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Icarus 257 (2015) 207–216 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Vesta’s missing moons: Comprehensive search for natural satellites of Vesta by the Dawn spacecraft 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 States Planetary Science Institute, Tucson, AZ 85719, United States c IGPP, UCLA, Los Angeles, CA 90095, United States d Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, United States e DLR – German Aerospace Center, Institute of Planetary Research, Berlin, Germany f Space Telescope Science Institute, Baltimore, MD 21218, United States g Institut für Geophysik und Extraterrestrische Physik (IGEP), University Braunschweig, Germany h Max-Planck Institute for Solar System Research, 37077 Göttingen, Germany b a r t i c l e i n f o Article history: Received 11 August 2014 Revised 25 March 2015 Accepted 29 April 2015 Available online 5 May 2015 Keywords: Asteroid Vesta Asteroids, dynamics Satellites of asteroids a b s t r a c t Earth-bound searches for natural satellites of 4 Vesta have been reported since 1987. With use of technological advances and observing capability has come a reduction in the detectable size of a possible satellite. The Dawn mission brought a small camera close to Vesta itself. In our search, which was carried out with a comprehensive data acquisition strategy and by experienced searchers, we ﬁnd no satellites to a detection limit as small as 3-m radius. Various observation and analysis strategies are discussed in detail. It is now time to factor the null result of this search into the context of satellite formation among other main belt asteroids and to conduct dynamical modeling to explore the suspected forces contributing to the absence of satellites at Vesta today. Ó 2015 Published by Elsevier Inc. 1. Introduction Within the Solar System many objects have natural satellites that are bound to the primary body as it also orbits the Sun. Earth’s moon, the Outer Planets’ satellite systems, some Kuiper Belt Objects (KBOs) (Veillet et al., 2002; Noll et al., 2008) and even small near-Earth objects (NEOs) (Margot et al., 2002) are examples. The presence or absence of a satellite has implications for the primary body’s collisional and dynamical history, and permits measurement of mass, size and bulk density. Within the Main Asteroid Belt, almost 100 asteroids with co-orbiting, smaller bodies within the gravitational sphere of inﬂuence (SOI, the region around an asteroid where the primary gravitational inﬂuence on an orbiting body is that body) (e.g. Bate et al., ⇑ Corresponding author at: Planetary Systems Laboratory, Code 693, Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, United States. E-mail address: [email protected] (L.A. McFadden). http://dx.doi.org/10.1016/j.icarus.2015.04.038 0019-1035/Ó 2015 Published by Elsevier Inc. 1971) of the larger asteroid are known (e.g. Johnston, 2014; Merline et al., 1999, 2002). We compare Vesta’s gravitational SOI with Earth, Jupiter, Ceres, a NEO and Pluto in Table 1. Ceres contains approximately a third of the current asteroid belt by mass (e.g. O’Brien and Sykes, 2011), with Vesta being the second most massive. Vesta has a reasonably-sized SOI relative to other bodies with natural satellites, and if the conditions exist for capture or retention of ejecta from an impact on Vesta, one might expect satellites to exist if not now, then in the past. 1999 KW4, a small Earth-crossing binary system (Ostro et al., 2006), has a SOI that is orders of magnitude smaller than Vesta’s. Further, its value varies by almost a factor of 2 throughout its orbit, yet its satellite remains. Dynamical models of the formation of the asteroid belt require migration of bodies from the Kuiper Belt to populate the asteroid belt (Levison et al., 2009; Walsh et al., 2012) and many KBO’s are multiple systems. Satellite capture requires a mechanism in which energy is lost to match the orbital velocity of the primary. 208 L.A. McFadden et al. / Icarus 257 (2015) 207–216 Table 1 Comparison of the gravitational sphere of inﬂuence (SOI) for some planets, asteroids and dwarf planets. Object name Mass (kg) 30 Sun Earth Jupiter Vesta Ceres 1999 KW4 1999 KW4 (perihelion) 1999 KW4 (aphelion) Pluto a Sphere of inﬂuence r A ¼ dA b 1.99 10 5.97 1024 1.90 1027 2.59 1020 9.34 1020 2.4 1012 2.4 1012 2.4 1012 1.31 1022 mA mSun 25 Distance from Sun (km) Radius (km) Sphere of inﬂuence (SOI)a (km) Relative SOIb – 1.50 108 7.79 108 3.54 108 4.14 108 9.61 107 1.62 108 2.99 107 5.87 109 – 6378.14 69911.00 262.70 476.0 1.5 1.5 1.5 1184 – 9.245 105 4.822 107 3.937 104 7.684 104 6.5 11.0 2.04 3.13 106 – 145 690 150 161 4.36 7.36 1.36 2644 , where dA is distance from Sun, mA mSun is mass relative to the Sun. SOI scaled to body’s radius. Binzel and Xu (1993) located asteroids with similar spectral signatures as Vesta’s lying in its orbital plane