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Star catalog position and proper motion corrections in asteroid astrometry II: The Gaia era
Icarus 339 (2020) 113596
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Star catalog position and proper motion corrections in asteroid astrometry II: The Gaia era Siegfried Eggl a, b, *, Davide Farnocchia a, Alan B. Chamberlin a, Steven R. Chesley a a b
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena 91101, CA, USA LSST/DIRAC Institute, Department of Astronomy, University of Washington, 15th Ave. NE, Seattle, WA 98195, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Asteroids Asteroids dynamics Orbit determination Astrometry Near-Earth objects
Astrometric positions of moving objects in the Solar System have been measured using a variety of star catalogs in the past. Previous work has shown that systematic errors in star catalogs can affect the accuracy of astrometric observations. That, in turn, can influence the resulting orbit fits for minor planets. In order to quantify these systematic errors, we compare the positions and proper motion of stellar sources in the most utilized star catalogs to the second release of the Gaia star catalog. The accuracy of Gaia astrometry allows us to unambiguously identify local biases and derive a scheme that can be used to correct past astrometric observations of solar system objects. Here, we provide substantially improved debiasing tables for 26 astrometric catalogs that were exten sively used in minor planet astrometry. Revised corrections near the galactic center eliminate artifacts that could be traced back to reference catalogs used in previous debiasing schemes. Median differences in stellar positions between catalogs now tend to be on the order of several tens of milliarcseconds (mas) but can be as large as 175 mas. Median stellar proper motion corrections scatter around 0.3 mas/yr and range from 1to 4 mas/yr for star catalogs with and without proper motion, respectively. The tables presented in this work contain a posteriori corrections meant to improve orbit fits based on optical observations that were measured against astrometric catalogs other than Gaia. However, astrometrists are strongly encouraged to make use of the most recent Gaia astrometric catalog when submitting new observations. Since previous debiasing schemes already reduced systematics in past observations to a large extent, correc tions beyond the current work may not be needed in the foreseeable future.
1. Introduction Over more than two centuries astronomers have collected approxi mately 200 million astrometric observations of minor planets in the Solar System1. This dataset of astrometric measurements is essential to estimate the trajectories of Solar System Objects (SSOs) such as nearEarth asteroids (Milani and Gronchi, 2010; Desmars et al., 2013). The vast majority of astrometry used for orbit determination of SSOs is op tical, i.e. pairs of Right Ascension (RA) and Declination (DEC) mea surements at given epochs. In contrast, only a tiny fraction of the SSO population has been observed by radar2. Improving the quality of optical astrometry is a worthwhile endeavor, especially if that means extending the arc of observations for objects of interest. Over the years, a variety of star catalogs has been used to measure astrometric positions of asteroids
to a common frame of reference such as the International Celestial Reference Frame (ICRF, Ma et al., 2009) (Table 1). With improving quality of astrometric measurements, it became evident that some ob servations of asteroids showed systematic errors that deviated from the expected scatter around the nominal trajectory (Carpino et al., 2003). Some of those systematic errors could be traced back to the use of spe cific astrometric catalogs in the observation reduction process. To assess these systematic errors, one can compare stellar positions and proper motion between various star catalogs. Based on its wide dynamic range and its rigorous ties to the ICRF, Chesley et al. (2010) selected the 2MASS catalog (Skrutskie et al., 2006) as a reference to identify local systematics in positions of stars in the USNO catalogs (Monet, 1998; Lasker et al., 1996a; Monet et al., 2003). Correcting for regional biases in star positions led to better ephemeris predictions and improved the error
* Corresponding author at: LSST/DIRAC Institute, Department of Astronomy, University of Washington, 15th Ave. NE, Seattle, WA 98195, USA. E-mail address: [email protected] (S. Eggl). 1 Minor Planet Center (MPC), http://www.minorplanetcenter.net/. 2 About one in a thousand asteroids, see NASA Jet Propulsion Laboratory (JPL), https://echo.jpl.nasa.gov/asteroids/index.html/. https://doi.org/10.1016/j.icarus.2019.113596 Received 19 July 2019; Received in revised form 1 November 2019; Accepted 6 December 2019 Available online 14 December 2019 0019-1035/Published by Elsevier Inc.
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Table 1 Star catalogs considered in this work. This table accounts for all the astrometry available up to March 23, 2018. The date of observation columns list the date of the oldest and most recent entry in the database including remeasurements. Catalog USNO A2.0 2MASS UCAC 2 UCAC 4 USNO B1.0 SST-RC4 Gaia DR 1 UCAC 3 USNO A1.0 Unspecified USNO SA2.0 SDSS DR 7 GSC 1.1 UCAC 1 GSC ACT CMC 14 Tycho 2 USNO SA1.0 PPM XL GSC (unspec.) ACT Other catalogs NOMAD PPM URAT 1 GSC 1.2 CMC 15 SDSS DR 8 UCAC 5
MPC designation
Number of observations
Date of observations
VizieR
ADES
Flag
Count
%
First
Last
CDS ID
USNOA2 2MASS UCAC2 UCAC4 USNOB1 SSTRC4 Gaia1 UCAC3 USNOA1 N/A USNOSA2 SDSS7 GSC1.1 UCAC1 GSCACT CMC14 Tyc2 USNOSA1 PPM XL GSC ACT N/A NOMAD PPM URAT1 GSC1.2 CMC15 SDSS8 UCAC5
c L r q o R U u a N/A d N i e m w g b t z l N/A v p S j Q n W
40,964,725 36,656,505 30,808,742 25,280,408 16,827,916 14,143,319 7,878,286 3,460,491 2,196,215 1,995,344 1,757,923 985,016 645,795 516,449 474,122 426,781 414,400 349,099 302,432 292,814 112,431 97,256 82,997 47,227 37,105 17,269 11,869 6157 1618
21.929 19.623 16.493 13.533 9.008 7.571 4.217 1.852 1.175 1.068 0.941 0.527 0.345 0.276 0.253 0.228 0.221 0.186 0.162 0.156 0.060 0.052 0.044 0.025 0.019 0.009 0.006 0.003 <0.001
1949/11/19 2004/06/19 1950/05/19 1851/05/28 1949/11/23 2004/08/22 1996/08/11 1949/03/29 1990/05/23 1607/09/28 1953/12/07 1997/01/11 1991/09/01 1998/09/19 1898/09/20 1993/03/18 1960/03/30 1950/02/17 1949/11/21 1979/11/19 1997/06/09 1929/11/27 1987/01/31 1827/06/21 1993/10/20 1950/12/09 2001/09/15 1998/09/19 2016/02/21
2018/03/15 2018/03/21 2018/03/22 2018/03/21 2018/03/22 2018/02/15 2018/03/22 2018/03/22 2015/12/05 2018/03/17 2018/01/18 2016/09/26 2015/01/18 2007/12/13 2018/03/18 2018/01/22 2017/09/23 2012/03/20 2018/03/18 2017/04/24 2009/01/22 2018/03/15 2018/03/15 2016/08/09 2018/03/22 2015/08/21 2018/03/15 2012/04/02 2018/02/10
I/252 II/246 I/289 I/322A I/284 N/A I/337 I/315 N/A N/A N/A II/294 I/220 I/268 I/255 I/304 I/259 N/A I/317 N/A I/246 N/A N/A I/146, I/193 I/329 I/254 I/327 II/306 I/340
statistics of astrometric observations of asteroids. Selecting the most accurate stars in the PPM XL catalog based on 2MASS astrometry, Farnocchia et al. (2015) improved the scheme by Chesley et al. (2010) and debiased practically all of the prevalent star catalogs used for asteroid astrometry. Farnocchia et al. (2015) included proper motion in the debiasing process which led to widespread im provements in the post-fit residuals of asteroids, most notably (99942) Apophis, (101955) Bennu and (6489) Golevka. The present work follows a similar approach with the advantage of having Gaia data, described in Section 2, as a reference. Following a brief outline of the debiasing process (Section 3), we calculate position and proper motion corrections for stellar catalogs that have been used extensively in minor planet astrometry (Sections 4– 6). In Section 7, we then assess the quality of ephemeris predictions based on the new debiasing scheme. A discussion of our results concludes this article.
