Icarus 257 (2015) 207–216

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Icarus

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Vesta’s missing moons: Comprehensive search for natural satellitesof Vesta by the Dawn spacecraft

http://dx.doi.org/10.1016/j.icarus.2015.04.0380019-1035/� 2015 Published by Elsevier Inc.

⇑ Corresponding author at: Planetary Systems Laboratory, Code 693, GoddardSpace Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, United States.

E-mail address: lucy.mcfadden@nasa.gov (L.A. McFadden).

Lucy A. McFadden a,⇑, David R. Skillman a, Nargess Memarsadeghi a, Jian-Yang Li b, S.P. Joy c,C.A. Polanskey d, Marc D. Rayman d, Mark V. Sykes b, Pasquale Tricarico b, Eric Palmer b,David P. O’Brien b, Stefano Mottola e, Uri Carsenty e, Max Mutchler f, Brian McLean f, Stefan E. Schröder e,Nicolas Mastrodemos d, Conrad Schiff a, H. Uwe Keller g, Andreas Nathues h, Pablo Gutiérrez-Marques h,C.A. Raymond d, C.T. Russell c

a NASA Goddard Space Flight Center, Greenbelt, MD 20771, United Statesb Planetary Science Institute, Tucson, AZ 85719, United Statesc IGPP, UCLA, Los Angeles, CA 90095, United Statesd Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, United Statese DLR – German Aerospace Center, Institute of Planetary Research, Berlin, Germanyf Space Telescope Science Institute, Baltimore, MD 21218, United Statesg Institut für Geophysik und Extraterrestrische Physik (IGEP), University Braunschweig, Germanyh Max-Planck Institute for Solar System Research, 37077 Göttingen, Germany

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 August 2014Revised 25 March 2015Accepted 29 April 2015Available online 5 May 2015

Keywords:Asteroid VestaAsteroids, dynamicsSatellites of asteroids

Earth-bound searches for natural satellites of 4 Vesta have been reported since 1987. With use of tech-nological advances and observing capability has come a reduction in the detectable size of a possiblesatellite. The Dawn mission brought a small camera close to Vesta itself. In our search, which was carriedout with a comprehensive data acquisition strategy and by experienced searchers, we find no satellites toa detection limit as small as 3-m radius. Various observation and analysis strategies are discussed indetail. It is now time to factor the null result of this search into the context of satellite formation amongother main belt asteroids and to conduct dynamical modeling to explore the suspected forces contribut-ing to the absence of satellites at Vesta today.

� 2015 Published by Elsevier Inc.

1. Introduction

Within the Solar System many objects have natural satellitesthat are bound to the primary body as it also orbits the Sun.Earth’s moon, the Outer Planets’ satellite systems, some KuiperBelt Objects (KBOs) (Veillet et al., 2002; Noll et al., 2008) andeven small near-Earth objects (NEOs) (Margot et al., 2002) areexamples. The presence or absence of a satellite has implicationsfor the primary body’s collisional and dynamical history, and per-mits measurement of mass, size and bulk density. Within theMain Asteroid Belt, almost 100 asteroids with co-orbiting, smallerbodies within the gravitational sphere of influence (SOI, theregion around an asteroid where the primary gravitationalinfluence on an orbiting body is that body) (e.g. Bate et al.,

1971) of the larger asteroid are known (e.g. Johnston, 2014;Merline et al., 1999, 2002). We compare Vesta’s gravitationalSOI with Earth, Jupiter, Ceres, a NEO and Pluto in Table 1. Cerescontains approximately a third of the current asteroid belt bymass (e.g. O’Brien and Sykes, 2011), with Vesta being the secondmost massive. Vesta has a reasonably-sized SOI relative to otherbodies with natural satellites, and if the conditions exist forcapture or retention of ejecta from an impact on Vesta, one mightexpect satellites to exist if not now, then in the past. 1999 KW4, asmall Earth-crossing binary system (Ostro et al., 2006), has a SOIthat is orders of magnitude smaller than Vesta’s. Further, its valuevaries by almost a factor of 2 throughout its orbit, yet its satelliteremains. Dynamical models of the formation of the asteroid beltrequire migration of bodies from the Kuiper Belt to populatethe asteroid belt (Levison et al., 2009; Walsh et al., 2012) andmany KBO’s are multiple systems. Satellite capture requires amechanism in which energy is lost to match the orbital velocityof the primary.

Table 1Comparison of the gravitational sphere of influence (SOI) for some planets, asteroids and dwarf planets.