with semi-major axes between the m6 secular resonance with Saturn at 2 AU and the 3:1 Kirkwood Gap at 2.5 AU. These asteroids comprise the dynamical Vesta family. Hubble Space Telescope images and subsequent analysis of Vesta’s shape (Thomas et al., 1997) suggested a large basin 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 basins likely produced the Vesta family (Marzari et al., 1996; Zappalà et al., 1984). Dynamical modeling prior to the Dawn mission suggested an impact by a 42 km body, 1 billion years (byr) ago (Asphaug, 1997). Remarkably, crater size frequency distributions support this age (Schenk et al., 2012; Marchi et al., 2012). An alternate and older age determination of these basins (3.5 and 3.7 byr) is presented by Schmedemann et al. (2014), assuming a lunar-like crater production function. Chaotic dynamics and secular perturbations (Wisdom, 1985) have resulted in fragments from Vesta colliding with Earth, surviving passage through Earth’s atmosphere and being found as meteorites; the Howardite–Eucrite–Diogenite (HED) group (McSween et al., 2011). There are samples of Vesta in the terrestrial meteorite collection, there are craters formed from collisions and reaccumulation of ejecta fragments on Vesta’s surface (e.g. Russell et al., 2012; Jaumann et al., 2012). Given the large amount of ejecta from Vesta and the varied dynamical outcomes that resulted, it is logical to ask if any fragments entered into orbit around Vesta, either directly or after a re-encounter. The above considerations lead us to ask if there are any 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 (McFadden et al., 2012) have been used to search for satellites orbiting Vesta in the past. None have been found to a previously reported size limit of 22 m radius. Until now, the region inside of 14 Vesta radii (3500 km) had not been searched due to scattered light from Vesta. Is it due to chance that neither satellites nor a debris ﬁeld are remnant in orbit around Vesta today? Were the instruments that searched for satellites in the past inadequate to detect anything orbiting Vesta? Or has the past collisional history removed any object or objects that once may have been in orbit around Vesta? The Dawn spacecraft spent more than a year at Vesta and we searched again for natural satellites. We designed a search that would improve upon past searches by looking closer to Vesta than possible in previous efforts. In this paper we describe the two observational sequences acquired for the satellite search using Dawn’s FC and report processing and preparation for search by the team of satellite searchers. Seven observers searched and reported that no satellites were found. However, we did ﬁnd moving objects including background asteroids, cosmic rays and something close to the camera and moving fast that is probably debris from the spacecraft. Next, we determine the upper limits of detection by implanting simulated objects with randomly chosen orbits and magnitude into a subset of the satellite search images. The observers searched again and report their ﬁndings in Section 6. Upper limits of detection in the meter-size range are then calculated assuming the same albedo and phase function as Vesta. We discuss our approach and consider changes for future satellite searches in the ﬁnal section and consider the implications for the absence of satellites in the context of the impact and ejecta history of Vesta in the discussion. The mission’s approach phase included searching for satellites around 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 not occulted by Vesta itself. Our upper limit of detection during approach was an object 5.3 m radius assuming Vesta’s global geometric albedo of 0.38 (Li et al., 2013). During a dedicated satellite search mosaic, carried out at three different times, the limiting radius of detection was 3.1 m and 4.3 m for 20 s and 270 s exposures respectively. We discuss the reason for the reverse relation between detection limits and exposure times in Section 6. If any larger collisional ejecta were in orbit around Vesta in the past, they are 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 of 150 mm, 5.5° 5.5° ﬁeld of view and pixel size of 19.23 arcsec as determined using Astrometrica software (Raab, 2011). The clear ﬁlter, designed for detecting stars, dust and the moon search, was always used to maximize photon collection and signal. Two data acquisition schemes were used; (1) direct pointing at Vesta beginning at 1.24 million km range, and (2) acquisition of a dedicated satellite search mosaic. The data sets were processed and analyzed using 5 different approaches, all of which complement each other and result in an increased reliability of the search results. We discuss the data acquisitions followed by the data processing that produced searchable images. 