KBO Astrometry Using Small Telescopes

Rachel Bowens-Rubin, Katheryn Decker French, Dora Gao, Christina A Jaworsky,

Carlos Zuluaga, Michael Person

3rd October 2008

Abstract

Astrometry of Kuiper Belt Objects has previously only been done with largetelescopes, however, our group aimed to make observations of the same qualitywith a small telescope. CCD images of Makemake (2005 FY9), the secondlargest KBO, were taken with a 14 inch telescope. The position of Makemakewas found by comparing its position on the frame to other stars in the frame.Observations were limited by the tracking capabilities of the telescopes and theairmass. It was found that the right ascension of the KBO was consistent withthe ephemris, but the declination offset differed significantly. It is possible todo KBO astrometry with small telescopes, however several hundred frames arerequired to equal the quality of observations on larger telescopes.

Introduction

The study of the Kuiper Belt is an important and relatively new field of plan-etary astronomy. The first Kuiper Belt Object (KBO) was discovered in 1992(Jewitt et. al., 1992). Since then, many more have been discovered. Under-standing the Kuiper belt is important in understanding solar system dynam-ics and evolution. Precise astrometry and determinations of orbits, sizes, andshapes of KBOs are necessary to increase our knowledge of the Kuiper belt. Oneimportant method for determining information about KBOs is to observe a stel-lar occultation (Elliot et. al., 2003). Precise astrometry of KBOs is required topredict stellar occultations.

Previous research in the field of KBO astrometry has required the use oflarge telescopes over long periods of time. Makemake was discovered using a1.2m telescope for 6 nights over the course of 2 months (Brown, MPEC 2005-O42). The Deep Ecliptic Survey (Millis et. al., 2002) (Elliot et. al., 2005) madeuse of 4m telescopes with a 2048 x 4096 pixel CCD camera.

We present astrometric results for the KBO Makemake (2005FY9) using14 inch telescopes at the George R. Wallace Astrophysical Obervatory (WAO)and STL-1001e SBIG CCD cameras. The STL-1001e camera made it possibleto observe the KBO with a small telescope. We observed Makemake over 29

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nights from June to August of 2008 (figure) and obtained astrometry for 728frames. We hope to be able to improve the existing astrometry for this objectand establish a procedure for observing KBOs and obtaining astrometry withsmall telescopes. Observing on smaller telescopes is often much easier and lessexpensive than with larger telescopes, and commonplace observations of KBOson small telescopes should be possible. This would help solar system populationstudies and the recovery of KBOs discovered in searches on larger telescopes.

Observations

The observations of Makemake were carried out on a 14” telescope at WallaceAstrophysical Observatory in Westford, Massachusetts. Images were taken withan SBIG camera and processed using CCDSoft. The telescope was mounted ona Paramount ME mount, making very precise tracking possible. Observationswere made starting in June and ending by mid August, when the observationwindow for Makemake became too small to obtain useful data.

The SBIG STL-1001E camera used had an array of 1024 by 1024 pixels. Thechip size was 24.6 square millimeters, and it had a field of view of approximately20 by 20 arcminutes. It had a peak quantum efficiency of 72%, and a gain of0.72 e-/ADU.

Nightly observations of Makemake were made in frames with a field of viewof 20 arc minutes. Five overlapping fields of view were used for the observationsas Makemake moved in the sky, shown in figure 1.

A new field of view was used each month, centered on the midmonth positionpredicted by Starry Night Pro 6 and JPL’s Horizons. Transitional frames wereused between the months of June and July. The frames contained an average of20 reference stars, which were used in the data analysis process. The referencestars, shown in figure 2, were spread across the entire frame to maximize theaccuracy of the astrometric fit.

The exposure time of the frames needed to be long enough to distinguishMakemake from the background, but short enough to prevent tracking errorsfrom distorting the frame. In the beginning of the summer, when Makemake wasstill relatively high in the sky, a series of twenty consecutive 3 minute exposureswas taken. But, as Makemake got lower in the sky, 3 minute exposures weretoo long. Stars were elongated in the frame because the telescopes track lessaccurately lower in the sky. So, a series of 60 consecutive 1 minute exposureswas used for the rest of the observations, because Makemake was still visible andvery few frames were unusable because of tracking inaccuracies. The differencein elongation is seen in figure 5.

After observing for 29 nights, Figure 3, the data had to be calibrated forthe reduction and analysis process. The goal of the calibrations was to re-duce systematic error introduced by the CCD. For each night, dark frames weresubtracted from each frame to remove extraneous signal due to hot pixels andrandom variation in the chip. In June, the autodark reduction feature in CCD-soft was used to subtract the dark frame. Autodark reduction subtracts a single

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Figure 1: This shows the fields that were used for each set of observations. Eachfield was used for a particular month or transition between months. Consistentfields were needed from night to night in order to observe the same standardstars.

