Searching for known asteroids

in the WFI archive using Astro-WISE

Jeffrey Bout

A ”small research” project for bachelor studentsSupervisors: Gijs Verdoes Kleijn and Edwin Valentijn

Kapteyn Astronomical InstituteUniversity of Groningen, the Netherlands

May 7, 2007

Abstract

This study is aimed at deriving new and/or improved photometry forknown asteroids using Wide Field Imager (WFI) archival images. Wepresent studies on a set of 354 asteroid occurrences of 144 different aster-oids found on WFI images using the Astro-WISE system. The set is likelyto be polluted with 3% non-asteroids. The set was found using a set of 798asteroid predictions obtained with the Skybot web service. So for 44% ofthe predictions, the asteroids were found on the WFI frames. Identifyingthe asteroids on the frames was done by comparing sizes and phase anglesof found sources within 15 arcsec of the predicted position with predictedvalues. Of the found asteroids, 88% were found within 3 arcsec from theirpredicted positions. The most plausible cause for not finding 56% of theasteroids is the big uncertainty in their orbital elements. Nevertheless,56% of the found asteroids were unnumbered asteroids, asteroids of whichtheir orbital elements are not yet known with high precision.The found asteroids were imaged using a B band filter, a V band filter orboth. For the V band, the measured luminosity is about 0.4 magnitudesweaker than the predicted visual magnitude. This is in agreement withthe value found by Juric et al, 2002 [1] of 0.41 magnitude with a rmsof 0.35. For the B band frames, the measured luminosity is about 1.0magnitudes weaker than the predicted visual magnitude. This is causedby a lower luminosity of asteroids in the B band. For 36 asteroids bothB band frames and V band frames were found. For these asteroids, B-Vestimations results in a B-V of 0.73 with a rms of 0.20. This is in agree-ment with the value found by Ivezic et al, 2001 [2]. They found that themajority of asteroids have a g-r of +0.65, which corresponds to a B-V of+0.85 when taking B-V is g-r + 0.2.

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1 Introduction

Within our solar system, hundreds of thousands of asteroids have been discov-ered. The big majority of these objects are discovered in the last 10 years. Theproperties of these objects are not well known. Only 40% of them have wellknown orbits and have an official number. Other properties like their colours,albedos and sizes are known for a tiny fraction of the known asteroids. To getthese properties photometric measurements are necessary. To get these mea-surements dedicated surveys can be done, but a lot of photometric measure-ments are also hidden inside frame archives of today’s observatories. Inside theAstro-WISE environment a number of these archives are stored. After develop-ing some algorithms, the photometric data of known asteroids can be retrievedfrom the archives. In this document, the results of such a study are presented.In chapters 2 and 3, the current knowledge about asteroids is presented as wellas techniques and software to study the properties of asteroids. The next twochapters deal with our steps in deriving the asteroid properties from archivalimages and with presenting conclusions about the found asteroid properties.

2 Asteroids and other small bodies within thesolar system

Besides planets, there are lots of small objects circling the Sun. Most of themwere undiscovered until a decade ago, but this is changing rapidly. Nowadaysmuch effort is done in discovering them mainly because a tiny fraction of themcan be a future threat for our planet. As a big side-effect, there is a big increaseof knowledge about the small objects within the solar system and the solar sys-tem itself.As we know more and more of the small objects, many types of small objectshave been found. For example: objects between Mars and Jupiter, objects inthe orbit of Jupiter, objects very far away from the sun, objects with extremeelliptical orbits and so on. Through the ages the ways of classifying these dif-ferent groups have changed a lot. For example: when Ceres was discovered in1801 it was first called a planet. After some years it was called an asteroid andsince 2006 it is called a dwarf planet. Within the International AstronomicalUnion (IAU) there have been lots of discussions about this the last couple ofyears which resulted in a number of definitions of different types of objects.

2.1 SSSBs

Objects within our solar system are divided in three main groups: planets,dwarf planets and small solar system bodies (SSSBs) [3]. SSSBs include as-teroids (also called ”minor planets” or ”planetoids”), comets and other smallbodies. Classically, the difference between asteroids and comets was quite clear:asteroids were small solid bodies, appearing as stellar objects (asteroid = Greekfor ”star-like”). Comets were identified by their nebulous envelopes made of ice

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and dust. The nebulous envelope of a comet is called ”coma” and is formedwhen the comet gets close to the sun on its highly elliptical orbit. It gives thecomet a ”fuzzy” appearance.Nowadays, there are objects found which are somewhere in between asteroidsand comets. When discovered no nebulous envelope was visible (so get listed inasteroid catalogues), but later on nebulosity appeared. Nevertheless, asteroidsand comets still get listed in their own catalogues.As the luminosity of comets is highly dependent on the existence of an activecoma, many previously discovered comets will be invisible when searching forthem on frames made many years before or later.

2.2 Asteroids

Within our solar system, an enormous number of asteroids exist. Estimationsof the total number of asteroids above 1 km in diameter are between 1.1 and1.9 million [4]. As of April 2007, over 370,000 asteroids have been discovered[5]. Of all these objects, only 220 of them have a diameter of 100 km or more.

Before 1995, most asteroids were discovered by visually comparing individualphotographs of a region in the sky using a special instrument called a ”stereo-scope”. As of April 1995, 27,000 asteroids were discovered [5]. In 1995, auto-mated systems for searching asteroids became available and have dramaticallyincreased the number of discoveries. As of April 2007, over 370,000 asteroidshave been discovered [5]. The present rate of discoveries is about 5000 asteroidsper month.Nowadays, the two most important projects for searching asteroids are ”LincolnNear-Earth Asteroid Research” (LINEAR) and ”Near-Earth Asteroid Tracking”(NEAT). In the near future a new project called ”Panoramic Survey Telescopeand Rapid Response System” (Pan-STARRS) will be added. The main pur-pose of these projects is searching asteroids that could be a future threat forour planet. Of these projects, the LINEAR project is running since 1998 andis responsible for most asteroid discoveries. As of October 2004, over 210,000asteroids were discovered [6] within the LINEAR project. Most of these aster-oids are found near the ecliptic plane, which is studied intensively because mostasteroids (especially Near Earth Objects, NEOs) are located inside this region.

