper motions. The average plate-minus-catalog di†erences and their standard deviations are presented in Table 1. The averages are not statistically signiÐcant and were not used as corrections. The small number of reference stars gave a somewhat poorer solution when using the Hipparcos Catalogue. The ACT is essentially the Tycho Catalogue with improved proper motions. However, the Tycho and ACT solutions are nearly equivalent. This is as expected, since the epochs of the observations are closer than 2 years to the catalog epoch. Even so, the standard deviations for the ACT solution are slightly smaller than those for the Tycho solution, and thus the former was adopted for the comparison 485 against the radio positions. The positions for the 12 nonHipparcos stars are presented in Table 2A, referred to the ACT catalog, and in Table 2B, referred to the Hipparcos and Tycho Catalogues. In order to use independent values not tied to the positions used for the match between the radio and optical, the proper motions (given in Table 2A) were obtained by comparing the positions given in the AC 2000 and the GSC 1.2 (Bucciarelli et al. 1994) catalogs. In two cases, however, the measured position had to be used : Oph 3 had no sure AC 2000 identiÐcation, and UX Cyg had no GSC 1.2 position. No proper-motion measure was found or could be calculated for LS 3299. This star was thus excluded from the comparison set. For Wolf 424, there were proper motions in SIMBAD, and the most precise ones were adopted. However, the only radio position found for Wolf 424 is given to a precision just short of 1A (White, Jackson, & Kundu 1989). The radio position of GG Tau/N is found 14A. 6 displaced from its optical position (Bieging, Cohen, & Schwartz 1984). Accordingly, these two stars were also excluded from the comparison set. As result, seven stars from the Campinas and LNA program were in the subsequent comparison of radio and optical positions. Other than these, the radio position database contains three stars observed with the Flagsta† Astrometric Scanning Transit Telescope (FASTT), tied directly to the extragalactic reference frame (Stone 1997). Of these, motions were known for two stars (Y Cas and U Lyn), which were then also used in the following comparison with the radio positions. 3. THE DATABASE The selection of radio-emitting stars was based on the lists of Wendker (1995) and Walter, Hering, & de Vegt (1990). Most of the radio positions were collected in the literature, from 1981 onward. A set of positions for 49 radio stars were retrieved from the US Naval Observatory VLA observations (McCarthy 1995). Although all e†orts were 600 .5 300 0h 0 6h 18h 24h -300 -.5 -600 FIG. 1.ÈSky distribution of the 112 stars represented in the database of radio positions. Open symbols show stars measured with continuum observations, and Ðlled symbols those with maser line observations. Circles and squares indicate that the optical positions were directly taken from the Hipparcos and Tycho Catalogues, respectively. Triangles represent optical positions from other astrometric programs (see ° 2). 486 ANDREI ET AL. made at a thorough search, we do not claim completeness for the database. In total, 288 radio positions were compiled. Next, the Hipparcos stars and three Tycho-only stars were sampled for a total of 103 stars. In addition, 10 stars imaged on astrographic plates and two imaged by mosaicking CCD images were added, having their positions placed on the Hipparcos/ICRS frame. Finally, three stars observed with FASTT (Stone 1993), relative to the extragalactic radio reference frame, were also included. From these additional stars, only nine could actually be used, because of a lack of reliable radio positions or proper motions. By far, most of the radio positions were observed with the VLA (5 GHz continuum measurements). However, precise