2.1. Direct pointing Direct pointing at Vesta served the project’s optical navigation (OpNav) requirements and for the satellite search, included 14 acquisitions each consisting of 20 successive, 1.5 s exposures pointed at Vesta. These were also used to design the ion propulsion 209 L.A. McFadden et al. / Icarus 257 (2015) 207–216 thrust sequences that put the spacecraft into orbit around Vesta and to determine exposure times and data compression settings for orbital science observations. There were two additional sequences called Rotational Characterization 1 (RC1) and Rotational Characterization 2 (RC2) to determine Vesta’s pole orientation. These sequences included ride along ‘‘OpNav’’ imaging consisting of alternating 0.008 s (for Vesta) and 1.5 s exposures (for stars), 36 in RC1 and 52 in RC2, taken within 3–6 min in time, a shorter interval than the 0.5–2.0 h of the ‘‘standard’’ OpNav sequences. We used the 1.5 s exposures to search for satellites. Images from each sequence were coadded and searched for the presence of satellites. An example is shown in Fig. 1. Table 2 presents observing circumstances at each OpNav and RC along with the size of Vesta in pixels and the limiting detectable radius derived from the experiment with implanted objects described in Section 5. The orbital period of satellites in circular orbit around 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 of motion of potential satellites across more than one pixel. 2.2. Satellite search mosaic The satellite search mosaic images extended 5000 km (20 Vestan radii) from Vesta’s surface. This region is designated the operational sphere in which the spacecraft orbited (Polanskey et al., 2011). The goal was to search for objects smaller than Hubble Space Telescope’s limit of 22 m in radius (McFadden et al., 2012) and closer to Vesta than previously searched (14 Vestan radii). The ﬁrst mosaic sequence was carried out before RC2, on 2011 July 9. At each image mosaic station, 4 sets of 3 images with 1.5 s, 20 s and 270 s exposures respectively, commanded at 5 s intervals were acquired (Fig. 2A). There are six mosaic stations (Fig. 2B) with data collection at intervals of 21 min each, with 10 min turn and settle periods between stations. A single mosaic took 2:45 h. This mosaic pointing and data acquisition was carried out twice before RC2 observations. Mosaic 3 began after a complete Vesta rotation of 5.4 h and was completed on 2011, July 10, 8:17. The goal was to have order of magnitude scaling in the image exposure durations and image time separations (Fig. 2C) because we are searching for objects with no known constraints in orbital characteristics other than being gravitationally bound to Vesta. As implemented, the time between the ﬁrst and second mosaic was 186 min and 785 min between the ﬁrst and third mosaic. A total of 216 images were commanded, two were corrupt resulting in 214 usable images. The station pointing is listed in Table 3. For reference, a body orbiting close to Vesta has an orbital period of 1.77565 h, while an orbit at 20 Vestan radii has a period of 452.12235 h (18.83843 days). 3. Data processing and search approaches Fig. 1. Eighteen RC2 images scaled and coadded to enhance stars and possible satellites. A satellite, if detected, would have a trail in a different direction relative to background stars and with the same number of detections as background stars, yet spaced according to its relative motion with respect to Vesta. The satellite search team used multiple methods of processing and searching and the data were scanned by many sets of eyes, an important point given that we found no satellite to the detection limits of the FC. Using different and independent approaches and searching with multiple and experienced eyes added certainty to our results. We designed our processing schemes from previous successful searches for satellites of Pluto (e.g. Stefﬂ et al., 2006) and considered the capabilities of the FC and the spacecraft’s motion. Image processing and algorithms used for data processing are Table 2 Observational circumstances during direct pointing satellite search with limiting magnitude 10.7 as determined from implanted objects into OpNav 16. OpNava Date Heliocentric distance (AU) Range to Vesta (km) Phase angle (°) Vesta apparent size (FC pixels) Limiting detectable radius (m) 1 2 3 4 5 6 7 8 9 10 RC1 13 RC2 16 17 18 2011-05-03T13:35 2011-05-10T07:03 2011-05-17T12:56 2011-05-24T08:52 2011-06-01T06:50 2011-06-08T16:04 2011-06-14T14:05 2011-06-17T13:05 2011-06-20T14:05 2011-06-24:04:35 2011-06-30T09:58 2011-07-04T01:34 2011-07-10T02:23 2011-07-13T04:04 2011-07-17T04:33 2011-07-18T21:34 2.176 2.179 2.183 2.187 2.192 2.197 2.201 2.203 2.205 2.207 2.212 2.215 2.219 2.222 2.225 2.226 1,217,991 1,008,802 809,438 645,024 482,837 352,165 264,683 226,313 190,540 152,454 97,730 70,195 37,030 25,072 14,073 10,728 42.73 42.47 41.86 40.92 39.48 37.15 34.76 33.36 31.82 29.76 26.11 23.57 29.18 42.79 80.76 107.78 5.1 6.1 7.6 9.6 12.8 17.6 23.4 27.4 32.5 40.6 63.4 88.3 167.0 247.0 440.0 577.0 270 223 178 141 104 74 54 46 38 29 18 13 7.0 5.7 5.3 7.2 a Note that numbering of the OpNavs has gaps for the following reasons: OpNav11 was lost due to spacecraft going into safe mode. OpNav14 was cancelled to make up thrust time lost during safe mode status. There were OpNav sequences added to RC1 and RC2 yet the naming is as listed in the table. 