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1 Spin Directions of Asteroids: Lightcurve Analysis of Koronis Family Members 158 Koronis and 72 Bohlinia by Lucy Crespo da Silva Submitted to the Department of Earth, Atmospheric, and Planetary Sciences in partial fulfillment of the requirements for the degree of BACHELOR OF SCIENCE at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY May 2 Lucy Crespo da Silva. All rights reserved. The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic copies of this thesis document in whole or in part. MASSACHUSES INSTITUTE OF TECHNOLOGY SEP LIBRARIES ARCHIVES Author... Certified by... Accepted by... The author hereby grants to MIT permission to reproduce and to distribute publicly paper and c ectroric copies of this thesis document in whola or in part in any medium now known or he-eafter created. Signature redacted... ' Department of Earth, Atmospheric, and Planetary Sciences May 15, 2 Signature redacted... Richard P. Binzel Professor of Planetary Science Thesis Supervisor Sianature redacted J Timothy L.Grove Chairman, Undergraduate Thesis Committee

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3 Spin Directions of Asteroids: Lightcurve Analysis of Koronis Family Members 158 Koronis and 72 Bohlinia by Lucy Crespo da Silva Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on May 15, 2, in partial fulfillment of the requirements for the degree of Bachelor of Science in Planetary Science. Abstract Clusters of asteroids within the main-belt are referred to as dynamical families because they are believed to have originated as the result of collisional destructions of large parent bodies. Family members are the remnants of the parent body break-up and often retain some of the parent body's original rotational information. Previous studies have indicated that the Koronis dynamical family may have been relatively recently formed due to the non-random nature of the orientation of its members spin vectors. This project was undertaken to contribute to the rotational data on Koronis family members in order to better understand the unusual properties observed. The goal of this project was to determine the directions of spin of Koronis family members 158 Koronis and 72 Bohlinia. Observations were made at the MIT Wallace Astrophysical Observatory in Westford, Massachusetts during Both of the targets were determined to have a retrograde sense of rotation, which is in agreement with the previously known sense of rotation of Koronis family member 243 Ida. In addition, the synodic period of 158 Koronis was confirmed by these observations, and a new value for the sidereal period of 72 Bohlinia was found to be hours. During the course of the observations, an uncataloged asteroid was discovered and has since been assigned the designation 1999 QQ2 by the IAU Minor Planet Center. Thesis Supervisor: Richard P. Binzel Title: Professor of Planetary Science

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5 Dedication NMIT is not a particularly nurturing environment, nor is it a fun place to spend four (or often more) years of one's life. Thankfully, I have survived with the support of friends and family who have made me realize there may be a life worth living outside this bleak world of concrete and steel. I would especially like to thank Allison Thomsen for pulling me out of particularly grim times and Janet Wu for being there for me, trying so hard to understand, and never growing up. This thesis is the culmination of one year's worth of work. Night after night during the summer of 1999 was spent gathering data for this project, and those nights became my days for weeks on end. Sleeping during the days, processing data during the evenings, and observing during the nights quickly became an all too familiar routine. I am grateful to those who kept me company at the observatory and to all those who accommodated my observing schedule. Bobby Bus generously donated his time and was a tremendous help throughout this project. Rick Binzel's insights and encouragement about this thesis and life in general have made him the best advisor I could ever have asked for. Finally, I would like to dedicate this work to my godfather, Joao Maria Machado. In spite of the brief time we have actually spent together, he has been a tremendous inspiration throughout my life. The inexplicable bond we share defines so much of who I am, and I am ever grateful. Obrigada. 5

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7 Contents Abstract 3 Dedication 5 1 Introduction Observations 2.1 Goals of the Observations Selection of Targets Instrumentation and Observation Procedures 2.4 Data Analysis Procedures Image processing Lightcurve techniques and observational results 2.5 Uncataloged Asteroid Discovery Analysis of Lightcurves 3.1 Overview of Photometric Astrometry Method Koronis Bohlinia Results and Discussion Conclusions and Future Work 29 Appendix 31 References 43 7

