Searching for known asteroids in the WFI archive using Astro-WISE

Transcription

1 Searching for known asteroids in the WFI archive using Astro-WISE Jeffrey Bout A small research project for bachelor students Supervisors: Gijs Verdoes Kleijn and Edwin Valentijn Kapteyn Astronomical Institute University of Groningen, the Netherlands May 7, 2007 Abstract This study is aimed at deriving new and/or improved photometry for known asteroids using Wide Field Imager (WFI) archival images. We present studies on a set of 354 asteroid occurrences of 144 different asteroids found on WFI images using the Astro-WISE system. The set is likely to be polluted with 3% non-asteroids. The set was found using a set of 798 asteroid predictions obtained with the Skybot web service. So for 44% of the predictions, the asteroids were found on the WFI frames. Identifying the asteroids on the frames was done by comparing sizes and phase angles of found sources within 15 arcsec of the predicted position with predicted values. Of the found asteroids, 88% were found within 3 arcsec from their predicted positions. The most plausible cause for not finding 56% of the asteroids is the big uncertainty in their orbital elements. Nevertheless, 56% of the found asteroids were unnumbered asteroids, asteroids of which their orbital elements are not yet known with high precision. The found asteroids were imaged using a B band filter, a V band filter or both. For the V band, the measured luminosity is about 0.4 magnitudes weaker than the predicted visual magnitude. This is in agreement with the value found by Juric et al, 2002 [1] of 0.41 magnitude with a rms of For the B band frames, the measured luminosity is about 1.0 magnitudes weaker than the predicted visual magnitude. This is caused by a lower luminosity of asteroids in the B band. For 36 asteroids both B band frames and V band frames were found. For these asteroids, B-V estimations results in a B-V of 0.73 with a rms of 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, which corresponds to a B-V of when taking B-V is g-r

2 1 Introduction Within our solar system, hundreds of thousands of asteroids have been discovered. The big majority of these objects are discovered in the last 10 years. The properties of these objects are not well known. Only 40% of them have well known 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 get these properties photometric measurements are necessary. To get these measurements dedicated surveys can be done, but a lot of photometric measurements are also hidden inside frame archives of today s observatories. Inside the Astro-WISE environment a number of these archives are stored. After developing some algorithms, the photometric data of known asteroids can be retrieved from 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 well as techniques and software to study the properties of asteroids. The next two chapters deal with our steps in deriving the asteroid properties from archival images and with presenting conclusions about the found asteroid properties. 2 Asteroids and other small bodies within the solar system Besides planets, there are lots of small objects circling the Sun. Most of them were undiscovered until a decade ago, but this is changing rapidly. Nowadays much effort is done in discovering them mainly because a tiny fraction of them can be a future threat for our planet. As a big side-effect, there is a big increase of knowledge about the small objects within the solar system and the solar system itself. As we know more and more of the small objects, many types of small objects have been found. For example: objects between Mars and Jupiter, objects in the orbit of Jupiter, objects very far away from the sun, objects with extreme elliptical orbits and so on. Through the ages the ways of classifying these different groups have changed a lot. For example: when Ceres was discovered in 1801 it was first called a planet. After some years it was called an asteroid and since 2006 it is called a dwarf planet. Within the International Astronomical Union (IAU) there have been lots of discussions about this the last couple of years 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 asteroids (also called minor planets or planetoids ), comets and other small bodies. Classically, the difference between asteroids and comets was quite clear: asteroids were small solid bodies, appearing as stellar objects (asteroid = Greek for star-like ). Comets were identified by their nebulous envelopes made of ice 2

