Rio survey of optical astrometric positions for 300 ICRF2 sources and the current optical/radio frame link status before Gaia

MNRAS 430, 2797 2814 (2013) doi:10.1093/mnras/stt081 Rio survey of optical astrometric positions for 300 ICRF2 sources and the current optical/radio frame link status before Gaia M. Assafin, 1 R. Vieira-Martins, 2 A. H. Andrei, 2,3 J. I. B. Camargo 2 andd.n.dasilvaneto 4 1 Observatório do Valongo/UFRJ, Ladeira Pedro Antonio 43, Rio de Janeiro, RJ 20.080-090, Brazil 2 Observatório Nacional/MCTI, R. General José Cristino 77, Rio de Janeiro, RJ 20921-400, Brazil 3 Shanghai Astronomical Observatory/CAS, 80 Nandan Road, Shanghai 200030, China 4 Centro Universitário Estadual da Zona Oeste, Av. Manual Caldeira de Alvarenga 1203, Rio de Janeiro, RJ 23.070-200, Brazil Accepted 2013 January 11. Received 2013 January 8; in original form 2012 November 27 ABSTRACT We obtained improved optical positions for 300 ICRF2 sources the Rio survey. We compared the Rio survey with 10 other selected optical astrometric surveys and studied the link between the Hipparcos Catalogue Reference Frame (HCRF) and the International Celestial Reference Frame, Second Realization (ICRF2). We investigated the possible causes for the observed non-coincidence between the optical and ICRF2 positions. The Rio survey positions were referred to the second version of the United States Naval Observatory CCD Astrograph Catalog (UCAC2), currently the best tested HCRF densification. The sources are between 90 < δ<+30. We used two telescopes with suitable diameters and focal lengths to properly link the observed ICRF2 sources with the UCAC2, using intermediate brightness stars. We certified the astrometry done with many statistical tests. The average optical minus ICRF2 offsets and respective standard deviations in (α, δ) were 3 mas (41 mas) and +4 (45 mas). The Rio survey represents well the zero-point offset of the other surveys. The standard error of 3.5 mas found for the HCRF/ICRF2 link indicates an error excess that can be originated by a non-coincidence between the observed optical/vlbi positions. We thus discussed the influence of the errors from the UCAC2. Then, we searched for correlations with the source morphology, represented by structure indices defined in the radio and in the optical domain. Finally, we studied how the position offsets could originate from the perturbation of the optical point spread function (PSF) of the source s core, by a second source of flux. We found an analytical relation that describes the resulting centroid shift, as a function of the atmospheric seeing, the brightness ratio and the relative distance between the two contributing flux sources. Two scenarios, modelled by this relation, are discussed: an extinction window in the dust torus nearby the core, and a Galactic star near the line of sight. Key words: methods: observational techniques: image processing surveys astrometry reference systems quasars: general. Based on observations made at Laboratorio Nacional de Astrofísica (LNA), Brazil. The complete set of positions and other information for the 300 ICRF sources (Table 2 in full) is available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?j/mnras/. Table 2 in full is also available as Supporting Information in the online version of this article. E-mail: massaf@astro.ufrj.br Affiliate researcher at Observatoire de Paris/IMCCE, 77 Avenue Denfert Rochereau, 75014 Paris, France. Affiliate researcher at Observatoire de Paris/IMCCE, 77 Avenue Denfert Rochereau, 75014 Paris, France. Affiliate researcher at Observatoire de Paris/SYRTE, 77 Avenue Denfert Rochereau, 75014 Paris, France. 1 INTRODUCTION In the XXIII General Assembly of 1997, the International Astronomical Union (IAU) adopted the International Celestial Reference System (ICRS) as the fundamental celestial reference frame (Arias et al. 1995). The primary materialization of the ICRS in the radio domain was the International Celestial Reference Frame (ICRF) (Ma et al. 1998), with 608 extragalactic sources (212 defining sources, 294 candidates and 109 other ones). The second realization of the International Celestial Reference Frame (ICRF2) was released in 2009 (Fey, Gordon & Jacobs 2009). The ICRF2 has 3414 members, measured by very long baseline interferometry (VLBI), but only 295 objects are defining sources (precision < = 0.4 mas). In the C 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society

2798 M. Assafin et al. optical domain, the primary representative of the ICRS is the Hipparcos Celestial Reference Frame (HCRF) (IAU 2002), based in the Hipparcos catalogue (ESA 1997). The first efforts to study the link between optical and radio reference frames in the pre-hipparcos era date back to the 80s. For example, see Walter & West (1980), White et al. (1990) and references therein. Our own group (the Rio group) has been working on the subject since the 90s (see Assafin & Vieira-Martins 1992; Assafin et al. 1996, 1997). In the Hipparcos era, one important task is to support efforts towards the maintenance and extension of the HCRF. In this context, the determination of the link between the HCRF and the ICRF is fundamental. The accuracy a of the link between the HCRF and the ICRF was first estimated by Kovalevsky et al. (1997), as a = 0.6 mas + t 1991.25 0.25 mas yr 1, at an epoch t. For 2012, a amounts to about 6 mas. The HCRF/ICRF2 frame link, especially the effect of rotation between the optical/radio frames, can be followed up by the comparison between the ICRF source positions with the positions of their optical counterparts, obtained in the HCRF frame. In practice, the most precise optical positions from the ground are obtained from the digitization of photographic plates, or better, with telescopes equipped with Charge Coupled Device (CCD) detectors. In this case, the reference frame is usually materialized by a star-dense astrometric catalogue, indirectly representing the HCRF, to cope with the smaller field of