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9 Chapter 1 Introduction In searching for the "missing planet" between Mars and Jupiter that was predicted by Bode's Law, Giuseppe Piazzi ( ) discovered Ceres on January 1, 181. At first it was believed that the missing planet had indeed been found, but when a second moving object was discovered in the same vicinity a little over a year later, it was realized that these two objects were significantly smaller than any of the other known planets. A new class of objects, called minor planets, was proposed, and it was theorized that these objects were the remains of a shattered planet. The name "asteroids," Greek for starlike, was suggested by William Herschel. However, it is now believed that the asteroid belt represents remnant planetesimals from the early solar system. Due to gravitational perturbations by Jupiter, a planet failed to accrete in that region between Mars and Jupiter, now known as the "main belt" of asteroids. Due to the non-spherical nature of asteroids, their rotations cause measurable periodic light intensity variations. From these lightcurves we can study several properties about asteroids, including their shapes and spin vectors. These periodic variations are relatively constant over time, as viewed from the background stars, and are referred to as the asteroids' sidereal periods. However, asteroids' rotation periods vary slightly when viewed from the Earth, owing to their relative motions, and the periods calculated from this viewpoint are known as the asteroids' synodic periods. Observations of an asteroid over a recorded span of a few months will show that a particular feature in its lightcurve will be observed to occur either slightly earlier or later than is theoretically expected. This shift in the asteroid's synodic period is due in part to the direction of the asteroid's rotation, and by measuring the direction of the shift it is possible to determine the asteroid's sense of rotation. Because asteroids have not undergone a substantial amount of geological evolution, they contain many important relics from the early solar system. On the other hand, many asteroids have undergone an extensive amount of collisional evolution. Collisions 9

10 are an important process in the formation and evolution of our solar system. The energies associated with collisions are much greater than can be reproduced in laboratory experiments, so by studying asteroid families, much can be learned about the physics of collisions. Collisions can alter asteroids' dynamics as well as their topographies. It is theorized that the fragments formed by the disruption of a parent body take on the orbital characteristics of that parent body. These groups of fragments are referred to as asteroid dynamical families and were discovered by K. Hirayama in By plotting all the asteroids in the main belt in orbital element space, such as proper inclination or proper eccentricity versus semi-major axis, one can see these clusters of asteroids. Although over thirty such families have since been identified, it is questionable whether all of them are statistically significant. Also, only a few of the larger families have members whose compositions are consistent with having originated from the same parent body. Among these families are the three original Hirayama families: Themis, Eos, and Koronis. For the above reasons, it is prudent to focus our studies on one of the three original families. The Koronis family has proved to be a particularly interesting family to study. Studies by Binzel (1986, 1987) showed that the mean amplitudes of several Koronis family asteroids' lightcurves were larger than expected. One possible hypothesis for this result is that the Koronis family is sufficiently young that their spin-vector orientations have not yet been randomized by collisions in the asteroid belt. A further study by Slivan (1995) indicated that several Koronis family members do indeed have similar spin-axis orientations, and an approximate minimum family age of fifty million years was calculated. By studying the lightcurves of the asteroids 158 Koronis and 72 Bohlinia and noting the changes in their synodic periods, the goal of this project is to determine the directions of spin of these two Koronis family asteroids. The spin direction of 243 Ida, another Koronis family member, was determined by a flyby of the Galileo Spacecraft, but no data are presently available regarding the spin directions of other Koronis family members. This project is intended to contribute to the growing collection of rotational data on Koronis family members and help provide an explanation for the unusual properties previously observed. 1

11 Chapter 2 Observations Observations of the rotational lightcurve of 72 Bohlinia were made at the MIT Wallace Astrophysical Observatory (WAO) in Westford, Massachusetts between UT 1999 July 14 and UT 1999 October 16. Observations of 158 Koronis were made by Slivan at WAO between UT 1999 April 14 and UT 1999 June 14 and were processed and analyzed as part of this project. The observing circumstances for these data are listed in Tables A.1 and A Goals of the Observations This project is a part of a larger study of Koronis family members. The goal of the larger project is to evaluate numerous family members for their rotational information and then analyze the entire set of spin vector results for randomness. Determining the age of the Koronis family helps answer the fundamental question of how often collisions produce families. Given a parent body with a certain angular momentum, the fragments produced in the disruption of this body are likely to retain some of that angular momentum. If a family is young, then its members may have common angular momentum results, such as spin directions and spin-vector orientations. An old family should have quite randomized rotational properties due to both large and small subsequent collisions. The goal of the observations carried out in this project is to contribute to the larger data set on Koronis family rotational dynamics. 2.2 Selection of Targets Both 158 Koronis and 72 Bohlinia were chosen as targets for this project in part because it was determined by Slivan that their rotational lightcurves could be successfully observed from WAO. Due to the often unreliable conditions at WAO, this needed to be determined before observations were attempted as part of an undergraduate thesis 11