3 and dust. The nebulous envelope of a comet is called coma and is formed when the comet gets close to the sun on its highly elliptical orbit. It gives the comet a fuzzy appearance. Nowadays, there are objects found which are somewhere in between asteroids and comets. When discovered no nebulous envelope was visible (so get listed in asteroid catalogues), but later on nebulosity appeared. Nevertheless, asteroids and comets still get listed in their own catalogues. As the luminosity of comets is highly dependent on the existence of an active coma, many previously discovered comets will be invisible when searching for them on frames made many years before or later. 2.2 Asteroids Within our solar system, an enormous number of asteroids exist. Estimations of the total number of asteroids above 1 km in diameter are between 1.1 and 1.9 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 individual photographs of a region in the sky using a special instrument called a stereoscope. As of April 1995, 27,000 asteroids were discovered [5]. In 1995, automated systems for searching asteroids became available and have dramatically increased the number of discoveries. As of April 2007, over 370,000 asteroids have been discovered [5]. The present rate of discoveries is about 5000 asteroids per month. Nowadays, the two most important projects for searching asteroids are Lincoln Near-Earth Asteroid Research (LINEAR) and Near-Earth Asteroid Tracking (NEAT). In the near future a new project called Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) will be added. The main purpose of these projects is searching asteroids that could be a future threat for our planet. Of these projects, the LINEAR project is running since 1998 and is responsible for most asteroid discoveries. As of October 2004, over 210,000 asteroids were discovered [6] within the LINEAR project. Most of these asteroids are found near the ecliptic plane, which is studied intensively because most asteroids (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 between the orbits of Mars and Jupiter, roughly between 2 and 3.5 AU. This group of asteroids is known as the Main Belt. Their orbits are elliptical, have eccentricities 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 asteroids should be visible near the equator. The mean density of known asteroids within 20 degrees from the ecliptic is about 10 to 20 asteroids per square degree or 2 to 5 asteroids on a 30 by 30 arcmin wide field detector. 3

4 In order to store the position and movement of discovered asteroids the properties of their orbits around the Sun have to be described. When the orbit of a celestial body is considered to be fixed, it can be given by a number of orbital elements. The traditionally used set of orbital elements is the set of Keplerian elements, which includes the inclination, longitude of the ascending node, eccentricity, 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 change due to many effects like the gravitational pull of other bodies within the solar system, nonsphericity of the sun, atmospheric drag, relativistic effects, radiation pressure and electromagnetic forces. Especially for asteroids the changes of their orbits 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 of most asteroids change with time. Fortunately, the evolution of orbital elements of asteroids can be predicted as will be shown in chapter 4. Estimating and improving the precision of the orbital elements of the extremely big amount of asteroids and other SSSBs is a time consuming process. Nowadays, it is done by the Minor Planet Center (MPC), a division of the Smithsonian Astrophysical Observatory [8]. In order to do this, the MPC collects all observations done for these objects. The MPC generally publishes new data on asteroids and other SSSBs on a monthly base. As the number of observations for each asteroid increases, the precision of the asteroid s orbit, size and albedo increases. As soon as the properties of an asteroid are well enough known, the object gets an official number. Nowadays, this is the case for only 40% of the known asteroids. To locate known asteroids on the night sky their ephemerides should be calculated. Ephemerides are a collection of properties of an object on a certain date and time. These properties include at least the position of the object on the night sky, but often also include lots of other properties like (apparent) luminosity, distance, (apparent) velocity and the elongation to the sun. The position of an object on the night sky is dependent of the location from which the observations are done. When an object is 1 AE away, the position on the night sky found from a certain location on Earth (called the topocentric coordinates of an object) can alter about ten arcsec from the position found if the observation was done from the centre of the Earth (called the geocentric coordinates of an object). These changes will get smaller for objects that are located 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 still not well known. This is because present asteroid discovery projects NEAT and LINEAR are focused on just finding asteroids and not on doing photometric 4