view (FOV). The United States Naval Observatory CCD Astrograph Catalog, in its second version, UCAC2 (Zacharias et al. 2004), is currently the most tested and used extension of the HCRF, for high-precision astrometry. The Gaia mission is coming (Robin et al. 2012). So now is the time to access the current status of the HCRF/ICRF2 frame link. For the best characterization of this status, we should use astrometric surveys of optical extragalactic source positions. In this work, we selected 10 surveys for study, which present at least one of three features: a large sky coverage, a large number of sources for the area covered and some extra care with the astrometry. We also produced an astrometric survey of our own, the Rio survey, which we will present here. The Rio survey displays all of these three qualities. We give a detailed description of these surveys in Section 7. We used published ICRF2 source positions in all the computations and statistics performed with the optical positions of the surveys used in this work, including the Rio survey. Between 1993 and 2006, the Rio group conducted a long-term CCD observational programme of ICRF sources at the Observatório do Pico dos Dias (OPD), Brasópolis, Brazil (IAU code 874). The OPD belongs to the Laboratorio Nacional de Astrofísica (LNA), Brazil, and possesses two telescopes of 0.6 m and 1.6 m diameters, used in the program. We wanted to extend the objectives reached by Assafin et al. (2003), which surveyed the Celestial Equator region within ±30. Our aim was to cover as much as possible the ICRF in the South, and up to about δ =+30, i.e. the entire region covered by the UCAC2, which is the best tested densification of the HCRF, up to date. In a pilot paper, we published positions for 31 sources from observations of this program (Assafin et al. 2005). The amount of observations from the OPD/LNA program was becoming huge. Fortunately, we eventually succeeded in our efforts to produce an automated, fast and precise astrometric package to cope with the task, the Package for Reduction of Astronomical Images Automatically, PRAIA (Assafin 2006). Along with our objectives, and in collaboration with Romanian astronomers, we used the 0.6 m Zeiss telescope at Belogradchik Observatory, Bulgaria, to cover most of the north part of the UCAC2, successfully using the PRAIA package in the reduction of 59 ICRF source positions (Assafin et al. 2007). The PRAIA package astrometric quality and computation efficiency have been certified by many other astrometric works conducted by the Rio group (see Sicardy et al. 2006; Assafin et al. 2010; Sicardy et al. 2011a,b; Assafin et al. 2012). Here, we conclude the efforts initiated in Assafin et al. (2005). All the observations of the OPD/LNA long-term program were reduced with the PRAIA package, and presented as the Rio survey. It consists of positions for 300 ICRF2 sources, homogeneously distributed in the celestial sphere between 90 <δ<+30. The positions are referred to the UCAC2. We present and analyse the Rio survey from Sections2to6. The ICRF2 sources in the Rio survey almost completely sample the sky range covered by the UCAC2. They also overlap with many of the sources of the studied surveys. We used the Rio survey and the other surveys to study the current status of the HCRF/ICRF2 reference frame link. This study is presented in Sections 7 and 8. The Rio survey completed a broader, South-Equator-North all-sky project, aimed to cover all the ICRF sources that could be properly observed with CCDs, and astrometrically referred to the UCAC2 frame with ground-based telescopes. This all-sky long-term project resulted from a joint international collaboration between two national Brazilian institutes located at the Rio de Janeiro city, the Observatório Nacional do Rio de Janeiro and the Observatório do Valongo da Universidade Federal do Rio de Janeiro, plus the United States Naval Observatory (Astrometry Department), the Observatoire de Paris/IMCCE and the Astronomical Institute of the Romanian Academy. Continuing with the previous works made by the group (da Silva Neto et al. 2002; Camargo et al. 2011), and supported by the analysis presented in Section 7, we investigated all the reasonable explanations for the non-coincidence between the optical/icrf2 positions that we observed. First, in Section 8.1, we discuss the effect of possible local errors in the UCAC2. Then, in Section 8.2, we revise the Standard Model for quasars and active galactic nuclei (AGNs), in this astrometric context. In Section 8.3, we explore the effects of the source morphology, using indices that can be associated with the morphology in the radio and in the optical domain, and search for statistical correlations with the position offsets. Finally, in Section 8.4, we study the effect of a perturbation in the optical point spread function (PSF) of the source, as the origin of a centroid shift in the optical, that can cause the position offset. We deduce an analytical expression that ties this shift with the seeing and with the relative distance and brightness of two hypothetical contributing point sources of flux (see Appendix A). We test two realistic scenarios that can be modelled by this relation. One is the effect of an extinction window nearby the source core, in the dust torus. The other is the presence of a galactic star nearby the line of sight of the source. We summarize the conclusions of this work in Section 9. 2 PROGRAM AND ASTROMETRIC STRATEGY OF THE RIO SURVEY In a long-term program at the OPD/LNA, we selected ICRF sources for observation south of +30 down to 90 declination. This allowed for a fair coverage of ICRF sources in the sky range covered by the UCAC2, within the visibility of the OPD/LNA site. The selection also overlapped with control targets observed in two parallel programs carried out by our group, in an international collaboration, covering the Equator region (Assafin et al. 2003) and the north part of the UCAC2 (Assafin et al. 2007).