radio positions obtained from line observations were also considered. Table 3 presents the distribution of the radio positions, sorted by instrument and type of observation. The average error for the radio positions is ^60 mas. There is a signiÐcant di†erence between the values for continuum (average error ^40 mas) and line (average error larger than ^100 mas) observations. As is evident from our sample, SiO and H O maser observations show distinctly di†erent 2 average errors. In Table 3 median errors are also given. The average and median di†er most noticeably for the VLBI entry, since the 1.6 and 8.4 GHz VLBI observations, which correspond to the earliest in our sample, are less precise than the 5 GHz ones. The sky distribution of the radio stars in the sample is shown in Figure 1. Table 3 shows that the H O maser radio positions are of 2 comparable precision to the continuum ones. That is not the case for the SiO maser radio positions, but they are included here nonetheless since the radio center of emission should lie relatively close to the optical center (Baudry, Lucas, & Guilloteau 1995). It should be stressed that 43% of all the observations and 51% of the continuum observations are from epochs prior to J1985.0. Thus, when the optical and radio positions agree well, these observations are useful to investigate the spin of the Hipparcos reference frame. Since the MERLIN and VLBI star positions, used to link the Hipparcos and the ICRF frames, are well studied, they are not included in this paper. On the other hand, 46 (out of 66) of the cardinal stars for linking the optical and radio reference systems, deÐned by Walter, Hering, & de Vegt (1997), are included here. 4. Vol. 117 COMPARISON BETWEEN RADIO AND OPTICAL POSITIONS All the radio positions were obtained relative to extragalactic radio sources, which, to the average precision of our sample, represent the ICRS. However, many of the oldest positions were referred to the FK4/B1950.0 system. These positions have been corrected for the motion of the equinox and removal of the E-terms of aberration through the Starlink software COCO, which uses the procedures of Aoki et al. (1983). Out of the 247 radio positions compared with their optical positions, 210 are found to be coincident to less than 500 mas in both right ascension and declination. Likewise, 136 radio positions are coincident to less than 100 mas, and 74 are found coincident to less than 50 mas. Table 4 gives details of the radio-minus-optical comparison. In Table 4, the entries follow those adopted in Table 3 plus an entry for the non-Hipparcos stars, i.e., those taken from the Campinas and Flagsta† programs. For these, all but three have radio positions obtained from 5 GHz continuum VLA observations. The remaining radio positions come from H O maser 22 GHz VLA observations, being at a similar 2 level of precision as the others. The radio position for UU Psc is found to be displaced from the optical position by D40A in declination, and as a result, this star was not considered. It is interesting that the distribution of radio observations is alike for the Hipparcos stars (78% from continuum observations) and non-Hipparcos stars (75% from continuum observations), even though the latter subsample is far smaller (N \ 12) than the Ðrst (N \ 235). However, the fraction of ““ radio minus optical ÏÏ o†sets smaller than 100 mas is signiÐcantly larger for the Hipparcos stars than for the non-Hipparcos ones. This indicates that the radio positions, in many cases resulting from astrophysical studies, are generally astrometrically sound to the extent of matching better with the superior Hipparcos positions. Analogously, the fraction of ““ radio minus optical ÏÏ o†sets smaller than 500 mas, encompassing the threshold of precision for the nonHipparcos stars, is alike for