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UCAC3: Astrometric Reductions

Charlie T. Finch, Norbert Zacharias, Gary L. Wycoff

finch@usno.navy.mil

U.S. Naval Observatory, Washington DC 20392–5420

ABSTRACT

Presented here are the details of the astrometric reductions from the x, y data to mean RightAscension (RA), Declination (Dec) coordinates of the third U.S. Naval Observatory (USNO) CCDAstrograph Catalog (UCAC3). For these new reductions we used over 216,000 CCD exposures.The Two-Micron All-Sky Survey (2MASS) data are extensively used to probe for coordinate andcoma-like systematic errors in UCAC data mainly caused by the poor charge transfer efficiency(CTE) of the 4K CCD. Errors up to about 200 mas have been corrected using complex look-uptables handling multiple dependencies derived from the residuals. Similarly, field distortions andsub-pixel phase errors have also been evaluated using the residuals with respect to 2MASS. Theoverall magnitude equation is derived from UCAC calibration field observations alone, indepen-dent of external catalogs. Systematic errors of positions at UCAC observing epoch as presentedin UCAC3 are better corrected than in the previous catalogs for most stars. The Tycho-2 catalogis used to obtain final positions on the International Celestial Reference Frame (ICRF). Residualsof the Tycho-2 reference stars show a small magnitude equation (depending on declination zone)that might be inherent in the Tycho-2 catalog.

Subject headings: astrometry — catalogs — methods: data analysis

1. INTRODUCTION

The U.S. Naval Observatory (USNO) CCDAstrograph Catalog (UCAC) project began ob-servations in the Southern Hemisphere at CerroTololo Interamerican Observatory (CTIO) in Jan-uary 1998. In October 2000 the first U.S. NavalObservatory CCD Astrograph catalog (UCAC1)(Zacharias et al. 2000) was published coveringabout 80% of the southern sky with positions andpreliminary proper motions for over 27 millionstars. The Astrograph was moved to the NavalObservatory Flagstaff Station (NOFS) in October2001 to complete the Northern Hemisphere ob-serving after 2/3 of the sky were completed fromCTIO. The second USNO CCD Astrograph cata-log (UCAC2) (Zacharias et al. 2004) was releasedin July 2003 with the same level of completenessas in UCAC1, but with improved reduction tech-niques, early epoch plates for improved propermotions and extended sky coverage. All sky cov-erage for UCAC observations were completed in

October 2004.

The third USNO CCD Astrograph Catalog(UCAC3) (Zacharias et al. 2010) is the first all-sky data release in the UCAC series, containingabout 100 million entries with a slightly fainterlimiting magnitude than in previous versions. Themagnitude range for UCAC3 is roughly 8.0 to16.3 mag in the UCAC bandpass (579-642 nm,hereafter UCAC magnitude). A detailed intro-duction into UCAC3 with comparisons to othercatalogs and warnings for the users are given in(Zacharias et al. 2010). Any user is also urged toread the extensive “readme” file provided with theDVD or on-line release.

The UCAC3 is based on a complete re-reductionof the pixel data aiming at more completenesswith the inclusion of double star fitting, problemcase investigations and the slightly deeper limitingmagnitude (Zacharias 2010). The final positionsare based on the Tycho-2 (Høg et al. 2000) refer-ence frame as in UCAC2. However, Two-Micron

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All Sky Survey (2MASS) (Skrutskie et al. 2006)residuals are used to probe for systematic errorsin astrometric reductions as will be explained be-low.

In UCAC1 and UCAC2 it was shown that the4K CCD in the astrograph camera has a rela-tively poor charge transfer efficiency (CTE), lead-ing to coma-like systematic errors in the uncor-rected stellar positions. The effect is seen mainlyin the x-axis (right ascension), which is the di-rection of the fast readout of charge, while they-axis (declination) shows a much smaller effect.In UCAC1 a simple empirical approach was usedto correct for this effect with the basic assumptionthat the effect was linear along the x-axis and noassumption for a dependency on magnitude. ForUCAC2 the empirical approach was extended witha more complex model as a function of x, y, andinstrumental magnitude derived from flip obser-vations of calibration fields. Flip observations areobtained by observing the same field with the tele-scope on one side of the pier (east or west) thenrepeat with the telescope on the other side. Thustwo images of the same area in the sky are ob-tained which are rotated by 180◦ with respect toeach other.

