Improvements in observing techniques The introduction and widespread availability of CCD (Charge Coupled Device) detectors have signicantly enhanced t

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1 Prospects in astrometry and orbital determination of minor bodies by M. Carpino Osservatorio Astronomico di Brera, via Brera, 28, Milano, Italy Abstract Astrometry of asteroids and comets is undergoing a signicant progress, both in accuracy and number of observations, as a consequence of the introduction of CCD devices and the availability of stellar catalogues dense enough to cope with CCD relatively small elds of view. Further substantial progress in accuracy is expected from the availability of Hipparcos catalogues. We review briey the main consequences of these changes and the new requirements they pose on the procedures for collecting, processing, archiving and distributing astrometric observations and on the software to be used for astrometric reduction and orbital analysis. Introduction Although astrometry is one of the oldest branches of observational astronomy and is often considered as an old-fashioned discipline, new technological developments occurred during the last few years have introduced new possibilities for the acquisition and reduction of astrometric data of minor bodies (asteroids and comets) and have produced a true revolution in the eld. In the present paper, we summarize some of the tools and methods which are available to present-day minor body astrometry and discuss briey how their full exploitation requires new concepts in the organization, processing and archiving of observations. 1

2 Improvements in observing techniques The introduction and widespread availability of CCD (Charge Coupled Device) detectors have signicantly enhanced the possibilities of ground-based astrometry of minor bodies: { the higher sensitivity of CCDs with respect to photographic plates has increased the limit magnitude which can be attained by a given instrument (allowing also telescopes of smaller size to be used for astrometry) and decreased the exposure times, thus increasing the eciency of the measurements; { the high linearity of CCD response allows a better computation of centroid coordinates of minor body images, thus increasing the astrometric precision; { the fact that the output of the observation is already in computer readable form allows a faster post-processing of the images, substituting slow and tiresome measurements with more automated procedures. CCD technology is benecial not only for professional astronomers, but also for amateurs, thanks to the availability of low-cost, easy-to-use commercial devices (as an example, a 50 cm telescope equipped with a CCD costing few thousand dollars is capable of good astrometry up to magnitude 19). As a result of the higher eciency of professional observatories including CCD-based systematic asteroid searches like Spacewatch (Scotti et al., 1992; Scotti, 1994) and NEAT (Helin et al., 1997; Rabinowitz et al., 1998) and the increasing involvement of amateur groups (especially in Japan and Italy), the database of astrometric observations of minor bodies is growing at an exponential rate. It is enough to quote here that, among all the observations stored at the Minor Planet Center (approximately 1;240;000 from the beginning of XIX century to March 1997), 167;000 (namely 13 %) were collected during 1996 alone; moreover, the total number of observations stored during 1996 is larger by 35 % with respect to 1995 (Minor Planet Center, 1997). It is likely that the present rate of growth is not going to decrease, also because new systematic searches are starting to work (like LINEAR, see Viggh et al., 1997) or are expected to become operational in the next future (like LONEOS, see Bowell et al., 1996). In the past, one of the main impediments to CCD astrometry was the lack of star catalogues dense enough to cope with the small elds of CCD images. For several years, CCD observations of asteroids have been reduced with the Guide Star Catalogue (Lasker et al., 1990; Russell et al., 1990), although this solution is far from optimal (the GSC was not developed for astrometric applications and has systematic errors in position of the order of 1{2 arcsec). Also from this point of view, the situation has signicantly improved in recent years: the GSC has undergone successive improvements (versions 1:1 and 1:2), introducing external checks and corrections for the deformations of the original Schmidt plates, improving 2

