HST Astrometry of Transneptunian Objects
aa r X i v : . [ a s t r o - ph . E P ] J un Accepted 28 June 2010 to appear in
ApJ Supplements
HST Astrometry of Transneptunian Objects
S. D. Benecchi and K. S. Noll Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, AZ 85719
ABSTRACT
We present 1428 individual astrometric measurements of 256 Transneptunian objectsmade with HST. The observations were collected over three years with two instruments,the Wide Field Planetary Camera 2 and the Advanced Camera for Surveys High Res-olution Camera, as part of four HST programs. We briefly describe the data and ouranalysis procedures. The submission of these measurements to the Minor Planet Centerincreased the individual arc length of objects by 1.83 days to 8.11 years. Of the 256total objects, 62 (24.2%) had arc length increases ≥ Subject headings:
Kuiper belt: general, Astrometry
1. Introduction
Where objects reside in the Kuiper Belt provides constraints for solar system formation models(Gomes et al. 2005; Morbidelli et al. 2005; Tsiganis et al. 2005; Levison et al. 2007). As of June2010 there are 1418 objects cataloged by the Minor Planet Center (MPC). These objects reside ina variety of orbits characterized by their orbital elements and their interaction, or non-interaction,with Neptune. Two classification schemes have been suggested: (1) the Deep Ecliptic Survey(DES; Chiang et al. 2003; Elliot et al. 2005), and (2) the Gladman classification (Gladman et al.2008) with the greatest distinction being the boundary between the Classical and Scattered objects.For the purposes of this paper we follow the DES scheme (Elliot et al. 2005) with more recentenhancements to include the scattering concept from Gladman et al. (2008). Objects with orbitsin mean motion resonances with Neptune are classified as Resonant. Objects with low inclinationand low eccentricity orbits that do not interact with Neptune are called Classical KBOs. Objectswith highly eccentric ( ≥ Planetary Science Institute, 1700 East Fort Lowell, Suite 106, Tucson, AZ 85719; [email protected] Space Telescope Science Institute, 3700 San Martin Dr., Baltimore MD 21218 ∼ ∼
20% and the eccentricity to ∼ ∼
2% in semi-major axis and ∼
10% in eccentricity after recovery in thesecond year and to less than 1% in both semi-major axis and eccentricity following observationsin year 3. The observational uncertainty of an object’s position after three years of observations isapproximately 0.5 arcseconds. The positional uncertainty increases by approximately 0.5 arcsecondseach year. For additional discussion of orbit determination and uncertainties see Jones et al. 2010.Observations with HST require the positional uncertainties of a TNO to be within the relativelymodest field of view (FOV) of the camera (on the order of 10s of arcseconds). Most of the objectswe observed already had positional uncertainties significantly better than this limit. The primarygoal of the observing programs was to look for binaries. The main requirement for observation wasthat the object have a predicted visual magnitude brighter than ∼
24 and an expected positionalaccuracy within the field of view of the HST instrument ( ∼
25 arcseconds for ACS/HRC and ∼
2. Observations
In this work we present astrometry measurements from four HST programs that observedTNOs for binary identification and photometric/binary orbit studies. The details of the proposalsand specific results can be found in Stephens et al. 2006, Noll et al. 2006, 2008, Grundy etal. 2007, 2008, 2009, and Benecchi et al. 2009. The data were obtained from HST programs10514, 10800, 11113 and 11178 and included 256 unique objects which were observed 3-4 times in asingle HST orbit with the telescope tracking at the rate of the TNO. A few objects were observedin multiple HST orbits. The programs which searched for binaries selected objects whose visiblemagnitudes were brighter than 24 and whose expected positional uncertainties were within the fieldof view of the camera being used at the time. The timing of these observations was not specific;data were collected when it was convenient to do so with the telescope. The programs aimed atphotometric and binary studies were specifically targeted in both time and object. Observationswere obtained using the Advanced Camera for Surveys High Resolution Camera (HRC) and theWide Field Planetary Camera 2 (WFPC2). All of the observations were dithered to avoid fixedpattern noise, properly sample the point-spread function (PSF), and provide for better statistics.Exposures were 260-300 seconds in duration and were obtained using a broad filter (Table 1) so asto obtain the best throughput possible for each object.