Survey of optical positions for 300 ICRF2 sources 2799 Since most sources were fainter than magnitude 17, we needed telescopes of about 1 metre in diameter to better suit our astrometric needs. Such telescopes, equipped with 1k 1k CCD detectors, usually do not present an FOV larger than about 5 5arcmin 2,and the number of reference stars from the primary catalogue becomes small. We overcome this problem by also using a smaller telescope of 0.6 m in diameter. The shorter focal length allowed for larger FOVs of about 10 10 arcmin 2. The number of reference stars was no longer small. With the smaller telescope, we constructed local secondary star catalogues, which served as reference frame for the observations with the larger telescope. The stars of the secondary catalogues have intermediate brightness, in the range between the bright primary catalogue stars and the faint ICRF2 sources. In this way, it was possible to properly exposure all objects with both telescopes. We avoided pixel saturation and obtained appropriate primary reference star images with high signal-to-noise ratio (S/N) with the smaller telescope. And, for both telescopes, we could optimize the S/N of the images of the secondary reference stars. This strategy improved the astrometry, since we could obtain better S/N for the ICRF2 source images with the larger telescope, but kept intact the primary (catalogue) and secondary (local catalogue) reference frames at the same time. The final positions come from the reduction of the observations of the larger telescope. In the absence of those, the final positions come directly from the observations with the smaller telescope, whenever the target was successfully imaged. In our case, this only represented 29 per cent of the sources. Since we do not know the proper motion of the stars from the local secondary catalogues, we observed the targets in both telescopes at epochs as close as possible to each other. The third version of the United States Naval Observatory CCD Astrographic Catalogue, UCAC3 (Zacharias et al. 2010), was released in 2009. It presented many problems in the proper motion system, first reported by Roeser, Demleitner & Schilbach (2010). The UCAC3 authors themselves reported typography/production errors in a significant part of the catalogue (Zacharias et al. 2011). For these reasons, the UCAC3 was not adopted in the reductions. Instead, we used the second version of the United States Naval Observatory CCD Astrographic Catalogue, the UCAC2 (Zacharias et al. 2004). The UCAC2 was the reference catalogue used in almost all the astrometric surveys that we study in Section 7, and is still the most tested and used HCRF densification up to date. After we have concluded the reductions of this work, the UCAC4 was then released. The authors claim that it is close to the UCAC2 system (Zacharias et al. 2011). Since it requires a huge effort to re-reduce the data with respect to the UCAC4, with no obvious gain in the system representation of the HCRF, we decided not to postpone the publication of our results, with the UCAC2 as the primary reference catalogue in our work. 3 OBSERVATIONS In our observations, we used two non-dedicated instruments, shared by the Brazilian astronomical community: the 0.6 m diameter Bollen & Chivens Cassegrain telescope (F/13.5, f = 8.1 m) and the 1.6 m diameter Perkin Elmer Cassegrain telescope (F/10, f = 16 m), located at the LNA observing site, the Observatório do Pico dos Dias, Brasópolis, Brazil (OPD/LNA) (IAU code 874; λ =+45 34 57, φ = 22 32 04, h = 1870 m). We added sources for observation later on, with the outcome of the ICRF-ext1 (Ma 2001) and of the ICRF-ext2 (Fey et al. 2008). Naturally, not all sources could be observed, due to prohibitive telescope time consuming. When the ICRF2 was finally released in 2009, the program at OPD/LNA had already finished. The telescopes were equipped with thin, back-illuminated CCD detectors (1024 1024 pixels of 24 µm sizes), resulting on CCD fields of view of 5 5arcmin 2,1pixel= 0.3 arcsec for the 1.6 m telescope, and of 10 10 arcmin 2,1pixel= 0.6 arcsec for the 0.6 m telescope. Aiming to minimize differential colour refraction to neglecting values, we observed all targets near the meridian, and used the V filter (Johnson system), in a compromise between the more redder bandpass of the UCAC astrograph (579 642 nm) and the typically bluer ICRF2 sources. Usually, we observed each target at least three times, with telescope shifts between exposures to avoid sampling the same pixels on the star images. For each telescope, exposure times ranged from 90 to 300 s, allowing for the efficient use of telescope time, i.e. fulfilling the nightly observation schedule of the targets, and affording adequate S/N for the targets, the primary and secondary reference stars. The sky magnitude limit for the OPD/LNA site was estimated as V = 21. The magnitude limit for the 0.6 m telescope observations was around V = 18, mainly due to relatively shorter exposures, since we wanted to avoid saturation of the primary reference stars. Observations covered the period between 1993 and 2006, i.e. they are consistent with the average epoch of the UCAC2 mean star positions, which are based in the UCAC astrograph CCD observations and on many other early epoch catalogues (Zacharias et al. 2004). The same sources were observed at each telescope on time intervals usually not longer than three years, minimizing to negligible levels the problem of unknown proper motions of the non-ucac2 stars (see the discussion in Sections 5.1 and 5.2). The mean epoch of observations was 2000.3 ±2.1 and 2000.7 ±3.0 yr for the 0.6 m and 1.6 m telescopes, respectively. Due to unfavourable meteorological conditions and to the end of the awarded telescope time, we did not observe all the scheduled ICRF targets. In some cases, we did not succeed to image the targets with the 1.6 m instrument, probably because the V magnitude of those sources was fainter than the sky limit. On the other hand, many sources were successfully imaged with the 0.6 m telescope. In some cases, usually for bright sources, we did not need to observe the source in the 1.6 m, since it had already been satisfactorily observed with the 0.6 m telescope. A total of 88 targets were only imaged with the 0.6 m telescope, 50 targets were only imaged with the 1.6 m instrument, and 162 sources were satisfactorily imaged with both telescopes (see Fig. 1). In all, we successfully imaged, reduced and averaged final positions for 300 ICRF sources (details are given in Section 5). 4 ASTROMETRY We reduced the positions with the astrometric package PRAIA (Assafin 2006). PRAIA tasks automatically identify objects in the fields, measure them with bi-dimensional Gaussian fits, recognize catalogue stars and perform right ascension and declination reductions with a variety of models. PRAIA also calculates magnitudes and seeing. Error estimates are computed and stored for all objects. In this work, we followed the same measuring and position reduction procedures described in Assafin et al. (2007) for the astrometry of northern ICRF source observations. We reduced 38 GB of images, comprising 3546 and 2445 CCD frames from the 0.6 m and 1.6 m telescopes, respectively. We computed magnitudes by fitting Gaussian profiles to the images. The zero-point was calibrated by a simple logarithmic relation, using UCAC2 star magnitudes. The magnitude bandwidth