5 measurements on them. A good option for obtaining photometric measurements is by studying the SDSS moving objects catalogue (SDSSMOC). In 2004 the 3rd release of this catalogue was released containing astrometric and photometric data for 204,305 moving objects. Of those, 67,637 are linked to 43,424 unique objects from the ASTORB file [9]. One example of a study of this catalogue was published in 2002 by Juric et al. [1]. Their findings on 2641 asteroids were obtained by searching for known asteroids in the SDSS archive. Nevertheless, on the majority of moving objects inside the SDSSMOC still no research has been published. The easiest of the three properties to determine is the colour (or spectral shape). It can be determined directly by doing photometric measurements (measuring the luminosity quantitatively) of the object through different filters. From the tiny fraction of asteroids on which photometric measurements are done so far, different types of asteroids were qualified. In 1975, Chapman et al. [10] have done research on 110 asteroids and developed a classification system based on their colour and albedo. They found three types of asteroids (called C-, S- and M-type asteroids). This classification system was later extended with various other asteroid types. Nowadays, the size of an asteroid can almost never be measured directly through modern techniques. Most asteroids are too small to be resolved even when imaged with the highest quality instruments like the Hubble Space Telescope. The usual way to determine the albedo of an asteroid is done by comparing the luminosity and the size of the object using the formula: L (λ) D 2 P F (λ) A (λ) (1) were L is the luminosity of the asteroid at wavelength λ, D is the size of the asteroid, P is the fraction of the surface being illuminated as seen from the observer, F is the incoming flux from the Sun at the asteroid at wavelength λ and A is the albedo of the asteroid at wavelength λ. So as long as the size of an asteroid is not known, its albedo isn t known as well. But when assuming a certain value for an asteroid s albedo while knowing its luminosity, the size of the asteroid can be calculated. Asteroid albedos are uncertain, but they depend on the colour (or asteroid type) of the object, because both the colour and albedo of an asteroid will depend on the object s composition of surface materials. So in an indirect way, colour information of asteroids combined with their luminosities tells us something about their sizes as well. And studying asteroid sizes is important as it will give us information about the total mass of the asteroid belt, about the sizes and masses of objects causing a threat for life on Earth and about the origin of the whole solar system. 5

6 3 Astro-WISE and the WFI archive Before 1995, most asteroids were discovered by visually comparing individual photographs of a region in the sky using a special instrument called a stereoscope. Nowadays, searching for known and unknown asteroids on large amounts of astronomical frames is relatively easy, as many frames are stored in computer databases. Computer algorithms can be developed in order to automatically analyse all objects on these frames and compare them with predicted positions when searching for known asteroids. So searching for objects like asteroids no longer have to be done manually. 3.1 Astro-WISE A very useful database containing archives of frames for searching asteroids is the database being part of the Astro-WISE environment [11]. Astro-WISE stands for Astronomical Wide-field Imaging System for Europe and is built by a partnership between OmegaCEN-NOVA / Kapteyn Institute (Groningen, The Netherlands; 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 is a computational environment which includes software tools for archiving, accessing, distributing and processing the frames stored in the environment. Results from processing (calibrated images, source catalogues) are kept in Astro-WISE and can be shared with other users. The pre-built routines facilitate the search for asteroids within the archived images. Astro-WISE has web-based interfaces to the calibration and analysis tools as well as a command line interface within the Python programming environment. It is a first step towards a truly virtual observatory, defined as a collection of data archives and software tools forming a computational environment allowing astronomers anywhere to search, access, analyse, and combine astronomical data for research. Astro-WISE includes determination of sources on frames, using the well known Sextractor routines [12]. Using these routines, asteroid candidates can be found within the obtained source collections. This far, the database of Astro-WISE contains frame archives from different wide field detectors like the Wide Field framer (WFI) of the 2.2m MPG/ESO telescope at La Silla [13], the Wide Field Camera (WFC) of the 2.5m INT telescope at La Palma [14], the Subaru Prime Focus Camera (Suprime-Cam) of the 8.2m Subaru telescope at Mauna Kea [15] and the OmegaCAM camera of the not jet operational 2.5m VST telescope at Paranal [16]. The big majority of frames in the database are made with the WFI detector (as of April 2007, about 15,000 raw science WFI observations of which about 2,000 are astrometrically and photometrically calibrated). So logically, in this project the WFI frames are used to search for known asteroids. 6