210 L.A. McFadden et al. / Icarus 257 (2015) 207–216 Table 3 Station pointing for satellite search mosaics. Station Station Station Station Station Station #1 #2 #3 #4 #5 #6 Mosaic #1 2011 July 09 17:36–20:32 Mosaic #2 2011 July 09 20:42–23:37 Mosaic #3 2011 July 10 5:21–8:17 RA DEC RA DEC RA DEC 304.4 305.6 301.0 297.9 296.1 300.6 8.7 4.3 2.2 3.6 7.9 10.3 304.7 305.9 301.3 298.2 296.3 300.9 9.1 4.8 2.7 4.1 8.4 10.8 305.5 306.7 302.2 299.0 297.2 301.8 10.3 5.9 3.8 5.3 9.6 12.0 Group 1 conducted three major tests that were used and reﬁned as 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]. Fig. 2. (A) Schematic representing the timing of exposures within a single mosaic station of the dedicated satellite search sequence. (B) Schematic representing the positions of the FC’s footprint (squares) relative to Vesta (center disk) and the planned orbits for the Dawn spacecraft (ellipses). (C) The cadence in time of the three satellite search mosaics designed to reduce the chance of the search aliasing with a satellite’s revolution. described in Memarsadeghi et al. (2012) and are summarized in Fig. 3. All procedures include image processing to subtract dark and bias frames and remove the instrument’s ﬂat ﬁeld. When calibrated data (level 1B) (Schröder et al., 2013) were released, we repeated the searches to see if satellites could be detected with the improved calibration. During the early OpNav sequences, the images were processed to generate Integrated Software for Imagers and Spectrometers (ISIS) cubes (Edwards, 1987; Anderson et al., 2011) with dark ﬁeld correction, a correction to eliminate shutter-induced smearing, and image stretch to compensate for scattered light. Then using the blink routine in ISIS, we searched through the stack of images looking for motion. The Motion-Vesta technique required the least amount of processing. The star ﬁeld moved only a few pixels within the image and between images for the early OpNav sequences. As Dawn got nearer, every star in the ﬁeld moved on the order of 10 or more pixels. A satellite orbiting Vesta would either be a point of light moving in a different direction than the stars, or if its orbital velocity were low, it would remain ﬁxed in the frame with the same relative position as Vesta. The Motion-Star search required co-registering stars to remove their motion. This was done using the coregistration (‘‘coreg’’) function in ISIS. Again, we used the blink routine to search for motion. For these image sets, the stars are ﬁxed in the frame while Vesta moves. If a satellite were present it would be noticed by its motion relative to stationary stars. This search technique was more useful than the Motion-Vesta technique until Dawn was nearer Vesta. At close range, the star ﬁeld changed too much between the ﬁrst and last image so co-registration, designed for small offsets, was not possible. The stacked technique was found to be an easier way to search for satellites, although it was not as robust. For this test, we stacked the OpNav images into a cube and read the 3D cube into IDL. For each sample and line of the 3D cube, we took the highest data number (DN) value to generate an image of the maximum values. Because the image is mostly black except for stars, the resulting maximum value images showed the star as trails while suppressing scattered light and noise (Fig. 3A). Vesta remained dominantly in the center of the frame while the background stars produced dotted trails in parallel lines. A satellite would be noticed as 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 scattered light. We used the ISIS routine, highpass with both samples and lines set to 11. This technique allowed us to see closer to L.A. McFadden et al. / Icarus 257 (2015) 207–216 211 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) Output from 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. Vesta even when the scattered light was signiﬁcant. To search for satellites with low orbital velocity in a sequence, after the high-pass ﬁlter, images were combined taking the median value of each pixel (median ﬁlter). This removes both cosmic rays and background stars, leaving only image artifacts (Fig. 3B) and satellites that moved less than a pixel during the sequence. This was done with data from OpNav 10, 13, 16, 17 and 18. No satellites were found. Another searcher, (named group 2), blinked images using a commercial software package Maxim-DL (2008) and Astrometrica (Raab, 2011) after calibration and solving to determine world coordinates using Astrometry.net (Lang et al., 2010). Animated gif ﬁles were produced providing another method of visual scanning. In these data products, a moving target would reveal itself in long exposures pointing at Vesta by motion in a different direction than the background stars when images in a time sequence were stacked and registered. Images with suspected moving targets were examined frame by frame for the following conditions that are required of a true detection of an object: (1) deviates from the system point spread 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 suspected satellite. When blinking many images, the eye can note and ignore cosmic rays as they are short lived and do not have a system PSF. An unsharp mask ﬁlter was used to enhance high frequency signal by one of the co-authors (group 3). This approach, coupled with 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 object detection and compared the identiﬁed objects to those in star catalogs (group 4a, b). The process used by group 4a, began with astrometric calibration followed by alignment of both raw and median ﬁltered data sets by reading into SAOImage DS9 (2014). They were then overlain with the Tycho-2 star catalog. All bright sources were identiﬁed with stars or hot pixels. Upon detecting object motion, the star-aligned and stacked image was compared with a ground-based archive image of the same sky region showing that no bright star is present at the position of the asteroid, and conﬁrming that other bright sources on the FC image correspond to stars. The second of group 4, 4b, used an automated star matching process. The raw data in Flexible Image Transport System (FITS) ﬁles from the Dawn Science Center were processed through Astrometry.net (Lang et al., 2010) to obtain an approximate World Coordinate System (WCS) transformation. Each image was then processed through a series of common pipeline steps including dark removal, bias subtraction, ﬂat-ﬁeld removal, and unsharp-masking. Following this, an image detection algorithm based on DAOPHOT (Stetson, 1987) was applied to ﬁnd objects with a Gaussian PSF and reject any objects found within a couple pixels of known hot/bad pixels. The approximate WCS solution was used to automatically identify stars from the Guide Star Catalog (Lasker et al., 2008) and UCAC3 (Zacharias et al., 2010) 212 L.A. McFadden et al. / Icarus 257 (2015) 207–216 catalogs. A new astrometric calibration based on a cubic polynomial ﬁt to the detector plane was computed with a typical rms (root mean square) of 15–20 arcsec. An approximate photometric calibration was also computed ﬁtting a polynomial between the ﬂuxes and catalog magnitudes that have typical rms of 0.3 magnitudes. The calibrations were put back into the FITS headers as new keywords. Objects from this series of image catalogs that did not match a known catalogue star became candidates for further processing. An example is shown in Fig. 3C. Candidates that appeared to move with respect to the background objects were visually examined for conﬁrmation or rejection. In a ﬁfth approach, the ﬁrst three images and the last three images in a sequence or OpNav were summed, and subtracted one from the other (Fig. 3D). If there were a moving object, the differenced image would show a dark–bright signature of different orientation and spacing between dark and bright signatures of the stationary background stars. The technique worked until the spacecraft was closer to and pointed at Vesta. At this point, the background stars were not stationary and image registration was required. 4. Results 4.1. OpNav and RC1, RC2 searches No satellites were found in the OpNav nor RC1 and RC2 sequences. Background asteroids and some fast moving things were detected and are described below. In advance of data acquisition, known background asteroids were identiﬁed in the camera’s ﬁeld of view using 553,917 objects in the Minor Planet Catalog. In order to be visible by Dawn, an asteroid has to be within 2.74° of the center of Vesta when it is in the center of the ﬁeld, as is the case for OpNav images and RC1 and RC2 sequences. 