In both previous UCAC catalogs sub-pixelphase and field distortion errors have also beeninvestigated. For UCAC1 the pixel phase wasmodeled with an empirical function showing anamplitude on the order of 12 mas resembling asine-function. For UCAC2 the pixel phase er-rors were investigated further and found to alsobe a function of the full width at half maximum(FWHM) of the stellar image profiles. The fielddistortion pattern was modeled in both previousreductions by binning reference star residuals fromindividual frames used in the reductions.

The new pixel data reductions up to x, y dataare described in (Zacharias 2010). This paper de-scribes the reductions following the x, y data upto the CCD-based mean RA, Dec positions. Earlyepoch data and procedures to derive proper mo-tions are presented in the UCAC3 release paper(Zacharias et al. 2010), while details about an im-portant part of the early epoch data, the SouthernProper Motion (SPM) data will be given elsewhere(Girard et al. 2010).

2. INPUT DATA

For the astrometric reductions of UCAC3 as de-scribed in this paper, two sets of input data areneeded: the x, y data from selected CCD obser-vations, and reference stars. Here two differentreference star catalogs are used for different pur-poses.

2.1. CCD Frame Selection

Out of the about 278,000 UCAC frames evertaken, all applicable survey frames, calibrationfield, and minor planet exposures are selected forthe reductions presented here. Poor quality framesare excluded. Quality criteria include limitingmagnitude, internal fit precision of high S/N stel-lar images, and mean image elongation. About15% of the observations are qualified as “poor”,see also (Zacharias et al. 2000). All frames whichpass those quality criteria are included. Then theall-sky completeness from the selected data are ex-amined and frames which almost meet the qualitycriteria are included as needed to provide a com-plete all-sky coverage.

The final UCAC3 catalog contains mainly thesurvey frame data. The minor planet observationswill be published separately, while the calibrationfield observations are only used in the first reduc-tion steps to derive corrections to systematic er-rors. A summary of the CCD observations is givenin Table 1. The frames taken along the path ofPluto are included here from a collaboration withL. Young (SWRI) for occultation predictions.

A total of about 50 fields in the sky observed atabout 10 to 30 different epochs with multiple expo-sures each time were used as astrometric calibra-tions. These typically low galactic latitude fieldsaround ICRF targets, equatorial calibration fields,and open clusters were observed about 10 to 30times during the project and with the telescopeflipped between orientations east and west of thepier to provide a reversal of RA, Dec orientationin x, y space. Data from these fields are utilizedto derive certain systematic error corrections (seebelow). However, these frames are not included inthe final UCAC3 reductions based on the Tycho-2reference catalog.

Frames around extragalactic link sources takenwith the astrograph at times of deep CCD obser-vations (mostly with the KPNO and CTIO 0.9 m

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telescopes) are not included here either. Thesedata are still under investigation and a separatepaper is in preparation regarding the optical linkto ICRF quasars.

2.2. x, y Data

For all astrometric reductions described belowonly the x, y results from pixel data profile fitmodel five (symmetric Lorentz profile with pre-set α, β shape parameters) are used. This fitmodel has five free parameters per single star im-age (background, amplitude, center x, y, widthof profile), similar to the more familiar two-dimensional Gauss model. However, the Lorentzprofile matches the observed point-spread func-tion (PSF) of our data significantly better thanthe Gaussian model. For more details and ex-plicit PSF model functions see the UCAC3 pixelreduction paper (Zacharias 2010).

Double star fits of blended images are basedon the same Lorentz image profile model, how-ever three more free parameters are used for thetwo center coordinates and the amplitude, respec-tively, of the secondary component. Both the pri-mary and secondary component are fit simultane-ously. A single width of the profiles for both com-ponents of a double star and a single backgroundlevel parameter is used in this fit.

The x, y data files also contain internal errorson the center coordinates derived from the least-square fits, two instrumental magnitudes based onthe profile fit model and a real aperture photom-etry, respectively, and several auxiliary flags fromthe raw pixel reduction step. For more informa-tion about the raw data reductions see the UCAC3pixel reduction paper (Zacharias 2010).