2800 M. Assafin et al. Figure 1. Hammer Aitoff sky distribution of the successfully imaged ICRF targets for each OPD/LNA telescope. A total of 88 targets were only imaged with the 0.6 m telescope (circles); 50 targets were only imaged with the 1.6 m telescope (crosses) and 162 sources were imaged with both telescopes. of the UCAC2 stars (579 643 nm) is not the same as that of our observations, which are in the Johnson V system. This can result in a systematic error for the individual magnitudes. However, we did not use colour terms to try to correct this, because the error in the magnitude of the UCAC2 standard stars dominates the error budget, and also because there are no available homogeneous sets of colours for the quasars. Anyway, the calculated magnitudes can be easily re-determined, when better colour information and better magnitude standards become available. We compared our computed magnitudes with the V magnitudes (between 500 and 600 nm) given by the LQAC2 in Souchay et al. (2012). The difference in the sense LNA minus LQAC2 for the 285 common objects was 0.81, with a standard deviation of 1.04. We thus corrected the the V zero-point of the computed magnitudes by adding +0.81 to all the 300 source magnitudes (the original values can be retrieved by subtracting 0.81 from the magnitudes.). The dispersion of 1.04 mag is in accordance with the S/N from the source images, and come from the known intrinsic variability of the sources, and from the intrinsic dispersion of the UCAC2 magnitude system, used to calibrate the magnitudes, frame by frame. We measured the (x, y) photocentres in an iterative procedure, by fitting the pixels within 2.5 times the full width at half-maximum (FWHM) from the centre, with a two-dimensional circular Gaussian function. This procedure improves the centre determination (see discussion in section 2 in Assafin et al. 2007). The seeing was typically within 1 to 2 arcsec (see Fig. 11, presented in another context, in Section 8.4). Fig. 2 displays the (x, y) measurement errors for the two telescope sets, as a function of the V magnitude, for all objects. Here, the (x, y) directions are associated with α and δ, respectively. For the targets alone, the average errors in each (x, y) coordinates were 52 and 37 mas for the 0.6 m and 1.6 m telescopes, respectively. Fig. 2 is proof of the successful strategy adopted for the telescope observations. The results were satisfactory, given the obtained S/N, which are consistent with the average seeing, and with the exposure times used, which in turn reflect a compromise between a reasonable S/N and the fulfilling of the scheduled list of targets for each telescope night. The (x, y) measurement errors for the 0.6 m and 1.6 m telescopes indicate that the bright UCAC2 stars and the local secondary catalogue stars in the intermediary magnitude range are satisfactorily imaged and, thus, measured. It also shows that the faint targets are also satisfactorily imaged/measured in the 1.6 m Figure 2. (x, y) photocentre measurement errors for the two telescope sets, as a function of the V magnitude, for all objects. The values are averages over 0.5 mag bins. Here, the (x, y) directions are associated with α and δ, respectively. telescope, as well as the brighter targets in the case of the 0.6 m telescope. We used the UCAC2 in the (α, δ) reductions of the 0.6 m telescope images. We utilized the standard six constant full linear model to relate the (x, y) measurements with the (X, Y) standard coordinates. The reference stars were eliminated in a one-by-one basis, until none displayed (O C) position residuals greater than 120 mas. This is, depending on the star magnitude, approximately two to three times the typical UCAC2 position errors, for the average epoch of the observations. We used 22 UCAC2 reference stars in average, per field. The (α, δ) reduction mean errors were, respectively, 45 mas and 43 mas, in average. In the case of the 1.60 m observations, we used the averaged star positions from the 0.6 m reductions to produce secondary star catalogues within 5 5arcmin 2 from each source position. We used these secondary catalogues as the reference frame for the 1.6 m position reductions. No proper motions were available for these secondary stars. But this was not problematic, since the time interval between the 0.6 m and 1.6 m observations was kept typically less than 3 years (see Section 5.1). The six constant model was used in the 1.6 m position reductions. We used the same (O C) criteria before to eliminate reference star outliers. We utilized 26 secondary reference stars per field in average. The (α, δ) reduction mean errors were 41 mas in average, for each coordinate. 5 THE TWO SETS OF TARGET POSITIONS FROM THE 0.6 M AND 1.6 M TELESCOPES After the astrometric procedures described in Section 4, we derived two sets of target positions, one for each telescope, after averaging the contributing individual CCD observations for each source. We eliminated some outlier positions in the averaging. For each telescope and target, we eliminated every outlier position which differed by more than 150 mas from the rest. This is about three times larger than the expected position error of UCAC2 stars, and is thus a clear indicator of a measurement problem. We derived positions for 212 targets with the 1.6 m observations, and for 250 targets with the 0.6 m telescope. For 162 common sources, positions were obtained from both 0.6 m and 1.6 m telescope observations. For 88 targets, there are only 0.6 m

telescope-based positions, and for 50 sources, only 1.6 m telescopebased positions. The two sets of target positions, obtained from each telescope, served to certify the astrometry done. We used these sets to check the consistency and robustness of the final positions (the Rio survey), which came from the 1.6 m telescope, and partly from the 0.6 m telescope, too. Survey of optical positions for 300 ICRF2 sources 2801 5.1 Epoch separation between the 0.6 m and 1.6 m telescope observations We investigated the epoch separation between the 0.6 m and 1.6 m telescope observations, as a possible cause of degradation of the local secondary catalogues of stars, which materialized the UCAC2 frame in the 1.6 m telescope position reductions. We studied how the unknown proper motions of the stars in the local secondary catalogues could affect the link between the 0.6 m and 1.6 m reference frames. For that, we computed the differences between the 0.6 m and 1.6 m telescope source positions for the 162 common targets, as a function of the respective epoch differences (modulus) (see Fig. 3). The objects displaying position differences larger than 70 mas at small epoch differences present large (x, y) measuring errors (low S/N). On the other hand, the large dispersion for the large epoch differences is genuine. We found it adequate to apply a non-parametric statistical test, to search for a possible correlation between the position and epoch differences. We used the Spearman rank-correlation statistic test for the samples. For improving the test sensitivity, we binned the position differences in integer units of 10 mas. We expected a continuous degrading effect with time, i.e. a strong correlation, as a result of the effects of galactic rotation, solar motion and possibly peculiar motion of the intermediate