12 project. The two asteroids were also chosen based on their coordinates during the summer and fall of 1999, the time period when the observations were planned to take place from WAO. 2.3 Instrumentation and Observation Techniques The on-chip differential photometry of 72 Bohlinia during the summer of 1999 was accomplished at WAO on the.61 m telescope using the PCCD camera system. The system had a 5:1 focal-length-reduction which yielded an effective focal ratio of f/3.33 and a plate scale of about 2.5"/pixel with a corresponding field size of approximately 15' x 2'. Due to the unavailability of the PCCD in the fall of 1999, a Photometrics STAR1 CCD camera was used on the.61m WAO telescope instead. That configuration yielded a field size of 15.7' x 23.5' with a corresponding image scale of approximately 2.3"/pixel. Because the STAR1 controls were located in the dome with the telescope, observations were more difficult and painstaking than with the PCCD, which was located in a separate room than the telescope. A problem with the STAR1 system, previously noted by Slivan (1995), was that the system's exposure clock hung up one second for every 64 seconds during exposures. As a result, the integration time on the STAR1 had to be set to 266 seconds in order to expose 72 Bohlinia for the desired 27 seconds. Ephemerides were generated using JPL's Ephemeris Generator web page at Prior observations made by Slivan indicated that successful collection of asteroid rotational data is not possible when the moon is illuminated more than 86% or is located less than 26 degrees away from the target. The rise and set times of the target for each desired night were computed by using the calc-altitude and timeofalt applications written by Slivan. Requests for time on the WAO.61 m telescope were made using this information, and luckily most of the time that was requested was granted for the project. Asteroid finder charts were made using the HST Guide Star Catalog CD-ROMs and Pickles program. Transparent overlays showing the outlines of the CCD image fields at the scale of the Pickles charts were used to select the specific locations of the fields. On most nights the fields were chosen by the locations of possible on-chip comparison 12

13 stars. However, 72 Bohlinia was at a stationary point in 1999 July, so one field for the entire month was chosen such that the same comparison star could be used on all the different nights. At a stationary point, the relative motions of the Earth and the asteroid exactly cancel out, making it appear as if the asteroid is not moving against the background of the stars. Figure 2-1 illustrates this concept by showing the positions of 72 Bohlinia from UT 1999 July The target each night was acquired at the telescope as soon as possible and successful observations were possible approximately 3 minutes into astronomical twilight. With the PCCD system, the target was acquired by using the continuous exposure and readout mode by locating bright stars in the area of the target field. This mode was not available with the STAR1 system, so locating the target took longer than expected. Once acquired, the target was positioned such that it was not in a known bad area of the CCD chip, such as in the shadow from the filter wheel mount. Imaging continued until the target was too low in the sky, the sky background became too bright due to twilight, or the sky became overcast. Some darks and zero-biases were taken during the course of the night when the field was temporarily obscured by clouds, but usually the calibration frames were taken at the end of each night after the target was no longer observable. Zero-bias, five second dark, and flat field frames were taken each night observations were performed. Longer dark frames, usually 27 seconds (the same integration time as most of the data images), were taken only on the first night in a series of observations and used to process all the images from that particular run. Most nights were concentrated on observing the differential lightcurve, so the telescope field did not have to be changed during the night. On the nights when standard star photometry was attempted in addition to lightcurve observations, field changes were done as quickly as possible to minimize gaps in the lightcurve. Landolt star Li was chosen because its color is similar to that of Koronis family members, and its coordinates were near those of the target. 13

14 + File : 72 Bohlinia July Pickles 4.11, by James McCartney, docs: Barbara McArthur, Univ. of Texa VI: Ra: 23h 32m 45.67s Dec: -5 54' 19.2" Roll:." Orient: 67.64* Veh.Roll: * AntiSun: 18* Moon: 128* Plate Roll: Tobs: /1/1.5 Tcat: /1/1.5 Now: /5/13 16:55:31 2' 1 '-1 ' -2'' *... o Figure 2-1: Positions of 72 Bohlinia from UT 1999 July

15 There were some minor technical problems encountered while using the WAO.61 m telescope. As the telescope tracked throughout the night, the filter wheel became unsecured in its mount. Since observations were being made in only one filter, at the beginning of each night the filter wheel was anchored in the R filter position with electrical tape. Another problem that was encountered was the backlash in the east and, to a lesser extent, in the south. When positioning on a field using the control paddle, it was necessary to overshoot the field in the east and south directions so that the last buttons used were the ones that moved the telescope west and north. Otherwise, the telescope would not stay fixed on the set coordinates, but rather drift slowly towards the east and south, causing the images to smear. Also, there was a problem writing several image files to disk using the STAR1 system. Although three full nights of observations were carried out in 1999 October, only one and a half nights of data were saved properly. Unfortunately, this was not discovered until those three nights of observations had been completed. Due to several factors, including clouds, appulses, and technical malfunctions, many data points and some entire nights of data were not used in the final lightcurve plots. Even if conditions were not ideal, observations were attempted on every scheduled night in which there was any possibility of gathering data. Table 2.1 shows the total number of nights allocated on the WAO.61 m telescope for the project, the total number of nights in which lightcurve data were collected, the percentage of nights that yielded useful data with respect to the total number of allocated nights, and the percentage of lightcurve data points that were accepted into the final solution with respect to the total number of lightcurve data points taken for each month. The percentages of accepted lightcurve data points for 1999 June and October are particularly low due to several appulses and computer malfunctions, respectively. 15