Monet (1998) Skrutskie et al. (2006) Zacharias et al. (2004b) Zacharias et al. (2013) Monet et al. (2003) Monet (2018) Lindegren et al. (2016) Zacharias et al. (2010) Lasker et al. (1996a) N/A Monet (1998) Abazajian et al. (2009) Lasker et al. (1996b) Zacharias et al. (2000) Lasker et al. (1999) Copenhagen University et al. (2006) Høg et al. (2009) Lasker et al. (1996a) Roeser et al. (2010) N/A Urban et al. (1998) N/A Zacharias et al. (2004a) Roeser and Bastian (1991) Zacharias et al. (2015) Morrison et al. (2001) Copenhagen University et al. (2011) Adelman-McCarthy and et al. (2011) Zacharias et al. (2017)
for Gmag ¼ 20. The Gaia astrometric catalog is, thus, a reference of unprecedented accuracy well suited to identify systematic errors in other star catalogs. 3. Star position and proper motion corrections Similar to Chesley et al. (2010) and Farnocchia et al. (2015), we compare the various star catalogs that were used for minor planet astrometry in the past to a reference catalog, in this case Gaia DR 2. By dividing the celestial sphere into 49,152 equal-area tiles (~0.8 square degrees each) using a HEALPix tesselation (Gorski et al., 2005) and comparing stellar positions and proper motion within a given tile, we can quantify local systematic differences. To this end, we extract stellar positions and proper motion at epoch J2000 from the reference and the test catalog. J2000 is the reference epoch for most of the catalogs considered in this work. Hence, J2000 is a natural choice for our catalog comparison as well. Given the variability in the number of stars per tile in each catalog, identification of common stars requires some attention. We first search for spatial correlation between astrometric sources within 100 of the reference position. If candidates are found, we apply the identification and outlier rejection criterion described in Farnocchia et al. (2015) to ensure spurious matches are excluded from the sample. The median of the differences in the astrometric quantities of each identified star per tile yields the local corrections for position (ΔαJ2000,ΔδJ2000), and proper motion (Δμα,Δμδ) at epoch J2000. Astro metric observations of minor planets can then be corrected for catalog systematics by subtracting
2. The Gaia catalogs Since 2013, the Gaia mission has been collecting astrometric infor mation on roughly 1.7 billion sources (Gaia Collaboration et al., 2018). A first data release based on a partially completed survey featured around a billion sources largely without proper motion (Lindegren et al., 2016). With the second Gaia data release (Gaia DR 2) published on April 25, 2018, this information has become publicly accessible through the Gaia Archive3. About 1.3 billion sources between 3 < Gmag < 21 come with a full five-parameter astrometric solution, i.e. right ascension and declination positions on the sky (α,δ), parallaxes, and proper motion for the epoch J2015.5 (TCB). Uncertainties in the parallaxes range between 0.04 milliarcseconds (mas) for sources with Gmag < 15 and 0.7 mas at Gmag ¼ 20. The corresponding uncertainties in the proper motion components start at 0.06 mas/yr for Gmag < 15 and reach 1.2 mas/yr
3
Reference
Δα ¼ ΔαJ2000 þ Δμα ⋅Δt; Δδ ¼ ΔδJ2000 þ Δμδ ⋅Δt; with Δt ¼ t 2,451,545.0, the difference between the epoch of obser vation and J2000 in JD (TT). Note that the timescale used for Gaia DR 2 is TCB. All differential quantities Δα, ΔαJ2000, and Δμα include the
Gaia Archive, https://gea.esac.esa.int/archive/. 2
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Table 2 The columns show the median (MED) and median absolute deviation (MAD) of corrections in position (right ascension and declination) and proper motion (right ascension and declination) over the entire sky as well as the fraction of sky coverage for each catalog. N� per tile gives the average number of stars per HEALPix tile for each catalog. The last column states whether or not a catalog contains data on stellar proper motion. Catalog 2MASS ACT CMC 14 CMC 15 GSC 1.1 GSC 1.2 GSC ACT Gaia DR 1 NOMAD PPM PPM XL SDSS DR 7 SDSS DR 8 SST-RC4, 5 & 5 Tycho 2 UCAC 1 UCAC 2 UCAC 3 UCAC 4 UCAC 5 URAT 1 USNO A1.0 USNO A2.0 USNO B1.0 USNO SA1.0 USNO SA2.0
ΔαJ2000 [mas]
ΔδJ2000 [mas]
Δμα [mas/yr]
Sky [%]
N�
Proper
MED
MAD
MED
MAD
MED
MAD
MED
MAD
coverage
per tile
motion
2.4 0.8 2.0 1.5 45.5 23.6 29.4 22.5 19.8 12.6 19.5 5.4 4.7 15.2 1.0 4.0 0.8 2.3 1.0 1.6 23.0 17.3 75.3 25.4 20.3 72.7
15.5 11.8 16.7 19.0 266.8 127.7 82.2 30.5 62.3 131.2 18.1 16.4 22.0 15.0 10.1 14.0 10.3 13.3 11.0 4.8 26.9 261.4 111.9 79.3 260.8 111.8
11.6 0.2 18.3 19.8 17.1 16.2 44.8 49.2 154.8 68.4 36.0 7.6 5.2 25.0 1.6 12.5 3.1 1.6 2.8 1.0 43.7 22.9 162.2 175.2 17.1 164.1
13.6 10.9 13.8 15.7 235.1 119.3 69.9 20.2 80.8 130.0 17.0 16.2 24.0 14.4 9.8 13.1 9.2 10.9 9.6 3.7 20.4 231.1 132.4 76.8 230.8 131.5
1.51 0.05 1.53 1.52 1.07 1.06 1.05 1.48 1.19 0.21 0.30 0.29 0.30 0.27 0.08 2.70 0.30 0.75 0.10 0.11 0.42 1.39 1.40 1.26 1.27 1.35
2.50 1.03 2.45 2.53 2.81 2.81 2.76 2.00 1.78 2.77 1.34 0.35 0.47 1.08 0.82 3.06 1.31 1.82 0.84 0.32 1.17 1.92 1.91 2.00 1.96 1.96
3.76 0.01 4.22 4.09 3.87 3.87 3.84 3.27 2.66 0.48 0.23 0.67 0.75 0.10 0.31 2.94 0.60 0.84 0.34 0.06 0.70 3.21 3.20 3.02 3.27 3.25
1.50 0.98 0.98 1.17 1.48 1.48 1.45 1.35 1.29 2.84 1.46 0.43 0.51 1.13 0.82 4.39 1.27 1.87 0.94 0.25 1.14 1.34 1.34 1.36 1.34 1.34
100 100 61 70 100 100 100 100 100 100 100 13 16 100 100 39 88 100 100 100 61 100 100 100 100 100
9582 20 1950 2506 383 383 383 23,248 22,738 8 18,524 7267 16,154 13,120 49 558 983 2050 2315 2192 4644 9929 10,707 21,264 1115 1126
No Yes No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No Yes No No
spherical metric factor cosδ.
submitted under SST-RC4. Astrometric standard stars in SST-RC5 are largely the same as in the 4th installment of the SST catalog, however (Monet, 2018). Hence, we use the same corrections to debias astro metric observations submitted under SST-RC4 and SST-RC5. � UCAC 5, is the 5th installment of the US Naval Observatory CCD Astrograph Catalog (UCAC) (Zacharias et al., 2017). By combining UCAC 5 with Gaia DR1 data, new proper motions on the Gaia co ordinate system for over 107 million stars were obtained with typical accuracies of 1–2 mas/yr for R ¼ 11–15 mag, and about 5 mas/yr through R ¼ 16 mag. � URAT, a follow-up project to the UCAC series featured and increased limiting magnitude that allowed for a roughly 4-fold increase in the average number of stars per square degree as compared to UCAC. Additionally, stars as bright as about 3rd magnitude were added to the catalog. The URAT 1 catalog (Zacharias et al., 2015) has its mean epoch between 2012.3 and 2014.6 supporting a magnitude range from 3 to 18.5 in R-band with a positional precision of 5 to 40 mas. It covers most of the Northern Hemisphere and some areas down to 24.8� in declination.