511 Davida was found 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, and because we did not know where, it is considered a found object. We thus consider 11.5 magnitudes an upper limit to detection because the images had to be stacked in order to satisfy the requirement noted in Section 3 that the PSF deviate from the system PSF. The brightest anticipated asteroid was 487 Venetia, which was observed in OpNav 4 on May 24, 2011 at V magnitude of 10.9 found by blinking images in the sequence. Both 487 Venetia and 511 Davida were detected by comparing the images to a ground-based ﬁeld of background stars (Fig. 4). If there is no background star and the image has the characteristics of the system PSF, the asteroid is considered detected. Through the course of the sequence, neither of these asteroid’s relative motion extended beyond a single pixel. Another asteroid of interest was 206,978 (2004 TP110), at magnitude 12.8 and 7 million km from Vesta. It was not detected, further bounding the detection limits of the camera and a check to the experimental simulation described in the next section. With this asteroid’s large motion of 8 arcsec/min it would have moved across 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 spacecraft is moving through the ﬁeld of view of the FC. It is so close that it is out of focus, as the PSF is large as is its motion relative to the spacecraft. These out-of-focus streaks have been seen regularly since launch in 2007 and have been determined to be unimportant for science or engineering. 4.2. Mosaic search Considering the orbital dynamics of expected objects in orbit around Vesta, combined with the motion of the spacecraft with 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 OpNav sequence (68.5 min). (B) Asteroid 487 Venetia is in the ﬁeld of view during OpNav 4 on 5/24/11 also with no detectable motion. respect to Vesta, almost all possible satellites will stay in a single pixel during a 20 s exposure, and almost all satellites will trail across multiple pixels during the 270 s exposures. In any search for reasonably fast moving objects using the 270 s exposures, the sought-after signature will be a trail of several, up to 20 pixels. We found no objects in orbit around Vesta after processing, blinking and scanning the mosaic search images. Minor planet 972 Cohnia was found at magnitude V = 11 in Mosaic 1 station 1 at RA = 20 10 57.0, DEC = +09 21 21. Its expected motion of 1.08 arcsec/min would have barely carried it to the next pixel during station 1’s data acquisition duration of 20 min. Due to some overlap in the stations, this asteroid also appears in station 6 taken almost 3 h later and the asteroid moved almost 10 pixels to RA = 20 10 51.82, DEC = +09 24 00.1 with S/N 9. Other asteroids are predicted to be in the ﬁeld of view and were not found because they were too faint. 5. Generating and implanting synthetic satellites to determine upper limits To implant synthetic satellites on the FC images, we used a software image simulator developed for the proposed German ‘‘AsteroidFinder’’ space mission (Mottola et al., 2008). The simulator realistically reproduces the basic steps of the image formation process: optical transfer through the optics, image projection onto the detector, charge accumulation in the CCD, charge transfer and the readout process. In order to represent moving objects, the exposure is divided into discrete time steps, the number of which is algorithmically determined based on the apparent speed of the object. For each time step, the input point source, a Dirac Delta L.A. McFadden et al. / Icarus 257 (2015) 207–216 213 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 that it is out of focus and close to the spacecraft. function, is convolved with the PSF of the FC optics (Sierks et al., 2011), which is approximated with a Gauss function with a Full Width at Half Maximum (FWHM) of 1.5 pixels. In order to provide a realistic image simulation, the CCD pixels are oversampled by a factor of 24 in each spatial dimension. The projected position of the light source onto the CCD at each time step is computed based on the apparent position of the object, which in turn depends on the object’s motion and on the spacecraft’s pointing instability. The latter is modeled in two parts: a random jitter and a systematic drift, the motion vector of which is assumed to be constant during an individual exposure, but its direction is changed in a random way between exposures. The input photon ﬂux for each sub-pixel and time step is then integrated and converted into electrons by multiplication by the sub-pixel Quantum Efﬁciency (QE). The FC CCD features a lateral anti-blooming gate to reduce charge spilling as under circumstances of extreme overexposure. However, because of this, the portion of the pixel beneath the anti-blooming gate (about 30% of the pixel surface) is insensitive to light. This effect is modeled in the simulator by introducing an intra-pixel QE map. After all sources have been integrated, photon noise is added for each pixel, following Poisson statistics. At this point, the parallel charge transfer process is simulated, in the course of which the effects of the electronic shutter smearing and charge transfer inefﬁciency are computed. Finally, the readout process is simulated, during which the conversion to digital units takes place, according to the camera system gain, and readout noise is optionally added. In this particular case, however, as the simulated image was added to a real FC image, no additional readout noise was added, as it is already present in