the two subsamples : 83% of the observations of Hipparcos stars and 78% of the observations for the non-Hipparcos stars. Another point that suggests the same conclusion is that many more close matches are found for H O maser obser2 vations than for the SiO maser ones. Nevertheless, as TABLE 4 RADIO-MINUS-OPTICAL DIFFERENCES : COMPARATIVE DISTRIBUTION POSITIONS MINUS STARS SUBSAMPLE Hipparcos . . . . . . . . . . . . Continuum . . . . . . . . . . VLA . . . . . . . . . . . . . . . . . . VLBI . . . . . . . . . . . . . . . . . Line . . . . . . . . . . . . . . . . . . SiO . . . . . . . . . . . . . . . . . . . H O .................. 2 Non-Hipparcos . . . . . . R [ O \ 500 mas 210 (89%) [ 91 160 (87%) [ 68 137 (86%) [ 64 23 (100%) [ 10 50 (96%) [ 23 19 (95%) [ 15 21 (100%) [ 15 10 (83%) [ 7 (88%) (85%) (84%) (100%) (100%) (100%) (100%) (78%) R [ O \ 100 mas 134 109 89 20 25 6 16 2 (57%) [ 70 (60%) [ 54 (56%) [ 51 (87%) [ 8 (48%) [ 16 (30%) [ 6 (76%) [ 12 (17%) [ 2 (68%) (68%) (67%) (80%) (70%) (40%) (80%) (22%) R [ O \ 50 mas 74 63 45 18 11 2 9 (31%) [ 44 (34%) [ 35 (28%) [ 31 (78%) [ 8 (21%) [ 9 (10%) [ 2 (43%) [ 8 1 (8%) [ 1 (43%) (44%) (41%) (80%) (39%) (13%) (53%) (11%) NOTES.ÈFor each level of the absolute value of the radio-minus-optical o†sets (i.e., smaller than 500 mas, 100 mas, and 50 mas), the number of radio positions and stars in the subsample are given. The indicated percentage is given relative to the total number of stars within each subsample class. No. 1, 1999 EARLY RADIO POSITIONS OF STARS Baudry et al. (1995) have pointed out, the center of the SiO maser radio emission lies nearer to its optical center as compared with the H O masers. A possible explanation is 2 that the H O line observations were made at the VLA at 2 precisions twice as high as the Hat Creek and IRAM SiO line observations. The high degree of good matches for the VLBI observations is of no surprise, then, not only because of the selection criterion for the stars aimed at, but also because of the inherent precision of the method. The average di†erences *a cos d and *d, in the sense radio minus optical, were calculated at the mean epoch of the Hipparcos Catalogue, referred to the ICRS. Their averages and errors, for the Hipparcos stars and some subsamples, are presented in Table 5. Smaller average matches are found for the VLBI observations. Relatively large averages are found for the H O subsample, indicating a poor 2 coincidence between the maser emission and its photocenter. The distributions of the averages around the equator and about the Galactic plane were also calculated. The angular radio-minus-optical o†sets are twice as large at southern declinations d ¹ [20¡ (170 ^ 41 mas) in comparison with those north of d º ]20¡ (95 ^ 20 mas). This pattern seems to follow the observational limitations of the radio instruments, which are mostly located in the Northern Hemisphere. This again would indicate a nonrandom quality of the radio positions in the sample. About the Galactic plane, there is a tendency to Ðnd negative *d o†sets and, to a lesser extent, positive *a cos d values for negative Galactic latitudes. These tendencies were checked by varying the width of the adopted Galactic plane, from 20¡ to 40¡, and either removing or keeping the less accurate negative declination observations. The radio-minus-optical o†sets are nevertheless similar. Table 6 presents all the positions for which each coincidence between the optical and radio positions, in right ascension and in declination, is smaller than 100 mas. By assuming the radio positions as placed on the ICRF, this set of radio-minus-optical o†sets, because of the large portion of radio positions observed prior to DJ1985, enables the spin rate of the Hipparcos frame relative to the extragalactic frame to be calculated. To obtain the rate of spin, we assumed