Object name Mass (kg) Distance from Sun (km) Radius (km) Sphere of influence (SOI)a (km) Relative SOIb

Sun 1.99 � 1030 – – – –Earth 5.97 � 1024 1.50 � 108 6378.14 9.245 � 105 145Jupiter 1.90 � 1027 7.79 � 108 69911.00 4.822 � 107 690Vesta 2.59 � 1020 3.54 � 108 262.70 3.937 � 104 150Ceres 9.34 � 1020 4.14 � 108 476.0 7.684 � 104 1611999 KW4 2.4 � 1012 9.61 � 107 1.5 6.5 4.361999 KW4 (perihelion) 2.4 � 1012 1.62 � 108 1.5 11.0 7.361999 KW4 (aphelion) 2.4 � 1012 2.99 � 107 1.5 2.04 1.36Pluto 1.31 � 1022 5.87 � 109 1184 3.13 � 106 2644

aSphere of influence rA ¼ dA

mAmSun

� �25, where dA is distance from Sun, mA

mSunis mass relative to the Sun.

b SOI scaled to body’s radius.

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Binzel and Xu (1993) located asteroids with similar spectral sig-natures as Vesta’s lying in its orbital plane with semi-major axesbetween the m6 secular resonance with Saturn at 2 AU and the3:1 Kirkwood Gap at 2.5 AU. These asteroids comprise the dynam-ical Vesta family. Hubble Space Telescope images and subsequentanalysis of Vesta’s shape (Thomas et al., 1997) suggested a largebasin that was subsequently resolved into two very large basins,Rheasilvia and Veneneia, imaged by Dawn’s Framing Camera (FC)as the spacecraft approached and orbited Vesta in 2011–2012(Jaumann et al., 2012; Schenk et al., 2012). Ejecta from these basinslikely produced the Vesta family (Marzari et al., 1996; Zappalàet al., 1984). Dynamical modeling prior to the Dawn mission sug-gested an impact by a 42 km body, 1 billion years (byr) ago(Asphaug, 1997). Remarkably, crater size frequency distributionssupport this age (Schenk et al., 2012; Marchi et al., 2012). An alter-nate and older age determination of these basins (3.5 and 3.7 byr)is presented by Schmedemann et al. (2014), assuming a lunar-likecrater production function. Chaotic dynamics and secular pertur-bations (Wisdom, 1985) have resulted in fragments from Vesta col-liding with Earth, surviving passage through Earth’s atmosphereand being found as meteorites; the Howardite–Eucrite–Diogenite(HED) group (McSween et al., 2011). There are samples of Vestain the terrestrial meteorite collection, there are craters formedfrom collisions and reaccumulation of ejecta fragments on Vesta’ssurface (e.g. Russell et al., 2012; Jaumann et al., 2012).

Given the large amount of ejecta from Vesta and the varieddynamical outcomes that resulted, it is logical to ask if any frag-ments entered into orbit around Vesta, either directly or after are-encounter. The above considerations lead us to ask if there areany satellites remaining in Vesta’s orbit today?

Direct imaging (Gehrels et al., 1987), coronographic imaging(Gradie and Flynn, 1988), speckle interferometry (Roberts et al.,1995) and imaging with Hubble Space Telescope (McFaddenet al., 2012) have been used to search for satellites orbiting Vestain the past. None have been found to a previously reported sizelimit of 22 m radius. Until now, the region inside of 14 Vesta radii(�3500 km) had not been searched due to scattered light fromVesta. Is it due to chance that neither satellites nor a debris fieldare remnant in orbit around Vesta today? Were the instrumentsthat searched for satellites in the past inadequate to detect any-thing orbiting Vesta? Or has the past collisional history removedany object or objects that once may have been in orbit aroundVesta?

The Dawn spacecraft spent more than a year at Vesta and wesearched again for natural satellites. We designed a search thatwould improve upon past searches by looking closer to Vesta thanpossible in previous efforts. In this paper we describe the twoobservational sequences acquired for the satellite search usingDawn’s FC and report processing and preparation for search bythe team of satellite searchers. Seven observers searched and

reported that no satellites were found. However, we did find mov-ing objects including background asteroids, cosmic rays and some-thing close to the camera and moving fast that is probably debrisfrom the spacecraft. Next, we determine the upper limits of detec-tion by implanting simulated objects with randomly chosen orbitsand magnitude into a subset of the satellite search images. Theobservers searched again and report their findings in Section 6.Upper limits of detection in the meter-size range are then calcu-lated assuming the same albedo and phase function as Vesta. Wediscuss our approach and consider changes for future satellitesearches in the final section and consider the implications for theabsence of satellites in the context of the impact and ejecta historyof Vesta in the discussion.

The mission’s approach phase included searching for satellitesaround Vesta for more than two months. During these sequences,Vesta was targeted on a regular basis and if there were a satellite,this was the time when it would most likely be observed and notocculted by Vesta itself. Our upper limit of detection duringapproach was an object 5.3 m radius assuming Vesta’s global geo-metric albedo of 0.38 (Li et al., 2013). During a dedicated satellitesearch mosaic, carried out at three different times, the limitingradius of detection was 3.1 m and 4.3 m for 20 s and 270 s expo-sures respectively. We discuss the reason for the reverse relationbetween detection limits and exposure times in Section 6. If anylarger collisional ejecta were in orbit around Vesta in the past, theyare not there now.