7 3.2 Wide Field Imager (WFI) The Wide Field Imager (WFI) of the 2.2m MPG/ESO telescope at La Silla is a wide field detector with a field of view of 34 by 33 arcminutes. It consists of a mosaic of eight 8M pixel CCDs where each CCD covers 487 by 975 arcsec (or square degrees) of the field of view of the detector. The pixel scale of the WFI CCDs is arcsec per pixel. When an exposure is taken with the detector, all 8 CCDs are exposed simultaneously. So (most of) the frames of 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. Only frames taken with some of the broad band filters will be suitable for detecting faint asteroids. Asteroids are expected to be detected most efficiently in the B and V band, due to the high solar emission, the high asteroid reflectivity and the high WFI detector sensitivity in these bands. Frames in other bands like U and 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 contains currently mostly uncalibrated frames which have to be calibrated first before being able to get high precision coordinates of sources. So just searching asteroids on all WFI frames is not easily done. The next step is obtaining predicted asteroid positions for the calibrated frames using some external modules. Different methods were tried before finally a quick and precise method was found. Finally, selection criteria have to be developed for getting the right sources from the frames near the predicted positions. In total, eight steps were done before a collection of good asteroid candidates was obtained. This chapter deals with these eight steps. As a result, 354 good candidates were found which were studied in chapter Step 1: Determining the set of to be studied frames For the WFI imager, the Astro-WISE environment contains mostly raw science frames (frames for which astrometry and photometry is not done yet). But when we want to search for known asteroids, we need images which are calibrated (they are called regridded frames in the Astro-Wise environment). To get these images, raw science frames can be led through the image pipeline of Astro-WISE. The resulting calibrated images could be studied for known asteroids. As creating calibrated frames for all the raw science frames in Astro-WISE would be a time consuming process, it was necessary to make a selection of raw images for calibration. Making this selection of images also was necessary, because calculating the asteroid ephemerides for each image was going to take some time as well. Making the selection should be done in a clever way in order 7

8 to find as many asteroids as possible at the end. When making the selection of images, the most important criterion was the area on the night sky on which the asteroids were going to be searched for. The big majority of asteroids is located more or less on the ecliptic plane, so it is wise to take only frames taken from areas in this region. Here, images were taken of which their central declination deviated no more than 20 degrees from the ecliptic plane. A second criterion for selecting images is by their integration time. This integration time should be long enough to get the (mostly) faint asteroids visible on the frames. A long integration time is also handy as it lets asteroids show their motion on the frame during the integration time. Here, a minimum integration time of 4 minutes was chosen. For this lower limit integration time, 97% of a typical set of asteroids will have a track length of more than 0.4 arcsec which is probably enough to be detected. Selecting raw science frames using the just mentioned criteria for the WFI imager 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 be reduced. This reduction had to be chosen so the aims of the project are met as good as possible. Searching for known asteroids on archived images and do photometric analysis on them are the main aims of this project. It can be done following two strategies: 1) Restricting that imaged areas were imaged for multiple filters during one observing night. With this restriction colour information (like B-V) for asteroids can be obtained. With this restriction the number of suitable frames is expected to be reduced dramatically. 2) Not making this restriction, but instead just take one observation from an imaged area during one observation night. When following this strategy photometric data will be found for many asteroids, but colour information will not be found. Here, both strategies were followed. As first a sample was created following the second strategy. A routine was developed which selected non overlapping areas on the night sky which were not imaged more than one time during one observing night and for which calibration observations were available. This routine resulted in 621 non overlapping raw science frames. This set of 621 raw science frames was used as input for the Astro-WISE pipeline to create calibrated frames. After inspecting some of these images, only the frames taken using a B filter (B/99, WFI #842) and a V filter (V/89, WFI #843) looked usable. The frames taken with other filters (U/38, Rc/162 and Ic/lwp) did not. This agrees with the expectation that asteroids are most efficiently detected in the B and V band, due to the high solar emission, the high asteroid reflectivity and the high WFI detector sensitivity in these bands. After excluding the frames for 8