16 Table 2.1: Assignment and Use of Observing Time Month # of nights Total # of nights % of nights that % of lightcurve (in 1999) allocated data were yielded useful data points collected data accepted April N/A 3 N/A 78 June July August October The observations were by far the largest and most difficult part of this project. In order to ascertain that the desired portions of the rotational lightcurves were being successfully acquired, data from each night were processed the following day. During 1999 July, there were a surprisingly large number of nights in Westford, MA that were clear enough to attempt observations. Consequently, the observer's life for approximately two weeks consisted solely of going to WAO in the evening, observing until dawn, sleeping for a few hours, processing the data from the previous night, and then returning to WAO again. After about a week, the stress of this routine became slightly overwhelming, and Slivan observed for a night in order to alleviate some of the primary observer's exhaustion. 2.4 Data Analysis Procedures Image processing The images taken with the PCCD were written to FITS format directly, but those taken with the STAR1 had to be converted to FITS format by using the ccd2fits application written by Slivan. All of the images were processed using IRAF. The data images were corrected for the readout bias, dark current, and flat fielding as follows. For each night of data, the zero-bias frames were averaged and subtracted from the averaged dark and flat field frames. Then the zero-bias corrected five-second dark frames were subtracted 16

17 from the flat field frames. The averaged zero-bias frames and zero-bias corrected longer dark frames were then subtracted from the data images. The data images were also divided by the averaged zero-bias and dark corrected flat field frames. It was discovered that the images processed in the above manner were not properly flattened. This was mostly due to a large reflection in the center of all the images which the normal method of flat field correction was not taking into account. An additional method of flattening the images was devised by Slivan to correct this problem. This method involved applying a sky correction to each image then dividing each of those images by their mean pixel values and saving them as new images. The final images were calculated by dividing the original images by the new images. The instrumental magnitudes for the target objects were obtained from the images by performing synthetic aperture photometry using the apphot package of IRAF. The signal from an object was measured by IRAF by summing the signals of all the pixels in the synthetic aperture then subtracting the signal contributed by the brightness of the sky background; the sky brightness was calculated by summing the signals from the pixels in a ring-shaped annulus around the target object. The size of the aperture was determined separately for each night of data by examining the point-spread functions of the target from several different data images and set just past the point where the signal blended into the background noise. The recommended aperture settings from Notes on CCD Photometry (Slivan, 1998) were used as a guide to set the inner radius, thickness of the annulus, and size of the centering box. Once an aperture was chosen, the same settings were used for all the images on a given night of data. Choosing an aperture size was crucial in determining the final lightcurves. An aperture which was too small would exclude some signal from the target and falsely decrease the errors in the lightcurve; an aperture which was too large, on the other hand, would include background contributions and unnecessarily increase the errors in the lightcurve. Table A.3 lists the final IRAF aperture setting which were chosen for each night. Occasionally, an appulse would occur in which the motion of the target asteroid brought it too close to one or more background stars. In these cases, synthetic aperture photometry could not be accurately performed without first removing the star(s) in question from the images. As long as the point-spread functions of the asteroid and back- 17

18 ground star(s) were separable, this method could be implemented. The procedure of removing background stars by using IRAF DAOPHOT is described in detail in Advanced Notes on CCD Photometry (Slivan, 1999). Once the nearby background star(s) were removed from the images, the instrumental magnitudes of the target were extracted by using the method described in the preceding paragraph. Two on-chip comparison stars and four check stars were chosen separately for each night, although whenever possible the fields were chosen to overlap so that the same comparison star could be used. The coordinates, as well as approximate V magnitudes from the HST Guide Star Catalog, of the comparison stars are listed in Table A.4. The check stars were used to monitor the conditions throughout the night and determine a standard deviation for the data. Images with the lowest background and highest standard deviation from each night were examined in order to eliminate any overexposed stars. Stars with pixel values between approximately one-half and three-quarters that of saturation were considered as possible comparison and/or check stars. The pointspread functions of these stars were examined, and the two brightest candidates were selected as comparison stars. Optimally, the four check stars would have a range of brightnesses which spanned the amplitude of the lightcurve, but often this was not possible. When there was a shortage of acceptable stars on the chip, one or both of the comparison stars were also used as check stars. On occasion, a star that was chosen as a comparison or check would appear to be variable; this could have been due to either intrinsic variability or color differences. By comparing the differences in magnitude between the comparison and check stars, it was often possible to detect which star(s) might be intrinsically variable. To be certain that none of the comparison stars chosen were variable, the stars in question would be eliminated, and new ones would be chosen. Although Slivan was the primary observer of 158 Koronis during both 1999 April and June, the data were processed as part of this project in the manner described above. The lightcurve of 158 Koronis was observed at WAO using the same telescope and camera system that was used to observe 72 Bohlinia during 1999 July and August. 18