2.3 Asteroid orbits

The big majority of known asteroids have orbits around the Sun lying betweenthe orbits of Mars and Jupiter, roughly between 2 and 3.5 AU. This groupof asteroids is known as the ”Main Belt”. Their orbits are elliptical, have ec-centricities between 0.01 and 0.3 and have inclinations, relative to the ecliptic,that range between 0 and 35 degrees [7]. So hundreds of thousands of asteroidsshould be visible near the equator. The mean density of known asteroids within20 degrees from the ecliptic is about 10 to 20 asteroids per square degree or 2to 5 asteroids on a 30 by 30 arcmin wide field detector.

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In order to store the position and movement of discovered asteroids the prop-erties of their orbits around the Sun have to be described. When the orbit of acelestial body is considered to be fixed, it can be given by a number of orbitalelements. The traditionally used set of orbital elements is the set of Keplerianelements, which includes the inclination, longitude of the ascending node, eccen-tricity, argument of perihelion, semi major axis and mean anomaly of an orbit.In reality, orbits of objects in the solar system are never fixed. They changedue to many effects like the gravitational pull of other bodies within the solarsystem, nonsphericity of the sun, atmospheric drag, relativistic effects, radiationpressure and electromagnetic forces. Especially for asteroids the changes of theirorbits are considerable. As most of them have orbits near the orbit of Jupiter,they are heavily pulled by this planet. As a result of this, the orbital elements ofmost asteroids change with time. Fortunately, the evolution of orbital elementsof asteroids can be predicted as will be shown in chapter 4.

Estimating and improving the precision of the orbital elements of the extremelybig amount of asteroids and other SSSBs is a time consuming process. Nowa-days, it is done by the Minor Planet Center (MPC), a division of the Smithso-nian Astrophysical Observatory [8]. In order to do this, the MPC collects allobservations done for these objects. The MPC generally publishes new data onasteroids and other SSSBs on a monthly base. As the number of observationsfor each asteroid increases, the precision of the asteroid’s orbit, size and albedoincreases. As soon as the properties of an asteroid are well enough known, theobject gets an official number. Nowadays, this is the case for only 40% of theknown asteroids.

To locate known asteroids on the night sky their ephemerides should be cal-culated. Ephemerides are a collection of properties of an object on a certaindate and time. These properties include at least the position of the object onthe night sky, but often also include lots of other properties like (apparent) lu-minosity, distance, (apparent) velocity and the elongation to the sun.The position of an object on the night sky is dependent of the location fromwhich the observations are done. When an object is 1 AE away, the positionon the night sky found from a certain location on Earth (called the topocentriccoordinates of an object) can alter about ten arcsec from the position found ifthe observation was done from the centre of the Earth (called the geocentriccoordinates of an object). These changes will get smaller for objects that arelocated further away.

2.4 Asteroid albedos, colours and sizes

Our knowledge about asteroids has increased dramatically over the last decade.Nevertheless, properties of asteroids like their albedos, colours and sizes are stillnot well known. This is because present asteroid discovery projects NEAT andLINEAR are focused on ’just’ finding asteroids and not on doing photometric

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measurements on them. A good option for obtaining photometric measurementsis by studying the SDSS moving objects catalogue (SDSSMOC). In 2004 the 3rdrelease of this catalogue was released containing astrometric and photometricdata for 204,305 moving objects. Of those, 67,637 are linked to 43,424 uniqueobjects from the ASTORB file [9]. One example of a study of this cataloguewas published in 2002 by Juric et al. [1]. Their findings on 2641 asteroids wereobtained by searching for known asteroids in the SDSS archive. Nevertheless,on the majority of moving objects inside the SDSSMOC still no research hasbeen published.

The easiest of the three properties to determine is the colour (or spectral shape).It can be determined directly by doing photometric measurements (measuringthe luminosity quantitatively) of the object through different filters. From thetiny fraction of asteroids on which photometric measurements are done so far,different types of asteroids were qualified. In 1975, Chapman et al. [10] havedone research on 110 asteroids and developed a classification system based ontheir colour and albedo. They found three types of asteroids (called C-, S- andM-type asteroids). This classification system was later extended with variousother asteroid types.

Nowadays, the size of an asteroid can almost never be measured directly throughmodern techniques. Most asteroids are too small to be resolved even when im-aged with the highest quality instruments like the Hubble Space Telescope.The usual way to determine the albedo of an asteroid is done by comparing theluminosity and the size of the object using the formula:

L (λ) ∝ D2 P F (λ) A (λ) (1)

were L is the luminosity of the asteroid at wavelength λ, D is the size of theasteroid, P is the fraction of the surface being illuminated as seen from theobserver, F is the incoming flux from the Sun at the asteroid at wavelength λand A is the albedo of the asteroid at wavelength λ. So as long as the size ofan asteroid is not known, its albedo isn’t known as well. But when assuminga certain value for an asteroid’s albedo while knowing its luminosity, the sizeof the asteroid can be calculated. Asteroid albedos are uncertain, but theydepend on the colour (or asteroid type) of the object, because both the colourand albedo of an asteroid will depend on the object’s composition of surfacematerials. So in an indirect way, colour information of asteroids combined withtheir luminosities tells us something about their sizes as well. And studyingasteroid sizes is important as it will give us information about the total mass ofthe asteroid belt, about the sizes and masses of objects causing a threat for lifeon Earth and about the origin of the whole solar system.

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3 Astro-WISE and the WFI archive

Before 1995, most asteroids were discovered by visually comparing individ-ual photographs of a region in the sky using a special instrument called a”stereoscope”. Nowadays, searching for known and unknown asteroids on largeamounts of astronomical frames is relatively easy, as many frames are storedin computer databases. Computer algorithms can be developed in order toautomatically analyse all objects on these frames and compare them with pre-dicted positions when searching for known asteroids. So searching for objectslike asteroids no longer have to be done manually.

3.1 Astro-WISE

A very useful database containing archives of frames for searching asteroidsis the database being part of the Astro-WISE environment [11]. Astro-WISEstands for ”Astronomical Wide-field Imaging System for Europe” and is built bya partnership between OmegaCEN-NOVA / Kapteyn Institute (Groningen, TheNetherlands; coordinator), Osservatorio Astronomico di Capodimonte (Naples,Italy), Terapix at IAP (Paris, France), ESO, Universitts-Sternwarte und Max-Planck Institut fr Extraterrestrische Physik (Munich, Germany). Astro-WISE isa computational environment which includes software tools for archiving, access-ing, distributing and processing the frames stored in the environment. Resultsfrom processing (calibrated images, source catalogues) are kept in Astro-WISEand can be shared with other users. The pre-built routines facilitate the searchfor asteroids within the archived images. Astro-WISE has web-based interfacesto the calibration and analysis tools as well as a command line interface withinthe Python programming environment. It is a first step towards a truly virtualobservatory, defined as a collection of data archives and software tools forminga computational environment allowing astronomers anywhere to search, access,analyse, and combine astronomical data for research. Astro-WISE includesdetermination of sources on frames, using the well known Sextractor routines[12]. Using these routines, asteroid candidates can be found within the obtainedsource collections.