3 the reliability of the catalogue and reducing the position error to 0:3{0:5 arcsec. Moreover, new catalogues have been produced by scanning whole-sky photographic surveys (POSS I, see Aldering et al., 1993, 1994) or by combining together dierent surveys (USNO-A1, see Monet, 1996). From the point of view of the accuracy, a major step forward is expected from the availability (June 1997) of Hipparcos ( 10 5 stars to an accuracy of 1{2 mas) and Tycho ( 10 6 stars to 30 mas) star catalogues; their density is not sucient for allowing a direct utilization in the astrometric reduction of CCD frames, but they supply an accurate reference for the estimation and correction of systematic errors in photographic plates, so that the next generation of scanned catalogues (GSC 2.0, USNO-B) will have a typical accuracy of the order of 0:1 arcsec. We can therefore forecast that, in the near future, this is the level of accuracy which could be reached also by small telescopes equipped with small-eld CCDs. In addition to ground-based optical observations, minor body astrometry will benet also from high precision data from space-borne (Hubble Space Telescope) and radar measurements; in particular, after the upgrade of the Arecibo facility, routine range measurements will become possible also for main belt objects. The intrinsic accuracy of this kind of measurement is of the order of 10 (?9 1; mas or few hundred meters in range). The rapid evolution of observing techniques calls for a change of perspective about the procedures and the tools necessary for the acquisition, processing, archiving and distribution of astrometric measurements and related quantities. In particular, the development of semi-automated processing methods is necessary in order to cope with the increasing number of observations produced; in turn, automated methods require the introduction of error models at all stages of the processing, from astrometric measurement to orbital determination and ephemeris prediction. Error models In the past years and up to the present, the astrometric observations of minor bodies and all the quantities which can be derived from them (orbital elements, ephemerides) are usually lacking any denite information on their precision. This does not mean, of course, that no evaluation of the precision of observations is adopted when they are used and processed, but this information is generally estimated by single research groups and not propagated to others in a systematic way and, in many cases, not even published. As an example, reference star catalogues do not supply error models from which it could be possible to estimate errors in astrometric positions obtained from them; in the same way, no error information is propagated from astrometric observations to orbital analysis. As a matter of fact, the most comprehensive and widely used database of astrometric observations 3

4 (supplied by the Minor Planet Center) does not contain any accuracy information (at least for optical observations). This situation is a historical consequence of the way in which observations were obtained and depends mainly on the photographic technology: the long time required to expose and reduce photographic plates meant that each observer could contribute only relatively few observations, and this did not allow a reliable statistical analysis of errors. Moreover, systematic eects introduced by atmospheric refraction and plate deformations cannot be easily modelled or estimated. The recent developments of observing techniques call for and, at the same time, make feasible a more rigorous and systematic analysis of errors. The format itself in which images are available (digital instead of analogic) allows automated methods to be applied since the rst stages of processing. Moreover, during the last years several new systematic observing programs have been undertaken, and more are expected to start in the next future; presently, the vast majority of observations is obtained by very few observing sites (1), and this trend is expected to continue in the future. It is likely that this \centralization" and homogenization of observations may facilitate the statistical analysis. A reasonable paradigm for the description of errors seems to be the adoption, for all the relevant quantities, of variance-covariance matrices, to be estimated by statistical analysis or propagated through all the stages of the computation (from errors in pixel coordinates and astrometric positions of reference stars, to reduced astrometric coordinates of minor planets, orbital elements and ephemerides). An approach of this kind is standard in many elds of experimental physics, can be easily implemented (at least, if linear propagation rules are assumed) and indeed has been used also for orbital analysis of minor bodies (Muinonen and Bowell, 1993; Muinonen et al., 1994); if adopted consistently, it would improve in several aspects the analysis of astrometric observations: { it would allow to compute reliable estimates for the weights to be adopted in least squares ts, both in the astrometric reduction of the image and in orbital determination; { it would allow to introduce automated criteria (based on objective statistical tests) for tasks which are usually performed by the user on the basis of his expertise, like selection of data (outlier rejection) and linkage of orbits (identi- cation of two or more preliminary orbits as belonging to the same object); (1) statistics performed on the observations published by the Minor Planet Center for 1995 and the rst half of 1996 shows that the three most productive observatories contributed with 33:0 %, 10:8 % and 5:7 % of the data; other 5 sites produced more than 3 % of the observations each, and all the others less than 3 % 4