reference stars. But we obtained a correlation coefficient of 0.24, with a deviation of only 3.08σ from the null hypothesis (no correlation), which is not indicative of a strong correlation. Looking at Fig. 3, we note two regimes of position differences, for epoch differences smaller and larger than 3 years. This suggests two distinct scales of position degradation. For the small epoch difference sample, the position degradation competes with the astro- Figure 4. Cumulative distribution of sources, as a function of the epoch differences between the 0.6 m and 1.6 m telescope observations. About 90 per cent of the sources lie in the 0 3 years range. metric errors. For the large epoch difference sample, the degradation may be somewhat larger than the overall astrometric errors. Mixing these two populations might mask the result of the test. Thus, we applied the test to each separate sample. We obtained small deviations for both the small and large epoch difference samples, respectively 1.12σ and 1.79σ. Now, these results confirm our expectation of a position degradation correlation with the increase of the epoch difference. Considering the position error budget, we note that this degradation starts to become significant only after 3 years. Fig. 4 shows the cumulative distribution of sources as a function of the epoch differences between the 0.6 m and 1.6 m telescope observations. About 90 per cent of the sources lay in the 0 to 3 years range. Because of that, the position degradation with time should have a negligible effect on the positions. This conclusion is supported by the positional differences obtained in the sense 0.6 m minus 1.6 m. They were +1 mas (30 mas) and +10 mas (31 mas), respectively, for right ascension and declination (standard deviations are in parentheses). This indicates that both telescope sets of positions are consistent with each other, in terms of the measurement errors and of the reference catalogue position errors. This conclusion is further confirmed by the results shown in the following section. Figure 3. Difference between the 0.6 m and 1.6 m telescope positions for 162 common sources, as a function of the respective epoch differences (modulus). The objects displaying position differences larger than 70 mas at small epoch differences present large (x, y) measuring errors (low S/N). On the other hand, the large dispersion for the large epoch differences is genuine. 5.2 The realization of the 0.6 m and 1.6 m telescope local frames We further investigated whether the realization of the two telescope sets of positions was representative of the UCAC2 the primary reference frame in the astrometric reductions. For that, we computed positional offsets in the sense optical minus ICRF2 for each target and telescope set. We used the two telescope sets of 162 common targets to test this hypothesis, point by point, for right ascension and declination, separately. For that, we compared the two telescope distribution sets of optical minus ICRF2 position offsets. We plot in Figs 5 and 6 these position offsets, respectively, for right ascension and declination. Here, we applied three statistic correlation tests, which we found adequate for the samples. Since the two tested distributions have the same nature, one of the tests was the parametric Pearson correlation test. But, since the samples came from independent

2802 M. Assafin et al. Figure 5. The two sets of optical minus ICRF2 right ascension offsets, for the 162 sources common to both telescopes. The diagonal line corresponds to a 1:1 correlation. Figure 6. The two sets of optical minus ICRF2 declination offsets, for the 162 sources common to both telescopes. The diagonal line corresponds to a 1:1 correlation. origins (distinct telescopes and observation conditions), we also applied for redundancy two non-parametric tests, the Spearman and the Kendall rank-correlation tests. For improving the sensitivity in the tests, we binned the position offsets in integer units of 10 mas. The Pearson correlation test furnished 0.69 and 0.77 coefficients for the right ascension and declination distributions, respectively, with significance levels of less than 0.1 per cent for the null hypothesis (no correlation). The Spearman coefficients were 0.72 and 0.77, respectively, for right ascension and declination, with deviations of more than 9.0σ from the same null hypothesis. The Kendall coefficients were 0.59 and 0.63 for right ascension and declination, with deviations of more than 11.0σ from the same null hypothesis. These tests clearly indicate a strong statistical correlation between the two sets, point by point, in accordance with the visual inspection of Figs 5 and 6. This high correlation also supports the conclusion drawn in Section 5.1 that we can neglect the effects of position degradation due to the epoch differences between the 0.6 m and 1.6 m telescope observations. We also studied the optical minus ICRF2 position offsets from sets and subsets of telescope positions, which could be interpreted as an independent group of positions by its own, in our investigation. We divided them in seven groups: (a) the 88 sources only imaged with the 0.6 m telescope; (b) the 50 sources only imaged with the 1.6 m telescope; (c) the 162 common sources imaged with the 0.6 m telescope; (d) the 162 common sources imaged with the 1.6 m telescope; (e) all the 250 sources imaged with the 0.6 m telescope; (f) all the 212 sources imaged with the 1.6 m telescope; (g) the 300 sources, with all the 212 source positions from the 1.6 m telescope, plus the 88 source positions only obtained with the 0.6 m telescope. In accordance with the designed astrometric strategy described in Section 2, it is not difficult to recognize the group (g), as the Rio survey of positions for the 300 ICRF2 sources of this work. Thus, we took this main set as the reference, in the following comparisons. First, we verified the hypothesis of independence of the sets of positions with respect to the Rio survey. For that, we found convenient to apply the F-test of distinct variances. We confirmed with more than 99 per cent probability that all sets presented a distinct variance with respect to the Rio survey. Next, we checked out if all the sets still preserved the same reference frame zero-point, with respect to the zero-point of the Rio survey. In this case, they should present the same average position offsets. For that, we found it correct to apply the Student s t-test (for distinct variances). For all the sets, we found probabilities higher than the 5 per cent threshold, rejecting the null hypothesis of unequal averages. This indicates that the zero-points of all the sets, given by the average optical minus ICRF2 position offsets, are statistically equivalent to each other. This indicates that the positions obtained, regardless of the telescope origin or observational conditions, robustly represent the reference frame of the primary reference catalogue used, i.e. the UCAC2. We list in Table 1 the averages and standard deviations of the optical minus ICRF2 position offsets for each of these groups, together with the results of the Student s t-tests. We conclude that all the sets of telescope positions studied are equally representative of the same reference frame. The standard deviations are in excellent agreement with the expected UCAC2 position errors for each instrument, for the epoch of the observations. In particular, the set of final positions, i.e. the Rio survey with 300 sources, realizes well the reference frame of the primary catalogue, the UCAC2, and consequently, the HCRF itself. 6 THE FINAL POSITIONS FOR THE 300 ICRF2 SOURCES: THE RIO SURVEY The analysis in Section 5 certified the astrometric quality of the obtained positions. We trust in the set of 300 positions (the g group in Table 1), as the final set of ICRF2 positions of this work, exactly as we planned in the astrometry design of the program, described in Section 2. This final set of positions, and related information, constitutes what we call here the Rio survey. We list in Table 2 the data for a small sample of the 300 sources. The complete data set with all the 300 ICRF2 sources is freely available in the electronic form at the Centre de Données astronomiques de Strasbourg (CDS). Table 2 is also available in full as Supporting