19 2.4.2 Lightcurve techniques and observational results In order to plot a rotational lightcurve, the instrumental magnitudes need to be measured at the same integration times. When the integration times vary during a night, a common exposure time must be chosen (conventionally, one second) and the magnitudes at that integration time need to be calculated. This was done by using the definition of magnitudes: mi - M 2 = -2.51og -- ) (2.1) where m and S are the magnitude and signal of the target, respectively. Also, corrections due to distance and changes in solar phase angle need to be applied to the instrumental magnitudes to yield reduced magnitudes. The equation for computing reduced magnitudes is given by: Mred = MAP--5log(rA) (2.2) where MAP is the target's approximate apparent visual magnitude, r is the target's apparent heliocentric range, and A is the target's apparent range; both r and A are measured relative to the observer. Note that MAP takes into account the complicated systematic changes due to a changing solar phase angle. The time light from the target takes to reach the Earth needs to be subtracted from the time variable of each data point. After all these corrections are applied, the difference between the target's and comparison star's reduced magnitudes can be plotted versus UT time to produce a lightcurve. The values of MAp r, A, and the one-way light-time can be found on the target's ephemeris along with other useful quantities. Often, there is more than one night's worth of data for a particular target, and the different data sets need to be composited in the following manner. First, a particular UT time needs to be selected as a reference for all the data points; this is most commonly chosen to be either hours UT of the first night data was collected or the UT time of the first data point. All the other data points must be related to this reference time by determining how many UT hours have elapsed since that time. If different comparison stars are used, their relative difference in magnitude must be taken into account and corrected 19

20 for as well. Finally, a composite lightcurve is made by plotting all the data on the same UT time and magnitude scale. The synodic periods of 158 Koronis and 72 Bohlinia had been determined prior to these observations (Slivan, 1995) to be and hours, respectively. Individual lightcurves were reduced for each night of observations and plotted using those initial periods. The individual lightcurves accumulated from each observing run were then combined to yield composite lightcurves for the months of 1999 April, June, July, August, and October (see Figures A-1 to A-5). All lightcurves were plotted using the magplot application written by Slivan, which was particularly useful in making the composite lightcurves. The pieces of the composite lightcurves from 1999 June and August do not line up on the vertical axes because it was not possible to perform comparison star photometry during the allotted time. The data from the six nights of useful observations taken in 1999 July did not overlap precisely within the error bars when plotted using the initial synodic period of 8.9 hours. Since the data were taken over the course of approximately one week and used the same comparison star, the bad fit could be corrected by slightly modifying the period. Because the asteroid was at a stationary point during the course of those observations, the period observed during 1999 July was the sidereal period of 72 Bohlinia. A new sidereal period of hours was determined by altering the initial synodic period in small increments and noticing when the data just fit together. In constructing the composite lightcurve, hours (the sidereal period) was used as the refined synodic period. The initial synodic period of 158 Koronis was confirmed by the observations. 2.5 Uncataloged Asteroid Discovery During the course of the lightcurve observations, a faint moving object was discovered in several of the images for the night of UT 1999 August 16. It turned out that this object was not catalogued, so further observations of this "mystery" object were made on UT 1999 August 19. Astrometric calculations were performed in order to determine the coordinates of this object on the two dates it was observed, and those coordi- 2

21 nates were subsequently sent to the IAU Minor Planet Center. Thanks to much help from Schelte J. Bus, the new asteroid has been assigned the designation 1999 QQ2 (in Minor Planet Circular 35812). It is a mainbelt asteroid with a diameter of probably about 5km. Further observations of the asteroid are necessary before it can be assigned a catalog number. Table 2.2 lists its orbital elements from the IAU Minor Planet Center, and Figure 2-2 shows its position on UT Table 2.2: 1999 QQ2 Orbital Elements Epoch 2 Feb. 26. TT = JDT Williams M (2.) P Q n Peri a Node e.2572 Incl P 4.17 H 14.4 G.15 U 3 21

22 1c Bohlinia (IRAF). I P. L <1.291e+41 * ~ 'a 41 4 I 'I 6 * I A a a. a I U 4 9 & 4 a a 4 a. *4 S a -a I. 4, a q 4 q * d I I S I I I cd)17.1(x)i - Bohlinia SAOimage lcrcspo@uranus.miledu Mon May 15 13:3:29 2(XX) Figure 2-2: Position of 1999 QQ2 on UT