This far, the database of Astro-WISE contains frame archives from differentwide field detectors like the Wide Field framer (WFI) of the 2.2m MPG/ESOtelescope at La Silla [13], the Wide Field Camera (WFC) of the 2.5m INT tele-scope at La Palma [14], the Subaru Prime Focus Camera (Suprime-Cam) of the8.2m Subaru telescope at Mauna Kea [15] and the OmegaCAM camera of thenot jet operational 2.5m VST telescope at Paranal [16]. The big majority offrames in the database are made with the WFI detector (as of April 2007, about15,000 raw science WFI observations of which about 2,000 are astrometricallyand photometrically calibrated). So logically, in this project the WFI framesare used to search for known asteroids.

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3.2 Wide Field Imager (WFI)

The Wide Field Imager (WFI) of the 2.2m MPG/ESO telescope at La Silla isa wide field detector with a field of view of 34 by 33 arcminutes. It consistsof a mosaic of eight 8M pixel CCDs where each CCD covers 487 by 975 arcsec(or 0.037 square degrees) of the field of view of the detector. The pixel scaleof the WFI CCDs is 0.238 arcsec per pixel. When an exposure is taken withthe detector, all 8 CCDs are exposed simultaneously. So (most of) the framesof WFI belong to collections of 8 frames having the same date of observation,integration time and telescope aiming direction.The WFI has a big collection of narrow, medium and broad band filters. Onlyframes taken with some of the broad band filters will be suitable for detectingfaint asteroids. Asteroids are expected to be detected most efficiently in the Band V band, due to the high solar emission, the high asteroid reflectivity andthe high WFI detector sensitivity in these bands. Frames in other bands like Uand R will be less effective for detecting asteroids.

4 Searching for known asteroids

Finding known asteroids in a big archive of frames consists of a number of steps.First the set of to be studied frames has to be determined. Astro-WISE containscurrently mostly uncalibrated frames which have to be calibrated first beforebeing able to get high precision coordinates of sources. So just searching aster-oids on all WFI frames is not easily done. The next step is obtaining predictedasteroid positions for the calibrated frames using some external modules. Dif-ferent methods were tried before finally a quick and precise method was found.Finally, selection criteria have to be developed for getting the right sources fromthe frames near the predicted positions.In total, eight steps were done before a collection of good asteroid candidateswas obtained. This chapter deals with these eight steps. As a result, 354 goodcandidates were found which were studied in chapter 5.

4.1 Step 1: Determining the set of to be studied frames

For the WFI imager, the Astro-WISE environment contains mostly raw scienceframes (frames for which astrometry and photometry is not done yet). Butwhen we want to search for known asteroids, we need images which are cali-brated (they are called ’regridded frames’ in the Astro-Wise environment). Toget these images, raw science frames can be led through the image pipeline ofAstro-WISE. The resulting calibrated images could be studied for known aster-oids.As creating calibrated frames for all the raw science frames in Astro-WISEwould be a time consuming process, it was necessary to make a selection ofraw images for calibration. Making this selection of images also was necessary,because calculating the asteroid ephemerides for each image was going to takesome time as well. Making the selection should be done in a clever way in order

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to find as many asteroids as possible at the end.

When making the selection of images, the most important criterion was thearea on the night sky on which the asteroids were going to be searched for. Thebig majority of asteroids is located more or less on the ecliptic plane, so it iswise to take only frames taken from areas in this region. Here, images weretaken of which their central declination deviated no more than 20 degrees fromthe ecliptic plane.A second criterion for selecting images is by their integration time. This inte-gration time should be long enough to get the (mostly) faint asteroids visible onthe frames. A long integration time is also handy as it lets asteroids show theirmotion on the frame during the integration time. Here, a minimum integrationtime of 4 minutes was chosen. For this lower limit integration time, 97% of atypical set of asteroids will have a track length of more than 0.4 arcsec which isprobably enough to be detected.

Selecting raw science frames using the just mentioned criteria for the WFI im-ager resulted in 10,824 frames, spread over the eight chips of the WFI imager.As processing these images still would take a lot of time, this number was to bereduced. This reduction had to be chosen so the aims of the project are met asgood as possible.Searching for known asteroids on archived images and do photometric analy-sis on them are the main aims of this project. It can be done following twostrategies:

1) Restricting that imaged areas were imaged for multiple filters during oneobserving night. With this restriction colour information (like B-V) forasteroids can be obtained. With this restriction the number of suitableframes is expected to be reduced dramatically.

2) Not making this restriction, but instead just take one observation from animaged area during one observation night. When following this strategyphotometric data will be found for many asteroids, but colour informationwill not be found.

Here, both strategies were followed. As first a sample was created following thesecond strategy. A routine was developed which selected non overlapping areason the night sky which were not imaged more than one time during one observ-ing night and for which calibration observations were available. This routineresulted in 621 non overlapping raw science frames. This set of 621 raw sci-ence frames was used as input for the Astro-WISE pipeline to create calibratedframes. After inspecting some of these images, only the frames taken using a Bfilter (B/99, WFI #842) and a V filter (V/89, WFI #843) looked usable. Theframes taken with other filters (U/38, Rc/162 and Ic/lwp) did not. This agreeswith the expectation that asteroids are most efficiently detected in the B andV band, due to the high solar emission, the high asteroid reflectivity and thehigh WFI detector sensitivity in these bands. After excluding the frames for

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the U/38, Rc/162 and Ic/lwp filters, 384 frames remained.

Next, a sample was created following the first strategy: selecting frames onareas on the night sky which were imaged multiple times during one observ-ing night. To this strategy the criterion was added that both B and V frameswere taken. This was done to be able to measure the B-V colour properties ofasteroids. Selecting frames resulted in 1081 raw science frames. Leading theseframes through the Astro-WISE pipeline did result in 1076 calibrated frames.Combining them with the 384 non-overlapping frames resulted in 1380 frames(80 less than perhaps expected, caused by an overlap between the two sets). Allthe calibrated frames were delivered by Gijs Verdoes Kleijn. The calibrationconsisted of de-biasing, flatfielding and astrometric and photometric calibrationin batch mode. For some nights no standard star field observations were avail-able. In those cases we applied the a typical zeropoint for WFI as derived froman analysis of the zeropoints as a function of time. We decided not to removebad pixels and columns and cosmic-rays during the calibration but perform thisduring the searching for asteroids.