Table 1. Optical minus ICRF2 positional offsets for study groups from the 0.6 m and 1.6 m telescope sets of positions. Group αcos δ δ σ α σ δ Pos. p (mas) (mas) (mas) (mas) No. (per cent) Survey of optical positions for 300 ICRF2 sources 2803 (a) Only 0.6 m +01 +11 42 48 088 06.3 (b) Only 1.6 m 11 +04 53 56 050 50.6 (c) Common 0.6 m 01 +11 42 48 162 21.6 (d) Common 1.6 m 02 +01 36 39 162 41.7 (e) All 0.6 m +00 +11 42 48 250 11.8 (f) All 1.6 m 04 +02 41 44 212 55.8 (g) 1.6 m + 0.6 m 03 +04 41 45 300 100.0 (Rio survey) Note. These study groups represent independent sets of positions, as verified by the F-test of distinct variances (see text). We furnish the averages, the standard deviation and the number of sources. In order, we have: (a) the 88 sources only imaged with the 0.6 m telescope; (b) the 50 sources only imaged with the 1.6 m telescope; (c) the 162 common sources imaged with the 0.6 m telescope; (d) the 162 common sources imaged with the 1.6 m telescope; (e) all the 250 sources imaged with the 0.6 m telescope; (f) all the 212 sources imaged with the 1.6 m telescope; (g) the 300 sources, with all the 212 source positions from the 1.6 m telescope, plus the 88 source positions only obtained with the 0.6 m telescope. The last group (g) represents, in fact, the Rio survey, with the set of final ICRF2 source positions of this work. The last column shows the results of the Student s t-test, in the comparison of the Rio survey with each position set. The test indicates if the distributions still have the same averages, although they represent independent distributions (distinct variances). We list the averaged right ascension/declination probabilities p. Probabilities p higher than 5 per cent indicate that the average offsets are statistically the same, i.e. the position sets share the same frame zero-point. Information in the online version of this article. For each source, we give the ICRS (J2000) and IERS (B1950) designation, the position, the V magnitude, the mean epoch of the position, the (x,y) photocentre measuring errors associated with (α, δ), the mean error from the (α, δ) reductions, the mean number of reference stars, the optical minus ICRF2 position offsets, the standard deviation of the contributing individual CCD positions, the number of contributing individual positions and the telescope origin of the position. We also furnish four indices based on the three indices extracted from the LQAC2, related to the optical PSF of the source. We further list two other indices (see Fey & Charlot 1997, 2000) related to the radio structure of the source core in the X and S radio bands, Figure 7. Optical minus ICRF2 position offsets with respect to right ascension and declination, for the 300 sources of the Rio survey. No systematic position errors and no signature of differential colour refraction are seen. extracted from the Bordeaux VLBI Image Database (BVID) and from the Radio Reference Frame Image Database (RRFID). These indices are presented in Section 8.2 and discussed later in detail in Section 8.3. Fig. 7 displays the optical minus ICRF2 position offsets with respect to right ascension and declination, for the 300 sources of the Rio survey. In Fig. 8, we plot the histogram of the offsets for both coordinates, with 30 bins of 10 mas size. We also plot the fit of a Gaussian function with (μ, σ ) of(+4 mas, 36 mas) and(+10 mas, 36 mas) for the right ascension and declination histograms. The fits produced a χ 2 of 8.93 and 6.81, respectively, resulting in a χ 2 test probability higher than 99.9 per cent that both sets of offsets follow a normal distribution. Since we observed close to the meridian, the differential colour refraction should produce an approximate linear trend in the δ δ graphic, which is not seen. In fact, no systematic errors are visible in Fig. 7. This is supported by the statistical analysis of the histograms of position offsets plotted in Fig. 8, which follow the normal distribution. We conclude that no systematic position errors and no signature of differential colour refraction are present in the Rio survey. Table 2. Results for a sample of three targets, out of the 300 ICRF2 sources of the Rio survey. Table 2 is available in full as Supporting Information in the online version of this article. m V Epoch σ x σ y E α E δ Ref. αcosδ δ σ α σ δ No. X S P K R N (yr) (mas) (mas) (mas) (mas) stars (mas) (mas) (mas) (mas) pos. 16.3 2004.0771 30 29 50 40 07 +07 20 36 42 13 3.07 2.01 1.34 0.96 0.58 0.73 17.1 1998.2215 35 37 50 49 25 +00 12 67 58 19 9.99 9.99 0.98 0.19 0.96 0.05 18.1 1999.8682 84 87 21 26 13 +07 06 80 62 05 3.44 1.00 2.32 1.53 1.67 0.51 Notes. The complete data set with all the 300 ICRF2 sources is freely available in the electronic form at the CDS. Table 2 is also available in full as Supporting Information in the online version of this article. For each source, we list the ICRS (J2000) and IERS (B1950) designations, the position, the V magnitude, the mean epoch of the position, the (σ x,σ y ) photocentre measuring errors associated with (α, δ), the mean errors (E α, E δ ) from the (α,δ) reductions, the mean number of reference stars, the optical minus ICRF position offsets, the standard deviation of the contributing individual CCD positions, the number of contributing individual positions, and the telescope origin of the position. We also furnish four indices (P, K, R and N, with P = K 2 + R 2 + N 2 ) based on the LQAC2, related to the optical PSF of the source. The K, R and N indices are, respectively, related to the skewness, roundness and normalness of the PSF. We also give two indices, X and S (see Fey & Charlot 1997, 2000), extracted from the BVID and from the RRFID, related to the radio structure of the source core in the X and S bands. These indices are presented in Section 8.2 and discussed in detail in Section 8.3. For the sake of layout clarity, we omitted from the table the source designations, positions and telescope origin. Complete table contents are fully available in the electronic form of the table for all the 300 sources. Codes 9.99 for the X or S radio indices, and 0.00 for the optical indices, mean no index available. We compute the standard deviations (σ α, σ δ )when there are three or more individual CCD contributing positions. In the case of two contributing positions, we give the distance between the coordinates. In the case of only one position available, we do not estimate σ (code 99998).