5 { it would allow the computation of error bars for other quantities derived from the orbital analysis (for instance, asteroid masses computed from the orbital changes during close approaches, see Carpino and Knezevic, 1996a and 1996b); { a realistic estimation of ephemeris uncertainty would allow an optimal planning of observation campaigns (Bowell et al., 1997), as well as the computation of the probability of exceptional events like stellar occultations and physical collisions. Although this approach seems natural and promising, there are some problems to be solved before it can be fully implemented: { the computation of correlations is usually troublesome, because it requires the modeling of systematic eects which are dicult to estimate. As an example, it is well known to orbit computers that, although the RMS error i of single astrometric measurements has signicantly improved from the last century to present days (going from 2{3 arcsec for typical late-xix century micrometric observations to 0:3{0:5 arcsec for present CCD measurements), it would be misleading to adopt directly these values for dening the weights w i to be used in the least square t according to the usual rule w i = 1= 2, because this i would result in a dangerous overweighting of recent data. This is due to the fact that CCD observations tend to be clustered in limited timespans around particular epochs, and the error of individual measurements belonging to these "batches" are not random, since a substantial fraction of it (produced by zonal errors in the stellar catalogues used for the astrometric reduction) is common to all the observations. For this reason, the increase in accuracy produced by the use of more observations is not described by the usual relationship (error / 1= p N) which holds for independent measurements. From a statistical point of view, a rigorous answer to this problem would require a detailed knowledge of the stochastic properties of catalogue errors (for instance, in the form of an auto-covariance function), which is not usually available. We have to notice, however, that the situation is improving, due to the improvement of star catalogues; { although a linear propagation of covariance matrices is often adequate, in some applications it is not sucient, and it is necessary to devise algorithms which could allow to take into account also non linear eects (Milani, 1998; Milani et al., 1998; Sansaturio et al., 1998); { orbit determination must rely also on observations performed in the past (in some cases, as far as 150 years ago), for which it is not possible to perform a detailed error analysis; in these cases, approximate error estimates can be possibly obtained by statistical analysis of post-t orbital residuals. 5

6 a) image display b) isophotal contour plot Figure 1. A small portion of a CCD frame (2424 pixels) containing the images of three point-like sources (stars): a) image display (higher light intensities are represented by darker hues); b) isophotal contour plot. Requirements for software and archiving procedures The increasing precision of astrometric observations imposes new accuracy requirements also on the software to be used for their reduction and analysis. For instance, software for orbit determination must use improved models for dynamic equations, the position of the observer and the reduction of observable quantities (apparent position range and radial velocity). The increasing number of observations poses new challenges to software performances and requires the adoption of more automated methods at all the stages of processing: image analysis and detection of moving objects, astrometric reduction, orbit determination, identication of objects against known orbits and linkage of single-opposition orbits, generation of ephemerides, planning and optimization of observations. Similar concepts are being implemented in a software package for astrometric reduction and orbital analysis, which is currently under development by A. Milani (University of Pisa), K. Muinonen (University of Helsinki), Z. Knezevic (Observatory of Belgrade) and myself. The package includes tools for the astrometric reduction of CCD images (program CCDAR (2) ) and for orbital computation: preliminary and precise orbit determination, ephemeris generation, orbital identication (program ORBFIT (3) ). (2) see (3) see ftp://copernico.dm.unipi.it/pub/orbfit/ 6

7 obs_name = 'Sormano'! observatory name obs_code = 587! observatory MPC code exp_time = ! exposure time (s) central_time = MJD UTC! observation time (center of exposure) c_astcoo = ! RA and DEC of the center of the frame c_astcoo_err = ! error in center's RA and DEC border_pixcoo = ! pixel coordinates of image borders c_pixcoo = ! pixel coordinates of image center scale = ! image scale (arcsec/pixel) scale_err = ! relative error in scale END_OF_HEADER! List of objects! ID X ErrX Y ErrY Mag ErrMag GP T F T F T F T F T... Figure 2. Example of inventory (object list) le, generated from the image shown in Figure 1. After a header (containing general information about the image), the le lists all the objects detected on the frame, giving for each of them pixel coordinates and uncalibrated magnitude (with their errors). The two brightest objects visible in Figure 1 are reported as items 73 and 65 in the list; a third, fainter object at approximate pixel coordinates (182; 120) was not detected and does not appear in the list. The fast evolution of techniques and available tools requires also a change of perspective about the criteria adopted and the procedures used for archiving and distributing the information. For instance, a consequence of the rapid improvement of stellar catalogues is that the results of the astrometric reduction of an image performed today may become obsolete in short time (as an example, new versions of USNO astrometric catalogue are expected to be available every year, at least for the next future); therefore, in order to allow a full exploitation of the information contained in the observation, it is necessary to store and to preserve for future use all the data needed in order to allow a complete astrometric reduction of the image (if not the complete image, at least the catalogue of all the objects detected on the 7