the two systems to be perfectly tied at the Hipparcos mean epoch (J1991.25). In this case, the usual methods (see, e.g., Lindegren & Kovalevski 1995) can be used to calculate the Ðrst time derivative of the three angles 487 deÐning the orientation between the radio and optical reference frames. As customary, the three orientation angles are deÐned by the equinox axis in the equatorial plane (Ðrst time derivative, u ), the axis orthogonal to the equinoctial 1 direction in the equatorial plane (second time derivative, u ), and the celestial pole axis (third time derivative, u ). 2 3 Spins u , u , and u were then calculated from the radio1 2 3 minus-optical di†erences. In order to increase the sensitivity and accuracy, a system of weighting was established that was directly proportional to the time span between the radio and the Hipparcos epochs of observation and inversely proportional to the o†set combined error. The rates of spin so calculated are given in Table 7. In the upper part of the table, the spin components are given for the Hipparcos-stars subsample and for the continuum radio observations only. Spin u is found always to be insigniÐ3 cant, while u and u appear to be consistently negative. 1 2 Their precisions compare well with the individual solutions given for the Hipparcos CatalogueÏs orientation (Kovalevsky et al. 1997). In the lower part of the table the results for two smaller subsamples are presented. In these cases much larger and less accurate values are found. For the H O maser radio observations, their larger average 2 radio-minus-optical o†sets in equatorial coordinates, and limited sample size, could explain the result. Concerning the VLBI observations, the average o†sets are small and the precision of the measures is generally high, thus requiring a di†erent understanding. For that, we calculated the estimator of the Spearman linear correlation coefficient for the time distribution of right ascensions, declinations, and the combined radio-minus-optical positional o†sets. In all three cases, the estimators were found to be positive and signiÐcant at 99.58% or higher. This points to a time evolution of the positional o†sets, which could be due to spin not accounted for in the orientation process of Hipparcos, supposing random proper-motion errors. On the other hand, the oldest VLBI observations, which dominate the spin solution, are much less precise than the ones close to J1991.25. Again, we have calculated the estimator of the Spearman linear correlation coefficient, now for the time distribution of the error in right ascension, declination, and the combined radio positional errors. They are also found to be signiÐcant, though moderately so, at 75.88% for a, at 80.11% for d, and at 90.58% for the combined errors. It is therefore difficult, using this subsample, to Ðlter out the contribution of the less precise positions. Thus, although TABLE 5 AVERAGE RADIO-MINUS-OPTICAL DIFFERENCES Solution O†set N *a cos d (mas) *d (mas) All observations . . . . . . R [ O \ 100 mas R [ O \ 50 mas R [ O \ 100 mas R [ O \ 50 mas R [ O \ 100 mas R [ O \ 50 mas R [ O \ 100 mas R [ O \ 50 mas R [ O \ 100 mas R [ O \ 50 mas 134 74 109 63 20 18 25 11 16 9 ]9.2 ^ 3.5 ]9.3 ^ 2.7 ]8.3 ^ 3.8 ]8.4 ^ 3.0 ]0.5 ^ 6.1 ]6.5 ^ 5.1 ]12.9 ^ 8.8 ]14.5 ^ 5.1 ]18.7 ^ 7.7 ]17.9 ^ 5.5 [8.8 ^ 4.0 [2.6 ^ 2.4 [12.1 ^ 4.2 [3.7 ^ 2.6 ]0.3 ^ 4.5 ]0.8 ^ 3.8 ]5.9 ^ 10.6 ]4.1 ^ 6.2 ]21.9 ^ 10.9 ]4.1 ^ 5.9 Continuum . . . . . . . . . . . VLBI . . . . . . . . . . . . . . . . . . Line . . . . . . . . . . . . . . . . . . . H O ................... 2 NOTE.ÈAverages are given for the main subsamples in the database of radio positions (see Table 3). TABLE 6 RADIO POSITIONS : R [ O OFFSET SMALLER THAN 100 mas RADIO [ OPTICAL (0A. 01) HIP NAME 10826 . . . . . . . . . . . . . 11093 . . . . . . . . . . . . . o Cet S Per 13133 . . . . . . . . . . . . . 