2.3. Reference Stars

The 2MASS catalog does not provide propermotions. However, the UCAC and 2MASS ob-servations were made almost at the same epochand the 2MASS positions are of high quality withrandom errors of about 70 mas per coordinatefor well exposed stars and small systematic errors(Zacharias et al. 2006). Due to the deep limitingmagnitude and high density the 2MASS catalog isan excellent tool to probe UCAC data for system-atic errors on a statistical basis, allowing to stackup many residuals as a function of a large number

of parameters, as will be described below. Table 2lists the number of available observations of refer-ence stars, each providing a residual along RA (x)and Dec (y).

For this purpose a subset of the 2MASS pointsource catalog is constructed. Stars are selectedfrom the Naval Observatory Merged Astromet-ric Dataset (NOMAD) using the 2MASS identifierand imposing a limit of V or R ≤ 16.5 to select116,247,341 2MASS stars. For these, the original2MASS positions are retrieved and matched withUCAC observations on a frame-by-frame basis.

Proper motions of this reference star catalog aretaken out of the NOMAD catalog. Even if theseare not very accurate for faint stars, they bridgethe few years of epoch difference to UCAC datato avoid large-scale biases from galactic dynamics.For most stars in the southern hemisphere, theepoch difference between 2MASS and UCAC is ∼± 1 yr, while it gradually increases for stars athigher declinations. Near the north celestial polethe epoch difference is about four years.

The 2MASS data are used only to derive mostof the systematic error corrections of the UCACx, y data. As with UCAC2, the Tycho-2 cata-log is used as the only source for reference starsin a final astrometric reduction to obtain UCAC3positions on the International Celestial ReferenceFrame (ICRF). Only stars from the Tycho-2 cata-log indicated as having good astrometry have beenused for this reduction. Tycho-2 proper motionshave been used to propagate the positions to theepoch of the individual UCAC x, y observations.

Both reference star catalogs are sorted by dec-lination and stored in binary direct access files.For each catalog a match to the x, y data are per-formed to produce cross-reference output files perCCD frame containing the record numbers fromthe x, y direct access data and the reference starcatalog, as well as the magnitude of the star, B−Vcolor, and astrometry flag (for Tycho-2). Thisscheme allows a fast runtime for the many passesthrough all the data to perform the astrometric re-ductions without the need for a match of referencestars each time.

3. ASTROMETRIC REDUCTIONS

For the astrometric reductions in UCAC3 ex-tensive systematic error investigations are per-

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formed. The largest systematic error is caused bythe poor charge transfer efficiency (CTE) of thedetector, followed by geometric field angle distor-tions. An iterative approach was adopted utilizing2MASS residuals to determine each of these effectsin turn as described below. The idea here is to usean empirical approach as done in the past, but in-vestigate further dependencies to better model theeffects seen in the 4K CCD pixel data. Preliminaryresults were presented earlier (Finch et al. 2009).A pure magnitude equation is derived from inter-nal calibration observations only. Finally the po-sition shifts as function of the sub-pixel locationof an image in the focal plane (the sub-pixel phaseerror) is derived, however, the x, y data used forthat are the original measures before applying theother corrections.

Systematic position offsets as a function of colorand differential color refraction due to Earth’s at-mosphere are small (about 5 mas) due to the nar-row UCAC spectral bandpass. No such correctionsare applied for the UCAC3 catalog.

3.1. Preliminary Field Distortion Pattern

In the first step of the astrometric reductions,the CTE caused systematic errors (coma-like) areapproximated by a linear model as a function ofmagnitude and x pixel coordinate, similar to theCTE modeling of UCAC1. This takes out about80% of the CTE effect. The pre-corrected x, y dataare then used in a preliminary astrometric reduc-tion with 2MASS reference stars to produce an ap-proximate field distortion pattern (FDP), i.e. sys-tematic errors purely based on the x, y location ofa stellar image on the area of the detector. Al-though the coma-like corrections for the CTE ef-fect should not bias the purely geometric FDP cor-rections, the scatter in the data is largely reducedby correcting for most of the CTE effect first. Thisleads to a more accurate FDP as would be gener-ated without applying any CTE corrections.

Maximal systematic errors in the FDP areabout 24 mas, with typical corrections in the 5to 10 mas range. This preliminary FDP is thenapplied to the otherwise uncorrected x, y data toanalyze the CTE effect from scratch in the fol-lowing step. The same reasoning applies here;with good FDP correction in hand the scatter ofthe residuals is reduced to accurately probe thesystematic errors induced by the poor CTE.