3. Data Reduction and Analysis3.1. HST Pipeline Processing
We processed the data through the standard HST pipeline (Baggett et al. 2002; Pavlovsky etal. 2006). The basic image reduction flags static bad pixels, performs A/D conversion , subtractsthe bias, and dark images, and corrects for flat fielding. It also updates the header with theappropriate photometry keywords. The flat-field-calibrated images, subscripted by flt for ACS and c0f for WFPC2, were the ones we analyzed. A/D conversion takes the observed charge in each pixel in the CCD and converts it to a number with theappropriate gain setting. The gain for ACS/HRC is 2.216.
The position for each TNO was determined using the Point Spread Function (PSF) fittingmethod described in Benecchi et al. (2009). These positions were then used in combination withthe guide star positions from the HST image headers and the appropriate geometric distortioncorrections to obtain the Right Ascension ( α ) and Declination ( δ ) of the TNO in the field. In thefollowing paragraphs we elaborate on the details of our analysis methods.PSF fitting provides the most accurate position of the center of light of the TNO in the HSTimages. Our analysis began by identifying the TNO on the image (the only non-smeared object inthe field since the telescope was tracking at the rate of the TNO) and obtaining a crude centroid(chosen by eye, good to about 0.5 pixel), flux (summed within a 1.5 pixel radius around the chosencenter) and sky background estimation. If the TNO was a binary, we reported the position as iffor a single object. For close binaries the position is effectively the center of light, for well resolvedbinaries the position is that of the primary. Next, a sub-pixel sampled model PSF was generatedusing Tiny Tim [generated for a solar spectral distribution using models 51 (HD 150205, a G5V star)and 57 (HD 154712, a K4V star) from the Bruzual-Persson-Gunn-Stryker Spectra Library; Krist& Hook 2004] with the crude position, flux and sky background characteristics. The model wassubtracted from the data and a χ was calculated to provide a reference point. Next we modifiedthe PSF to account for changes in focus (thermally-induced breathing) and for small motions ofthe spacecraft known as jitter that occur on orbital timescales. We iterated the determinationof the focus and jitter values with an automated fitting routine, amoeba [Press et al. 1992; thisroutine performs multidimensional minimization of a function containing our object variables (x,y, background and flux) using the downhill simplex method], until the χ converged. Typically, 4-5iterations were required to reach a final PSF model.From our fits, we obtained the nominal x and y position of the TNO on the HST image ( flt or c0f ). The next piece of information required for astrometry is the position of the reference stars. Weused the guide star position values (referenced in the world coordinate system (WCS), Pavlovsky,C. et al. 2006, section 6.2) within the header of the image, combined with the geometric distortiontable for the HRC (found in the idc files) and the PYRAF xytosky routine to obtain the ( α, δ )of the TNO in the field. The process was similar for the WFPC2 image with the exception ofthe application of the geometric distortion corrections, of which there are none . The positions ofthe guide stars are accurate to ∼ The keywords for the reference position are found under the heading ”World Coordinate System and RelatedParameters” in the .fits headers. The values from the keywords
CRPIX1 , CRPIX2 , CRVAL1 , CRVAL2 , CD1 1 , CD1 2 , CD2 1 and
CD2 2 are used in the PYRAF script. When the analysis for this paper was done the WFPC2 images needed to be converted from GEIS to FITS imageformat prior to extracting the astrometry. The conversion was accomplished with the IRAF routine strfits. Since thetime of this work, the HST archive was updated to provide all images in standard FITS format. α, δ ) of the TNO, the position of HST in itsx-,y-,z-axis at the time of the observation is required. This information is contained within thearchive table files with extensions spt for HRC and shf for WFPC2. The reference keywords are
POSTNSTX , POSTNSTY and