2. Observations and search approaches

The satellite search was carried out with Dawn mission’s FC(Sierks et al., 2011) an F/7.5 imager with a focal length of150 mm, 5.5� � 5.5� field of view and pixel size of 19.23 arcsec asdetermined using Astrometrica software (Raab, 2011). The clear fil-ter, designed for detecting stars, dust and the moon search, wasalways used to maximize photon collection and signal. Two dataacquisition schemes were used; (1) direct pointing at Vesta begin-ning at 1.24 million km range, and (2) acquisition of a dedicatedsatellite search mosaic. The data sets were processed and analyzedusing 5 different approaches, all of which complement each otherand result in an increased reliability of the search results. We dis-cuss the data acquisitions followed by the data processing that pro-duced searchable images.

2.1. Direct pointing

Direct pointing at Vesta served the project’s optical navigation(OpNav) requirements and for the satellite search, included 14acquisitions each consisting of 20 successive, 1.5 s exposurespointed at Vesta. These were also used to design the ion propulsion

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thrust sequences that put the spacecraft into orbit around Vestaand to determine exposure times and data compression settingsfor orbital science observations. There were two additionalsequences called Rotational Characterization 1 (RC1) andRotational Characterization 2 (RC2) to determine Vesta’s pole orien-tation. These sequences included ride along ‘‘OpNav’’ imaging con-sisting of alternating 0.008 s (for Vesta) and 1.5 s exposures (forstars), 36 in RC1 and 52 in RC2, taken within 3–6 min in time, ashorter interval than the 0.5–2.0 h of the ‘‘standard’’ OpNavsequences. We used the 1.5 s exposures to search for satellites.Images from each sequence were coadded and searched for thepresence of satellites. An example is shown in Fig. 1. Table 2 pre-sents observing circumstances at each OpNav and RC along withthe size of Vesta in pixels and the limiting detectable radiusderived from the experiment with implanted objects described inSection 5. The orbital period of satellites in circular orbit around

Fig. 1. Eighteen RC2 images scaled and coadded to enhance stars and possiblesatellites. A satellite, if detected, would have a trail in a different direction relativeto background stars and with the same number of detections as background stars,yet spaced according to its relative motion with respect to Vesta.

Table 2Observational circumstances during direct pointing satellite search with limiting magnitu

OpNava Date Heliocentric distance (AU) Range to V

1 2011-05-03T13:35 2.176 1,217,9912 2011-05-10T07:03 2.179 1,008,8023 2011-05-17T12:56 2.183 809,4384 2011-05-24T08:52 2.187 645,0245 2011-06-01T06:50 2.192 482,8376 2011-06-08T16:04 2.197 352,1657 2011-06-14T14:05 2.201 264,6838 2011-06-17T13:05 2.203 226,3139 2011-06-20T14:05 2.205 190,54010 2011-06-24:04:35 2.207 152,454RC1 2011-06-30T09:58 2.212 97,73013 2011-07-04T01:34 2.215 70,195RC2 2011-07-10T02:23 2.219 37,03016 2011-07-13T04:04 2.222 25,07217 2011-07-17T04:33 2.225 14,07318 2011-07-18T21:34 2.226 10,728

a Note that numbering of the OpNavs has gaps for the following reasons: OpNav11 wthrust time lost during safe mode status. There were OpNav sequences added to RC1 an

Vesta ranges from 1.77 to 159 h for orbits from 1 to 20 Vestan radii.The variation in the duration of the OpNavs allows for detection ofmotion of potential satellites across more than one pixel.

2.2. Satellite search mosaic

The satellite search mosaic images extended 5000 km (�20Vestan radii) from Vesta’s surface. This region is designated theoperational sphere in which the spacecraft orbited (Polanskeyet al., 2011). The goal was to search for objects smaller thanHubble Space Telescope’s limit of 22 m in radius (McFaddenet al., 2012) and closer to Vesta than previously searched (14Vestan radii). The first mosaic sequence was carried out beforeRC2, on 2011 July 9. At each image mosaic station, 4 sets of 3images with 1.5 s, 20 s and 270 s exposures respectively, com-manded at 5 s intervals were acquired (Fig. 2A). There are sixmosaic stations (Fig. 2B) with data collection at intervals of21 min each, with 10 min turn and settle periods between stations.A single mosaic took 2:45 h. This mosaic pointing and data acqui-sition was carried out twice before RC2 observations. Mosaic 3began after a complete Vesta rotation of 5.4 h and was completedon 2011, July 10, 8:17. The goal was to have order of magnitudescaling in the image exposure durations and image time separa-tions (Fig. 2C) because we are searching for objects with no knownconstraints in orbital characteristics other than being gravitation-ally bound to Vesta. As implemented, the time between the firstand second mosaic was 186 min and 785 min between the firstand third mosaic. A total of 216 images were commanded, twowere corrupt resulting in 214 usable images. The station pointingis listed in Table 3. For reference, a body orbiting close to Vestahas an orbital period of 1.77565 h, while an orbit at 20 Vestan radiihas a period of 452.12235 h (18.83843 days).