8 ! ID RA DEC MAG dra ddec dmag Identification! num (deg) (deg) (") (") 'S' 'GSC1.1_5526_01169' 'S' 'GSC1.1_5526_01167' 'S' 'GSC1.1_5526_01247' '?' 'S' 'GSC1.1_5526_01261' '?' '?' '?'... Figure 3. Astrometric coordinates of stars computed by program CCDAR on the basis of pixel coordinates listed in the inventory le (see Figure 2); for each object, the program reports right ascension, declination and calibrated magnitude, with their error bars. J95S03M C Figure 4. Format adopted by the Minor Planet Center for storing astrometric observations of minor bodies, reporting date and time, right ascension and declination, magnitude, reference (MPC page 29387) and observatory code (587). A detailed description of the format is available through WWW at frame, with their pixel coordinates and measured uxes) (4). This requires a new, \dynamic" organization of the database of astrometric observations: astrometric coordinates are not to be considered as primitive, unchangeable quantities, but as the result of a complex elaboration of more fundamental datasets (images or object catalogues derived thereof, which of course have to be included in the database or be anyway available), to be re-computed at any time an improvement in stellar catalogues or reduction software is available. This in turn requires the adoption of well dened and documented standards and formats for storing images and object lists (see Figures 1{4 for an example). This concept is by no means new and, for instance, was well clear to people involved in micrometric measurements of asteroid positions, who used to publish, (4) of course, storage of object lists would imply a substantial increase in the size of astrometric databases (probably by 2{3 orders of magnitude) with respect to current practice; technical problems related to maintenance of archives of such dimension could be substantial, especially in the case of systematic surveys based on large size (mosaic) CCDs 8

9 together with the reduced result, also the dierence in coordinates with respect to the reference stars: starting from these data, the Minor Planet Center has undertaken a systematic activity of re-analysis and reduction of the observations against modern stellar catalogues, which is leading to the (apparent) paradox that, in many cases, micrometric observations from the end of last century are more accurate and reliable that many more recent photographic observations, for which we do not have the original plate measurements and therefore a new astrometric reduction is impossible or very cumbersome. Conclusions Recent progresses in the techniques for the acquisition of astrometric measurements of minor bodies and the continuous evolution of star catalogues suggest that the methods and software used for their analysis should evolve in the direction of { consistent adoption of realistic error models (based on estimation and propagation of covariance matrices) at all the stages of processing (from image analysis to orbit determination); { introduction of more automated algorithms; { new denition of requirements for archiving and distribution of observations; in particular, it is highly advisable that not only the nal result of astrometric reductions, but also raw pixel measurements (centroids) or even images, be stored and preserved for future utilization. Acknowledgment I am grateful to A. Milani for helpful discussion and to the referees (B. Gladman and K. Muinonen) for the improvements suggested. 9