the original image. The magnitude zero point is based on the optics’ theoretical performance and on the CCD data sheet provided by the manufacturer. A subsequent analysis of photometry calibrated to the V magnitude of stars in the UCAC3 star catalog yielded a photometric equation with a zero-point shift of 0.165 magnitudes, only a few percent different from that used to generate the satellites in this experiment. We therefore consider the upper limits to have an uncertainty of 0.2 magnitudes. We selected OpNav 16 (Fig. 6) and the three exposures at mosaic station 5 to insert simulated satellites using the method described above. OpNav 16 was selected as an optimum sequence because the spacecraft was close to Vesta and scattered light did not dominate the signal from stars. Station 5 images were selected because of the absence of abundant and inhomogeneous scattered light from Vesta. In other words, these data sets were selected to test the faintest detections that our searchers would make. We deﬁne this as the limiting magnitude. It was not practical to search all images again. The satellites are in randomly oriented circular orbits with radii 1.1–100 Vesta radii, starting position angle, inclination (between cos i = 1 to cos i = 0), and l, the ascending node, are also randomized as is their magnitudes, though limited to a range of 7–13. 6. Search for implanted objects: results The team searched the selected images containing randomly implanted satellites with randomly generated magnitudes, and reported the positions of each satellite found. We present the compiled detection efﬁciency achieved by each searcher in each image set in Fig. 7A–C. All false detections were reexamined to be sure they were not real objects. None were. In OpNav 16, at a magnitude range of 8.5–9.0 (see Supplementary material Table S1), corresponding to radii of 15.6–12.4 m, 50% of the searchers found 50% of the objects and 50% did not. This is roughly equivalent to a search completeness. The faintest object found was 10.7 magnitude corresponding to a radius of 5.7 m. The size of an object detected at each OpNav is calculated by scaling the limiting magnitude at OpNav 16 assuming Vesta’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 smallest detectable radius was 5.3 m at OpNav 17. The mission’s OpNav observations span 3 months, a factor contributing to the robust nature 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 the RC1 sequences to radius 18.1 m. Nothing was found larger than 5.3 m radius. In Fig. 7B the fraction of objects found by 4 searchers at half-magnitude intervals, referred to as search or detection efﬁciency, are shown for station 5, 20 s exposures (see Supplementary material Table S2 for details of each searcher). The 50% detection efﬁciency magnitude is between 10.5 and 11.0, corresponding to radii of 8.0 and 6.3 m, respectively. The faintest object found in the 20-s exposures was 12.57 magnitude or 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 the 270-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 11.82 magnitude or 4.3 m radius. We expected fainter objects to be detected in 270-s exposures, while in fact the opposite is true. Most likely, this results from higher background noise from scattered light from Vesta in the longer exposure, as well as the fact that any fainter and fast-moving objects would spread across more pixels, resulting in a brighter limiting magnitude of detection. Thus, the 20 s exposures when co-added provide fainter detection limits than the 270 s exposures. But the completeness level is fainter in the 270 s exposures. Examining both Fig. 7 and Tables S1–S3 show that different observers had different search efﬁciencies. Some searchers missed some brighter objects, yet found very faint ones. Visual acuity is one criterion for effective searching, experience another, and method of searching, yet another variable. The ﬁgures, as well as results from previous satellite discoveries (Pluto’s moons for 214 L.A. McFadden et al. / Icarus 257 (2015) 207–216 possible that this repeated encounter has a pumping action that clears Vesta of any satellites? As far as we know, this line of inquiry has not previously been proposed and it may be worthy of further study. Another candidate explanation is the idea that stable orbits around Vesta are precluded by the particular structure of its gravitational ﬁeld. Vesta’s gravity ﬁeld is lumpy and contains spin–orbit resonances that make some orbital regimes dynamically unstable as discussed by Tricarico and Sykes (2010). They also point out regimes in which spin–orbit resonances are stable. While their results were computed based on relatively short-term numerical integrations prior to Dawn’s arrival at Fig. 6. Synthetic satellites were inserted into OpNav 16 images. Satellites with random orbits are seen with a trajectory that is markedly different from the