4. Added astrometric catalogs In addition to the 20 catalogs4 that were discussed in Farnocchia et al. (2015), we added the following six catalogs to be compared to Gaia DR 2: � CMC 15 is the 15th installment of the Carlsberg Meridian Catalogue generated through the Carlsberg Meridian Telescope, formerly the Carlsberg Automatic Meridian Circle (Copenhagen University et al., 2011). CMC 15 has been compiled between March 1999 and March 2011, encompasses around 134,000,000 entries, and claims a posi tional accuracy between 35 and 100 mas for a declination range from 40 to þ50 � . � Gaia DR 1 as described in Section 2. � The 8th data release of the Sloan Digital Sky Survey (SDSS) added roughly 4 times the number of sources published in data release 7, namely about 325 million (Adelman-McCarthy and et al., 2011). The fact that astrometric data together with proper motion is available has made SDSS DR 7 (Abazajian et al., 2009) attractive for minor planet astrometry. Almost 1 million observations of minor planets were reduced with SDSS DR 7 (Table 1). SDSS DR 8, although of fering a significant increase in source density, has not been as pop ular, which is partly due to known issues with the astrometry (Aihara et al., 2011). � The Space Surveillance Telescope (SST) has been relying on a pro prietary catalog based on selected sources from a variety of other astrometric and photometric catalogs for the reduction of its 14þ million observations of asteroids in the Solar System. Although not in the public domain, the 5th version of the SST catalog (SST-RC5) has been kindly made available for this study (Monet, 2018). Most of the astrometric observations considered in this work have been
4
Δμδ [mas/yr]
Table 2 shows that roughly 1% of observations do not have a catalog descriptor and can, therefore, not be corrected. About 300,000 obser vations have been submitted without specifying which version of the GSC catalog was used. Since the various installments of the GSCs have different correction tables, those observations are difficult to debias as well. Observations reduced by catalogs not explicitly mentioned in Table 1 account for less than 0.05% of all database entries. Their weight on the bulk of orbit solutions is deemed small enough not to merit explicit debiasing. 5. Catalog comparison results With more than 40 million entries in the Minor Planet Center data base, the USNO A2.0 catalog has been one of the most popular choices for reducing astrometric observations of minor planets. Figs. 1 and 2 show the proposed corrections derived from a comparison with Gaia DR
This includes PPMXL that as in part used as the reference catalog. 3
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Fig. 1. USNO A2.0 catalog systematics with respect to Gaia DR 2. The top panels display local differences in right ascension and declination, the bottom panels show the systematics caused by the missing proper motion.
collected over the entire sky. The visual impression from Fig. 1, namely that there is an overall bias towards higher declination values in stellar positions, is confirmed in the distribution of ΔδJ2000. The lack of proper motion as well as a median bias of 162 mas in declination with a mode closer to a quarter arcsecond all suggest that astrometric observations reduced with USNO A2.0 could benefit from a correction. Table 2 re ports the size of the corrections in terms of the all sky median (MED) and median absolute deviation (MAD) for each studied catalog. Of particular interest is the comparison between PPM XL and Gaia DR 2, since a subset of the former was used as a reference for stellar positions and proper motion in Farnocchia et al. (2015). The corresponding graphs are pre sented in Figs. 3 and 4. The range of position corrections is only about one sixth of that in USNO A2.0 and the subset of 2MASS stars used for astrometry also has a relatively small positional bias as can be gathered from Table 2. A comparison between Gaia DR 2 and UCAC 4 (Figs. 5 and 6) reveals that the relatively large corrections seen by Farnocchia et al. (2015, Figures 9 to 12) near the galactic center (α � 270� , δ � 30� ) appear to actually be associated to the PPM XL reference, rather than the UCAC catalogs. This is indicated by the signature seen near the galactic center in all four panels of Fig. 3 that is now substantially absent from all four panels of Fig. 5. With the exception of the artificial structures close to the Galactic center introduced through PPM XL, our results for UCAC, USNO and CMC catalogs are very similar to those found in Farnocchia et al. (2015). The corresponding Figures are provided in the Appendix. Among the newly added catalogs UCAC 5 continues the tradition of the UCAC family with an increase in the overall quality of the catalog. Local corrections are mostly due to differences between stellar positions in Gaia DR 2 and Gaia DR 1. The latter were ingested into UCAC 5. URAT 1 has a higher source density compared to UCAC 4, but it also exhibits larger deviations from Gaia DR 2 in both stellar positions and proper motion. We confirm the known issues with astrometric accuracy around the north celestial pole in SDSS DR 8 (Aihara et al., 2011), which were addressed in the following data releases SDSS DR 9–15. However, no observation in the MPC database is reduced against the latter. Apart from minor systematics stemming from survey
Fig. 2. Summary statistics of USNO A2.0 catalog systematics with respect to Gaia DR 2. The top panel displays the distribution of local differences in right ascension and declination. The signature of the missing proper motion is shown in the bottom panel. The legend contains the median (MED) and median ab solute deviation (MAD) for the respective quantities.
2. The regional biases in stellar positions first found by Chesley et al. (2010) and later confirmed by Farnocchia et al. (2015) are clearly visible in the top panels of Fig. 1. Fig. 2 shows the distribution of the corrections 4
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Fig. 3. Same as Fig. 1 but for the PPM XL catalog. Note the larger corrections near the galactic center (α � 270� , δ � 30� ).
thus, encouraged to switch to Gaia DR 2 as soon as possible for both, measuring and remeasuring of asteroid observations. We debias all ob servations where corrections are available with the exception of those reduced with ACT, Gaia DR 1, Tycho-2 and UCAC-5, since the latter show no large scale structures in local position and proper motion systematics. 6. Smoothing of debiasing tables Due to the discrete nature of calculating corrections to astrometric measurements on HEALPix tiles, transitions between neighboring cor rections are not guaranteed to be smooth. As an example, Fig. 7 shows that adjacent USNO A2.0 tiles can have significantly different bias values. Corrections for minor planet observations that cross such a border would see an artificial jump in the corresponding coordinate. A finer HEALPix tessellation could be used to mitigate such a problem. However, a finer tessellation would mean that fewer stars per tile are available to estimate the magnitude of the correction. In order to circumvent reducing the sample size of stars per tile, we use radial basis functions (RBFs, Schaback, 1995) to interpolate data from neighboring tiles onto a finer HEALPix tessellation. To this end, we increased the number of tiles from 49,152 to 786,432 and subsequently interpolated the catalog corrections from the coarser tessellation onto the new tile centers. This process reduces artificial discontinuities along tile borders while at the same time retaining a sufficient number of stars in each of the stencil tiles. In Fig. 8, the distribution of inter-tile corrections in RA is shown for USNO A2.0 before and after smoothing. The smoothing of catalog corrections leads to a substantial reduction of the variance (�90%) and maximum magnitude (�40%) in the distribution of discontinuous transitions between HEALPix tiles. The results for the DEC coordinate are essentially identical and therefore omitted. Reductions in the discontinuities in other catalogs due to smoothing are similar to those shown for USNO-A2.0.
Fig. 4. Same as Fig. 2 for the PPM XL catalog.
incompleteness, Gaia DR 1 had excellent stellar positions at the epoch of its publication (J2015, Lindegren et al., 2016). Since Gaia DR 1 largely lacks proper motion, the differences to Gaia DR 2 become significant at the epoch of comparison (J2000), however. This is reflected in Fig. 14 as well as in Table 2. The quality of stellar positions, even if measured through the Gaia satellite, degrades relatively quickly with time if no proper motion corrections are applied. Minor planet astrometrists are,
7. Ephemeris prediction test We follow the example of Chesley et al. (2010, Sec. 6), Farnocchia 5
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Fig. 5. Same as Fig. 3 but for the UCAC 4 catalog. Systematics are small in positions, but traces of stellar proper motion errors in the galactic plane are visible.
Fig. 7. Zoom into a region with a large jump between positive and negative catalog corrections in ΔαJ2000 for the USNO A2.0 catalog. Smoothing can reduce the magnitude of discontinuous transitions between HEALPix tiles with opposite bias values.
respectively, we construct predictions close to the center of the third apparition, near the middle of the true observational arc. The pre dictions are then compared to the reference solution that uses the full arc. The analysis is performed in a consistent way such that a given debiasing scheme is used for both the short arcs derived from a subset of apparitions and the full arc. All astrometric data is weighted according to the scheme presented in Vere�s et al. (2017). Fig. 9 shows the corresponding results. The prediction errors in the orbital semimajor axes5 of 700 NEOs derived from astrometry debiased
Fig. 6. Same as Fig. 2 for the UCAC 4 catalog.
et al. (2015, Sec. 4.3) and Vere�s et al. (2017) and evaluate the impact of the new debiasing scheme on asteroid orbit determination and predic tion. To achieve that, we compare the prediction performance for an ensemble of 700 near-Earth objects (NEOs), each of which had at least five apparitions since 1998. Every one of those apparitions has at least ten observations over 15 days. Using the astrometric observations from either the first two apparitions or the penultimate apparition,
5 The semimajor axis was chosen as an indicator in this study as it is the key orbital parameter driving prediction uncertainties through Kepler shear.