3. Data processing and search approaches

The satellite search team used multiple methods of processingand searching and the data were scanned by many sets of eyes,an important point given that we found no satellite to the detec-tion limits of the FC. Using different and independent approachesand searching with multiple and experienced eyes added certaintyto our results. We designed our processing schemes from previoussuccessful searches for satellites of Pluto (e.g. Steffl et al., 2006) andconsidered the capabilities of the FC and the spacecraft’s motion.Image processing and algorithms used for data processing are

de 10.7 as determined from implanted objects into OpNav 16.

esta (km) Phase angle (�) Vesta apparentsize (FC pixels)

Limiting detectableradius (m)

42.73 5.1 27042.47 6.1 22341.86 7.6 17840.92 9.6 14139.48 12.8 10437.15 17.6 7434.76 23.4 5433.36 27.4 4631.82 32.5 3829.76 40.6 2926.11 63.4 1823.57 88.3 1329.18 167.0 7.042.79 247.0 5.780.76 440.0 5.3

107.78 577.0 7.2

as lost due to spacecraft going into safe mode. OpNav14 was cancelled to make upd RC2 yet the naming is as listed in the table.

Fig. 2. (A) Schematic representing the timing of exposures within a single mosaicstation of the dedicated satellite search sequence. (B) Schematic representing thepositions of the FC’s footprint (squares) relative to Vesta (center disk) and theplanned orbits for the Dawn spacecraft (ellipses). (C) The cadence in time of thethree satellite search mosaics designed to reduce the chance of the search aliasingwith a satellite’s revolution.

Table 3Station pointing for satellite search mosaics.

Mosaic #1 Mosaic #2 Mosaic #32011 July 09 2011 July 09 2011 July 1017:36–20:32 20:42–23:37 5:21–8:17

RA DEC RA DEC RA DEC

Station #1 304.4 8.7 304.7 9.1 305.5 10.3Station #2 305.6 4.3 305.9 4.8 306.7 5.9Station #3 301.0 2.2 301.3 2.7 302.2 3.8Station #4 297.9 3.6 298.2 4.1 299.0 5.3Station #5 296.1 7.9 296.3 8.4 297.2 9.6Station #6 300.6 10.3 300.9 10.8 301.8 12.0

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described in Memarsadeghi et al. (2012) and are summarized inFig. 3. All procedures include image processing to subtract darkand bias frames and remove the instrument’s flat field.

Group 1 conducted three major tests that were used and refinedas Dawn approached Vesta:

� Visual motion detection with Vesta at the center[Motion-Vesta].� Visual motion detection with the star field co-registered

[Motion-Star].� Stacked images showing star and satellite trails [Stacked].

When calibrated data (level 1B) (Schröder et al., 2013) werereleased, we repeated the searches to see if satellites could bedetected with the improved calibration. During the early OpNavsequences, the images were processed to generate IntegratedSoftware for Imagers and Spectrometers (ISIS) cubes (Edwards,1987; Anderson et al., 2011) with dark field correction, a correctionto eliminate shutter-induced smearing, and image stretch to com-pensate for scattered light. Then using the blink routine in ISIS, wesearched through the stack of images looking for motion. TheMotion-Vesta technique required the least amount ofprocessing. The star field moved only a few pixels within the imageand between images for the early OpNav sequences. As Dawn gotnearer, every star in the field moved on the order of 10 or morepixels. A satellite orbiting Vesta would either be a point of lightmoving in a different direction than the stars, or if its orbital veloc-ity were low, it would remain fixed in the frame with the same rel-ative position as Vesta.

The Motion-Star search required co-registering stars to removetheir motion. This was done using the coregistration (‘‘coreg’’)function in ISIS. Again, we used the blink routine to search formotion. For these image sets, the stars are fixed in the frame whileVesta moves. If a satellite were present it would be noticed by itsmotion relative to stationary stars. This search technique was moreuseful than the Motion-Vesta technique until Dawn was nearerVesta. At close range, the star field changed too much betweenthe first and last image so co-registration, designed for small off-sets, was not possible.

The stacked technique was found to be an easier way to searchfor satellites, although it was not as robust. For this test, westacked the OpNav images into a cube and read the 3D cube intoIDL. For each sample and line of the 3D cube, we took the highestdata number (DN) value to generate an image of the maximum val-ues. Because the image is mostly black except for stars, the result-ing maximum value images showed the star as trails whilesuppressing scattered light and noise (Fig. 3A). Vesta remaineddominantly in the center of the frame while the background starsproduced dotted trails in parallel lines. A satellite would be noticedas a trail of light that had a different direction and point spacing,assuming there was not an exact match with the star motion.