3.2. CTE Effect

When the CCD reads out an image, the elec-trons are transferred from pixel−to−pixel untilthe charge reaches the output register. The lowCTE of the 4K CCD causes charge to be left be-hind as this transfer occurs, leading to slightlyasymmetric images. The amount of asymmetryand the derived x, y center of stellar images withrespect to the unaffected position depend on thex pixel location, the brightness of the star, thelength of the exposure, and other factors.

As found here and in previous UCAC reduc-tions the CTE effect is by far the most substantialsystematic error seen in the raw UCAC x, y dataamounting up to about 200 mas. The effect is pre-dominantly seen in the x-axis along right ascensionand increases from no effect near x = 0 pixel to amaximum near x = 4094 pixel, as evident in Fig-ure 1. A similar effect is also seen in the y-axis,but to a lesser degree because of a slower chargetransfer in the direction of declination.

For the reductions, the UCAC frames are sep-arated into individual data sets depending on ob-servation site (CTIO or NOFS) and telescope ori-entation (east or west). Over 216,000 frames areused for the reductions, see Table 1. Most framesat CTIO were observed with the telescope west ofthe pier, while at NOFS the regular observing wasperformed east of the pier.

Because the instrument had to be disassem-bled for the move from CTIO to NOFS the cam-era alignment and other instrument properties areslightly different at both sites. This explains theslightly different patterns for systematic error cor-rections found for the two sites. However, the2MASS reference star catalog is dense enough toprovide a sufficient number of residuals for statis-tically significant results even on relatively smallsub-sets of the UCAC data.

For UCAC3 we found that the CTE systematicsshow a dependence on FWHM, brightness of thestar, exposure time, location on the chip (x, y),camera orientation (east, west) and observing site(CTIO, NOFS). For example as Figures 1 and 2show the CTE caused different systematic positionoffsets for the x coordinate as a function of mag-nitude for 20 and 150 sec exposures, respectively.

The residuals with respect to the 2MASS refer-ence stars are split into two major data sets for in-

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vestigating the CTE effect, CTIO west and NOFSeast. A plotting program is then used to displayand determine empirical corrections to create acomplex look-up table. The table is split up intofour different FWHM bins keeping a roughly equalnumber of frames per bin, with half step magni-tude bins ranging from 8 to 16 magnitude for allstandard exposure times of 20−200 seconds dura-tion, and 5 bins along the x, y axes. Each dataset is evaluated and look-up tables are created tocorrect for the residuals, (see sample, Table 3).

For each of the main data sets, CTIO west andNOFS east, tables are created separately for thex and y axes. After testing we found that thesetables could also be used for the data of the otherconfigurations, (CTIO east and NOFS west) cor-responding to the observation site. After apply-ing corrections and re-running the residuals thecorrection tables are continuously updated untilthe residuals flattened out. The largest correctionfrom the residuals for CTIO is 204 mas in the x-axis and −32 mas in the y-axis. For NOFS thelargest correction from the residuals is 216 mas inthe x-axis and −67 mas in the y-axis.

3.3. Pure Magnitude Equation

The 2MASS positions are uncorrelated to thex, y pixel coordinates of the UCAC observa-tions. Thus any systematic errors seen in the2MASS−UCAC residuals as a function of UCACx, y and also as a function of magnitude timesthese coordinates (coma terms) are inherent inthe UCAC data and can be corrected with theabove procedure.

However, this is not the case for a pure mag-nitude dependent systematic error, which couldoriginate in either or both catalogs. With the sys-tematic error corrections applied to the UCAC x, y

data as described above any possible pure magni-tude equation from 2MASS was transferred intothe UCAC positions. Different catalogs have typ-ically different magnitude equations. As an ex-ample Figure 3 shows the residuals as function ofmagnitude from a reduction of UCAC data withTycho-2 reference stars, after applying all system-atic error corrections based on the 2MASS reduc-tions. This clearly shows a difference in magni-tude equation between 2MASS (= UCAC systemat this point) and Tycho-2 without knowing whatthe error free positions might be.

The flip observations of calibration fields areused to determine the overall, pure magnitude de-pendent systematic errors in the UCAC data in-dependent of any external reference star catalog.With these observations the same field in the skyhas been observed with sets of frames rotated by180◦ with respect to each other. Any x, y coor-dinate offset as function of magnitude shows upin the residuals of a transformation of east versuswest frames x, y data. We derived overall magni-tude equation slope terms for long and short ex-posure frames and both sites separately. Theseare then applied globally in the final astrometricreductions.