10 References Aldering, G., Humphreys, R. M., Odewahn, S. C., Cornuelle, C. S. and Thurmes, P. (1993) Astrometric Characteristics of the APS Catalog of POSS I, Bull. American Astron. Soc. 183, #73:02 Aldering, G., Humphreys, R. M., Odewahn, S. and Thurmes, P. (1994) The Automated Plate Scanner On-Line Database of POSS I, in Crabtree, D. R., Hanisch, R. J. and Barnes, J. (eds.), Astronomical Data Analysis Software and Systems III, A.S.P. Conference Series 61, 219 Bowell, E., Koehn, B. W., Howell, S. B., Homan, M. and Muinonen, K. (1996) Lowell Observatory Near-Earth-Object Search, in Beginning the Spaceguard Survey, 27 Bowell, E., Koehn, B. W., Wasserman, L. H. and Muinonen, K. (1997) Hierarchical Observing Protocol (HOP) for Asteroids, Bull. American Astron. Soc., DPS meeting no. 29, #07:13 Carpino, M. and Knezevic, Z. (1996a) Asteroid mass determination: (1) Ceres, in S. Ferraz-Mello et al. (eds.), Dynamics, Ephemerides and Astrometry of the Solar System (IAU Symposium 172), Paris, France, 203{206 Carpino, M. and Knezevic, Z. (1996b) Determination of asteroid masses from mutual close approaches, in A. Manara et al. (eds.), Proc. 1 st Italian Meeting of Planetary Science, Bormio, Italy, 62{74, see Helin, E. F., Rabinowitz, D. L., Pravdo, S. H. and Lawrence, K. J. (1997) Near- Earth Asteroid Tracking (NEAT): First Year Results, Bull. American Astron. Soc., DPS Meeting no. 29, #03:10 Lasker, B. M., Sturch, C. R., McLean, B. J., Russell, J. L., Jenkner, H. and Shara, M. M. (1990) The Guide Star Catalog. I. Astronomical and Algorithmic Foundations, Astron. J. 99, 2019{2058 Milani, A. (1998) The Asteroid Identication Problem I: recovery of lost asteroids, Icarus, in press Milani, A., La Spina, A., Sansaturio, M.-E. and Muinonen, K. (1998) The Asteroid Identication Problem II: proposing identications, in preparation Minor Planet Center (1997) Archive Statistics, Monet, D. (1996) The 491,848,883 Sources in USNO-A1.0, Bull. American Astron. Soc. 188, #54:04 Muinonen, K. and Bowell, E. (1993) Asteroid orbit determination using Bayesian probabilities, Icarus 104, 255{279 10

11 Muinonen, K., Bowell, E. and Wasserman, L. H. (1994) Orbital uncertainties of single-apparition asteroids, Planetary and Space Science 42, 307{313 Rabinowitz, D. L., Helin, E. F., Lawrence, K. J. and Pravdo, S. H. (1998) JPL's Near-Earth Asteroid Tracking (NEAT) Program: A fully automated, remotely controlled, digital sky survey, Bull. American Astron. Soc. 192, #55:02 Russell, J. L., Lasker, B. M., McLean, B. J., Sturch, C. R. and Jenkner, H. (1990) The Guide Star Catalog. II. Photometric and Astrometric Calibrations, Astron. J. 99, 2059{2081 Sansaturio, M.-E., Milani, A., La Spina, A. and Muinonen, K. (1998) The asteroid identication problem, in Impact of Modern Dynamics in Astronomy, IAU Colloquium 172, Namur (Belgium), 6-11 July 1998 Scotti, J. V. (1994) Computer aided Near Earth Object detection, in Milani, A., Di Martino, M. and Cellino, A. (eds.), Asteroid, Comets, Meteors 1993, Kluwer Acad. Publ., 19{30 Scotti, J. V., Gehrels, T. and Rabinowitz, D. L. (1992) Automated detection of asteroids in real-time with the Spacewatch telescope, in Harris, A. W. and Bowell, E. (eds.), Asteroid, Comets, Meteors 1991, Lunar and Planetary Inst., 541{544 Viggh, H. E. M., Stokes, G. H., Shelly, F. C., Blythe, M. S. and Stuart, J. S. (1997) Recent Results from the Lincoln Near Earth Asteroid Research (LINEAR) Project, Bull. American Astron. Soc., DPS Meeting no. 29, #03:02 11

Improving the Absolute Astrometry of HST Data with GSC-II

The 2005 HST Calibration Workshop Space Telescope Science Institute, 2005 A. M. Koekemoer, P. Goudfrooij, and L. L. Dressel, eds. Improving the Absolute Astrometry of HST Data with GSC-II A. M. Koekemoer,