23 Chapter 3 Analysis of Lightcurves 3.1 Overview of Photometric Astrometry Photometric astrometry is the method of measuring the time intervals between a particular lightcurve feature that is observed at different geometries (Magnusson, 1989). Assuming the target's spin axis is not perpendicular to the Earth's, the shift in the target's synodic period will increase as the period of time between successive observations increases. The primary goal of this project was to observe the lightcurves of 158 Koronis and 72 Bohlinia several times over the course of a few months with small enough errors to be able to notice a shift in time in their synodic periods. A particular maximum for each lightcurve was chosen as a reference point from which to measure any potential shift so that potential shadowing effects in the minima would not be a concern. The direction of such a shift, if observed, would directly correspond to the direction of rotation of the target about its axis. An increasing synodic period, or a particular lightcurve feature being observed later in time than theoretically expected, would indicate a prograde period; a decreasing synodic period, or a particular feature being observed earlier in time than expected, would indicate a retrograde period. Once such a shift was found, it could be measured to yield the rotation rate of the target. 3.2 Method I n order to measure a shift in the synodic period of an asteroid, the same piece(s) of the asteroid's rotational lightcurve must first be observed at different relative geometries to the Earth. Once the lightcurve is obtained at two different positions in the target's orbit, the pieces should be composited by the method described in section Although it is not necessary to have the relative differences in the comparison stars' magnitudes, it is helpful since then there is no vertical shift in addition to the time shift to worry about. It is also advantageous to obtain the full rotational lightcurve at both geom- 23

24 etries so that a more accurate calculation of the shift can be performed. The amount of shift expected in the synodic period is given by: P ExpectedShift = (3.1) where P is the target's synodic period and is the angle between the different positions in its orbit. From the composite lightcurve, the shift can be measured manually by comparing two lightcurves or numerically by using a cross-correlation program. These two methods will be discussed further in sections and Koronis During the month of 1999 April, one of the two rotational lightcurve maxima was recorded. In 1999 June, an attempt was made to record that same lightcurve maximum again. Pieces of the maximum, each approximately one third to one half of the full maximum measured from trough to trough, were recorded over the course of 5 nights. Because only two sets of these nights of data used the same comparison stars, the result was three pieces of the lightcurve maximum which were not corrected for their different relative brightnesses. The amount of time scheduled at WAO did not allow for the relative comparison star photometry, needed in order to assemble the maximum, to be performed. However, since the goal of this project was to determine the direction of rotation of the two asteroids, fixing all of the data to the same brightness scale was not absolutely necessary, although it would have further constrained the solution. The data from 1999 June were added to the composite from 1999 April by making the corrections described in section and using hours UT on UT 1999 April 14 as the reference time (see Figure A-6). In order to compare the 1999 April composite to the three 1999 June segments, the brightness offsets were estimated and corrected. However, adjusting the brightness offsets alone did not account for the time offsets; the 1999 June segments were shifted earlier in time with respect to the 1999 April composite. It was attempted to slightly modify the synodic period to account for the misalignment, however, this only caused the composite lightcurve to deteriorate. By making a second copy of the composite lightcurve on a transparency, it was possible to manually superimpose the 1999 June lightcurve onto the 1999 April one. The 24

25 1999 April composite was held fixed while the 1999 June segments were shifted in time until the best fit with the 1999 April data was found. The segments from UT 1999 June 7, 8, and 14 did not help constrain the solution, so only the segments from UT 1999 June 4, 5, and 11 were used in finding the result. However, due to the magnitude of the error bars and because the vertical offsets from the 1999 April composite and the 1999 June segments were not fixed, possible values of the time shift from 1999 April to June ranged from 3 to 56 minutes. This final range of shifts was determined from the overlap of the shifts calculated separately for the data from UT 1999 June 4, 5 and Bohlinia The quantity and quality of data collected for the target at WAO during the month of 1999 October were not sufficient to calculate a shift from 1999 July. Instead, data taken by Slivan in 1999 October and November 1 were used in conjunction with the data from 1999 July to compute the shift. Although no relative comparison star photometry was performed for this data set, the full rotational lightcurves were obtained for the target in both 1999 July and October/November. The data from 1999 July and October/November were composited by the method described in section and using hours UT on UT 1999 July 14 as the reference time (see Figure A-7). The lightcurve from 1999 October/November was found to be shifted earlier in time compared to the lightcurve from 1999 July. Note that the direction of this shift is the same as that found for 158 Koronis. This shift was still apparent even when estimated corrections for the brightness offsets were applied; adjusting the rotation period caused each of the composites to fall apart, and the time offset was still present. Therefore, the two lightcurves were superimposed as described in the previous section in order to determine the approximate magnitude of the shift. Since the full lightcurves for each month were available, a cross-correlation algorithm was used to more precisely determine the amount of the shift. A smoothing spline 2 1. Data was obtained at the Colgate University Foggy Bottom Observatory in Hamilton, New York using a.4m reflector at its f/13.9 Cassegrain focus. A Photometrics PM3 nitrogen-cooled CCD camera and R filter were also used, and IRAF was used at MIT for all data processing and synthetic aperture photometry. 2. The application used was adapted by Dave Schleiker at Lowell Observatory. 25