POSTNSTZ for HST position X-axis, Y-axis and Z-axis, respec-tively. The units of the values are in km and they are given to an accuracy of 8 decimal places.Added in quadrature these values give the instantaneous distance of HST from the Earth’s center( ∼ photflam and photzpt values in the image header which aregiven in the Space Telescope magnitude system (STmag). Finally, we used synphot After astrometry is compiled for all our observations we compare our measured position tothe calculated position at the time of observation based on the orbit of the object in the MPCdatabase. We call the difference between these two values, observed minus calculated, the residual.We observed both numbered, objects which the MPC has deemed to have reliable positions far 6 –into the future (typically observed at four or more oppositions), and unnumbered objects, objectswhich have been designated by the MPC with observations longer than 24 hours, but which don’thave reliable long term orbits. For numbered objects the residual is determined solely from theorbit in the MPC database. For unnumbered objects, we calculate a new orbit using the Bernsteinformalism (Bernstein & Khushalani, 2000) and determine the residuals between our observationsand the positions of the TNO for both the new and old orbit. In total, 1428 positions for 256unique objects were submitted to the MPC. From the original sample there were 22 objects thatwe did not find in our images, likely due to bad magnitude estimates or poorer positional accuracythan expected.In most cases, since we were looking at objects with well-determined orbits, our observationsdo not significantly improve the orbits. However, in many cases our observations extend the arcon the orbit deminishing the chance the object will be lost in the future. Twenty-six percentof the objects we measured had positional improvements by 1.5-12 arcseconds; none were in theposition of being lost (we define lost as having a positional uncertainty of & α and δ positionof the object, column 7 is the magnitude of the object in the respective filter, proposal ID andinstrument (columns 8, 9 and 10). Columns 11 and 12 are the residuals (observed-reference) in α and δ space measured in arcseconds. Residuals for numbered objects are referenced to the existingorbit and residuals for unnumbered objects are referenced to the new orbit. In columns 13 and 14we list the increase of the arc length in years and the fractional arc length extension.As an additional evaluation of our measurements, we plotted the residuals returned to us fromthe MPC to ensure that there are no systematics in our positions. As expected, we show in Figure2 a random distribution for the residuals.
4. Discussion
In order to test the significance of the contribution of our astrometry, we investigated theorbits of the some of the objects in our survey that had the longest arc length increase (1997 SZ ,1998 U R , 1998 W S , 1998 W Y , 19299 and 24952) and a similar number of objects which hadthe largest fractional arc length increase (2002 CW , 2000 J F , 2000 Y X , 24952 and 19299).In both cases, we ran the Bernstein code with all the astrometric datapoints excluding the HSTobservations and once again with the HST astrometry included. In all cases the objects had anarc length of at least 3 years previous to the addition of the HST datapoints. The addition ofthe HST datapoints do not change the nominal orbit solutions or the dynamical classifications.The dynamical classifications are calculated in as described in Elliot et al. (2005). The nominal Table 1. Astrometry (sample, full table electronic only)
Object a Year Month Decimal Day RA (J2000.0) DEC (J2000.0) M HST
Filter PropID Instr Resid (”) b Resid (”) b Prearc c Postarc d .
47 +21 : 16 : 52 . · · · · · · · · · .
43 +21 : 16 : 52 . · · · · · · · · · · · · -2.71 0.77 · · · · · ·· · · · · · · · · .
37 +21 : 16 : 52 . · · · · · · · · · · · · -2.79 0.92 · · · · · ·· · · · · · · · · .
34 +21 : 16 : 52 . · · · · · · · · · · · · -2.41 1.12 · · · · · · .
05 +12 : 37 : 49 . · · · · · · · · · .
06 +12 : 37 : 49 . · · · · · · · · · · · · -0.46 0.06 · · · · · ·· · · · · · · · · .
08 +12 : 37 : 49 . · · · · · · · · · · · · -0.27 0.10 · · · · · ·· · · · · · · · · .
09 +12 : 37 : 49 . · · · · · · · · · · · · -0.24 0.07 · · · · · · .
93 +25 : 15 : 38 . · · · · · · · · · .
97 +25 : 15 : 38 . · · · · · · · · · · · · -0.43 -0.26 · · · · · ·· · · · · · · · · .
01 +25 : 15 : 38 . · · · · · · · · · · · · -0.30 -0.10 · · · · · ·· · · · · · · · · .
05 +25 : 15 : 38 . · · · · · · · · · · · · -0.27 0.06 · · · · · · .
57 +16 : 47 : 12 . · · · · · · · · · .
52 +16 : 47 : 11 . · · · · · · · · · · · · · · · · · ·· · · · · · · · · .
12 +16 : 47 : 10 . · · · · · · · · · · · · · · · · · ·· · · · · · · · · .
08 +16 : 47 : 09 . · · · · · · · · · · · · · · · · · · .