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Figure 2: This is a sample image of the August field of view. Makemake is boxedand the reference stars are in cross hairs. The comparison stars are distributedthroughout the field to produce a better astrometric fit

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dark frame taken at the beginning of the series from all the exposures in theseries. However, because autodark only uses one dark frame, it does not accountfor cosmic rays and random errors over time, and was not used in July or Au-gust. Instead, ten one minute dark frames were averaged and subtracted fromthe frames to dark correct the data from July on. Observations of Makemakewere limited by the tracking of the telescopes. Because of this limitation, itwas impossible to take frames where the pixel counts of Makemake were severaltimes higher than the pixel counts of the background; the image elongated asexposure time was increased. Instead, in the observations, Makemake’s pixelcounts are only 10 to 20 percent higher than the counts in the backgrounds.Stacking the images to boost the signal was unsuccessful because the alignmentprocess distorted the image to line stars up between frames.

Analysis

The first step in analyzing the images was to create a network of companionstars for each field. The correct field was determined from the coordinates in thefits header. Coordinates for the comparison stars were found using the USNO-Band UCAC catalogs. Due to pointing calibrations of the telescope, there was anoffset between the catalog and the actual frame. [See figure where it shows theinitial fit, with offset] To account for the offset, an initial astrometric fit was runon several stars to find a function relating right ascension and declination tothe pixel coordinates. A six-parameter model using a point-spread function wasused to calculate a fit.The parameters for the model were platescale, rotationangle, central RA and DEC of the chip, and two linear cross-terms for theplatescale and rotation angle.

Upon obtaining an initial astrometric fit, the next step was to make a moreextensive fit including more stars in the frame. As many stars as possible wereincluded, unless they would have reduced the quality of the fit. Stars with apixel count of over 65k were considered saturated and were not included. Starstoo close to the edge of the frame were likely to not be in all frames for agiven night and were also not used. When two stars were very close together,they were not included because their point-spread functions were not separable.This more extensive fit generated a final network of stars with a center rightascension, declination, and pixel coordinate.

Next, each frame was centroided so that each star in the frame is directlymatched to its X,Y location. Using the catalog generated from the last step, theprocess was repeated using the new network instead of the UCAC catalog. Theright ascension and declination of the network was updated for the time of eachframe so that a direct correlation between the map of the sky at a specific timein the night (when the frame was taken) and the right ascension of the centerof the frame could be established. Because each frame shifted with respect tothe other frames, minor calibrations were still required. By manually inputting

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Date* Time Started * Frames Taken Frames Used ExpTime Autodark Observers

6/8 02:15 20 0 4 yes RBR, KDF6/9 03:27pm 20 18 3 yes DG, CAJ6/10 01:45pm 20 20 3 yes KDF,CAJ6/11 01:38pm 20 0 3 yes KDF,DG6/12 02:22pm 20 0 3 yes KDF,CAJ6/13 02:17pm 20 0 3 yes RBR,DG6/18 02:49pm 20 20 3 yes RBR,DG6/21 02:46pm 20 0 3 yes DG,CAJ6/22 01:58pm 20???? 22 3 yes RBR,CAJ6/26 03:27pm 60 55 1 yes RBR,CAJ6/27 03:25pm 60 0 1 yes DG,CAJ6/28 01:42pm 42 0 1 yes DG,CAJ7/2 03:00pm 32 21 1 no RBR,KDF7/3 02:05pm 60 57 1 no RBR,KDF7/7 01:54pm 60 60 1 no RBR,KDF7/8 02:14pm 60 58 1 no DG,CAJ7/9 01:54pm 60 33 1 no KDF,CAJ7/11 01:30pm 60 58 1 no KDF,CAJ7/12 01:41pm 60 49 1 no KDF,CAJ7/13 01:35pm 60 9 1 no DG,CAJ7/16 01:50pm 60 42 1 no RBR,DG7/17 01:56pm 90 51 1 no DG,CAJ7/27 01:32pm 60 0 1 no RBR,KDF7/29 01:32pm 57 30 1 no KDF,CAJ7/30 02:20pm 60 0 1 no DG,CAJ8/2 01:11pm 60 0 1 no KDF,CAJ8/5 01:12pm 60 9 1 no RBR,DG8/10 01:04pm 40 29 1 no RBR,DG8/13 00:41pm 40 29 1 no KDF,CAJ

Figure 3: *Date and Time are in UT

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the X,Y pixel coordinates of a specific reference star, the offset was determined.The shift in the X,Y coordinates was applied to the rest of the frame using apoint spread function for each star.