26 was fitted to each of the two lightcurves so that the small variations due to noise were eliminated but the overall shape and features were retained. The splines were necessary in order to use the fast Fourier transformation routine in IDL which requires evenly sampled curves. The two smoothed lightcurves were sampled at three minute intervals, and the greatest correlation between them was found to be when the 1999 July curve was held fixed and the 1999 October/November curve was shifted forward approximately 2 minutes in time. Although the data from 1999 August and October from WAO were not used in calculating the final solution, they were consistent with the "earlier" direction found for the shift. 3.3 Results and Discussion The expected amount of shift for each target was calculated by using equation 3.1; for each target, was computed as the difference between the average of the target's observer-centered ecliptic longitude of the first month and second month in which data were collected. For 158 Koronis, the expected shift was found to be 21.4 minutes, while for 72 Bohlinia the expected shift was computed to be 19.5 minutes. Both of these expected shifts are in agreement with the directions of shifts determined during this project. A mathematical analysis was performed on the 158 Koronis data in the same manner as described in section which confirmed the amount and direction of the shift found in section The results suggest no ambiguity in the direction of the shifts. As previously mentioned, however, the amount of the shift for 158 Koronis has a range of possible values from 3 to 56 minutes. This solution is not consistent with the expected value of the shift. Thus, this exaggerated shift is most likely due to errors in the 1999 June lightcurve fragments and the fact that a complete lightcurve from 1999 June was not available. For 72 Bohlinia, the result obtained from the numerical analysis is the point at which there was the highest degree of correlation between the two lightcurves. Although the result is approximately 2 minutes, due to the time resolution in sampling the lightcurves, the pre- 1. The observer-centered ecliptic longitude of the target's apparent position was taken from the target's ephemeris and was already corrected for light-time, the gravitational deflection of light, and stellar aberration. 26

27 cise value of highest degree of correlation is not known. However, it definitely lies between 18 and 24 minutes. Since both of the targets' synodic periods appeared to be decreasing, each has a retrograde sense of rotation. There is effectively no uncertainty in the senses of rotation since they are derived directly from the directions of the shift as described in section 3.2. Due to a flyby by the Galileo Spacecraft in 1993, the sense of rotation of 243 Ida is also known to be retrograde. 27

28

29 Chapter 4 Conclusions and Future Work The goal of this project was to determine the senses of rotation for the Koronis family asteroids 158 Koronis and 72 Bohlinia. Usable data from 7 nights over 3 months were obtained for 158 Koronis; for 72 Bohlinia, usable data were obtained during 16 nights over 5 months. In both cases, the synodic periods were found to be decreasing over tirne, indicating that both asteroids have retrograde rotations. This correlates interestingly with the retrograde rotation for the third measured Koronis family member, 243 Ida. By using a Binomial distribution, it is possible to calculate the probability that three out of three Koronis family members would randomly have retrograde senses of rotation. The Binomial distribution is given by: P(x) = (N! x N-x (4.1) x! (N - x)! where P(x) is the probability of exactly x successes in N trials, and p is the probability of success on any one trial. For the case where three out of three asteroids have the same sense of rotation, x=n=3 and p=.5. Therefore, the probability that all three asteroids randornly have the same sense of rotation is 12.5%, indicating there is an 87.5% probability the results are not random. I n standard hypothesis testing, a result with a probability >9% is considered possibly significant and >95% is considered significant. The current data sample for Koronis family members (N=3) is too small to reach these levels of significance, but the results are encouraging. For example, if a fourth Koronis family member is observed to be retrograde, the probability that the results are non-random increases to 93.75%. A fifth observed retrograde Koronis family member would further increase the probability to % and would be considered statistically significant. The current results are consistent with the hypothesis that many Koronis family members "remember" the angular momentum of the parent body. If this is the case, then 29

30 the Koronis family is geologically quite young. However, future observations of other Koronis family members' spin directions need to be made in order to confirm this hypothesis. Although not realized at the onset of this project, it is recommended to observe each target's full lightcurve rather than just the maxima at two different geometries. Having full lightcurves at both aspects allows a more accurate shift to be calculated. 3

31 Appendix Table A.1: Observing Circumstances for 158 Koronis 32 Table A.2: Observing Circumstances for 72 Bohlinia 33 Table A.3: IRAF Aperture Settings Used in Data Processing 34 Table A.4: Coordinates of On-Chip Comparison Stars 35 Figure A-1: 158 Koronis April 36 Figure A-2: 158 Koronis June 37 Figure A-3: 72 Bohlinia July 38 Figure A-4: 72 Bohlinia August 39 Figure A-5: 72 Bohlinia October 4 Figure A-6: 158 Koronis with Shift in Synodic Period from 1999 April to June 41 Figure A-7: 72 Bohlinia with Shift in Synodic Period from 1999 July to November 42 31