For the total set of 1380 frames, asteroid occurrences will be predicted andcandidates will be searched for in the following steps. For the 1380 frames,integration times were between 240 and 900 seconds. They were taken betweenJune 13th, 1999 and May 6th, 2003. Other statistics are not mentioned here,as they will become more interesting after further processing steps are done.

4.2 Step 2: Calculating predicted asteroid ephemerides

As the area of a WFI CCD is 0.037 square degrees and the known asteroiddensity near the ecliptic is about 10 to 20 per square degree, the number ofpredicted asteroid occurrences on the frames will be in the order of 500 to 1000.To predict the positions of known asteroids on the 1380 selected WFI frames,the ephemerides of many asteroids had to be calculated with high precision forthe dates and times of all frames. Different methods were tried before finally aquick and precise method was found.

The first method used was calculating the ephemerides of many asteroids usingthe PyEphem library together with the Astorb table. PyEphem is a pythonlibrary for calculating the ephemerides of celestial bodies on particular dates[17]. Internally, it calculated the positions using routines from the XEphem as-tronomical ephemeris package made by E. C. Downey [18]. The Astorb table isa table containing high-precision, up-to-date orbital elements and ephemeridesuncertainties of over 300,000 asteroids [19]. The orbital elements are based ondata from the Minor Planet Centre. The epoch for the orbital elements for acertain version equals the publication date of the version. Ephemerides of mostnon-Earth-approaching asteroids can be calculated with the table to arcsec ac-curacy within 50 days of this epoch using an ephemerides tool like PyEphem.Using this method resulted in quick but uncertain calculations. Calculating the

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ephemerides for one frame took just 3 seconds, but visually checking framesfor asteroids on predicted positions showed uncertainties of many arcminutes.This was probably caused by the big difference of epochs of the frames and theAstorb table. With just one version of the Astorb table this difference couldnot be kept small as the studied frames were taken from 1999 to 2003.

A possible solution for the uncertainties in the calculated ephemerides was cal-culating the orbital elements for the date and time of each frame. Then theepochs of the frames and the orbital elements should be the same and calculat-ing the ephemerides using PyEphem might be done with a minimal error.Calculating orbital elements for certain dates could be done with OrbFit. Thisis a software package for computing orbital elements for asteroids for any epochgiven their current orbital elements, among many other features. So when com-bining this package with the PyEphem package and the Astorb orbital elementstable, positions of asteroids on the celestial sphere in the past or future can becalculated [20]. OrbFit predicts orbital elements using all planets as perturbingmasses. It incorporates multiple numerical integration schemes, choosing thestep size automatically to achieve a prescribed truncation error. It also incor-porates general relativistic perturbations for the gravitational field of the Sunas well as the Earth (only for near Earth asteroids). When calculating the ob-server location, the package takes into account the motion of the Earth aroundthe Earth-Moon barycentre as well as precession, nutation and Earth rotation[21].With the combination of OrbFit, PyEphem and Astorb, ephemerides could becalculated with high (arcsec) precision. Unfortunately, calculating them for oneframe took about 1.5 hour. Most of the 1380 frames were taken with the 8 chipsWFI detector, so these 1380 frames belonged to more or less 172 different datesand times. The process for calculating the ephemerides would take 11 days.This was acceptable for calculating ephemerides for our collection of frames,but not very flexible when used on other collections in the future. Then wewere notified of the existence of Skybot.

The Virtual Observatory Sky Body Tracker (or short: Skybot) is a web ser-vice (an on-line tool) providing high precision ephemerides of asteroids [22]. Itcalculates the ephemerides for a given field of view at a given date and time.The web service is able to provide ephemerides fast and with high precision,because it uses a database of pre-computed ephemerides for all known solar sys-tem objects for many epochs (interval of 10 days), which were issued from theAstorb table. As of April 2007, Skybot does the calculations for over 360,000asteroids. Calculations for one frame typically take about 15 seconds.Calculated topocentric or geocentric ephemerides by Skybot include the objectname and number, the astrometric J2000 equatorial coordinates, the asteroidclass, the apparent visual magnitude, the error on the position, the apparentangular size, the motion on the celestial sphere (velocity in arcsec per hour plusdirection) among other properties.

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For the 1380 frames, topocentric asteroid ephemerides were calculated in lessthan 6 hours or 15 seconds per frame. The fact that many frames had the samedate and time was ignored, as this made the routines for requesting and storingasteroid ephemerides much easier to develop.819 occurrences of asteroids were predicted on the 1380 frames. This value iswithin the range of expected occurrences of 500 to 1000. The occurrences wereof 265 different asteroids (of which 91 have an official number) and were dis-tributed over 514 of the 1380 frames. So on 37% of the frames, one or moreasteroids were predicted.

At this stage, two interesting properties of the predicted asteroids are theirtrack length and apparent visual magnitude distributions. These properties saysomething about the probability of detecting and recognising asteroids on theframes as very faint asteroids are likely to remain undetected and slow asteroidscould not be separated from stars.

Figure 1: Histogram of the expected track lengths (in arcsec) of 819 asteroidoccurrences during the integration times of the studied frames.

The expected track length of the asteroids can be calculated using their ex-pected motion in arcsec per hour and the integration time of the frames theyare on. A histogram of the expected track length is shown in figure 1. Of the819 asteroid occurrences only 21 will have a track length of 0.4 arcsec or less.These asteroids are removed from our list as their motion is too low to measurecompared to seeing effects (see section 4.6) and we keep 798 occurrences of 261different asteroids (of which 91 have an official number), distributed over 503frames.The frames on which no asteroids were predicted were no longer interesting.They were excluded from further processing steps. So on continuing steps, 503frames were processed containing 798 predicted occurrences of asteroids. Ofthe occurrences, 170 were of asteroids which have no official number. These

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asteroids do not have an official number, because their orbit is not well known.Their predicted positions on the sky are expected to differ from observed posi-tions more than asteroids which do have an official number.

Figure 2: Histogram of the expected visual magnitudes of 798 asteroid occur-rences.