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been studied in Farnocchia et al. (2015) are included in this work. The quality of catalog corrections presented here is significantly improved compared to previous work, in particular for the UCAC series. The switch to the new debiasing scheme based on Gaia DR 2 delivers only incremental improvement of the quality of near-Earth asteroid orbits over (Farnocchia et al., 2015), however. This suggests that further debiasing attempts may not be necessary. The procedure suggested in this work can help mitigate some of the systematics introduced by the use of star catalogs other than Gaia. Note that the debiasing tables are intended to correct astrometric measurements as part of the orbit determination process. They should not be considered a valid substitute for measuring or remeasuring astrometric positions with respect to the latest Gaia astrometric catalog. We strongly recommend that contem porary Solar System astrometry be conducted with Gaia DR 2 and its successors. Data availability
Fig. 8. Distribution of discontinuities between neighboring HEALPix tiles in the RA correction tables for USNO A2.0 with and without smoothing.
Tables containing standard resolution and interpolated catalog cor
Fig. 9. Cumulative distributions of orbit prediction errors for the debiasing schemes presented in this work (blue line), Farnocchia et al. (2015) (red line) and the theoretical Gaussian (black line) are shown. The first and second apparitions have been used in the left graph and the penultimate apparition in the right graph. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
with respect to Gaia DR 2 are only slightly smaller that those using the debiasing scheme presented in Farnocchia et al. (2015). These results suggest that most of the statistical bias was de facto eliminated with the previous debiasing approach. Using interpolated debiasing tables as discussed in the previous section did not significantly affect the above prediction statistics, either. Given the larger size of the interpolated table and the potential loss in computational efficiency, we recommend using interpolated values only when discontinuities in the former debiasing table are an obstacle to high-fidelity orbit determination.
rections derived in this work are publicly available at ftp://ssd.jpl.nasa. gov/pub/ssd/debias/debias_2018.tgz and ftp://ssd.jpl.nasa. gov/pub/ssd/debias/debias_hires2018.tgz. Acknowledgments This research has received funding from the Jet Propulsion Labora tory through the California Institute of Technology postdoctoral fellowship program, under a contract with the National Aeronautics and Space Administration. VizieR catalogue access tools, CDS, Strasbourg, France, have been essential to this research project (Ochsenbein et al., 2000). This work made use of the IAU Minor Planet Center observations database as well as results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is htt ps://www.cosmos.esa.int/gaia. The Gaia archive website is https ://archives.esac.esa.int/gaia.
8. Conclusions The Gaia astrometric catalog published with the second Gaia data release has become the new standard for minor planet astrometry. Its uniformity and high quality in both stellar positions and proper motion allow us to improve prior astrometric observations of minor planets by correcting for potential systematics in other astrometric catalogs. In this work, we have used Gaia DR 2 as a reference to calculate debiasing ta bles for 26 astrometric catalogs. New tables for six catalogs (PPM XL, SST-RC5, Gaia DR 1, CMC 15, URAT, UCAC 5 and SDSS 8) that had not
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Appendix A The appendix shows local position and proper motion systematics for stellar catalogs not presented in the main body of the article (Figs. 10– 25). For catalogs without proper motion, only the bias values in right ascension and declination are provided. Proper motion corrections for those catalogs resemble those of USNO A2.0 displayed in Fig. 1.
Fig. 10. Corrections in stellar positions for the 2MASS catalog (top panels), CMC 14 (center panels) and CMC 15 (bottom panels). None of the above catalogs come with proper motion.
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Fig. 11. Same as Fig. 10 for the GSC 1.1 catalog (top panels), the GSC 1.2 catalog (center panels) and GSC ACT (bottom panels).
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Fig. 12. Same as Fig. 10 for the USNO A1.0 (top panels), the USNO SA1.0, (center panels) and the USNO SA2.0 catalogs (bottom panels).
Fig. 13. Corrections in stellar positions and proper motion for the ACT catalog.
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Fig. 14. Corrections in stellar positions at the epoch of the release of Gaia DR 1 (J2015) as well as positions and proper motion for the Gaia DR 1 catalog at epoch J2000. Note the difference in scale between the corrections in positions at epoch J2000 (arcsec) and J2015 (mas).
Fig. 15. Corrections in stellar positions and proper motion for the NOMAD catalog.
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Fig. 16. Corrections in stellar positions and proper motion for the PPM catalog.
Fig. 17. Corrections in stellar positions and proper motion for the SDSS DR 7 catalog.
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Fig. 18. Corrections in stellar positions and proper motion for the SDSS DR 8 catalog.
Fig. 19. Corrections in stellar positions and proper motion for the SST-RC5 catalog.
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Fig. 20. Corrections in stellar positions and proper motion for the Tycho 2 catalog.
Fig. 21. Corrections in stellar positions and proper motion for the UCAC 1 catalog.
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Fig. 22. Corrections in stellar positions and proper motion for the UCAC 2 catalog.
Fig. 23. Corrections in stellar positions and proper motion for the UCAC 3 catalog.
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Fig. 24. Corrections in stellar positions and proper motion for the UCAC 5 catalog.
Fig. 25. Corrections in stellar positions and proper motion for the URAT 1 catalog.
References
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Abazajian, K.N., Adelman-McCarthy, J.K., Agüeros, M.A., Allam, S.S., Prieto, C.A., An, D., Anderson, K.S., Anderson, S.F., Annis, J., Bahcall, N.A., et al., 2009. The seventh data release of the Sloan Digital Sky Survey. Astrophys. J. Suppl. Ser. 182, 543. Adelman-McCarthy, J.K., et al., 2011. VizieR Online Data Catalog: The SDSS Photometric Catalog, Release 8 (Adelman-McCarthyþ, 2011). VizieR Online Data Catalog, II/306. � Balbinot, E., Beers, T.C., Aihara, H., Prieto, C.A., An, D., Anderson, S.F., Aubourg, E., et al., 2011. Erratum: “The eighth data release of the Sloan Digital Sky Survey: first data from SDSS-III” (2011, ApJS, 193, 29). Astrophys. J. Suppl. Ser. 195, 26. https:// doi.org/10.1088/0067-0049/195/2/26. Carpino, M., Milani, A., Chesley, S.R., 2003. Error statistics of asteroid optical astrometric observations. Icarus 166, 248–270. Chesley, S.R., Baer, J., Monet, D.G., 2010. Treatment of star catalog biases in asteroid astrometric observations. Icarus 210, 158–181.