After centrioding, a third astrometric fit was made. As before, a six-parametermodel was used. The root mean square of the fit was found to evaluate the qual-ity of the fit. When multiplied by the plate scale, the typical rms was about0.07 arc seconds. Any frames with a rms of higher 0.12 were discarded to keepthe data set as consistent as possible. This third astrometric fit was used tofind a new function relating the pixel coordinates to RA and DEC. Using thisnew function, the RA and DEC of the KBO was determined for each frame.

After obtaining the third function relating X,Y coordinations to right ascen-sion and declination, the final step was to find the RA and DEC of Makemakein each frame based on its X,Y coordinates. Then, a fourth astrometric fit wasmade to get a better approximation of Makemake’s pixel coordinates. To furtherincrease the accuracy of the fit, the KBO in the frame was checked to assurethat it was a bright, clear round point. Frames where the KBO was elongatedor near hot pixels were discarded [Figure where we have an example of a goodKBO, and a bad KBO]. With the remaining frames, the fourth function corre-lating RA and DEC to pixel coordinates was used to find a more accurate RAand DEC for Makemake. Having found a new right ascension and declinationfor the KBO, the last step was to analyze the offset obtained by the differencebetween our result and the initially predicted ephemeris.

Discussion

The results from the analysis (Figures 8 and 9) were compared to those foundby the MIT ECM (Ephemeris Correction Model) (Figures 10 and 11). Theresiduals between the observed and predicted ephemerides were found to beconsistent. The RA offsets were close to zero in both models, and the DECoffsets were consistently negative.

There were several sources of error in the data (Figures 12 and 13). One ofthe most significant sources of error was the Earth’s atmosphere. The error waspredicted to be higher at higher airmasses, when the object was low in the sky.A strong trend was not generally observed for a single night (See figures 14 and15 ), but the trend of increasing error with increasing airmass was clearly visibleover the course of all of the observations (See figures 16 and 17 ). This is believedto be because observations were only taken over short ranges of airmasses forany given night. The plot the error over the course of all observations covers awider range of airmasses, and so a stronger correlation can be seen.

Towards the end of the observing period, Makemake was setting early inthe night, and there was only a short time window between sunset and whenMakemake set. In an attempt to get more images, observations were madebefore astronomical twilight on some nights. A clear trend of increasing errorwith increasing solar altitude was observed when the solar altitude was above-14 degrees. (See figures 18 and 19)

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0 200 400 600 8000

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Figure 4: The network of stars is distributed evenly across each frame. Dis-tributing the the star choice helps to make a better astrometric fit.

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Figure 5: The image on the left was taken with an exposure time of 1 minute.The image on the right was taken with an exposer time of 3 minutes. Due tothe telescope tracking, the stars in the 3 minute frame look elongated. Becausethe KBO was small the elongation affects position more than in a large brightstar.

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535 540 545 550

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Figure 6: This shows a before and after image of the script to center Makemakewhen Makemake was successfully centered.

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Figure 7: This shows a before and after image of the script to center Makemakewhen it is near a hot pixel. The hot pixel is detected as the center of the frameinstead of Makemake.

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54 630 54 640 54 650 54 660 54 670 54 680 54 6902

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Makemake RA Residuals

Figure 8: The Residuals for the RA are consistently near zero. The proximityto zero indicates that the predicted ephemeris for Makemake’s RA is close towhat was observed.

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54 630 54 640 54 650 54 660 54 670 54 680 54 6902

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Makemake DEC Residuals

Figure 9: The Residuals for the DEC are consistently negative. The negativevalues indicate that Makemake was observed to be slightly below the predictedephemeris.

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54 630 54 640 54 650 54 660 54 670 54 680 54 6900.5

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Figure 10: The RA residuals predicted by the MIT ephemeris correction modelare close to zero, which is consistent with the observed positions.

When data was taken after the sun was below -14 degrees, solar altitude wasnot a source of error, but its effects can be seen for nights such as 20080710(See figures 20 and 21 when data was taken starting at a solar altitude of -11degrees.

The random error in our data was analyzed by studying its change withexposure time. (See figures 22 and 23) As expected, the error was less in 3minute exposures than in 1 minute exposures. The mean RA error was 0.212for the 60 second exposures, and 0.124 for the 180 second exposures. The meanDEC error was 0.183 for the 60 second exposures and 0.106 for the 180 secondexposures.

The quality of the astrometry of the images was found to depend on thenumber of stars used in the fit. (See figures 24 and 25) To reduce the error,images where less that 9 stars avaliable for the fit were not used.