The predicted visual magnitudes of the asteroid occurrences are between 15and 24, as visible in figure 2. The majority of visual magnitudes are between18.5 and 22.5. A fraction of the fainter asteroids are expected to be invisible onthe frames as you will need a lot of integration time if you want to detect suchfaint objects.

4.3 Step 3: Extracting imaged sources near the predictedpositions

To search for sources on the frames the Sextractor module can be used, whichis integrated inside the Astro-WISE environment. When a source is found bySextractor, lots of properties are given for the source like the luminosity, theposition, the shape and the position angle (which is the direction of movementin case of a moving object).

When searching for sources around a predicted asteroid position, a maximumdistance for selected sources had to be chosen. This distance should be bigenough that not well known asteroids still get selected. Inspection of the er-rors in position given by Skybot showed that this error was of little value: thefound deviation of asteroids when visually inspecting frames was very often incontradiction with the error given by Skybot. So the maximum distance had tobe found in a different way. To choose this maximum distance the number ofsources for different distances was studied (see figure 3).

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Figure 3: Histogram of the radial distances of the 2269 found sources within 15arcsec from the expected asteroid positions.

When studying the area around an expected asteroid position, two types ofsources are expected to be found: asteroids and randomly positioned objects(stars, galaxies, bad pixels, cosmic rays, etc.). The number of randomly po-sitioned objects within a thin ring is expected to be proportional to the ringradius, because the surface of a thin ring is the thickness of the ring times twotimes pi times the radius of the ring. In the histogram the randomly positionedobjects are visible as the linearly increasing number of objects between 4 and15 arcsec away from the expected asteroid position. A line trough these valuesreaches zero for 0 arcsec position deviation as expected.In the histogram also a high peak of non random objects are visible between 0and 3 arcsec away from the expected asteroid position. As they are non random,they are likely to be the asteroids we are looking for. From this we can concludethat the majority of asteroids will be less than 3 arcsec away from the expectedposition. Nevertheless, to avoid that not well known asteroids are excluded fromour selection of sources, all sources having a distance of 15 arcsec or less wereselected. In later steps this distance could be lowered if needed.

Searching for sources within 15 arcsec of the 798 predicted asteroid occurrencesresulted in 2269 sources distributed over 649 of the asteroid occurrences. Sofor 149 asteroid occurrences no sources were found within 15 arcsec and for649 asteroid occurrences about 3 objects per asteroid occurrence were found.Inspection of the images showed that the Sextractor module on some occasionssplit highly elliptical asteroid sources into two sources. This will to be correctedin step 5 (section 4.5). Also a lot of sources seemed to be derived from badsources of the frames (bad pixels, bad columns, cosmic rays). These had to beexcluded from our set of sources first.

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4.4 Step 4: Excluding bad sources

When studying sources found by the Sextractor module, a lot of them turnedout to be bad sources like bad pixels, bad columns and cosmic rays. Fortunatelymost of them were easily distinguished from other sources: on the WFI framesthey are very small (less than 1 arcsec). We performed a visual inspection toensure that these sources are indeed not astronomical sources: no PSF profileappeared for these sources. Removing sources smaller than 1 arcsec hopefullyremoved most bad sources.

Figure 4: Histogram of the minor axes in arcsec of the 2269 found sources within15 arcsec from the expected asteroid position.

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Figure 5: Cut-outs centered on 50 of the 1310 sources which were removed bythe selection criterion, because their minor axes were smaller than 1 arcsec.These sources are bad pixels, bad columns and cosmic rays.

Figure 6: Histogram of the radial distance of 959 sources which survived theselection criterion, because their minor axes were bigger than 1 arcsec. Non-random positioned objects appear within 3 arcsec.

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In figure 4 the high number of small sources is clearly visible. 1310 of the2269 sources were removed in this process. They are shown in figure 5. 959sources survived the new selection criterion. They were found for 532 of the649 asteroid occurrences. 117 asteroid occurrences lost their sources during thisselection criterion. Visual inspection of the remaining sources showed that theprocess did not remove all bad columns from the set of sources. They are of lit-tle concern here. It will turn out that proceeding steps will remove them as well.

After removing the bad sources it is expected that a lot of random objectsare removed from our set of sources. The histogram of position deviations infigure 6 shows that this is the case. As before, the remaining random objectsare visible as the linearly increasing number of objects between 3 and 15 arcsecaway from the expected asteroid position. A line trough these values reacheszero for 0 arcsec position deviation as expected. Fluctuations from the linearbehaviour is caused by asteroids which were imaged many times in order todetermine their colour information.

4.5 Step 5: combining split up sources

During retrieving sources from the frames by the Sextractor module, a numberof highly elliptical sources (asteroids?) were split into two sources. A routinefor combining these sources (obliging the position angles of two sources and theline connecting the two to be within 10 degrees from each other and obligingthe sum of the major axes of the sources to be at least half the length of thecalculated major axis of the combined source) found 54 sources which couldbe combined to 27 combined sources. After combining the 54 split up sources932 remain in the set of sources for the 532 asteroid occurrences. Two of thecombined sources are bad columns. As before, this is of little concern here. Thebad column will be removed in proceeding steps.

4.6 Step 6: Searching for asteroids by using the expectedtrack length

After the previous steps, most of the 932 sources will be astronomical objects.A way to distinguish asteroids from other astronomical sources is by comparingthe differences between the expected track length of the to be found asteroidand measured track lengths of the sources. The measured track lengths of thesources (from now called ’source length’) can be calculated by subtracting thesource minor axis (’B’ in the Sextractor module) from the source major axis(’A’ in the Sextractor module). In figure 7 these differences are show. On thehorizontal axis, the source lengths of the sources are shown. On the verticalaxis, the track length differences are shown.

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Figure 7: Scatter of the absolute track length deviations (arcsec) and the sourcelength (arcsec) of 932 sources having minor axes bigger than 1 arcsec. Sourceswith absolute track length deviations bigger than 2 arcsec will be excluded bythe selection criterion as well as sources with source lengths smaller than 0.5arcsec that have a position deviation larger than 2 arcsec.

In the figure, three groups of objects are seen:

1) A horizontal group of objects for which the track length difference issmaller than about 2 arcsec, independent of the (expected) source lengths.Their source length range from 0 to 12 arcsec. These objects are asteroidcandidates.