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Høg, E., Fabricius, C., Makarov, V., Urban, S., Corbin, T., Wycoff, G., Bastian, U., Schwenkendick, P., Wicenec, A., Turon, C., 2009. The Tycho-2 Catalogue of the 2.5 million brightest stars. Commentary. Astron. Astrophys. 500, 583–588. Lasker, B., Russel, J., Jenkner, H., 1999. The HST Guide Star Catalog, Version GSC-ACT (Laskerþ 1996–99), I/255. VizieR Online Data Catalog. Lasker, B., Russel, J., Jenkner, H., Sturch, C., McLean, B., Shara, M., 1996. The 491,848,883 Sources in USNO-A1.0. Bull. Am. Astron. Soc. 28, 905. Lasker, B., Russel, J., Jenkner, H., Sturch, C., McLean, B., Shara, M., 1996. The HST Guide Star Catalog Version 1.1. The Association of Universities for Research in Astronomy, Inc. Lindegren, L., Lammers, U., Bastian, U., Hern� andez, J., Klioner, S., Hobbs, D., Bombrun, A., Michalik, D., Ramos-Lerate, M., Butkevich, A., et al., 2016. Gaia data release 1-astrometry: one billion positions, two million proper motions and parallaxes. Astron. Astrophys. 595, A4. Ma, C., Arias, E.F., Bianco, G., Boboltz, D.A., Bolotin, S.L., Charlot, P., Engelhardt, G., Fey, A.L., Gaume, R.A., Gontier, A.-M., Heinkelmann, R., Jacobs, C.S., Kurdubov, S., Lambert, S.B., Malkin, Z.M., Nothnagel, A., Petrov, L., Skurikhina, E., Sokolova, J.R., Souchay, J., Sovers, O.J., Tesmer, V., Titov, O.A., Wang, G., Zharov, V.E., Barache, C., Boeckmann, S., Collioud, A., Gipson, J.M., Gordon, D., Lytvyn, S.O., MacMillan, D.S., Ojha, R., 2009. The Second Realization of the International Celestial Reference Frame by Very Long Baseline Interferometry. In: IERS Technical Note, 35. Milani, A., Gronchi, G., 2010. Theory of Orbit Determination. Cambridge University Press. Monet, D.G., 1998. The 526,280,881 objects in the USNO-A2. 0 catalog. In: Bulletin of the American Astronomical Society, 30, p. 1427. Monet, D.G., 2018. SST RC 5 Star Catalog private communication. Monet, D.G., Levine, S.E., Canzian, B., Ables, H.D., Bird, A.R., Dahn, C.C., Guetter, H.H., Harris, H.C., Henden, A.A., Leggett, S.K., et al., 2003. The USNO-B Catalog. Astron. J. 125, 984. Morrison, J., Roeser, S., McLean, B., Bucciarelli, B., Lasker, B., 2001. The guide star catalog, version 1.2: an astrometric recalibration and other refinements. Astron. J. 121, 1752. Ochsenbein, F., Bauer, P., Marcout, J., 2000. The Vizier database of astronomical catalogues. Astron. Astrophys., Suppl. Ser. 143, 23–32. Roeser, S., Bastian, U., 1991. PPM Star Catalogue North. Positions and proper motions of 181.731 stars north of 2.5 degrees declination for equinox and epoch. J2000. 0. Vol. 1: Zonesþ 80 deg. toþ 30 deg.; Vol. 2: Zonesþ 20 deg. to-0 deg.. In: Predictability, Stability, and Chaos in N-Body Dynamical Systems, 1,2.
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Contents lists available at ScienceDirect
Icarus journal homepage: www.elsevier.com/locate/icarus
Star catalog position and proper motion corrections in asteroid astrometry II: The Gaia era Siegfried Eggl a, b, *, Davide Farnocchia a, Alan B. Chamberlin a, Steven R. Chesley a a b
Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena 91101, CA, USA LSST/DIRAC Institute, Department of Astronomy, University of Washington, 15th Ave. NE, Seattle, WA 98195, USA
A R T I C L E I N F O
A B S T R A C T
Keywords: Asteroids Asteroids dynamics Orbit determination Astrometry Near-Earth objects
Astrometric positions of moving objects in the Solar System have been measured using a variety of star catalogs in the past. Previous work has shown that systematic errors in star catalogs can affect the accuracy of astrometric observations. That, in turn, can influence the resulting orbit fits for minor planets. In order to quantify these systematic errors, we compare the positions and proper motion of stellar sources in the most utilized star catalogs to the second release of the Gaia star catalog. The accuracy of Gaia astrometry allows us to unambiguously identify local biases and derive a scheme that can be used to correct past astrometric observations of solar system objects. Here, we provide substantially improved debiasing tables for 26 astrometric catalogs that were exten sively used in minor planet astrometry. Revised corrections near the galactic center eliminate artifacts that could be traced back to reference catalogs used in previous debiasing schemes. Median differences in stellar positions between catalogs now tend to be on the order of several tens of milliarcseconds (mas) but can be as large as 175 mas. Median stellar proper motion corrections scatter around 0.3 mas/yr and range from 1to 4 mas/yr for star catalogs with and without proper motion, respectively. The tables presented in this work contain a posteriori corrections meant to improve orbit fits based on optical observations that were measured against astrometric catalogs other than Gaia. However, astrometrists are strongly encouraged to make use of the most recent Gaia astrometric catalog when submitting new observations. Since previous debiasing schemes already reduced systematics in past observations to a large extent, correc tions beyond the current work may not be needed in the foreseeable future.
1. Introduction Over more than two centuries astronomers have collected approxi mately 200 million astrometric observations of minor planets in the Solar System1. This dataset of astrometric measurements is essential to estimate the trajectories of Solar System Objects (SSOs) such as nearEarth asteroids (Milani and Gronchi, 2010; Desmars et al., 2013). The vast majority of astrometry used for orbit determination of SSOs is op tical, i.e. pairs of Right Ascension (RA) and Declination (DEC) mea surements at given epochs. In contrast, only a tiny fraction of the SSO population has been observed by radar2. Improving the quality of optical astrometry is a worthwhile endeavor, especially if that means extending the arc of observations for objects of interest. Over the years, a variety of star catalogs has been used to measure astrometric positions of asteroids
to a common frame of reference such as the International Celestial Reference Frame (ICRF, Ma et al., 2009) (Table 1). With improving quality of astrometric measurements, it became evident that some ob servations of asteroids showed systematic errors that deviated from the expected scatter around the nominal trajectory (Carpino et al., 2003). Some of those systematic errors could be traced back to the use of spe cific astrometric catalogs in the observation reduction process. To assess these systematic errors, one can compare stellar positions and proper motion between various star catalogs. Based on its wide dynamic range and its rigorous ties to the ICRF, Chesley et al. (2010) selected the 2MASS catalog (Skrutskie et al., 2006) as a reference to identify local systematics in positions of stars in the USNO catalogs (Monet, 1998; Lasker et al., 1996a; Monet et al., 2003). Correcting for regional biases in star positions led to better ephemeris predictions and improved the error
* Corresponding author at: LSST/DIRAC Institute, Department of Astronomy, University of Washington, 15th Ave. NE, Seattle, WA 98195, USA. E-mail address: [email protected] (S. Eggl). 1 Minor Planet Center (MPC), http://www.minorplanetcenter.net/. 2 About one in a thousand asteroids, see NASA Jet Propulsion Laboratory (JPL), https://echo.jpl.nasa.gov/asteroids/index.html/. https://doi.org/10.1016/j.icarus.2019.113596 Received 19 July 2019; Received in revised form 1 November 2019; Accepted 6 December 2019 Available online 14 December 2019 0019-1035/Published by Elsevier Inc.