After applying all corrections a small magni-tude term of a few mas/mag is still seen in theresiduals of the Tycho-2 reductions of UCACdata as shown in the UCAC3 release paper(Zacharias et al. 2010). This indicates such amagnitude equation is present in the Tycho-2 cat-alog itself, which is found to vary as a function ofdeclination zone as one would expect.

It would be preferable to derive all systematicerror corrections from internal calibration observa-tions. However, the flip observations alone do notallow us to do so because of the degeneracy be-tween a pure magnitude equation and coma-liketerms. Only after correcting the UCAC x, y datafor coordinate dependent (including coma) termsdo the flip observations allow for a unique solu-tion of the magnitude equation. Of course the as-sumption here is a constant magnitude equation,not changing from exposure to exposure. This as-sumption can not easily be made for photographicastrometry, which is affected by a highly non-linear detector, but should hold better for CCDdata.

3.4. Field Distortions

Field distortion patterns (FDPs) are derivedfor UCAC3 by binning thousands of reference starresiduals of individual CCD frames using the sameprocedure as in the previous UCAC reductions.These reductions are performed on the CTE cor-rected data but without applying the preliminaryFDP used before.

From deriving FDPs of various subsets of thedata we found that the FDP is almost constant ex-cept for a small difference depending on observing

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site (CTIO or NOFS). Residuals are created us-ing all good survey frames with respect to 2MASSreference stars split into CTIO west and NOFSeast data sets. The data using opposite cameraorientations than used for most of the observa-tions (i.e. CTIO east and NOFS west) did not havesignificantly different field distortions so only twocorrection tables are used for the final reductions.FDP corrections for frames taken with the cameraorientation not used frequently are applied by ro-tating the FDP of the data with the large amountof observations at that site.

Figure 4 (top) shows the FDP for CTIO westwith vectors up to 23 mas in length. The FDP forNOFS east is slightly different with vectors up to24 mas at some bins. In Figure 4 (bottom), weshow the difference (CTIO west−NOFS east) ofthe two data sets. Although these differences aresmall (below 6 mas) they are systematic and welldetermined. Therefore we choose to use a separateFDP map to correct the data of each site.

3.5. Subpixel Phase Errors

After the above mentioned systematic errorshave been corrected the 2MASS reference star cat-alog is used again to generate residuals from all ap-plicable UCAC survey frames. Residuals are an-alyzed as a function of the original x and y pixelcoordinate fraction (sub-pixel phase) before othercorrections are applied. Various sub-sets of thedata are looked at. Systematic errors are foundto be a function of the FWHM of the image pro-files. Figure 5 gives some examples. The resultsare found to be independent of exposure time, asexpected. However, a slight difference between theCTIO and NOFS data is found.

The amplitude of the sub-pixel phase depen-dent systematic errors in the star positions isshown in Figure 6, here for the corrections tothe x coordinate; those for the y coordinate aresomewhat smaller. All sub-pixel phase systematiccorrections are smaller than what was found inUCAC2. This is a consequence of using an imageprofile model in UCAC3 (Lorentz profile) whichbetter fits the true PSF than was the case forUCAC2 (Gauss model).

However, the function of the sub-pixel phasesystematic errors are more complex in the UCAC3than UCAC2 data, where a simple sine and co-

sine term were sufficient. For the UCAC3 datawe had to expand to three sine and three cosineterms in order to fit the sub-pixel phase errors suf-ficiently well (Figure 5). These six parameters aredetermined separately for 12 sets of data binned byFWHM (from 1.5 to 3.0 pixels), and split by NOFSand CTIO data. Calibration tables are then gen-erated for equal steps along FWHM by interpo-lation and x, y corrections applied, separately foreach coordinate, based on these tables.

4. MEAN POSITIONS

Positions of all detected objects are obtainedframe-by-frame from a final astrometric reductionwith the Tycho-2 reference star catalog and cor-recting raw x, y data first for the sub-pixel phaseerrors, then for systematic errors as a function ofx, y (FDP), then for mixed terms of coordinatewith magnitude (CTE effect), and finally for apure magnitude equation, as explained above. Ap-parent places and refraction are corrected rigor-ously using the Software for Analyzing Astromet-ric CCD (SAAC) code (Winter 1999), which alsoutilizes the Naval Observatory Vector AstrometrySubroutines (NOVAS) code (Kaplan 1989)1. Thethus obtained positions are on the ICRF at in-dividual epoch of each CCD frame (between 1998and 2004) and are output to FPOS (final position)files.