2) A vertical group of objects for which their source length is smaller thanabout 0.5 arcsec, independent of the track length difference. Their tracklength difference range from 0 to 11 arcsec. These objects are more or lesscircular objects, for example stars and QSO’s.

3) A group of objects having both a source length bigger than 0.5 arcsec anda track length deviation bigger than 2 arcsec. These objects are ellipticallyshaped were the asteroid is suspected to be differently shaped. So they areelliptically shaped objects, but not the predicted asteroid. So for examplegalaxies.

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So a first criterion for searching candidate asteroids is having a track lengthdifference smaller than 2 arcsec. Unfortunately, when visually inspecting thesources with a bigger track length difference, 3 combined sources (which seemto be asteroids) from the previous step have this property. This was caused byuncertain determinations of the source lengths of the combined sources in theprevious step. When for combined sources the track length differences are keptsmaller than 5 arcsec, these 3 combined sources survive the criterion.From the three groups of objects, the first two overlap. The overlapping regioncontains both asteroids and non asteroid objects. They are objects with both asmall source length (smaller than 0.5 arcsec) and a small track length difference.If we were to add the criterion that the source length should be bigger than 0.5arcsec, a lot of non-random positioned objects (asteroids?) would get excluded.To prevent this, the criterion was expanded by only excluding objects with asource length smaller than 0.5 arcsec if their position deviation is more than 2arcsec (non-random appearing sources in figure 6).In figure 7 groups of sources with a slope of -1 are visible. These groups aresources from different frames belonging to the same asteroid (in order to getcolour information for those asteroids).

After the criterion was run on the set of sources, 468 sources were excludedand 464 of the 932 sources remained for 401 of the 532 asteroid occurrences.131 asteroid occurrences lost their sources during this selection criterion. Theexcluded sources are shown in figure 8.

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Figure 8: Cut-outs centered on 50 of the 932 sources which were removed bythe selection criterion, because their source lengths were incomparable with theexpected track lengths of the asteroids.

4.7 Step 7: Searching for asteroids by using the expecteddirection of movement

Asteroids move on the sky with a certain direction. For all the predicted aster-oids this direction of movement was delivered by Skybot. As the direction ofmovement is a direct function of the orbit of the asteroid, the value deliveredby Skybot can be assumed to be very precise. Figure 9 shows a histogram ofthe difference between the predicted directions of movement and the measureddirections of movement for the 464 sources. The majority of sources in thehistogram has a deviation of less than 12 degrees. These sources are asteroidcandidates and insisting that the deviation is less than 12 degrees seems to bea good criterion.

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Figure 9: Histogram of the absolute angle deviations in degrees of 464 sources.Non-randomly oriented sources have measured directions of movement deviatingless than 12 degrees from the expected directions of movement of the asteroids.

Figure 10: Scatter of the absolute angle deviations (in degrees) and the sourcelengths (in arcsec) of 464 sources. Increasing absolute angle deviations withdecreasing source lengths are visible.

It is interesting to study how the deviation in direction of movement is relatedto the source length of the sources. This is shown in figure 10. You can expectthat with decreasing source length the deviation in direction of movement get

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higher. This is caused by an increasing uncertainty in measuring the directionof movement from the frame by the Sextractor module. In the figure this effectis well visible. The figure shows that for sources with source lengths of morethan 2 arcsec, the direction of movement can be measured within 5 degree un-certainty. When the source length gets lower than 2 arcsec, the deviation indirection of movement increases dramatically.In the previous step, objects with a measured track length of less than 0.5 arc-sec only passed the criterion when the position deviation was less than 2 arcsec.As they are likely to be asteroids and their direction of movement cannot bemeasured accurately, the direction of movement criterion was not executed onthese objects.

After the criterion was run on the set of sources, 98 sources were excludedand 366 of the 464 remained for 360 of the 401 asteroid occurrences. 41 aster-oid occurrences lost their sources during this selection criterion. The excludedsources are shown in figure 11.

Figure 11: Cut-outs centered on 50 of the 98 sources which were removed bythe selection criterion, because their their directions of movement were incom-parable with the expected directions of movement of the asteroids.

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4.8 Step 8: Excluding asteroid occurrences with multiplecandidates

After the previous steps only 6 (or 2%) of the 360 asteroid occurrences havetwo possible candidates. All other 354 different asteroid occurrences have justone possible candidate. As the processing steps were quite strict, most of thesecandidates will in fact be the asteroid. More selection criteria (like searchingfor objects in star catalogues and insisting certain magnitude deviations) can bedone in future. For the 6 asteroid occurrences with multiple candidates the can-didates simply were removed from the set of sources. So 354 (or 44%) of the 798asteroid occurrences we started with remain with an asteroid candidate. Thesecandidates are studied in chapter 5. This chapter is concluded with an overviewof the processes done during this chapter for retrieving source candidates forthe asteroid occurrences. This overview is shown in table 1.

Table 1: Processes done for retrieving source candidatesProcess Passed Asteroid occurrences Passed SourcesStep 2: Predicting asteroids 798 -Step 3: Extracting sources 649 2269Step 4: Excluding bad sources 532 959Step 5: Combining split sources 532 932Step 6: Excluding bad lengths 401 464Step 7: Excluding bad angles 360 366Step 8: Excluding multiple sources 354 354

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5 Found asteroids

Figure 12: Cut-outs centered on 50 of the 354 found asteroid candidates.

For the 798 predicted asteroid occurrences, we found 354 good candidates whichare 44% of the total. These objects are shown in figure 12. The 354 found oc-currences were of 144 different asteroids of which 64 have an official number.So 144 or 55% of the 261 searched for asteroids were possibly found and 64 or70% of 91 numbered asteroids were possibly found.

Before studying the found candidates, we want to know how many of the ob-jects are indeed the searched for asteroids. So we want to know how many nonasteroids (could) have survived the previous selection criteria or how much pol-lution our data contains. This can be done by running the selection criteria ondifferent parts of the frames we have used (so where no asteroids are likely tobe found). When doing this a couple of times 2064 sources were lead throughthe criteria. This did result in 11 possible candidates so about 11/2064 = 0.5%succeeded to pass the criteria. As we started with 2269 to be studied sourceswithin 15 arcsec of the predicted asteroid positions, about 0.5% or 11 non as-teroids sources are expected to pass the selection criteria. So about 11 (or 3%)of the 354 sources we found are perhaps not asteroids and the remaining 97%are the asteroids we were looking for.