32 +14 : 42 : 41 . · · · · · · · · · .
28 +14 : 42 : 41 . · · · · · · · · · · · · -3.25 -5.10 · · · · · ·· · · · · · · · · .
24 +14 : 42 : 41 . · · · · · · · · · · · · -3.07 -5.02 · · · · · ·· · · · · · · · · .
20 +14 : 42 : 41 . · · · · · · · · · · · · -2.94 -4.94 · · · · · · . −
21 : 06 : 41 . · · · · · · · · · . −
21 : 06 : 41 . · · · · · · · · · · · · · · · · · ·· · · · · · · · · . −
21 : 06 : 40 . · · · · · · · · · · · · · · · · · ·· · · · · · · · · . −
21 : 06 : 40 . · · · · · · · · · · · · · · · · · · . −
09 : 49 : 32 . · · · · · · · · · . −
09 : 49 : 32 . · · · · · · · · · · · · -0.23 -1.21 · · · · · ·· · · · · · · · · . −
09 : 49 : 32 . · · · · · · · · · · · · -0.09 -1.18 · · · · · ·· · · · · · · · · . −
09 : 49 : 32 . · · · · · · · · · · · · -0.14 -1.17 · · · · · · a Object name in MPC packed format. b Provided by B. Marsden. c Orbit arc length in years previous to HST measurements. d Orbit arc length in years including HST measurements. ∼
10 Myr with tests (in the order listed) for resonance membership, or forclassification as a Centaur, Scattered or Classical object. All three orbits must give the same resultfor the object to be deemed classified. In a few cases the semi-major axis changes on the orderof 0.05 AU, but most of the time the changes are smaller than 0.01 AU. If an object were closeto a resonance such an orbit adjustment might reclassify an object dynamically (resonant to non-resonant or vice versa), however we do not see any cases of that in our particular dataset. It is alsotrue that our observations decrease the uncertainities on the orbital elements (in particular thosefor semi-major axis, eccentricity and inclination) by a factor of ∼
10 (e.g. from 0.01 AU to 0.001AU on semi-major axis, from 0.0005 to 0.0001 on eccentricity and 0.001 to 0.0001 on inclination)for the objects with the largest fractional arc length increases.Our results are in agreement with studies done by Elliot et al. (2005) and Wasserman etal. (2006) which show that observations over three years measured at two lunations on years oneand two and at least one lunation in year three are sufficient to determine the orbit of a TNOto the accuracy required for finding the object in an typical CCD field for at least 10 years. Forexample, the object (49673) 1999 RA was discovered in 1999 and has an arc length of 3.1 years.The current 1-year uncertainty on the orbit is 2.71 arcseconds. To summarize the contribution ofour observations we plot in Figure 3, a measure of the fraction of objects whose arc lengths wereincreased in year increments and the fractional arc length increases for all our objects.
5. Summary
We have presented the steps required for extracting astrometry from HST images for submissionto the MPC. The position of HST is a critical component of the measurement for moving objectsin our solar system. Of the 256 TNOs measured, the individual arc length of objects were extendedby 1.83 days to 8.11 years. 62 (24.2%) objects had their arc length of observation increased by ≥ Facilities:
HST (ACS, WFPC2). 9 –
Fig. 1.—
Sample MPC file structure.
The MPC file is space delimited, the first line for anobject gives the position of the TNO, the second line gives the position of HST when the observationwas taken. 10 –Fig. 2.—
Orbit residuals.
The difference between the observed position and expected positionin the orbit of the TNO. Unnumbered objects are plotted as points and numbered objects are plussymbols. The numbered object residuals are based on orbits maintained by the MPC while theunnumbered object residuals are based on orbits calculated to include the new HST measurements.There do not appear to be any systematics among the residuals. 11 –Fig. 3.—
Orbit Improvement. (left) A plot of fraction of objects versus their arc length extensionin years provided by the HST measurements. Of the 256 total objects, 24.2% had their arc lengthsextended by 3 years or more and 38 objects had their arc lengths extended beyond 8 years. (right) Aplot of the fraction of objects versus their fractional arc length extension (i.e. arc length extensiondivided by total arc length). 23.4% of objects (60) had their fractional arc lengths improved by afactor of two or greater. 12 –
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