Previously identified and flagged observationsof minor planets and high proper motion stars areoutput to separate files. All other individual po-sitions are output by declination zones and thensorted by declination. Weighted mean positionsare calculated from the individual images of eachstar, generating a running star number, MPOS(mean position file) on the fly. Over 139 millionobjects are identified at this step.

All MPOS entries are then matched with earlyepoch star catalogs and another, more compre-hensive 2MASS extract containing about 338 mil-lion objects. These 2MASS stars are selecteddirectly from the 2MASS point source catalogwithout going through NOMAD. The R magni-tude was estimated based on the 2MASS near-infrared J−K color and stars with R ≤ 17.0 or J ≤

15.5 are selected. The unique identifier for stars

1http://aa.usno.navy.mil/software/novas/novas info.php

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matched across catalogs is the MPOS star num-ber. Individual early epoch positions are outputtogether with MPOS entries (CCD epoch obser-vations) and sorted by MPOS number. Weightedproper motions and mean positions are then cal-culated to obtain the UCAC3 release catalog data(Zacharias et al. 2010). Objects which did nothave either a reasonable proper motion deter-mined or could not be matched with 2MASS aredropped at this point. Only these compiled cat-alog mean positions and proper motions are pub-lished in UCAC3, not the MPOS or FPOS data,which likely will be made available for the finalUCAC4 release after further updates.

5. COMPARISON WITH HIPPARCOS

A total of 1510 Hipparcos stars in the 8 to 12magnitude range are randomly selected (about 300all sky per magnitude interval) and flagged in theUCAC data. These stars are not used as referencestars in test reductions using Tycho-2 referencestars. Thus the obtained positions are field starpositions from UCAC observations independent ofthe Hipparcos and Tycho catalog positions. In-dividual UCAC observed positions are then com-pared to the original (ESA 1997) and new Hippar-cos reductions (van Leeuwen 2007) at the epoch ofUCAC observations, using Hipparcos mean posi-tions, proper motions and parallaxes.

After excluding outliers (≥ 200 mas positiondifference in either coordinate), RMS values overobservations in each bin are calculated (Table 4).Similarly sorting all observations by magnitude orcolor, respectively and binning over 100 observa-tions lead to the plots shown in Figure 7 and 8.

The expected position errors from UCAC3 andHipparcos data at the epoch of our UCAC obser-vations are also presented in Table 4 together withthe expected RMS of the combined error and theratio of expected to observed scatter, separatelyfor each coordinate. In all cases the observed er-rors (from the scatter of the UCAC3−Hipparcosposition differences) is slightly smaller than theexpected errors as calculated from the combinedformal errors for the same observations, thus atleast some of these are overestimated (see also dis-cussion section below).

UCAC position differences of those sampledHipparcos stars do not show systematic errors as a

function of magnitude or color exceeding about 10mas over the range sampled. Plots with respect tothe original or new Hipparcos catalog are almostidentical.

However, 23 Hipparcos stars (1.5% of this sam-ple) show very large differences (between 300 and600 mas in either coordinate) when comparingthe new reduction Hipparcos positions with theUCAC3 positions at UCAC epoch. A similar num-ber of stars is found when comparing with the orig-inal Hipparcos Catalogue; however, for not exactlythe same stars. All possible combinations of incon-sistencies between the two Hipparcos solutions andUCAC data are found, with two of the three po-sitions or all three separated by several standarderrors of their internal errors.

6. DISCUSSION

The use of an image profile model better match-ing the actual PSF than a Gaussian model is es-sential for the astrometric reductions of blendedimages. A better matching model also does reducethe amplitude of the sub-pixel phase error and isadvisable to be used when no such corrections arebeing applied to the data. In particular, a compar-ison of Figure 6 with a similar figure of the UCAC2paper show that with a Gaussian model and 2.0pixel/FWHM sampling the pixel phase error hasan amplitude of 11 mas, while with the image pro-file model 5 as used in UCAC3 this amplitude isonly about 6 mas.