32 Table A.1: Observing Circumstances for 158 Koronis UT Date R.A. m s) Dec. (' (J2.O) (J2)Logtd " Ecliptic Filter Detector Observer R PCCD Slivan R PCCD Slivan R PCCD Slivan R PCCD Slivan R PCCD Slivan R PCCD Slivan R PCCD Slivan R PCCD Slivan R PCCD Slivan 32

33 Table A.2: Observing Circumstances for 72 Bohlinia UT Date R.A. (h m s) Dec. ( ) Ecliptic Filter Detector Observer (J2.) (J2.O) Longitude R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Slivan R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Crespo R PCCD Crespo R STAR1 Crespo R STARI Crespo R STARI Crespo R PM3 Slivan R PM3 Slivan R PM3 Slivan R PM3 Slivan R PM3 Slivan 33

34 Table A.3: IRAF Aperture Settings Used in Data Processing UT Date Aperture (pixels)

35 Table A.4: Coordinates of On-Chip Comparison Stars UT Dates Observed R.A. (h m s) Dec. (' ") Approximate (J2.) (J2.) V Magnitude 1999 April 14, April June 4, June 7, June June July 14-16, August August 1, August October 12,

36 158 Koronis (P= hr) I a I +<D O4%6I S UT hours on 1999 Apr 14 1] 1999 April 14 > 1999 April 18 A 1999 April 21 Figure A-1: 158 Koronis April 36

37 158 Koronis (P= hr) / UT hours on 1999 Jun 4 15 I. E] 1999 June 4 KQ 1999 June 5 A 1999 June 7 V 1999 June 8 M 1999 June 11 Figure A-2: 158 Koronis June 37

38 - I I 72 Bohlinia (P=8.92 hr) I I I I I III d C S-3-47 mwm < writt 47If I I o UT hours on 1999 Jul 14 E 1999 July 14 <> 1999 July 15 A 1999 July 16 V 1999 July 2 M 1999 July 21 x 1999 July 22 Figure A-3: 72 Bohlinia July 38

39 A I 72 Bohlinia (P=8.92 hr) I a a a a {, ~ I I I I I I UT hours on 1999 Aug August 9 K> 1999 August 13 A 1999 August 16 Figure A-4: 72 Bohlinia August 39

40 72 Bohlinia (P=8.92 hr) II I I %m 4* 'U I I I I I I I o UT hours on 1999 Oct October October 13 Figure A-5: 72 Bohlinia October 4

41 / 158 Koronis (P= hr) I I 'U ,,^~ 9 44' ~II ' UT hours on 1999 Jun 4 L. * 1999 April 14 x 1999 April 18 X 1999 April 21 o 1999 June 4 < 1999 June 5 A 1999 June 7 V 1999 June 8 M 1999 June 11 Figure A-6: 158 Koronis with Shift in Synodic Period from 1999 April to June 41

42 72 Bohlinia (P=8.92 hr) I I S $ pp.1, t r 1 me I I - I ~ I I I o UT hours on 1999 Jul BOTTOM TOP n 1999 July 14 E 1999 October 3 c 1999 July 15 1 l999 October 31 A 1999 July 16 A 1999 November 1 v 1999 July 2 V 1999 November 5 X 1999 July 21 M 1999 November 8 x 1999 July 22 Figure A-7: 72 Bohlinia with Shift in Synodic Period from 1999 July to November 42

43 References Binzel, R. P Collisional Evolution in the Asteroid Belt: An Observational and Numerical Study Ph.D. thesis, University of Texas at Austin. Binzel, R. R A photoelectric survey of 13 asteroids. Icarus 72: Magnusson, P., Barucci, M. A., Drummond, J. D., Lumme, K., Ostro, S. J., Surdej, J., Taylor, R. C., and Zappala, V Determination of pole orientations and shapes of asteroids. In Asteroids //, ed. R. P. Binzel (Tucson: University of Arizona Press). p Reinsch, C. H Smoothing by Spline Functions. Numerische Mathematik 1: Slivan, S. M Spin-Axis Alignment of Koronis Family Asteroids. Ph.D. thesis, Massachusetts Institute of Technology. Slivan, S. M Notes on CCD Photometry Unpublished course notes for the MIT Observational Techniques of Optical Astronomy. Slivan, S. M Advanced Notes on CCD Photometry - Salvaging Appulsed Asteroid Data from an Otherwise Uncrowded Field. Unpublished notes written at the MIT Department of Earth, Atmospheric, and Planetary Sciences. 43