14576 . . . . . . . . . . . . . RZ Cas b Per 16042 . . . . . . . . . . . . . UX Ari 16846 . . . . . . . . . . . . . HR 1099 19431 . . . . . . . . . . . . . 19762 . . . . . . . . . . . . . 20070 . . . . . . . . . . . . . EI Eri HD 283447 b Per 20097 . . . . . . . . . . . . . V410 Tau 20388 . . . . . . . . . . . . . SAO 76567 20390 . . . . . . . . . . . . . Campinas . . . . . . . . 21251 . . . . . . . . . . . . . 26311 . . . . . . . . . . . . . T Tauri V826 Tau HD 28867 v Ori 26714 . . . . . . . . . . . . . 27989 . . . . . . . . . . . . . 28041 . . . . . . . . . . . . . 32015 . . . . . . . . . . . . . 33165 . . . . . . . . . . . . . TW Lep a Ori U Ori SV Cam EZ CMa 34042 . . . . . . . . . . . . . Z CMa 35197 . . . . . . . . . . . . . 35487 . . . . . . . . . . . . . 35600 . . . . . . . . . . . . . 36669 . . . . . . . . . . . . . 36773 . . . . . . . . . . . . . SS Cam R CMa AR Mon Z Pup KQ Pup 2453-1918-1 . . . . . . 39348 . . . . . . . . . . . . . 40534 . . . . . . . . . . . . . YY Gem 54 Cam R Cnc 44164 . . . . . . . . . . . . . 48036 . . . . . . . . . . . . . TY Pyx R Leo a 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 9 19 22 22 48 08 08 08 08 08 08 08 08 08 08 26 26 26 26 26 26 26 26 26 36 36 36 36 36 36 09 14 18 18 18 18 21 21 21 32 33 36 36 40 55 55 41 54 54 03 03 03 16 19 20 32 33 33 34 02 16 16 59 47 20.78 51.71 51.71 55.50 10.12 10.13 10.13 10.13 10.13 10.13 10.13 10.13 10.13 10.13 35.32 35.32 35.32 35.33 35.33 35.34 35.33 35.33 35.34 47.33 47.33 47.33 47.33 47.32 47.32 40.86 12.92 14.53 14.56 31.09 31.10 58.83 58.84 59.42 15.82 33.04 12.81 12.81 39.69 10.27 49.18 18.74 13.04 13.04 43.17 43.17 43.16 24.74 28.02 48.45 38.06 47.96 47.97 37.67 35.84 33.82 33.82 42.76 33.49 d [02 ]58 ]58 ]69 ]40 ]40 ]40 ]40 ]40 ]40 ]40 ]40 ]40 ]40 ]28 ]28 ]28 ]28 ]28 ]28 ]28 ]28 ]28 ]00 ]00 ]00 ]00 ]00 ]00 [07 ]28 ]50 ]50 ]28 ]28 ]28 ]28 ]19 ]18 ]18 [01 [01 [20 ]07 ]20 ]82 [23 [23 [11 [11 [11 ]73 [16 [05 [20 [14 [14 ]31 ]57 ]11 ]11 [27 ]11 58 35 35 38 57 57 57 57 57 57 57 57 57 57 42 42 42 42 42 42 42 42 42 35 35 35 35 35 35 53 12 17 17 27 27 18 18 32 01 01 12 12 17 24 10 16 55 55 33 33 33 19 23 15 39 31 31 52 16 43 43 48 25 36.8 11.5 11.3 02.9 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 56.5 56.3 56.3 56.1 56.0 55.9 56.0 56.0 56.1 19.1 18.7 18.5 18.5 18.6 18.6 35.6 12.5 44.8 44.4 16.5 16.4 06.8 06.6 06.5 38.8 00.3 06.8 06.9 55.5 25.2 30.7 04.5 42.1 42.1 06.2 06.2 06.3 57.1 40.9 35.7 29.1 26.1 26.1 11.6 25.8 34.5 34.6 58.1 43.9 EPOCH (1900]) *a cos d *d TYPE INTERF. FREQUENCY (GHz) 88.95 91.33 85.05 86.30 83.22 89.28 89.29 89.29 89.30 83.57 83.79 82.42 86.30 84.78 78.95 79.94 80.19 81.21 82.43 83.68 83.57 83.79 83.22 79.94 82.43 83.63 83.68 83.22 83.79 87.01 90.10 82.43 88.95 82.11 90.10 85.04 90.10 90.25 90.10 90.10 86.22 86.22 89.00 82.42 88.95 86.30 83.68 89.32 81.22 82.11 83.90 86.30 86.22 86.22 88.95 89.31 83.68 85.22 85.73 88.95 91.32 87.03 91.33 ]3 ]0 ]3 ]2 [6 ]1 ]1 ]1 ]1 ]3 ]4 ]6 ]4 ]3 [1 [1 ]2 ]6 [1 ]3 ]0 [1 ]5 ]5 ]6 ]7 ]7 [4 [0 ]2 ]3 ]4 [0 [9 ]1 [3 [1 ]6 [0 ]2 ]1 [2 [9 ]1 ]1 [9 ]1 [3 ]6 [2 [5 [2 ]2 ]3 ]7 [7 ]5 [4 [3 ]2 ]1 ]0 [1 ]7 ]5 [9 [3 [5 [0 [0 [1 [1 ]0 ]4 [6 [3 [1 [1 [5 [7 [9 [6 [6 [0 ]1 ]4 [7 [9 [9 [9 [1 ]2 [3 [2 ]4 ]3 [5 [0 [3 [9 ]1 ]6 ]3 ]6 [1 [7 [3 [1 ]4 [6 [7 ]0 ]6 [5 ]5 ]1 [0 ]9 [9 [3 [7 [5 [0 ]4 ]0 [3 H O 2 SiO OH Algol Algol Algol Algol Algol Algol Algol Algol Algol Algol Algol RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn T Tauri T Tauri T Tauri T Tauri T Tauri T Tauri T Tauri T Tauri T Tauri T Tauri a Cyg a Cyg RS CVn Flare H O 2 RS CVn W-R W-R T Tauri T Tauri T Tauri RS CVn Algol RS CVn H O 2 VV Cephei VV Cephei Flare RS CVn H O 2 SiO RS CVn SiO VLA IRAM VLA VLA VLBI VLBI VLBI VLBI VLBI VLBI VLBI VLA VLA VLBI VLA VLA VLA VLA VLA VLA VLBI VLBI VLBI VLA VLA VLA VLA VLBI VLBI VLBI VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA IRAM VLBI IRAM 22 86 1.6 5 8.4 5 5 5 5 5 1.6 5 5 5 5 5 5 5 5 5 5 1.6 8.4 5 5 5 5 8.4 1.6 5 5 5 5 5 5 5 5 8.4 5 5 5 5 5 5 22 5 5 5 5 5 5 5 5 5 22 5 5 5 5 22 86 5 86 488 REFERENCES 1 2 3, 4 5 6, 7 8 8 8 8 6, 9, 10 6 11 5 12 13 13 13 13 13 13 6, 9, 10 6 6 13 13 13 13 6, 10 6 7, 9 14 7, 9, 15 16 17 14 11 14 18 14 14 11 5 5 5 1 5 7, 9, 15 16 19 17 20 5 5 5 1 16 7, 9, 15 21 16 1 2 7, 9 2 TABLE 6ÈContinued RADIO [ OPTICAL (0A. 01) HIP 49018 53809 57917 59600 59796 .......... .......... .......... .......... .......... NAME DH Leo R Crt S Crt HU Vir DK Dra 63642 . . . . . . . . . . RT Vir 64293 . . . . . . . . . . 65915 . . . . . . . . . . 66257 . . . . . . . . . . RS CVn FK Com HR 5110 70401 . . . . . . . . . . RX Boo 71380 . . . . . . . . . . 73473 . . . . . . . . . . 78512 . . . . . . . . . . 79233 . . . . . . . . . . Campinas . . . . . . 79607 . . . . . . . . . . RV Lib d Lib AG Dra RU Her Oph 1 TZ CrB 90488 . . . . . . . . . . U Her 81519 82817 84014 85852 WW Dra Wolf 630 V792 Her DR Dra .......... .......... .......... .......... 87965 . . . . . . . . . . Z Her 88469 . . . . . . . . . . 88838 . . . . . . . . . . 90115 . . . . . . . . . . 9 Sgr VX Sgr FR Sct 90303 . . . . . . . . . . 92420 . . . . . . . . . . RY Sct b Lyr 93820 . . . . . . . . . . R Aql 94013 . . . . . . . . . . 94910 . . . . . . . . . . V1762 Cyg U Sge 98220 . . . . . . . . . . RR Aql 98298 . . . . . . . . . . Cyg X-1 100214 . . . . . . . . . V444 Cyg 100287 . . . . . . . . . V1687 Cyg 101341 . . . . . . . . . Cyg OB 2-5 108317 . . . . . . . . . VV Cep 108728 . . . . . . . . . RT Lac a 10 11 11 12 12 12 13 13 13 13 13 13 13 13 13 14 14 14 15 16 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 21 21 22 00 00 52 13 15 15 02 02 10 30 34 34 34 34 34 24 24 35 00 01 10 11 14 14 14 14 25 25 39 55 10 32 32 58 58 03 08 23 23 25 50 50 50 50 06 06 06 06 08 18 18 57 57 58 58 19 19 20 20 20 32 32 56 56 01 01.96 33.87 45.10 20.69 41.53 41.53 37.94 37.95 36.95 46.86 47.68 47.68 47.68 47.68 47.71 11.60 11.60 48.44 58.41 41.04 14.51 08.92 41.20 41.23 41.23 41.10 47.48 47.49 03.94 29.58 25.60 41.42 41.43 07.01 06.99 52.44 04.04 22.79 22.79 31.48 04.79 04.79 04.79 04.79 22.24 22.24 22.24 22.24 25.94 48.41 48.40 36.07 36.07 21.68 21.67 32.43 32.41 27.98 27.98 27.98 22.42 22.42 39.15 39.15 30.64 d ]24 [18 [07 [09 ]72 ]72 ]05 ]05 ]35 ]24 ]37 ]37 ]37 ]37 ]37 ]25 ]25 [18 [08 ]66 ]25 [19 ]33 ]33 ]33 ]33 ]18 ]18 ]60 [08 ]48 ]74 ]74 ]15 ]15 [24 [22 [12 [12 [12 ]33 ]33 ]33 ]33 ]08 ]08 ]08 ]08 ]52 ]19 ]19 [01 [01 ]35 ]35 ]38 ]38 ]43 ]43 ]43 ]41 ]41 ]63 ]63 ]43 33 19 35 04 33 33 11 11 56 13 10 10 10 10 10 42 42 02 31 48 04 04 51 51 51 51 53 53 41 19 57 13 13 08 08 21 13 40 40 41 21 21 21 21 13 13 13 13 25 36 36 53 53 12 12 43 43 51 51 51 18 18 37 37 53 10.4 29.5 48.0 46.8 04.6 04.6 08.6 08.5 05.2 58.1 56.8 56.8 56.8 56.8 56.8 14.2 13.7 11.2 08.0 10.1 14.4 46.7 32.4 32.5 32.5 32.0 33.0 32.9 59.5 57.7 56.6 38.0 37.9 20.6 21.0 38.5 26.4 51.8 51.7 24.0 45.6 45.6 45.6 45.6 49.0 49.2 49.2 48.7 33.4 37.6 37.6 10.7 10.6 05.8 05.8 54.0 54.0 16.2 16.2 16.3 19.0 18.9 32.0 32.0 25.2 EPOCH (1900]) *a cos d *d TYPE INTERF. FREQUENCY (GHz) 85.03 88.95 88.95 89.00 85.04 85.03 85.06 88.95 88.98 83.63 82.42 82.36 83.63 83.57 87.51 82.22 92.03 86.30 86.22 86.30 92.05 90.10 83.57 82.42 82.36 88.42 88.95 85.11 86.30 85.22 86.30 86.22 86.30 83.68 89.14 89.16 85.06 89.23 83.63 92.62 82.42 82.36 86.54 83.63 85.11 82.22 82.22 88.95 86.22 85.04 85.03 88.95 85.11 83.57 89.89 83.68 85.03 88.93 83.63 82.42 88.91 83.63 89.07 83.63 82.43 ]2 [0 ]1 [5 ]4 ]7 ]5 ]3 [1 ]2 [4 [4 [4 [3 [3 ]6 [7 ]4 ]5 ]7 ]9 ]1 [5 ]3 ]3 [0 ]4 ]9 ]8 [1 ]3 [4 ]1 ]5 ]2 ]1 [2 ]0 ]4 ]8 [1 [0 ]1 ]2 [6 ]2 ]5 ]1 ]5 ]9 [3 ]0 [8 [0 ]0 ]4 [8 [0 ]1 ]2 [0 ]4 ]6 ]6 ]2 ]2 ]0 [1 ]5 [0 [5 [1 [2 [7 ]3 [1 [2 ]1 ]1 ]1 [7 [7 ]8 ]9 [5 ]5 ]1 ]4 [1 ]1 [0 ]4 [5 [4 ]9 ]2 ]5 [1 [8 [2 ]4 ]7 [5 [2 ]9 [5 ]1 [4 [3 ]1 ]9 ]7 ]1 ]1 [9 [8 ]2 ]1 [1 [0 ]2 ]5 [2 [3 [2 ]1 [1 ]4 [1 ]0 RS CVn H O 2 H O 2 RS CVn RS CVn RS CVn H O 2 H O 2 RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn H O 2 SiO RS CVn Algol Z And SiO T Tauri RS CVn RS CVn RS CVn RS CVn H O 2 OH RS CVn Flare RS CVn RS CVn RS CVn RS CVn RS CVn RS CVn H O 2 VV Cephei VV Cephei Algol b Lyrae b Lyrae b Lyrae b Lyrae OH H O 2 H O 2 H O 2 RS CVn Algol Algol H O 2 OH X-ray X-ray Algol Algol W-R W-R W-R b Lyrae b Lyrae VV Cephei VV Cephei RS CVn VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLBI VLA VLA IRAM VLA VLA VLA IRAM VLA VLBI VLA VLA VLBI VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA VLBI VLBI VLA VLA VLA VLA VLA VLA VLA VLA VLA VLA 5 22 22 5 5 5 22 22 5 5 5 5 5 5 5 22 86 5 5 5 86 5 5 5 5 5 22 1.6 5 5 5 5 5 5 5 5 22 5 5 15, 8.4 5 5 5 5 1.6 22 22 22 5 5 5 22 1.6 5 5 5 5 5 5 5 5 5 5 5 5 489 REFERENCES 5 1 1 11 11 5 22 1 16 7, 9, 15 15 7, 15 15 6, 9, 10 16 3, 23, 24 2 5 5 5 2 14 6, 10 15 7, 15 25 1 3, 4 5 21 5 11 5 7, 9, 15 16 16 22 16 7, 9, 15 26 15 7, 15 16 9, 15 3, 4 1 23, 24 1 5 11 5 1 23 6, 7, 9, 10 27 11 5 16 9, 15 7, 15 16 7, 9, 15 16 7, 9, 15 7, 9, 15 490 ANDREI ET AL. Vol. 117 TABLE 6ÈContinued RADIO [ OPTICAL (0A. 01) HIP NAME 109303 . . . . . . AR Lac 114114 . . . . . . 114639 . . . . . . R Peg SZ Psc 117915 . . . . . . II Peg a 22 22 22 23 23 23 23 23 01 08 08 06 13 13 55 55 d 30.68 40.87 40.90 39.15 23.76 23.77 03.28 03.57 ]43 ]45 ]45 ]10 ]02 ]02 ]28 ]28 53 44 44 32 40 40 38 38 25.4 31.6 31.2 36.0 31.1 31.2 00.6 00.7 EPOCH (1900]) *a cos d *d TYPE INTERF. FREQUENCY (GHz) 89.01 89.71 82.43 92.03 83.63 89.11 82.43 88.85 ]1 ]5 [1 [5 [6 [4 ]1 ]7 ]1 ]2 [2 [9 ]2 [1 [1 [9 RS CVn RS CVn RS CVn SiO RS CVn RS CVn RS CVn RS CVn VLA VLA VLA IRAM VLA VLA VLA VLA 5 5 5 86 5 5 5 5 REFERENCES 16 16 7, 9, 15 2 7, 9, 15 16 7, 9, 15 16 NOTES.ÈFor YY Gem, the number refers to the Tycho Catalogue, while for V826 Tau and Oph 1 the ““ Campinas ÏÏ entry refers to the authorsÏ observations as discussed in ° 2. All other reference numbers are for the Hipparcos Catalogue. Masers are indicated by line observations. Position and epoch are relative to the radio measure. REFERENCES.È(1) Bowers & Johnston 1994 ; (2) Baudry et al. 1995 ; (3) Baudry et al. 1990 ; (4) Bowers, Johnston, & de Vegt 1989 ; (5) K. J. Johnston & C. de Vegt 1992, private communication, cited in electronic catalog by Walter et al. 1997 ; (6) Lestrade et al. 1988 ; (7) Walter et al. 1990 ; (8) McCarthy 1995 ; (9) Morrison et al. 1990 ; (10) Niell et al. 1988 ; (11) Lestrade et al. 1993 ; (12) Lestrade et al. 1990 ; (13) Johnston et al. 1985b ; (14) White, Pallavicini, & Kundu 1992 ; (15) Florkowski et al. 1985 ; (16) Argyle et al. 1996 ; (17) Bieging et al. 1984 ; (18) Skinner & Brown 1994 ; (19) Cohen, Bieging, & Schwartz 1982 ; (20) Cohen & Bieging 1986 ; (21) Jackson, Kundu, & White 1989 ; (22) Bowers, Claussen, & Johnston 1993 ; (23) de Vegt et al. 1987 ; (24) Johnston, Spencer, & Bowers 1985a ; (25) Lestrade et al. 1992 ; (26) Gehrz et al. 1995 ; (27) Andrei & Bartel 1996. the weighted and unweighted solutions show similar results, their degree of certainty remains unsure. 5. CONCLUSIONS A set of 247 radio positions, obtained in 1981È1993, representing 112 stars, was gathered from the literature. Because of the complex relation between the radio and optical emission mechanisms for stars, and the fact that many of these positions were obtained by projects whose primary scope was not astrometry, we investigated in this paper which of these positions were in agreement with their corresponding optical positions in the Hipparcos reference frame. A total of 136 radio positions, representing 72 stars, are found to agree to better than 100 mas with their corresponding optical positions. A total of 46 of the cardinal stars, as deÐned by Walter et al. (1997), are represented in