2804 M. Assafin et al. Figure 8. Histogram of the optical minus ICRF2 position offsets for right ascension and declination, for the 300 sources of the Rio survey. Frequency is in relative percentage (per cent) to the total source number. We used 30 bins of 10 mas size. Also plotted is the fit of a Gaussian function with (μ, σ )of(+4 mas, 36 mas) and (+10 mas, 36 mas) for the right ascension and declination histograms. The fits produced χ 2 s of 8.93 and 6.81 (count units), respectively, resulting in a χ 2 test probability higher than 99.9 per cent that both sets of offsets follow a normal distribution. 7 THE RIO SURVEY, THE 10 MOST RELEVANT OPTICAL SURVEYS OF ICRF SOURCE POSITIONS AND THE CURRENT STATUS OF THE OPTICAL/RADIO FRAME LINK The astrometric surveys selected for study in this work present at least one of three features: a large sky coverage, encompassing a significant area covered by the UCAC2, a large number of sources for the area covered and some extra care with the astrometry. First, we summarize the properties of each of these surveys, and label their respective sets of positions, for reference. Then, we compare them with the Rio survey, and draw conclusions about the current status of the link between the optical/radio frames. Zacharias et al. (1999) presented 327 all-sky source positions based on short focus astrographs and long focus reflectors and plate/ccd observations. The positions were directly referred to the HCRF. They modelled the solar motion and the galactic rotation to account for the unknown proper motions of the secondary stars, used to link the short and long focus fields. The paper listed positions with (ZC) and without (ZN) these kinematic corrections. da Silva Neto et al. (2000) was another important all-sky survey of 315 positions measured with the Digital Sky Survey (DSS). Three sets of positions, SN HIP,SN TYC and SN ACT, are presented, relative to the respective reference catalogues Hipparcos, Tycho (ESA 1997) and Astrographic Catalogue-Tycho (ACT; Urban, Corbin & Wycoff 1998). A more recent example of an all-sky survey was the Large Quasar Reference Frame (LQRF; Andrei et al. 2009). It was recently updated. The new version, LQRF2, with 187 504 quasars and AGNs, is available together with the new, second version of the Large Quasar Astrometric Catalogue, LQAC2 (Souchay et al. 2012). The LQRF2 is a compilation of optical positions from many all-sky astrometric catalogues, based on ground-based observations with photographic plates, CCD and infrared detectors. CCD observations have the small FOV as a drawback. In the Hipparcos era, the first efforts of extending the HCRF towards dense star catalogues were made by the United States Naval Observatory, with the USNO A2.0 catalogue (Monet 1998), and by the Space Telescope Science Institute, with the Guide Star Catalogue 2.2 (GSC 2.2). 1 Fienga & Andrei (2002) were the first in the 2000s to use such catalogues, to depend only on CCD observations to derive source positions. They published 38 northern source positions, using the 1.2 m telescope at Observatoire de Haute-Provence, France. They used the zonal corrections for the USNO A2.0 catalogue, furnished in Assafin et al. (2001). We labelled the USNO A2.0 and the GSC 2.2 position sets as FAU and FAG, respectively. A problem is that none of these catalogues lists proper motions and the mean epoch of the catalogue star positions is about 20 years or more apart from the CCD observations. Assafin et al. (2003) published 172 positions for ICRF sources within 30 from the equator, entirely based on CCD observations, made with the 90 cm telescope at the Cerro Tololo Inter-American Observatory, Chile (CTIO). The CTIO survey was the first one to use the United States Naval Observatory CCD Astrograph Catalogue, UCAC2 (Zacharias et al. 2004), as the reference frame, representing the HCRF. Camargo et al. (2005) published positions of southern quasars using infrared detectors with the European Southern Observatory (ESO) 3.5 m NTT/SOFI instrument. They obtain precise positions for 30 and 14 sources, using the equipment in single and mosaic mode, respectively (NTTS and NTTM surveys). They used the UCAC2 in the position reductions. Recently, Aslan et al. (2010) published CCD positions using two instruments, the 1.5 m RTT150 Russian Turkish Telescope at the TÜBİTAK National Observatory, Turkey, and the 1 m telescope at the Yunnan Astronomical Observatory, China. They used the UCAC2 and the Two Micron All Sky Survey (2MASS; Cutri et al. 2003) as reference catalogues. They reduced 130 and 182 ICRF2 source positions with the UCAC2 and 2MASS (ASU and AS2 surveys), covering the Equatorial belt and the sky for δ > = 40, respectively. More recently, using the UCAC2 as reference frame, Camargo et al. (2011) published the WFISO survey of precise positions for 24 south ICRF2 sources, using the ESO 2.2 m Wide Field Imager, and the 4 m Southern Astrophysical Research (SOAR) Telescope in Chile. In a pilot paper, we published positions for 31 southern sources from observations of the OPD/LNA program (Assafin et al. 2005). We obtained 27 positions from the 0.6 m telescope observations (PL60 survey), and 28 positions from the 1.6 m telescope (PL160 survey), all referred to the UCAC2. In a collaboration with Romanian astronomers, we used the 0.6 m Zeiss telescope at Belogradchik Observatory, Bulgaria, and published 59 northern ICRF source positions (ROM survey), in the UCAC2 frame (Assafin et al. 2007). We thus separated 17 groups of positions from these 10 optical surveys, which we judge that form independent sets of positions. And we compared the Rio survey with all of them. For simplicity, we refer to these groups indistinguishably as surveys too. Table 3 displays, for the common sources, the average and the standard deviation of the optical minus ICRF2 position offsets, obtained in this work, and from the surveys. We also furnish the averages and standard deviations for all sources measured in each respective survey. We checked if these position sets were statistically independent of the Rio survey by conveniently using the F-test of distinct variances. We confirmed this hypothesis with confidence 1 http://tdc-www.harvard.edu/catalogs/gsc2.html