Additionally, once Vesta became large in the field of view(OpNav 6), we began to use a high pass filter to remove the scat-tered light. We used the ISIS routine, highpass with both samplesand lines set to 11. This technique allowed us to see closer to

Fig. 3. (A) OpNav images stacked into a cube and filtered selecting the highest data number (DN) value. This image shows Vesta dominating with background stars as trails.(B) A high-pass filter removes background stars, leaving only bodies moving less than a pixel during the sequence and/or persistent and known image artifacts. (C) Outputfrom automated processing pipeline. Circles denote known catalog stars and squares are ‘unidentified objects’ needing follow-up examination. (D) Difference of two images,one created by coadding the first three images in the sequence, the other coadding the last three images in the sequence.

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Vesta even when the scattered light was significant. To search forsatellites with low orbital velocity in a sequence, after thehigh-pass filter, images were combined taking the median valueof each pixel (median filter). This removes both cosmic rays andbackground stars, leaving only image artifacts (Fig. 3B) and satel-lites that moved less than a pixel during the sequence. This wasdone with data from OpNav 10, 13, 16, 17 and 18. No satelliteswere found.

Another searcher, (named group 2), blinked images using a com-mercial software package Maxim-DL (2008) and Astrometrica(Raab, 2011) after calibration and solving to determine world coor-dinates using Astrometry.net (Lang et al., 2010). Animated gif fileswere produced providing another method of visual scanning. Inthese data products, a moving target would reveal itself in longexposures pointing at Vesta by motion in a different direction thanthe background stars when images in a time sequence were stackedand registered. Images with suspected moving targets were exam-ined frame by frame for the following conditions that are requiredof a true detection of an object: (1) deviates from the system pointspread function (PSF) because of motion of the putative satellite, (2)the appearance of the object in each frame in the time sequence and(3) absence of image artifacts or hot pixels at the position of the sus-pected satellite. When blinking many images, the eye can note andignore cosmic rays as they are short lived and do not have a systemPSF. An unsharp mask filter was used to enhance high frequencysignal by one of the co-authors (group 3). This approach, coupledwith visual searching, with no detection software, has yielded

positive results in the past (Weaver et al., 2006; Stern et al., 2007;Showalter et al., 2012).

Two independent groups used algorithms for automated objectdetection and compared the identified objects to those in star cat-alogs (group 4a, b). The process used by group 4a, began withastrometric calibration followed by alignment of both raw andmedian filtered data sets by reading into SAOImage DS9 (2014).They were then overlain with the Tycho-2 star catalog. All brightsources were identified with stars or hot pixels. Upon detectingobject motion, the star-aligned and stacked image was comparedwith a ground-based archive image of the same sky region showingthat no bright star is present at the position of the asteroid, andconfirming that other bright sources on the FC image correspondto stars.

The second of group 4, 4b, used an automated star matchingprocess. The raw data in Flexible Image Transport System (FITS)files from the Dawn Science Center were processed throughAstrometry.net (Lang et al., 2010) to obtain an approximateWorld Coordinate System (WCS) transformation. Each image wasthen processed through a series of common pipeline steps includ-ing dark removal, bias subtraction, flat-field removal, andunsharp-masking. Following this, an image detection algorithmbased on DAOPHOT (Stetson, 1987) was applied to find objectswith a Gaussian PSF and reject any objects found within a couplepixels of known hot/bad pixels. The approximate WCS solutionwas used to automatically identify stars from the Guide StarCatalog (Lasker et al., 2008) and UCAC3 (Zacharias et al., 2010)

Fig. 4. (A) Circle marks asteroid 511 Davida found in OpNav 3 on May 17, 2011.Because it is a distant asteroid, its motion is less than a pixel during the OpNavsequence (68.5 min). (B) Asteroid 487 Venetia is in the field of view during OpNav 4on 5/24/11 also with no detectable motion.

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catalogs. A new astrometric calibration based on a cubic polyno-mial fit to the detector plane was computed with a typical rms(root mean square) of 15–20 arcsec. An approximate photometriccalibration was also computed fitting a polynomial between thefluxes and catalog magnitudes that have typical rms of 0.3 magni-tudes. The calibrations were put back into the FITS headers as newkeywords. Objects from this series of image catalogs that did notmatch a known catalogue star became candidates for further pro-cessing. An example is shown in Fig. 3C. Candidates that appearedto move with respect to the background objects were visuallyexamined for confirmation or rejection.

In a fifth approach, the first three images and the last threeimages in a sequence or OpNav were summed, and subtractedone from the other (Fig. 3D). If there were a moving object, the dif-ferenced image would show a dark–bright signature of differentorientation and spacing between dark and bright signatures ofthe stationary background stars. The technique worked until thespacecraft was closer to and pointed at Vesta. At this point, thebackground stars were not stationary and image registration wasrequired.