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Table 1 Star catalogs considered in this work. This table accounts for all the astrometry available up to March 23, 2018. The date of observation columns list the date of the oldest and most recent entry in the database including remeasurements. Catalog USNO A2.0 2MASS UCAC 2 UCAC 4 USNO B1.0 SST-RC4 Gaia DR 1 UCAC 3 USNO A1.0 Unspecified USNO SA2.0 SDSS DR 7 GSC 1.1 UCAC 1 GSC ACT CMC 14 Tycho 2 USNO SA1.0 PPM XL GSC (unspec.) ACT Other catalogs NOMAD PPM URAT 1 GSC 1.2 CMC 15 SDSS DR 8 UCAC 5
MPC designation
Number of observations
Date of observations
VizieR
ADES
Flag
Count
%
First
Last
CDS ID
USNOA2 2MASS UCAC2 UCAC4 USNOB1 SSTRC4 Gaia1 UCAC3 USNOA1 N/A USNOSA2 SDSS7 GSC1.1 UCAC1 GSCACT CMC14 Tyc2 USNOSA1 PPM XL GSC ACT N/A NOMAD PPM URAT1 GSC1.2 CMC15 SDSS8 UCAC5
c L r q o R U u a N/A d N i e m w g b t z l N/A v p S j Q n W
40,964,725 36,656,505 30,808,742 25,280,408 16,827,916 14,143,319 7,878,286 3,460,491 2,196,215 1,995,344 1,757,923 985,016 645,795 516,449 474,122 426,781 414,400 349,099 302,432 292,814 112,431 97,256 82,997 47,227 37,105 17,269 11,869 6157 1618
21.929 19.623 16.493 13.533 9.008 7.571 4.217 1.852 1.175 1.068 0.941 0.527 0.345 0.276 0.253 0.228 0.221 0.186 0.162 0.156 0.060 0.052 0.044 0.025 0.019 0.009 0.006 0.003 <0.001
1949/11/19 2004/06/19 1950/05/19 1851/05/28 1949/11/23 2004/08/22 1996/08/11 1949/03/29 1990/05/23 1607/09/28 1953/12/07 1997/01/11 1991/09/01 1998/09/19 1898/09/20 1993/03/18 1960/03/30 1950/02/17 1949/11/21 1979/11/19 1997/06/09 1929/11/27 1987/01/31 1827/06/21 1993/10/20 1950/12/09 2001/09/15 1998/09/19 2016/02/21
2018/03/15 2018/03/21 2018/03/22 2018/03/21 2018/03/22 2018/02/15 2018/03/22 2018/03/22 2015/12/05 2018/03/17 2018/01/18 2016/09/26 2015/01/18 2007/12/13 2018/03/18 2018/01/22 2017/09/23 2012/03/20 2018/03/18 2017/04/24 2009/01/22 2018/03/15 2018/03/15 2016/08/09 2018/03/22 2015/08/21 2018/03/15 2012/04/02 2018/02/10
I/252 II/246 I/289 I/322A I/284 N/A I/337 I/315 N/A N/A N/A II/294 I/220 I/268 I/255 I/304 I/259 N/A I/317 N/A I/246 N/A N/A I/146, I/193 I/329 I/254 I/327 II/306 I/340
statistics of astrometric observations of asteroids. Selecting the most accurate stars in the PPM XL catalog based on 2MASS astrometry, Farnocchia et al. (2015) improved the scheme by Chesley et al. (2010) and debiased practically all of the prevalent star catalogs used for asteroid astrometry. Farnocchia et al. (2015) included proper motion in the debiasing process which led to widespread im provements in the post-fit residuals of asteroids, most notably (99942) Apophis, (101955) Bennu and (6489) Golevka. The present work follows a similar approach with the advantage of having Gaia data, described in Section 2, as a reference. Following a brief outline of the debiasing process (Section 3), we calculate position and proper motion corrections for stellar catalogs that have been used extensively in minor planet astrometry (Sections 4– 6). In Section 7, we then assess the quality of ephemeris predictions based on the new debiasing scheme. A discussion of our results concludes this article.
Monet (1998) Skrutskie et al. (2006) Zacharias et al. (2004b) Zacharias et al. (2013) Monet et al. (2003) Monet (2018) Lindegren et al. (2016) Zacharias et al. (2010) Lasker et al. (1996a) N/A Monet (1998) Abazajian et al. (2009) Lasker et al. (1996b) Zacharias et al. (2000) Lasker et al. (1999) Copenhagen University et al. (2006) Høg et al. (2009) Lasker et al. (1996a) Roeser et al. (2010) N/A Urban et al. (1998) N/A Zacharias et al. (2004a) Roeser and Bastian (1991) Zacharias et al. (2015) Morrison et al. (2001) Copenhagen University et al. (2011) Adelman-McCarthy and et al. (2011) Zacharias et al. (2017)
for Gmag ¼ 20. The Gaia astrometric catalog is, thus, a reference of unprecedented accuracy well suited to identify systematic errors in other star catalogs. 3. Star position and proper motion corrections Similar to Chesley et al. (2010) and Farnocchia et al. (2015), we compare the various star catalogs that were used for minor planet astrometry in the past to a reference catalog, in this case Gaia DR 2. By dividing the celestial sphere into 49,152 equal-area tiles (~0.8 square degrees each) using a HEALPix tesselation (Gorski et al., 2005) and comparing stellar positions and proper motion within a given tile, we can quantify local systematic differences. To this end, we extract stellar positions and proper motion at epoch J2000 from the reference and the test catalog. J2000 is the reference epoch for most of the catalogs considered in this work. Hence, J2000 is a natural choice for our catalog comparison as well. Given the variability in the number of stars per tile in each catalog, identification of common stars requires some attention. We first search for spatial correlation between astrometric sources within 100 of the reference position. If candidates are found, we apply the identification and outlier rejection criterion described in Farnocchia et al. (2015) to ensure spurious matches are excluded from the sample. The median of the differences in the astrometric quantities of each identified star per tile yields the local corrections for position (ΔαJ2000,ΔδJ2000), and proper motion (Δμα,Δμδ) at epoch J2000. Astro metric observations of minor planets can then be corrected for catalog systematics by subtracting
2. The Gaia catalogs Since 2013, the Gaia mission has been collecting astrometric infor mation on roughly 1.7 billion sources (Gaia Collaboration et al., 2018). A first data release based on a partially completed survey featured around a billion sources largely without proper motion (Lindegren et al., 2016). With the second Gaia data release (Gaia DR 2) published on April 25, 2018, this information has become publicly accessible through the Gaia Archive3. About 1.3 billion sources between 3 < Gmag < 21 come with a full five-parameter astrometric solution, i.e. right ascension and declination positions on the sky (α,δ), parallaxes, and proper motion for the epoch J2015.5 (TCB). Uncertainties in the parallaxes range between 0.04 milliarcseconds (mas) for sources with Gmag < 15 and 0.7 mas at Gmag ¼ 20. The corresponding uncertainties in the proper motion components start at 0.06 mas/yr for Gmag < 15 and reach 1.2 mas/yr
3
Reference
Δα ¼ ΔαJ2000 þ Δμα ⋅Δt; Δδ ¼ ΔδJ2000 þ Δμδ ⋅Δt; with Δt ¼ t 2,451,545.0, the difference between the epoch of obser vation and J2000 in JD (TT). Note that the timescale used for Gaia DR 2 is TCB. All differential quantities Δα, ΔαJ2000, and Δμα include the
Gaia Archive, https://gea.esac.esa.int/archive/. 2
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Table 2 The columns show the median (MED) and median absolute deviation (MAD) of corrections in position (right ascension and declination) and proper motion (right ascension and declination) over the entire sky as well as the fraction of sky coverage for each catalog. N� per tile gives the average number of stars per HEALPix tile for each catalog. The last column states whether or not a catalog contains data on stellar proper motion. Catalog 2MASS ACT CMC 14 CMC 15 GSC 1.1 GSC 1.2 GSC ACT Gaia DR 1 NOMAD PPM PPM XL SDSS DR 7 SDSS DR 8 SST-RC4, 5 & 5 Tycho 2 UCAC 1 UCAC 2 UCAC 3 UCAC 4 UCAC 5 URAT 1 USNO A1.0 USNO A2.0 USNO B1.0 USNO SA1.0 USNO SA2.0
ΔαJ2000 [mas]
ΔδJ2000 [mas]
Δμα [mas/yr]
Sky [%]
N�
Proper
MED
MAD
MED
MAD
MED
MAD
MED
MAD
coverage
per tile
motion
2.4 0.8 2.0 1.5 45.5 23.6 29.4 22.5 19.8 12.6 19.5 5.4 4.7 15.2 1.0 4.0 0.8 2.3 1.0 1.6 23.0 17.3 75.3 25.4 20.3 72.7
15.5 11.8 16.7 19.0 266.8 127.7 82.2 30.5 62.3 131.2 18.1 16.4 22.0 15.0 10.1 14.0 10.3 13.3 11.0 4.8 26.9 261.4 111.9 79.3 260.8 111.8
11.6 0.2 18.3 19.8 17.1 16.2 44.8 49.2 154.8 68.4 36.0 7.6 5.2 25.0 1.6 12.5 3.1 1.6 2.8 1.0 43.7 22.9 162.2 175.2 17.1 164.1
13.6 10.9 13.8 15.7 235.1 119.3 69.9 20.2 80.8 130.0 17.0 16.2 24.0 14.4 9.8 13.1 9.2 10.9 9.6 3.7 20.4 231.1 132.4 76.8 230.8 131.5
1.51 0.05 1.53 1.52 1.07 1.06 1.05 1.48 1.19 0.21 0.30 0.29 0.30 0.27 0.08 2.70 0.30 0.75 0.10 0.11 0.42 1.39 1.40 1.26 1.27 1.35
2.50 1.03 2.45 2.53 2.81 2.81 2.76 2.00 1.78 2.77 1.34 0.35 0.47 1.08 0.82 3.06 1.31 1.82 0.84 0.32 1.17 1.92 1.91 2.00 1.96 1.96
3.76 0.01 4.22 4.09 3.87 3.87 3.84 3.27 2.66 0.48 0.23 0.67 0.75 0.10 0.31 2.94 0.60 0.84 0.34 0.06 0.70 3.21 3.20 3.02 3.27 3.25
1.50 0.98 0.98 1.17 1.48 1.48 1.45 1.35 1.29 2.84 1.46 0.43 0.51 1.13 0.82 4.39 1.27 1.87 0.94 0.25 1.14 1.34 1.34 1.36 1.34 1.34
100 100 61 70 100 100 100 100 100 100 100 13 16 100 100 39 88 100 100 100 61 100 100 100 100 100
9582 20 1950 2506 383 383 383 23,248 22,738 8 18,524 7267 16,154 13,120 49 558 983 2050 2315 2192 4644 9929 10,707 21,264 1115 1126
No Yes No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No Yes No No
spherical metric factor cosδ.