Survey of optical positions for 300 ICRF2 sources 2805 Table 3. Comparison of the Rio survey with 17 sets of positions, taken from the 10 most relevant astrometric surveys of optical ICRF source positions, found in the literature up to date. Survey (all sources) Survey (common sources) This work (common sources) αcosδ δ σ α σ δ αcosδ δ σ α σ δ αcosδ δ σ α σ δ p Survey (mas) (mas) (mas) (mas) No. (mas) (mas) (mas) (mas) (mas) (mas) (mas) (mas) No. (per cent) Rio 03 +04 41 45 300 03 +04 41 45 03 +04 41 45 300 100.0 PL60 20 +09 89 58 27 +04 +01 41 42 +02 +04 37 37 24 49.4 PL160 14 06 53 61 28 11 01 53 56 04 +09 38 39 27 33.8 CTIO 08 14 36 32 172 10 13 36 32 04 +06 41 40 148 03.6 ZN +00 +49 75 79 365 08 +54 77 80 04 +05 40 44 226 22.4 ZC 05 +26 71 80 365 13 +36 74 83 04 +05 40 44 226 29.6 SN HIP 05 20 226 229 313 21 21 222 234 03 +05 39 42 188 47.0 SN TYC 06 35 188 197 290 15 22 184 194 03 +06 39 42 180 39.3 SN ACT +12 20 176 196 315 +11 02 174 193 03 +05 39 42 190 08.1 ASU 04 +15 53 45 130 10 +16 48 45 06 +08 40 41 87 41.8 AS2 +13 +27 101 87 182 06 +32 77 81 06 +05 39 42 101 01.7 WFISO 18 12 46 54 24 18 12 46 54 04 +03 36 33 24 14.2 LQRF2 +03 08 146 144 285 +03 08 146 144 03 +05 41 44 285 32.5 NTTS +04 +05 64 82 30 +02 +06 66 85 +03 +11 38 35 28 75.1 NTTM +11 +02 38 25 16 +11 +02 38 25 01 +07 42 31 16 45.8 ROM +06 +07 51 57 59 +05 +07 58 63 +00 +07 44 32 33 43.5 FAU +49 +244 170 137 38 +50 +255 149 141 11 +02 47 35 30 03.4 FAG +68 +69 127 128 38 +74 +74 128 135 11 +02 47 35 30 00.2 Note. We list the average and the standard deviation between the optical minus ICRF2 position offsets, for the common sources measured in this work and in the surveys. We also give the averages and standard deviations found for all sources in each respective survey. Rio stands for this work. PL60 and PL160 stand for the 0.6 m and 1.6 m position sets from our pilot paper (Assafin et al. 2005). CTIO comes from the work by Assafin et al. (2003). ZN and ZC refer to the optical positions in Zacharias et al. (1999), respectively without and with galactic kinematic corrections. SN HIP, SN TYC and SN ACT stand for the positions referred to the Hipparcos, Tycho and ACT catalogues from da Silva Neto et al. (2000). ASU and AS2 come, respectively, from the UCAC2 and 2MASS catalogue-based positions published in Aslan et al. (2010). WFISO comes from the ESO2p2/WFI and SOAR/SOI telescope-based positions in Camargo et al. (2011). LQRF2 refers to the second version of the LQRF by Andrei et al. (2009), which was published in Souchay et al. (2012). NTTS and NTTM come from the 3.5 m NTT telescope-based positions using, respectively, single and mosaic CCD fields (Camargo et al. 2005). ROM stand for the set of optical positions by Assafin et al. (2007). FAU and FAG stand in this order for the USNO A2.0 and GSC 2.2 catalogue-based positions given by Fienga & Andrei (2002). We applied the Student s t-test (for distinct variances; see discussion about the F-test in the text), to check out if the position sets shared the same reference frame zero-point, i.e. the average offsets in right ascension and in declination. The last column lists the right ascension/declination averaged probabilities p. Values higher than 5 per cent indicate that the zero-points are statistically equivalent. For the Rio survey, we took the 1.6 m + 0.6 m values given in Table 1. For the LQRF2 all-source statistics, we repeated the common-source statistics, because there were already a large representative number of sources available in the comparison. levels higher than 99 per cent for all compared sets. Next, we applied the Student s t-test (for distinct variances) to check which of these sets still represented the same reference frame, i.e. if their zeropoints in right ascension and in declination were the same. The results of the test, applied to the position offsets, are also listed in Table 3. In the Student s t-test, probabilities higher than 5 per cent indicate that the zero-points, given by the average optical minus ICRF2 position offsets, are statistically the same. According to Table 3, the AS2, the FAU and FAG surveys do not display compatible reference frame zero-points with the Rio survey. This makes sense, since the reference frames of these surveys do not have anything in common with the UCAC2. This result, together with the averages and standard deviations found for these surveys, suggests that the 2MASS, USNO-A.2 and GSC 2.2 catalogues are not better representatives of the HCRF, than the UCAC2 is. The CTIO survey also presented a low probability. In this case, we found p = 7.3 per cent for right ascension, but p below 0.1 per cent for declination. This was because the standard deviation for the declination offsets was only 36 mas for this survey, but the average was significant, 14 mas. From Table 3, the Rio, CTIO, NTTM and ASU surveys present the smallest standard deviations for the optical minus ICRF2 position offsets. The most discrepant results, by more than 3 σ (Rio survey), come from the FAU, FAG, SNs, and from the LQRF2 surveys. The standard deviations of the other surveys agree within 2σ with the Rio survey, with closer results for our PL160 pilot program, for the WFISO and for the ROM surveys. In all, the results are in agreement, when considering the error budget from each survey and from our work. Apart from a few exceptions, most of which are expected, the vast majority of the surveys studied here have frame zero-points statistically compatible with the Rio survey. This is further verified in Fig. 9, which displays the average optical minus ICRF2 offsets for right ascension and declination for all the surveys, including the Rio survey. The error bars stand for the respective standard errors, computed by dividing the standard deviations by the square root of the number of sources (see Table 3, Columns 2 to 6). The analysis shows that among all these surveys, the Rio survey is the one which presents the best compromise between the three fundamental qualities that we pursue: source number, precision/accuracy and UCAC2 area coverage. Thus, we can assume that the Rio survey is the best representative of the afore studied surveys. Now, recognizing the advantage of homogeneity in working with only one position set, we justify the use of the Rio survey alone in the following investigation of the current status of the link between the HCRF and the ICRF2 reference frames. Fig. 9 illustrates the current status of the zero-point alignment of the HCRF/ICRF2 reference frames in the Hipparcos era, before the Gaia mission. The Rio survey represents well the average of