4. Results

4.1. OpNav and RC1, RC2 searches

No satellites were found in the OpNav nor RC1 and RC2sequences. Background asteroids and some fast moving thingswere detected and are described below. In advance of data acqui-sition, known background asteroids were identified in the camera’sfield of view using 553,917 objects in the Minor Planet Catalog. Inorder to be visible by Dawn, an asteroid has to be within 2.74� ofthe center of Vesta when it is in the center of the field, as is the casefor OpNav images and RC1 and RC2 sequences. 511 Davida wasfound during OpNav 3 on May 17, 2011 at V magnitude of 11.5.We knew ahead of time that Davida was in the field of view, andbecause we did not know where, it is considered a found object.We thus consider 11.5 magnitudes an upper limit to detectionbecause the images had to be stacked in order to satisfy therequirement noted in Section 3 that the PSF deviate from the sys-tem PSF. The brightest anticipated asteroid was 487 Venetia, whichwas observed in OpNav 4 on May 24, 2011 at V magnitude of 10.9found by blinking images in the sequence. Both 487 Venetia and511 Davida were detected by comparing the images to aground-based field of background stars (Fig. 4). If there is no back-ground star and the image has the characteristics of the systemPSF, the asteroid is considered detected. Through the course ofthe sequence, neither of these asteroid’s relative motion extendedbeyond a single pixel.

Another asteroid of interest was 206,978 (2004 TP110), at mag-nitude 12.8 and 7 million km from Vesta. It was not detected, fur-ther bounding the detection limits of the camera and a check to theexperimental simulation described in the next section. With thisasteroid’s large motion of �8 arcsec/min it would have movedacross multiple pixels were it detected.

Fig. 5 shows a fast moving object that was seen in four frames.The most probable explanation is that small debris from the space-craft is moving through the field of view of the FC. It is so close thatit is out of focus, as the PSF is large as is its motion relative to thespacecraft. These out-of-focus streaks have been seen regularlysince launch in 2007 and have been determined to be unimportantfor science or engineering.

4.2. Mosaic search

Considering the orbital dynamics of expected objects in orbitaround Vesta, combined with the motion of the spacecraft with

respect to Vesta, almost all possible satellites will stay in a singlepixel during a 20 s exposure, and almost all satellites will trailacross multiple pixels during the 270 s exposures. In any searchfor reasonably fast moving objects using the 270 s exposures, thesought-after signature will be a trail of several, up to �20 pixels.We found no objects in orbit around Vesta after processing, blink-ing and scanning the mosaic search images.

Minor planet 972 Cohnia was found at magnitude V = 11 inMosaic 1 station 1 at �RA = 20 10 57.0, DEC = +09 21 21. Itsexpected motion of 1.08 arcsec/min would have barely carried itto the next pixel during station 1’s data acquisition duration of20 min. Due to some overlap in the stations, this asteroid alsoappears in station 6 taken almost 3 h later and the asteroid movedalmost 10 pixels to �RA = 20 10 51.82, DEC = +09 24 00.1 withS/N � 9. Other asteroids are predicted to be in the field of viewand were not found because they were too faint.

5. Generating and implanting synthetic satellites to determineupper limits

To implant synthetic satellites on the FC images, we used a soft-ware image simulator developed for the proposed German‘‘AsteroidFinder’’ space mission (Mottola et al., 2008). The simula-tor realistically reproduces the basic steps of the image formationprocess: optical transfer through the optics, image projection ontothe detector, charge accumulation in the CCD, charge transfer andthe readout process. In order to represent moving objects, theexposure is divided into discrete time steps, the number of whichis algorithmically determined based on the apparent speed of theobject. For each time step, the input point source, a Dirac Delta

Fig. 5. A sequence of 4 exposures acquired during Mosaic 1. (A) (Far right) 270 s exposure shows a streak moving from right to left. The second through fourth frames are (B)1.5, (C) 20 and (D) 270 s exposures respectively and show trails proportional to the exposures. The object was in the field of view for almost 2 min. Its large PSF indicates thatit is out of focus and close to the spacecraft.

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function, is convolved with the PSF of the FC optics (Sierks et al.,2011), which is approximated with a Gauss function with a FullWidth at Half Maximum (FWHM) of 1.5 pixels. In order to providea realistic image simulation, the CCD pixels are oversampled by afactor of 24 in each spatial dimension. The projected position ofthe light source onto the CCD at each time step is computed basedon the apparent position of the object, which in turn depends onthe object’s motion and on the spacecraft’s pointing instability.The latter is modeled in two parts: a random jitter and a systematicdrift, the motion vector of which is assumed to be constant duringan individual exposure, but its direction is changed in a randomway between exposures.

The input photon flux for each sub-pixel and time step is thenintegrated and converted into electrons by multiplication by thesub-pixel Quantum Efficiency (QE). The FC CCD features a lateralanti-blooming gate to reduce charge spilling as under circum-stances of extreme overexposure. However, because of this, theportion of the pixel beneath the anti-blooming gate (about 30%of the pixel surface) is insensitive to light. This effect is modeledin the simulator by introducing an intra-pixel QE map.