submitted under SST-RC4. Astrometric standard stars in SST-RC5 are largely the same as in the 4th installment of the SST catalog, however (Monet, 2018). Hence, we use the same corrections to debias astro metric observations submitted under SST-RC4 and SST-RC5. � UCAC 5, is the 5th installment of the US Naval Observatory CCD Astrograph Catalog (UCAC) (Zacharias et al., 2017). By combining UCAC 5 with Gaia DR1 data, new proper motions on the Gaia co ordinate system for over 107 million stars were obtained with typical accuracies of 1–2 mas/yr for R ¼ 11–15 mag, and about 5 mas/yr through R ¼ 16 mag. � URAT, a follow-up project to the UCAC series featured and increased limiting magnitude that allowed for a roughly 4-fold increase in the average number of stars per square degree as compared to UCAC. Additionally, stars as bright as about 3rd magnitude were added to the catalog. The URAT 1 catalog (Zacharias et al., 2015) has its mean epoch between 2012.3 and 2014.6 supporting a magnitude range from 3 to 18.5 in R-band with a positional precision of 5 to 40 mas. It covers most of the Northern Hemisphere and some areas down to 24.8� in declination.
4. Added astrometric catalogs In addition to the 20 catalogs4 that were discussed in Farnocchia et al. (2015), we added the following six catalogs to be compared to Gaia DR 2: � CMC 15 is the 15th installment of the Carlsberg Meridian Catalogue generated through the Carlsberg Meridian Telescope, formerly the Carlsberg Automatic Meridian Circle (Copenhagen University et al., 2011). CMC 15 has been compiled between March 1999 and March 2011, encompasses around 134,000,000 entries, and claims a posi tional accuracy between 35 and 100 mas for a declination range from 40 to þ50 � . � Gaia DR 1 as described in Section 2. � The 8th data release of the Sloan Digital Sky Survey (SDSS) added roughly 4 times the number of sources published in data release 7, namely about 325 million (Adelman-McCarthy and et al., 2011). The fact that astrometric data together with proper motion is available has made SDSS DR 7 (Abazajian et al., 2009) attractive for minor planet astrometry. Almost 1 million observations of minor planets were reduced with SDSS DR 7 (Table 1). SDSS DR 8, although of fering a significant increase in source density, has not been as pop ular, which is partly due to known issues with the astrometry (Aihara et al., 2011). � The Space Surveillance Telescope (SST) has been relying on a pro prietary catalog based on selected sources from a variety of other astrometric and photometric catalogs for the reduction of its 14þ million observations of asteroids in the Solar System. Although not in the public domain, the 5th version of the SST catalog (SST-RC5) has been kindly made available for this study (Monet, 2018). Most of the astrometric observations considered in this work have been
4
Δμδ [mas/yr]
Table 2 shows that roughly 1% of observations do not have a catalog descriptor and can, therefore, not be corrected. About 300,000 obser vations have been submitted without specifying which version of the GSC catalog was used. Since the various installments of the GSCs have different correction tables, those observations are difficult to debias as well. Observations reduced by catalogs not explicitly mentioned in Table 1 account for less than 0.05% of all database entries. Their weight on the bulk of orbit solutions is deemed small enough not to merit explicit debiasing. 5. Catalog comparison results With more than 40 million entries in the Minor Planet Center data base, the USNO A2.0 catalog has been one of the most popular choices for reducing astrometric observations of minor planets. Figs. 1 and 2 show the proposed corrections derived from a comparison with Gaia DR
This includes PPMXL that as in part used as the reference catalog. 3
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Fig. 1. USNO A2.0 catalog systematics with respect to Gaia DR 2. The top panels display local differences in right ascension and declination, the bottom panels show the systematics caused by the missing proper motion.
collected over the entire sky. The visual impression from Fig. 1, namely that there is an overall bias towards higher declination values in stellar positions, is confirmed in the distribution of ΔδJ2000. The lack of proper motion as well as a median bias of 162 mas in declination with a mode closer to a quarter arcsecond all suggest that astrometric observations reduced with USNO A2.0 could benefit from a correction. Table 2 re ports the size of the corrections in terms of the all sky median (MED) and median absolute deviation (MAD) for each studied catalog. Of particular interest is the comparison between PPM XL and Gaia DR 2, since a subset of the former was used as a reference for stellar positions and proper motion in Farnocchia et al. (2015). The corresponding graphs are pre sented in Figs. 3 and 4. The range of position corrections is only about one sixth of that in USNO A2.0 and the subset of 2MASS stars used for astrometry also has a relatively small positional bias as can be gathered from Table 2. A comparison between Gaia DR 2 and UCAC 4 (Figs. 5 and 6) reveals that the relatively large corrections seen by Farnocchia et al. (2015, Figures 9 to 12) near the galactic center (α � 270� , δ � 30� ) appear to actually be associated to the PPM XL reference, rather than the UCAC catalogs. This is indicated by the signature seen near the galactic center in all four panels of Fig. 3 that is now substantially absent from all four panels of Fig. 5. With the exception of the artificial structures close to the Galactic center introduced through PPM XL, our results for UCAC, USNO and CMC catalogs are very similar to those found in Farnocchia et al. (2015). The corresponding Figures are provided in the Appendix. Among the newly added catalogs UCAC 5 continues the tradition of the UCAC family with an increase in the overall quality of the catalog. Local corrections are mostly due to differences between stellar positions in Gaia DR 2 and Gaia DR 1. The latter were ingested into UCAC 5. URAT 1 has a higher source density compared to UCAC 4, but it also exhibits larger deviations from Gaia DR 2 in both stellar positions and proper motion. We confirm the known issues with astrometric accuracy around the north celestial pole in SDSS DR 8 (Aihara et al., 2011), which were addressed in the following data releases SDSS DR 9–15. However, no observation in the MPC database is reduced against the latter. Apart from minor systematics stemming from survey
Fig. 2. Summary statistics of USNO A2.0 catalog systematics with respect to Gaia DR 2. The top panel displays the distribution of local differences in right ascension and declination. The signature of the missing proper motion is shown in the bottom panel. The legend contains the median (MED) and median ab solute deviation (MAD) for the respective quantities.
2. The regional biases in stellar positions first found by Chesley et al. (2010) and later confirmed by Farnocchia et al. (2015) are clearly visible in the top panels of Fig. 1. Fig. 2 shows the distribution of the corrections 4
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Fig. 3. Same as Fig. 1 but for the PPM XL catalog. Note the larger corrections near the galactic center (α � 270� , δ � 30� ).
thus, encouraged to switch to Gaia DR 2 as soon as possible for both, measuring and remeasuring of asteroid observations. We debias all ob servations where corrections are available with the exception of those reduced with ACT, Gaia DR 1, Tycho-2 and UCAC-5, since the latter show no large scale structures in local position and proper motion systematics. 6. Smoothing of debiasing tables Due to the discrete nature of calculating corrections to astrometric measurements on HEALPix tiles, transitions between neighboring cor rections are not guaranteed to be smooth. As an example, Fig. 7 shows that adjacent USNO A2.0 tiles can have significantly different bias values. Corrections for minor planet observations that cross such a border would see an artificial jump in the corresponding coordinate. A finer HEALPix tessellation could be used to mitigate such a problem. However, a finer tessellation would mean that fewer stars per tile are available to estimate the magnitude of the correction. In order to circumvent reducing the sample size of stars per tile, we use radial basis functions (RBFs, Schaback, 1995) to interpolate data from neighboring tiles onto a finer HEALPix tessellation. To this end, we increased the number of tiles from 49,152 to 786,432 and subsequently interpolated the catalog corrections from the coarser tessellation onto the new tile centers. This process reduces artificial discontinuities along tile borders while at the same time retaining a sufficient number of stars in each of the stencil tiles. In Fig. 8, the distribution of inter-tile corrections in RA is shown for USNO A2.0 before and after smoothing. The smoothing of catalog corrections leads to a substantial reduction of the variance (�90%) and maximum magnitude (�40%) in the distribution of discontinuous transitions between HEALPix tiles. The results for the DEC coordinate are essentially identical and therefore omitted. Reductions in the discontinuities in other catalogs due to smoothing are similar to those shown for USNO-A2.0.