this subsample. At an agreement level of better than 50 mas, 74 radio positions are found, representing 44 stars. Analysis shows that the radio-minus-optical di†erences are larger for the southern stars and for the non-Hipparcos ones. The o†sets from H O VLA line observations are typi2 cally smaller than those from the less precise Hat Creek and IRAM SiO maser observations. These conclusions, in a general way, give statistical support to the nonaccidental character of the closest radio and optical matches found between the radio and optical positions within the sample. There seems to be an apparent asymmetry of the values of the positional o†sets relative to the Galactic plane. A statistically signiÐcant trend in the time distribution of VLBI o†sets is found. This result is, however, unsure because of the high errors of the oldest VLBI observations. The components of the spin rate of the Hipparcos frame have been calculated relative to a sample of selected radio star positions, which are referenced to extragalactic radio sources representing the ICRF. The degree of precision attained is comparable to that of the individual solutions used to deÐne the orientation of the Hipparcos Catalogue. The component about the polar axis (u ) is found to be 3 negligible, but this is not the case for the other two components. We are thankful to the referee for the valuable remarks and suggestions made regarding the text. We also thank the LNA/MCT for the allocated nights and sta† assistance at the 1.60 m telescope. We acknowledge the use of data from the Digitized Sky Survey and the Guide Star Catalog 1.2 of the Space Telescope Science Institute. This work has also TABLE 7 RATE OF SPIN OF THE Hipparcos FRAME RELATIVE TO THE EXTRAGALACTIC RADIO REFERENCE FRAME Solution All observations . . . . . . . . . Continuum . . . . . . . . . . . . . . VLBI (weighted) . . . . . . . . . VLBI (unweighted) . . . . . . H O ...................... 2 O†set R[O R[O R[O R[O R[O R[O R[O R[O R[O R[O \ \ \ \ \ \ \ \ \ \ 100 mas 50 mas 100 mas 50 mas 100 mas 50 mas 100 mas 50 mas 100 mas 50 mas u 1 (mas yr~1) u 2 (mas yr~1) u 3 (mas yr~1) [0.3 ^ 0.4 [0.9 ^ 0.3 [0.3 ^ 0.4 [0.9 ^ 0.3 ]3.8 ^ 0.7 ]3.6 ^ 0.6 ]2.1 ^ 1.2 ]1.5 ^ 1.0 ]3.0 ^ 1.5 ]4.9 ^ 3.1 [0.8 ^ 0.4 [1.2 ^ 0.2 [0.3 ^ 0.4 [1.1 ^ 0.2 ]2.0 ^ 0.6 ]1.8 ^ 0.5 ]2.2 ^ 1.3 ]2.9 ^ 1.1 ]11.6 ^ 1.6 ]2.1 ^ 1.8 ]0.1 ^ 0.2 [0.1 ^ 0.2 ]0.3 ^ 0.3 [0.1 ^ 0.2 ]2.2 ^ 0.4 ]1.1 ^ 0.4 ]1.0 ^ 1.1 [0.3 ^ 0.9 [9.0 ^ 1.1 [7.3 ^ 1.5 NOTE.ÈThe lower groups represent particular solutions that are discussed in the main text. No. 1, 1999 EARLY RADIO POSITIONS OF STARS made use of the SIMBAD database of the Centre de Donnees Astronomiques de Strasbourg (CDS), the Hipparcos and Tycho Catalogues of the European Space Agency, and the AC 2000 and ACT catalogs at the US Naval Observatory. This research was partially supported 491 by FundacÓa8 o Universitaria Jose Bonifacio/Universidade Federal do Rio de Janeiro grant 3914-4. S. P. P. thanks CNPq for grant 300017/93-0, and E. G. J. likewise for grant 300016/93-6. REFERENCES Andrei, A. H., & Bartel, N. 1996, in VIII Reunion Regional LatinoameriGehrz, R. D., et al. 1995, ApJ, 439, 417 cana de Astronomia, ed. E. E. Falco, J. A. Fernandez, & R. Freire Jackson, P. D., Kundu, M. R., & White, S. M. 1989, A&A, 210, 284 Ferrero (Rev. Mexicana Astron. AstroÐs. Ser. Conf. 4) (Xochicalco, Johnston, K. J., Spencer, J. H., & Bowers, P. F. 1985a, ApJ, 290, 660 Mexico : Inst. Astron., Univ. Nac. Autonoma Mexico), 122 Johnston, K. J., Wade, C. M., Florkowski, D. R., & de Vegt, C. 1985b, AJ, Andrei, A. H., Jilinski, E. G., & Puliaev, S. P. 1995, AJ, 109, 428 90, 1343 Aoki, S., Soüma, M., Kinoshita, H., & Inoue, K. 1983, A&A, 128, 263 Kovalevsky, J., et al. 1997, A&A, 323, 620 Argyle, R. W., Einicke, O. H., Pilkington, J. D. 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