After all sources have been integrated, photon noise is added foreach pixel, following Poisson statistics. At this point, the parallelcharge transfer process is simulated, in the course of which theeffects of the electronic shutter smearing and charge transfer inef-ficiency are computed. Finally, the readout process is simulated,during which the conversion to digital units takes place, accordingto the camera system gain, and readout noise is optionally added.In this particular case, however, as the simulated image was addedto a real FC image, no additional readout noise was added, as it isalready present in the original image.

The magnitude zero point is based on the optics’ theoreticalperformance and on the CCD data sheet provided by the manufac-turer. A subsequent analysis of photometry calibrated to the Vmagnitude of stars in the UCAC3 star catalog yielded a photometricequation with a zero-point shift of 0.165 magnitudes, only a fewpercent different from that used to generate the satellites in thisexperiment. We therefore consider the upper limits to have anuncertainty of 0.2 magnitudes. We selected OpNav 16 (Fig. 6)and the three exposures at mosaic station 5 to insert simulatedsatellites using the method described above. OpNav 16 wasselected as an optimum sequence because the spacecraft was closeto Vesta and scattered light did not dominate the signal from stars.Station 5 images were selected because of the absence of abundantand inhomogeneous scattered light from Vesta. In other words,these data sets were selected to test the faintest detections thatour searchers would make. We define this as the limiting magni-tude. It was not practical to search all images again. The satellitesare in randomly oriented circular orbits with radii 1.1–100 Vestaradii, starting position angle, inclination (between cos i = 1 tocos i = 0), and l, the ascending node, are also randomized as is theirmagnitudes, though limited to a range of 7–13.

6. Search for implanted objects: results

The team searched the selected images containing randomlyimplanted satellites with randomly generated magnitudes, andreported the positions of each satellite found. We present the com-piled detection efficiency achieved by each searcher in each imageset in Fig. 7A–C. All false detections were reexamined to be surethey were not real objects. None were.

In OpNav 16, at a magnitude range of 8.5–9.0 (seeSupplementary material Table S1), corresponding to radii of15.6–12.4 m, 50% of the searchers found 50% of the objects and50% did not. This is roughly equivalent to a search completeness.The faintest object found was 10.7 magnitude corresponding to aradius of 5.7 m. The size of an object detected at each OpNav is cal-culated by scaling the limiting magnitude at OpNav 16 assumingVesta’s phase law and V-band geometric albedo of 0.38 (Li et al.,2013) until Vesta filled the field of view (Table 2). The smallestdetectable radius was 5.3 m at OpNav 17. The mission’s OpNavobservations span 3 months, a factor contributing to the robustnature of the search. The earlier detection size (at 50% efficiency)of 22 m radius, determined with Hubble Space Telescope(McFadden et al., 2012), was reduced between OpNav 10 and theRC1 sequences to radius 18.1 m. Nothing was found larger than5.3 m radius.

In Fig. 7B the fraction of objects found by 4 searchers athalf-magnitude intervals, referred to as search or detection effi-ciency, are shown for station 5, 20 s exposures (seeSupplementary material Table S2 for details of each searcher).The 50% detection efficiency magnitude is between 10.5 and11.0, corresponding to radii of 8.0 and 6.3 m, respectively. Thefaintest object found in the 20-s exposures was 12.57 magnitudeor 3.1 m in radius for the observing circumstances (rh = 2.219 AU,D = 37,929 km, phase = 28.7�) of the mosaic acquisition. For the270-s exposures (Fig. 7C and Supplementary material Table S3),the 50% efficiency occurred at 11.0–11.5 magnitudes or 6.3–5.0 m radii, respectively. One searcher found an object at 11.82magnitude or 4.3 m radius. We expected fainter objects to bedetected in 270-s exposures, while in fact the opposite is true.Most likely, this results from higher background noise from scat-tered light from Vesta in the longer exposure, as well as the factthat any fainter and fast-moving objects would spread across morepixels, resulting in a brighter limiting magnitude of detection.Thus, the 20 s exposures when co-added provide fainter detectionlimits than the 270 s exposures. But the completeness level isfainter in the 270 s exposures.

Examining both Fig. 7 and Tables S1–S3 show that differentobservers had different search efficiencies. Some searchers missedsome brighter objects, yet found very faint ones. Visual acuity isone criterion for effective searching, experience another, andmethod of searching, yet another variable. The figures, as well asresults from previous satellite discoveries (Pluto’s moons for

Fig. 6. Synthetic satellites were inserted into OpNav 16 images. Satellites withrandom orbits are seen with a trajectory that is markedly different from thebackground stars that trail in the direction of spacecraft motion when thespacecraft is pointed at Vesta.

Fig. 7. (A) Detection efficiency (fraction found) for satellites inserted in OpNav 16sequence binned at 0.5 magnitude intervals from 4 searchers’ efforts. (B) Same forstation 5 of the satellite search mosaic, 20 s exposure images from 4 searchers. (C)Same for station 5, 270 s exposures conducted by 7 searchers.