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144 or 55% of the 261 searched for asteroids were possibly found. This lowfraction of found asteroids can have a number of causes:

1) Badly done position predictions caused by a big uncertainties in the orbitalelements of the asteroid.

2) The asteroids were too faint to be detected.

3) Bad astrometry for a fraction of the frames. From inspection of the frameswe conclude that this option is unlikely.

Badly done position predictions are a likely cause for not finding the aster-oids. Juric et al, 2002 [1] did not find 34% of their predicted asteroid occurrencesand their most plausible explanation for this was the big uncertainty in manyof the predicted asteroid positions due to big uncertainties in their orbital ele-ments.Asteroids being too faint to be detected is also a likely cause for not finding theasteroids. Of the 798 predicted asteroid occurrences 70 (see figure 2) or 9% arefainter than visual magnitude 22.0. Of the 354 found candidates only 3 or 1%are fainter than magnitude 22.0. So the big majority of the asteroids fainterthan magnitude 22.0 no candidate was found. They were probably just too faintto be detected on the WFI during the integration times of the frames. Limitingourselves to searching for asteroids brighter than magnitude 22.0 would haveresult in 798 minus 70 equals 728 predictions with 354 minus 3 equals 351 can-didates. So the fraction of found asteroid occurrences would have been increasedfrom 44 to 48% when limiting the brightness of the asteroids to magnitude 22.

5.1 Found asteroid positions

Figure 13: Histogram of the radial distances from the expected asteroid posi-tions of the 354 asteroid candidates.

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When the position deviations are shown, 281 (or 79%) of the 354 asteroid can-didates (or 35% of the 798 predicted asteroid occurrences) are within 3 arcsecfrom the expected position. This is visible in figure 13. These occurrences areof 127 or 88% of the 144 found asteroids. 243 (or 69%) of the 354 asteroidcandidates (or 30% of the 798 predicted asteroid occurrences) are even within1 arcsec from the expected position. It is most likely that the candidates areindeed the asteroids searched for as the 3 arcsec area is only 4% of the 15 arcsecarea. So for the found asteroid occurrences, the majority of the expected po-sitions seem to be calculated with very high precision. 79 (or 55%) of the 144found unique asteroids are of asteroids which do not have an official numberyet. These asteroids’ orbital elements are not yet known with high precision.From the big fraction of 88% of asteroids found within 3 arcsec we can concludethat the initial search for sources within 15 arcsec from the expected positionseems to be big enough. Only 12% of the candidates were found between 3 and15 arcsec and it is expected that the fraction of candidates found between 15and (for example) 30 arcsec is less. Increasing the search area will probablyresult in just a few percent of found asteroids and in extra pollution of wrongcandidates as well. Nevertheless, as mentioned before, a big fraction of asteroidsis not found which is caused by badly known orbits of many of the asteroidsresulting in badly done position predictions.

5.2 Found asteroid magnitudes

The magnitude predicted by Skybot is a visual magnitude, but does not equalthe V-band magnitude. The frames studied for known asteroids were taken us-ing two different filters: a B band filter (B/99, WFI #842) and a V band filter(V/89, WFI #843). In figure 14 a histogram of the differences between mea-sured B and V band magnitudes and the predicted visual magnitudes is shownfor the 354 asteroid candidates. For the V band frames, the measured luminos-ity is about 0.4 magnitudes weaker than the predicted visual magnitude. Thisis in agreement with the value found by Juric et al, 2002 [1] of 0.41 magnitudewith a rms of 0.35. For the B band frames, the measured luminosity is about1.0 magnitudes weaker than the predicted visual magnitude. This higher valueis caused by a lower luminosity of asteroids in the B band.

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Figure 14: Histogram of the magnitude deviations in the B band (full curve)and V band (dashed curve) of the 354 asteroid candidates.

For 36 of the 144 asteroids, candidates were found imaged in both the B bandfilter and the V band filter. For these 36 asteroids, B-V could be estimated.These B-V values are presented in figure 15. The mean B-V is 0.73 with arms of 0.20. This value is in agreement with the value found by Ivezic et al,2001 [2]. They found that the majority of asteroids have a g-r of +0.65, whichcorresponds to a B-V of +0.85 when taking B-V is g-r + 0.2.

In figure 14 the magnitude deviations are visible. The figure shows some ob-servations of asteroids with luminosities higher than expected. This can havemultiple causes:

1) The asteroid can have an abnormal composition. Due to this, the reflec-tion of the asteroid can be different for certain bands. But deviations inbrightness of multiple magnitudes are very unlikely.

2) The luminosity can be badly measured, caused by a badly done photome-try. From inspection of the frames we conclude that this option is unlikely.

3) A wrong source near the predicted position was assigned to be the asteroid.A good indication for this error can be a big deviation of the position ofthe source. When looking at these deviations (as shown in figure 16),2 sources were found for which both the luminosity was more than 1magnitude to high and the position was more than 6 arcsec away from thepredicted position. These sources could possibly be removed from the setof asteroid candidates.

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Figure 15: Histogram B-V measurements for 36 unique asteroid candidates.The mean B-V is 0.73 with a rms of 0.20.

Figure 16: Scatter of the magnitude deviations (objects with a positive deviationare brighter than expected) and the position deviations of the 354 asteroid can-didates. Circles are B band measurements. Crosses are V band measurements.Two objects are visible that are too bright and far away from the expectedposition of the asteroids.

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6 Conclusions and next steps

As this research consisted of both developing asteroid searching algorithms andstudying found data, conclusions can be made about these both subjects.

Concerning searching algorithms for asteroids the following conclusions can bemade:

1) Asteroids are expected to be detected most efficiently in the B and Vband, due to the high solar emission, the high asteroid reflectivity and thehigh WFI detector sensitivity in these bands.

2) In order to calculate asteroid positions with arcsec accuracy, the asteroids’orbital elements should be known for an epoch within 50 days of the dateof observation of the studied frame. A very usable way to calculate aster-oid positions with high accuracy and high speed is by using the Skybotweb service.

3) When isolating asteroids from other astronomical objects, two good crite-ria can be used. As first, asteroid candidates should have a source length(major axis minus minor axis) that differs less than two arcsec from theexpected track length during the exposure. As second, asteroid candidatesshould have a position angle that differs less than five degrees from theexpected direction of movement. The values mentioned might depend onthe used instrument and analysis.After using these criteria and excluding bad sources, for just a tiny frac-tion of the asteroid predictions multiple sources will be found. So moreselection criteria (like searching for objects in star catalogues and insistingcertain magnitude deviations) seem not to be necessary. From simulationswe conclude that only 3% of the found candidates are not the searched forasteroids.