Fig. 4. Same as Fig. 2 for the PPM XL catalog.
incompleteness, Gaia DR 1 had excellent stellar positions at the epoch of its publication (J2015, Lindegren et al., 2016). Since Gaia DR 1 largely lacks proper motion, the differences to Gaia DR 2 become significant at the epoch of comparison (J2000), however. This is reflected in Fig. 14 as well as in Table 2. The quality of stellar positions, even if measured through the Gaia satellite, degrades relatively quickly with time if no proper motion corrections are applied. Minor planet astrometrists are,
7. Ephemeris prediction test We follow the example of Chesley et al. (2010, Sec. 6), Farnocchia 5
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Fig. 5. Same as Fig. 3 but for the UCAC 4 catalog. Systematics are small in positions, but traces of stellar proper motion errors in the galactic plane are visible.
Fig. 7. Zoom into a region with a large jump between positive and negative catalog corrections in ΔαJ2000 for the USNO A2.0 catalog. Smoothing can reduce the magnitude of discontinuous transitions between HEALPix tiles with opposite bias values.
respectively, we construct predictions close to the center of the third apparition, near the middle of the true observational arc. The pre dictions are then compared to the reference solution that uses the full arc. The analysis is performed in a consistent way such that a given debiasing scheme is used for both the short arcs derived from a subset of apparitions and the full arc. All astrometric data is weighted according to the scheme presented in Vere�s et al. (2017). Fig. 9 shows the corresponding results. The prediction errors in the orbital semimajor axes5 of 700 NEOs derived from astrometry debiased
Fig. 6. Same as Fig. 2 for the UCAC 4 catalog.
et al. (2015, Sec. 4.3) and Vere�s et al. (2017) and evaluate the impact of the new debiasing scheme on asteroid orbit determination and predic tion. To achieve that, we compare the prediction performance for an ensemble of 700 near-Earth objects (NEOs), each of which had at least five apparitions since 1998. Every one of those apparitions has at least ten observations over 15 days. Using the astrometric observations from either the first two apparitions or the penultimate apparition,
5 The semimajor axis was chosen as an indicator in this study as it is the key orbital parameter driving prediction uncertainties through Kepler shear.
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been studied in Farnocchia et al. (2015) are included in this work. The quality of catalog corrections presented here is significantly improved compared to previous work, in particular for the UCAC series. The switch to the new debiasing scheme based on Gaia DR 2 delivers only incremental improvement of the quality of near-Earth asteroid orbits over (Farnocchia et al., 2015), however. This suggests that further debiasing attempts may not be necessary. The procedure suggested in this work can help mitigate some of the systematics introduced by the use of star catalogs other than Gaia. Note that the debiasing tables are intended to correct astrometric measurements as part of the orbit determination process. They should not be considered a valid substitute for measuring or remeasuring astrometric positions with respect to the latest Gaia astrometric catalog. We strongly recommend that contem porary Solar System astrometry be conducted with Gaia DR 2 and its successors. Data availability
Fig. 8. Distribution of discontinuities between neighboring HEALPix tiles in the RA correction tables for USNO A2.0 with and without smoothing.
Tables containing standard resolution and interpolated catalog cor
Fig. 9. Cumulative distributions of orbit prediction errors for the debiasing schemes presented in this work (blue line), Farnocchia et al. (2015) (red line) and the theoretical Gaussian (black line) are shown. The first and second apparitions have been used in the left graph and the penultimate apparition in the right graph. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
with respect to Gaia DR 2 are only slightly smaller that those using the debiasing scheme presented in Farnocchia et al. (2015). These results suggest that most of the statistical bias was de facto eliminated with the previous debiasing approach. Using interpolated debiasing tables as discussed in the previous section did not significantly affect the above prediction statistics, either. Given the larger size of the interpolated table and the potential loss in computational efficiency, we recommend using interpolated values only when discontinuities in the former debiasing table are an obstacle to high-fidelity orbit determination.
rections derived in this work are publicly available at ftp://ssd.jpl.nasa. gov/pub/ssd/debias/debias_2018.tgz and ftp://ssd.jpl.nasa. gov/pub/ssd/debias/debias_hires2018.tgz. Acknowledgments This research has received funding from the Jet Propulsion Labora tory through the California Institute of Technology postdoctoral fellowship program, under a contract with the National Aeronautics and Space Administration. VizieR catalogue access tools, CDS, Strasbourg, France, have been essential to this research project (Ochsenbein et al., 2000). This work made use of the IAU Minor Planet Center observations database as well as results from the European Space Agency (ESA) space mission Gaia. Gaia data are being processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC is provided by national institutions, in particular the institutions participating in the Gaia MultiLateral Agreement (MLA). The Gaia mission website is htt ps://www.cosmos.esa.int/gaia. The Gaia archive website is https ://archives.esac.esa.int/gaia.
8. Conclusions The Gaia astrometric catalog published with the second Gaia data release has become the new standard for minor planet astrometry. Its uniformity and high quality in both stellar positions and proper motion allow us to improve prior astrometric observations of minor planets by correcting for potential systematics in other astrometric catalogs. In this work, we have used Gaia DR 2 as a reference to calculate debiasing ta bles for 26 astrometric catalogs. New tables for six catalogs (PPM XL, SST-RC5, Gaia DR 1, CMC 15, URAT, UCAC 5 and SDSS 8) that had not
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Appendix A The appendix shows local position and proper motion systematics for stellar catalogs not presented in the main body of the article (Figs. 10– 25). For catalogs without proper motion, only the bias values in right ascension and declination are provided. Proper motion corrections for those catalogs resemble those of USNO A2.0 displayed in Fig. 1.
Fig. 10. Corrections in stellar positions for the 2MASS catalog (top panels), CMC 14 (center panels) and CMC 15 (bottom panels). None of the above catalogs come with proper motion.
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Fig. 11. Same as Fig. 10 for the GSC 1.1 catalog (top panels), the GSC 1.2 catalog (center panels) and GSC ACT (bottom panels).
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Fig. 12. Same as Fig. 10 for the USNO A1.0 (top panels), the USNO SA1.0, (center panels) and the USNO SA2.0 catalogs (bottom panels).
Fig. 13. Corrections in stellar positions and proper motion for the ACT catalog.
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Fig. 14. Corrections in stellar positions at the epoch of the release of Gaia DR 1 (J2015) as well as positions and proper motion for the Gaia DR 1 catalog at epoch J2000. Note the difference in scale between the corrections in positions at epoch J2000 (arcsec) and J2015 (mas).
Fig. 15. Corrections in stellar positions and proper motion for the NOMAD catalog.
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Fig. 16. Corrections in stellar positions and proper motion for the PPM catalog.
Fig. 17. Corrections in stellar positions and proper motion for the SDSS DR 7 catalog.
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Fig. 18. Corrections in stellar positions and proper motion for the SDSS DR 8 catalog.
Fig. 19. Corrections in stellar positions and proper motion for the SST-RC5 catalog.
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Fig. 20. Corrections in stellar positions and proper motion for the Tycho 2 catalog.
Fig. 21. Corrections in stellar positions and proper motion for the UCAC 1 catalog.
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Fig. 22. Corrections in stellar positions and proper motion for the UCAC 2 catalog.
Fig. 23. Corrections in stellar positions and proper motion for the UCAC 3 catalog.
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Fig. 24. Corrections in stellar positions and proper motion for the UCAC 5 catalog.
Fig. 25. Corrections in stellar positions and proper motion for the URAT 1 catalog.
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