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example Weaver et al., 2006), indicate that the discovery of anysmall body bears a component of chance. The faintest objectdetected, of magnitude 12.57, was found by blinking and visualdetection by an experienced observer who has found asteroids pre-viously. There were detections by the semi-automatic approachthat were missed by the visual searchers and vice versa. In theOpNav 16 sequence with 1.5 s exposures, two visual observersdetected objects fainter than 9th magnitude, yet missed objectsof 6th magnitude. It is clear that to increase the detection limitof a search, multiple, experienced observers are needed and thatmultiple approaches improve the chances of detection.

7. Discussion

Why might we expect to find natural satellites gravitationallybound to Vesta? First it is a fairly common state for minor planetswith a number of cases found among the Main Asteroid Belt, theKuiper Belt and Near Earth populations. Second, bound systemspersist, seeming to be robust to perturbations. 1999 KW4, a smallEarth-crossing binary system (Ostro et al., 2006), follows a highlyelliptical orbit with aphelion and perihelion distances of 1.08 and0.20 AU respectively. Its motion exposes the binary to large varia-tions in tidal forces, especially as it passes near to the Sun, yet itcurrently has a satellite. Is there something peculiar to Vesta thatprevents it having a companion? We offer three possible explana-tions to account for its ‘‘missing moons.’’

First is that there is no mechanism preventing Vesta from hav-ing moons except for the ‘‘luck of the draw.’’ Vesta has a reasonablylarge SOI. Yet there must be a mechanism that allows a body tolose energy in order to be captured. The conditions of capturemay never have existed for Vesta.

Secondly, there may be a mechanism that strips Vesta of anyorbiting satellites. In this context, any object that avoids the fatesof either colliding with Vesta or failing to capture, could only per-sist in bound motion for a short period of time. One possible mech-anism is the periodic encounter between Vesta and Asteroid 197Arete. Every 18 years, Arete passes within 0.04 AU of Vesta fromwhich an early mass of Vesta was derived (Hertz, 1968). Is it

possible that this repeated encounter has a pumping action thatclears Vesta of any satellites? As far as we know, this line of inquiryhas not previously been proposed and it may be worthy of furtherstudy.

Another candidate explanation is the idea that stable orbitsaround Vesta are precluded by the particular structure of its grav-itational field. Vesta’s gravity field is lumpy and contains spin–or-bit resonances that make some orbital regimes dynamicallyunstable as discussed by Tricarico and Sykes (2010). They alsopoint out regimes in which spin–orbit resonances are stable.While their results were computed based on relativelyshort-term numerical integrations prior to Dawn’s arrival at

L.A. McFadden et al. / Icarus 257 (2015) 207–216 215

Vesta, they strongly suggest that the lack of orbiting satellites can-not be caused by irregularities in Vesta’s gravitational field.

Numerical simulations of impacts (e.g. Durda et al., 2004) con-strain the amount of material that could be launched into orbit,and long-term integrations might be used to constrain the lifetimeof such satellites. If the formation and lifetime of orbiting bodiesaround Vesta were examined one result might provide insight intothe question of whether Rheasilvia, if it were the primary source ofejected material, is on the order of 1 byr old (Marchi et al., 2012) ormuch older (>3 byr) as determined by Schmedemann et al. (2014).The formation of the more recent and smaller Marcia crater(Williams et al., 2014) should also be considered while modelingthe lifetime of material in orbit around Vesta. In any event, theabsence of a natural satellite in orbit around Vesta today is a factto be considered in any modeling scenario of Vesta’s impact history.

8. Conclusion

The satellite search carried out with the Framing Camera onDawn is comprehensive in terms of the proximity of the spacecraftto Vesta, the time spent searching and the number of searchers anddiversity of analysis approaches used. We have reduced the limit-ing radius of any possible satellite by a factor of four over previousstudies. At this point, we take the lack of moons around Vesta as asupported fact with little probability of being overturned. Ratherthan regarding it as a simple null result, we believe it offers cluesto Vesta’s collisional history and dynamical environment.

Acknowledgments

We thank Herbert Raab for working with us to modifyAstrometrica so that asteroids could be projected into the Dawnspacecraft’s frame of reference. The Dawn Flight Team made theobservations possible and we thank them for their superior drivingand operations implementation. This work was supported by theDawn mission through NASA’s Discovery Program, NASA’s Dawnat Vesta Participating Scientist Program through GrantsNNX10AR56G to University of Maryland at College Park andNNX13AB82G to Planetary Science Institute. Part of this workwas carried out at the Jet Propulsion Laboratory, CaliforniaInstitute of Technology, under a contract with NASA to UCLANASA contract number, NNM05AA86C. The Framing Camera pro-ject is financially supported by the Max Planck Society –Germany and the German Space Agency, DLR.

Appendix A. Supplementary material

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.icarus.2015.04.038.

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