Concerning the found asteroid candidates the following conclusions can be made:

4) For the 798 predicted asteroid occurrences we found 354 candidates (or44%) of 144 different asteroids of which we think about 97% are indeedthe searched for asteroids. 4% were probably not found because they weretoo faint (fainter than visual magnitude 22.0). The remaining 52% wereprobably not found caused by big uncertainties in their orbits resulting inbadly done position predictions.

5) When we find a good asteroid candidate within 15 arcsec from the pre-dicted position, there is a probability of 88% of finding it within 3 arcsec.When this is the case, it is most likely that the candidate is indeed theasteroid searched for as the 3 arcsec area is only 4% of the 15 arcsec area.

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55% of the objects are unnumbered asteroids, asteroids of which their or-bital elements are not jet known with high precision.

6) For the V band, the measured luminosity is about 0.4 magnitudes weakerthan the predicted visual magnitude. This is in agreement with the valuefound by Juric et al, 2002 [1] of 0.41 magnitude with a rms of 0.35. For theB band frames, the measured luminosity is about 1.0 magnitudes weakerthan the predicted visual magnitude. This is caused by a lower luminosityof asteroids in the B band.For 36 asteroids both B band frames and V band frames were found. Forthese asteroids, B-V estimations results in a B-V of 0.73 with a rms of0.20. This is in agreement with the value found by Ivezic et al, 2001[2]. They found that the majority of asteroids have a g-r of +0.65, whichcorresponds to a B-V of +0.85 when taking B-V is g-r + 0.2.

To end this report, some proposed next steps are given.

1) With the big developments in storing image archives, the processes inretrieving occurrences of known asteroids from them get less time con-suming. So in the future, there are more and more opportunities to doresearch on asteroids without the need to do new observations. Also for thearchives stored inside the Astro-WISE environment, many asteroid occur-rences can still be found using the algorithms developed for this research.Finding these occurrences depends mostly on the amount of calibratedscience frames stored in the database. As of April 2007, the Astro-WISEcontains about 120,000 raw science frames of which only 1380 were studiedhere.

2) During this research, lots of asteroids were found near the predicted po-sitions. Nevertheless, the majority of asteroids were not found. This wasprobably caused by big uncertainties in their orbital elements. When theselection criteria presented here are run on very big areas around predictedpositions and the resulting collections of candidates are reduced by asso-ciating candidates with objects from stellar catalogues, perhaps a numberof asteroids can be found which were highly deviated from their predictedorbits.

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7 Acknowledgment

I would like to thank my two supervisors Gijs Verdoes Kleijn and Edwin Valen-tijn for giving me the opportunity to do this research. During this research Ihave learned a lot about the Python programming language, the Astro-WISEenvironment, the needed architecture in storing astronomical images, under-standing your data and doing scientific research. I also would like to thank therest of the Astro-WISE team for helping me around with their great systemwhen Gijs was not available.

References

[1] Juric et al. Comparison of positions and magnitudes of asteroids observedin the sloan digital sky survey with those predicted for known asteroids.ApJS, 124:1776, 2001.

[2] Z. Ivezic et al. Solar system objects observed in the sloan digital sky surveycommissioning data. ApJS, 122:2749–2784, 2001.

[3] Iau resolution 5: Definition of a planet in the solar system. http://www.iau.org/Resolutions_at_GA-XXVI.340.0.html, April 2007.

[4] New study reveals twice as many asteroids as previously believed. http://www.esa.int/esaCP/ESAASPF18ZC_index_0.html, April 2007.

[5] Mpc archive statistics. http://cfa-www.harvard.edu/iau/lists/ArchiveStatistics.html, April 2007.

[6] Lincoln near earth asteroid research (linear) project. http://www.ll.mit.edu/LINEAR/, April 2007.

[7] Encrenaz et al. The Solar System, 3rd edition. 2004.

[8] Minor planet centre. http://cfa-www.harvard.edu/iau/mpc.html, April2007.

[9] The 3rd release of the sloan digital sky survey moving object cat-alog. http://www.astro.washington.edu/ivezic/sdssmoc/sdssmoc.html, April 2007.

[10] C. R. Chapman et al. Surface properties of asteroids - a synthesis of po-larimetry, radiometry, and spectrophotometry. Icarus, 25:104–130, May1975.

[11] Astro-wise. http://www.astro-wise.org/, April 2007.

[12] Emmanuel Bertin. Sextractor. http://terapix.iap.fr/rubrique.php?id_rubrique=91/, April 2007.

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[13] Wide field imager (wfi). http://www.ls.eso.org/lasilla/Telescopes/2p2T/E2p2M/WFI/, April 2007.

[14] Wide field camera (wfc). http://www.ing.iac.es/Astronomy/instruments/wfc/, April 2007.

[15] Suprime-cam. http://www.subarutelescope.org/Observing/Instruments/SCam/index.html, April 2007.

[16] Omegacam. http://www.astro.rug.nl/~omegacam/, April 2007.

[17] Brandon Craig Rhodes. Pyephem. http://www.rhodesmill.org/brandon/projects/pyephem-manual.html, April 2007.

[18] Elwood Downey. Xephem. http://www.clearskyinstitute.com, April2007.

[19] Edward Bowell. Astorb. http://www.naic.edu/~nolan/astorb.html,April 2007.

[20] Orbfit. http://newton.dm.unipi.it/orbfit/OrbFit/doc/help.html,April 2007.

[21] Andrea Milani et al. The asteroid identification problem. iii. proposingidentifications. Icarus, 144:39–53, June 2000.

[22] Virtual observatory sky body tracker (skybot). http://www.imcce.fr/webservices/skybot/, April 2007.

A Appendices

A.1 Found asteroid candidates

A table of the properties of the found asteroid candidates can be found at:http://www.intra.astro.rug.nl/~bout/small-research/354asteroids.txt

A.2 Used WFI frames

A table of the dates and chipnames of the used WFI frames can be found at:http://www.intra.astro.rug.nl/~bout/small-research/1380prop.txt

A table of the Astro-WISE filenames of the used WFI frames can be foundat:http://www.intra.astro.rug.nl/~bout/small-research/1380filenames.txt

A.3 Python code of the used algorithms

The python code of the developed algorithms can be found at:http://www.intra.astro.rug.nl/~bout/small-research/code.py

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