The use of such a PSF profile model (still withthe same number of fit parameters per star as thetraditional Gaussian model) allows to neglect po-sitional errors as function of sub-pixel phase com-pletely for a sampling of about 2.5 pixel/FWHMor larger without the need to investigate possibleother dependencies of this systematic error as afunction of other things. However, for single starsand with calibration data in hand to correct forthe position offsets caused by a sub-pixel phasedependency, the use of a more sophisticated im-age profile model than a Gaussian might not havean apparent advantage for astrometric reductions.

The slight difference in amplitude of the sub-pixel phase corrections between CTIO and NOFSdata is surprising. It could be caused by a slightlydifferent, observed PSF between the two sites,even for the same seeing (FWHM). Whether this

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is caused by differences in the instrument, guidingor atmosphere is currently not known.

The small systematic errors of UCAC based po-sitions of randomly selected Hipparcos stars con-firms the good correction of UCAC3 epoch posi-tions as function of magnitude and color, at leastfor the 8 to 12 magnitude range. With UCAC3positions agreeing with Hipparcos data the mag-nitude equation seen in residuals with respect toTycho-2 is an indication for such small systematicerrors in the Tycho-2 catalog. These are likelyintroduced through the proper motions, thus theearly epoch, ground-based data, as also indicatedin the UCAC3 release paper.

The random errors in the observed UCAC−Hipparcosposition differences are even slightly smaller thanthe expected, combined formal errors. For the newHipparcos reductions the difference is only a fewpercent, while for the comparison with the originalHipparcos Catalogue data the observed errors areabout 10% smaller than expected. This indicatesa slightly overestimated error in the original Hip-parcos Catalogue proper motions. The formal po-sition errors for the individual UCAC observationsdo include the formal image profile fit error, andthe conventional plate adjustment error propaga-tion. The weighting scheme used in this individualCCD frame least-square adjustments also includean estimated error contribution from the turbu-lence in the atmosphere, scaled by the exposuretime. The mismatch between the actual PSF andthe image profile model can lead to an overestima-tion of the center position errors, particularly forstars as bright as this sample of Hipparcos stars,which would explain the slightly smaller than ex-pected scatter in the Hipparcos to UCAC positiondifferences. The exclusion of outliers at an arbi-trary limit of 200 mas could be another possibleexplanation. At the faint end of Hipparcos (11thmagnitude) the Hipparcos catalog positions areof comparable precision to typical mean UCACpositions (based on 4 images) at their about 2000epoch. The next step after UCAC, the USNORobotic Astrometric Telescope (URAT) program(Zacharias 2008) to begin in 2010 thus will likelybe capable of improving proper motions of indi-vidual Hipparcos stars significantly.

The entire UCAC team is thanked for makingthis all-sky survey a reality. For more detailed

information about “who is who” in the UCACproject the reader is referred to the readme fileand UCAC3 release paper. The California Insti-tute of Technology is acknowledged for the pgplot

software. More information about this project isavailable athttp://www.usno.navy.mil/usno/astrometry/.

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Zacharias, N. et al. submitted to AJ (UCAC3 re-lease paper)

Zacharias, N. 2010, in preparation for AJ (UCAC3pixel red.paper)

This 2-column preprint was prepared with the AAS LATEXmacros v5.2.

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Fig. 1.— CTIO west residuals in x with respectto 2MASS reference stars as a function of UCACmodel magnitude using frames taken at 20 secondexposures (short). The top plot shows the residu-als for low x near pixel 1 and the bottom plot forhigh x near pixel 4094. Each dot represents themean over 1000 residuals.

Fig. 2.— CTIO west residuals in x with respectto 2MASS reference stars as a function of UCACmodel magnitude using frames taken at 150 secondexposures (long). The top plot shows the residualsfor low x near pixel 1 and the bottom plot for highx near pixel 4094. Each dot represents the meanover 1000 residuals.

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Fig. 3.— Residuals in x (top) and y (bottom) forCTIO west with respect to Tycho-2 reference starsas a function of UCAC model magnitude. Eachdot represents the mean over 3000 residuals.

Fig. 4.— Field distortion pattern (FDP) plot of2MASS stacked residuals for CTIO west (top) andthe difference between vectors of CTIO west andNOFS east (bottom). The scaling of the vectorsis 10,000 which makes the largest corrections forCTIO west (top) 23 mas and the largest differencevector (bottom) 6 mas.