The overall error was greater for the right ascension measurements thanfor the declination measurements. For the 60 second exposures, the mean RAerror was 0.212, and the mean DEC error was 0.183. This was most likely causedby slight imperfections in the Paramount telescope mount tracking accumulatedover time. Imperfect tracking could have caused the images to be slightly blurredduring an attempt to point at a steady right ascension coordinate. This effectwould have affected the right ascension astrometry measurements more thanthe declination measurements, which is consistent with our calculated errors.

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54 630 54 640 54 650 54 660 54 670 54 680 54 6900.5

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Makemake MIT DEC ECM

Figure 11: The DEC residuals predicted by the MIT ephemeris correction modelare slightly negative, which predicts that Makemake should be slightly belowthe Minor Planet Center ephemeris. The DEC residuals are again consistentwith the observed positions.

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54 630 54 640 54 650 54 660 54 670 54 680 54 690

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Figure 12: The error in right ascension plotted for each night of images wassmaller for nights at the beginning of the observing period. This is believed tobe caused by a combination of longer exposure times and lower air masses

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54 630 54 640 54 650 54 660 54 670 54 680 54 690

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Makemake DEC Position Errors

Figure 13: The error in declination appears to follow the same trend as the rightascension error. The error at the start of the observing period is lower overallthan the end.

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1.5 1.6 1.7 1.80.0

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07/11/2008 Makemake RA Position Errors

Figure 14: This is a plot of the errors in the RA error vs the airmass. The errorvs airmass for the night of July 11th, 2008 shows no strong correlation.

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07/11/2008 Makemake DEC Position Errors

Figure 15: This is a plot of the errors in the RA error vs the airmass. The errorvs airmass in one night of observing had a weak trend.

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Makemake RA Position Errors

Figure 16: RA error increases with higher airmasses as expected. Images takenthough airmasses above 2.3 result in significantly more error than those below.

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1.5 2.0 2.5 3.00.0

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Figure 17: Like RA error, DEC error also increases with higher airmasses asexpected. Images taken though airmasses above 2.3 result in significantly moreerror than those below.

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-12 -14 -16 -18 -20 -22 -240.0

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Figure 18: The RA error for each solar altitude was found to be higher foraltitudes above -14 degrees and fairly consistent below -14 degrees. Severalnights of images were affected by higher errors resulting from observations takentoo early in the night

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Figure 19: The DEC error for each solar altitude was found to be higher foraltitudes above -14 degrees and fairly consistent below -14 degrees, similar tothe RA error. Several nights of images were affected by higher errors resultingfrom observations taken too early in the night

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07/10/2008 Makemake RA Position Errors

Figure 20: For the night of July 10th, 2008 observations were taken starting at asolar altitude starting at -11 degrees (right side of graph). The RA error at solaraltitudes between -11 and -14 degrees was observed to be greater than the errorat lower solar altitudes. This night was atypical and the effect of solar altitudewas insignificant in the error in the majority of nights of the observations.

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18 17 16 15 14 13 12 110.0

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07/10/2008 Makemake DEC Position Errors

Figure 21: For the night of July 10th, 2008 observations were taken starting ata solar altitude starting at -11 degrees (right side of graph). The DEC errorat solar altitudes between -11 and -14 degrees was observed to be greater thanthe error at lower solar altitudes. This night was atypical and the effect ofsolar altitude was insignificant in the error in the majority of nights of theobservations.

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1 2 3

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Makemake RA Position Errors vs Exposure Time

Figure 22: The RA error was less for greater exposure times. This is expectedbecause the error is proportional to the square root of the number of photonsreceived

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Figure 23: The DEC error was less for greater exposure times, similar to RA.This is expected because the error is proportional to the square root of thenumber of photons received

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Figure 24: The RA position error showed a slight dependance of the number ofstars used in the astrometric fit. The more stars that were used, the lower theerror was.

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=

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Figure 25: he DEC position error showed a slight dependance of the number ofstars used in the astrometric fit. The more stars that were used, the lower theerror was.

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The following recommendations are made to those wishing to carry out simi-lar astrometry measurements on KBOs with small telescopes. Take images withthe maximum exposure time possible without saturating stars to be used in theastrometry fit. With the equipment used here (described in Section 1), this wasaround 180 seconds. Do not start taking data until the sun is more than 14degrees below the horizon. Although more frames can potentially be obtainedthis way, it is a large source of error. Similarly, observe the KBO through aslittle airmass as possible. Choose a field around the KBO with the most starsthat csn be used to make an astrometric fit.

The possiblility of using small telescopes for KBO astrometry measurementsopens the door for much more work to be done in the field. More extensivesurveys are possible with smaller telescopes because time on them will be lessexpensive. Despite the fact that data taken on larger telescopes can have lowererror, it is more practical to take many frames on a smaller telescope to reducethe error. We would like to see small telescopes used to calculate and correctthe ephemeres of many KBOs.

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