background stars that trail in the direction of spacecraft motion when the spacecraft is pointed at Vesta. example Weaver et al., 2006), indicate that the discovery of any small body bears a component of chance. The faintest object detected, of magnitude 12.57, was found by blinking and visual detection by an experienced observer who has found asteroids previously. There were detections by the semi-automatic approach that were missed by the visual searchers and vice versa. In the OpNav 16 sequence with 1.5 s exposures, two visual observers detected objects fainter than 9th magnitude, yet missed objects of 6th magnitude. It is clear that to increase the detection limit of a search, multiple, experienced observers are needed and that multiple approaches improve the chances of detection. 7. Discussion Why might we expect to ﬁnd natural satellites gravitationally bound to Vesta? First it is a fairly common state for minor planets with a number of cases found among the Main Asteroid Belt, the Kuiper Belt and Near Earth populations. Second, bound systems persist, seeming to be robust to perturbations. 1999 KW4, a small Earth-crossing binary system (Ostro et al., 2006), follows a highly elliptical orbit with aphelion and perihelion distances of 1.08 and 0.20 AU respectively. Its motion exposes the binary to large variations in tidal forces, especially as it passes near to the Sun, yet it currently has a satellite. Is there something peculiar to Vesta that prevents it having a companion? We offer three possible explanations to account for its ‘‘missing moons.’’ First is that there is no mechanism preventing Vesta from having moons except for the ‘‘luck of the draw.’’ Vesta has a reasonably large SOI. Yet there must be a mechanism that allows a body to lose energy in order to be captured. The conditions of capture may never have existed for Vesta. Secondly, there may be a mechanism that strips Vesta of any orbiting satellites. In this context, any object that avoids the fates of either colliding with Vesta or failing to capture, could only persist in bound motion for a short period of time. One possible mechanism is the periodic encounter between Vesta and Asteroid 197 Arete. Every 18 years, Arete passes within 0.04 AU of Vesta from which an early mass of Vesta was derived (Hertz, 1968). Is it Fig. 7. (A) Detection efﬁciency (fraction found) for satellites inserted in OpNav 16 sequence binned at 0.5 magnitude intervals from 4 searchers’ efforts. (B) Same for station 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. L.A. McFadden et al. / Icarus 257 (2015) 207–216 Vesta, they strongly suggest that the lack of orbiting satellites cannot be caused by irregularities in Vesta’s gravitational ﬁeld. Numerical simulations of impacts (e.g. Durda et al., 2004) constrain the amount of material that could be launched into orbit, and long-term integrations might be used to constrain the lifetime of such satellites. If the formation and lifetime of orbiting bodies around Vesta were examined one result might provide insight into the question of whether Rheasilvia, if it were the primary source of ejected material, is on the order of 1 byr old (Marchi et al., 2012) or much 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 modeling the lifetime of material in orbit around Vesta. In any event, the absence of a natural satellite in orbit around Vesta today is a fact to be considered in any modeling scenario of Vesta’s impact history. 8. Conclusion The satellite search carried out with the Framing Camera on Dawn is comprehensive in terms of the proximity of the spacecraft to Vesta, the time spent searching and the number of searchers and diversity of analysis approaches used. We have reduced the limiting radius of any possible satellite by a factor of four over previous studies. At this point, we take the lack of moons around Vesta as a supported fact with little probability of being overturned. Rather than regarding it as a simple null result, we believe it offers clues to Vesta’s collisional history and dynamical environment. Acknowledgments We thank Herbert Raab for working with us to modify Astrometrica so that asteroids could be projected into the Dawn spacecraft’s frame of reference. The Dawn Flight Team made the observations possible and we thank them for their superior driving and operations implementation. This work was supported by the Dawn mission through NASA’s Discovery Program, NASA’s Dawn at Vesta Participating Scientist Program through Grants NNX10AR56G to University of Maryland at College Park and NNX13AB82G to Planetary Science Institute. Part of this work was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA to UCLA NASA contract number, NNM05AA86C. The Framing Camera project is ﬁnancially supported by the Max Planck Society – Germany and the German Space Agency, DLR. Appendix A. 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