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Fig. 5.— CTIO west residuals in x with respect to2MASS reference stars as a function of sub-pixelphase. The top and bottom plot show residualswith an average FWHM of 1.54 and 2.11 pixelrespectively. Each dot represents the mean over5000 residuals. The fitted curve is from a least-squares adjustment using a model with a total ofsix Fourier terms.

Fig. 6.— Amplitude of the sub-pixel phase depen-dent positional correction as a function of imageprofile width (FWHM) for the CCD astrographframes taken at CTIO (filled) and NOFS (opencircles), respectively.

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Fig. 7.— Position differences UCAC−Hipparcos(new reductions) as a function of V magnitude ofa random sample of Hipparcos stars reduced asfield stars in UCAC processing. Each dot is themean of 100 individual UCAC observations.

Fig. 8.— Position differences UCAC−Hipparcos(new reductions) as a function of B−V color of arandom sample of Hipparcos stars reduced as fieldstars in UCAC processing. Each dot is the meanof 100 individual UCAC observations.

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Table 4: RMS position differences and expectederrors of observed UCAC3 − Hipparcos positions.

difference Hipparcos err UCAC3 err combined err rationumber Vmag range RA Dec RA Dec RA Dec RA Dec RA Decobserv. mag mas mas mas mas mas mas mas mas diff/c.err

Hipparcos (original)423 8.0 − 8.5 41.9 46.3 10.7 8.8 46.9 47.1 48.1 47.9 0.87 0.97717 8.5 − 9.0 45.2 41.9 12.7 11.7 47.8 48.0 49.4 49.4 0.92 0.85802 9.0 − 10.0 43.6 44.6 21.8 18.3 47.3 47.6 52.1 51.0 0.84 0.88

1227 10.0 − 11.0 45.6 45.5 28.3 22.5 43.3 43.9 51.7 49.3 0.88 0.92978 11.0 − 99.0 52.8 48.2 42.7 35.7 42.2 42.7 60.0 55.6 0.88 0.87

Hipparcos (new reduction)423 8.0 − 8.5 42.3 45.8 8.9 7.3 46.9 47.1 47.7 47.6 0.89 0.96722 8.5 − 9.0 46.4 44.2 12.0 10.0 47.8 48.0 49.3 49.1 0.94 0.90801 9.0 − 10.0 45.3 42.6 14.0 11.6 47.3 47.5 49.3 48.9 0.92 0.87

1238 10.0 − 11.0 47.4 44.1 20.8 16.9 43.4 43.9 48.1 47.1 0.99 0.94993 11.0 − 99.0 52.3 49.9 36.7 27.5 42.2 42.8 56.0 50.9 0.93 0.98

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Table 1

Summary of UCAC frames a

Site/orientation number of number of number of number ofCalibration Frames Survey Frames Minor Planet Frames Pluto Frames

CTIO east 1582 5 14 00 3 14 0

CTIO west 1583 163460 828 100 155143 796 0

NOFS east 2452 66940 1340 840 58523 1156 74

NOFS west 1525 2580 32 00 2397 28 0

Total 7142 232985 2214 940 216066 2068 74

aFirst row number represents the total number of UCAC frames while the second row number gives thenumber of frames used in the final UCAC3 reduction.

Table 2

Number of reference star observations used for reductions

number of number ofsite/orientation 2MASS star Tycho-2 star

observations observations

CTIO east 8772812 1600CTIO west 203915168 9683015NOFS east 58493251 4071859NOFS west 7856501 186557

Total 279037732 13943031

Table 3

Example CTIO west CTE lookup table for frames taken at 20 second exposures with

corrections given in mas

8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5 16.0

mag mag mag mag mag mag mag mag mag mag mag mag mag mag mag mag mag

xbin1 147 148 143 134 119 108 95 81 66 49 33 18 -8 -44 -69 -76 -86

xbin2 116 111 115 111 105 90 80 69 53 42 27 18 -4 -32 -52 -59 -74

xbin3 101 92 95 85 76 67 60 44 41 33 24 14 2 -17 -31 -39 -48

xbin4 68 61 61 59 56 43 38 33 29 23 19 11 2 -10 -17 -21 -30

xbin5 52 47 42 41 43 37 32 28 25 23 17 13 11 3 1 0 -10

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