9 the U/38, Rc/162 and Ic/lwp filters, 384 frames remained. Next, a sample was created following the first strategy: selecting frames on areas on the night sky which were imaged multiple times during one observing night. To this strategy the criterion was added that both B and V frames were taken. This was done to be able to measure the B-V colour properties of asteroids. Selecting frames resulted in 1081 raw science frames. Leading these frames 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). All the calibrated frames were delivered by Gijs Verdoes Kleijn. The calibration consisted of de-biasing, flatfielding and astrometric and photometric calibration in batch mode. For some nights no standard star field observations were available. In those cases we applied the a typical zeropoint for WFI as derived from an analysis of the zeropoints as a function of time. We decided not to remove bad pixels and columns and cosmic-rays during the calibration but perform this during the searching for asteroids. For the total set of 1380 frames, asteroid occurrences will be predicted and candidates will be searched for in the following steps. For the 1380 frames, integration times were between 240 and 900 seconds. They were taken between June 13th, 1999 and May 6th, 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 square degrees and the known asteroid density near the ecliptic is about 10 to 20 per square degree, the number of predicted asteroid occurrences on the frames will be in the order of 500 to 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 for the dates and times of all frames. Different methods were tried before finally a quick and precise method was found. The first method used was calculating the ephemerides of many asteroids using the PyEphem library together with the Astorb table. PyEphem is a python library for calculating the ephemerides of celestial bodies on particular dates [17]. Internally, it calculated the positions using routines from the XEphem astronomical ephemeris package made by E. C. Downey [18]. The Astorb table is a table containing high-precision, up-to-date orbital elements and ephemerides uncertainties of over 300,000 asteroids [19]. The orbital elements are based on data from the Minor Planet Centre. The epoch for the orbital elements for a certain version equals the publication date of the version. Ephemerides of most non-earth-approaching asteroids can be calculated with the table to arcsec accuracy within 50 days of this epoch using an ephemerides tool like PyEphem. Using this method resulted in quick but uncertain calculations. Calculating the 9

10 ephemerides for one frame took just 3 seconds, but visually checking frames for asteroids on predicted positions showed uncertainties of many arcminutes. This was probably caused by the big difference of epochs of the frames and the Astorb table. With just one version of the Astorb table this difference could not be kept small as the studied frames were taken from 1999 to A possible solution for the uncertainties in the calculated ephemerides was calculating the orbital elements for the date and time of each frame. Then the epochs of the frames and the orbital elements should be the same and calculating the ephemerides using PyEphem might be done with a minimal error. Calculating orbital elements for certain dates could be done with OrbFit. This is a software package for computing orbital elements for asteroids for any epoch given their current orbital elements, among many other features. So when combining this package with the PyEphem package and the Astorb orbital elements table, positions of asteroids on the celestial sphere in the past or future can be calculated [20]. OrbFit predicts orbital elements using all planets as perturbing masses. It incorporates multiple numerical integration schemes, choosing the step size automatically to achieve a prescribed truncation error. It also incorporates general relativistic perturbations for the gravitational field of the Sun as well as the Earth (only for near Earth asteroids). When calculating the observer location, the package takes into account the motion of the Earth around the Earth-Moon barycentre as well as precession, nutation and Earth rotation [21]. With the combination of OrbFit, PyEphem and Astorb, ephemerides could be calculated with high (arcsec) precision. Unfortunately, calculating them for one frame took about 1.5 hour. Most of the 1380 frames were taken with the 8 chips WFI detector, so these 1380 frames belonged to more or less 172 different dates and 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 we were notified of the existence of Skybot. The Virtual Observatory Sky Body Tracker (or short: Skybot) is a web service (an on-line tool) providing high precision ephemerides of asteroids [22]. It calculates 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 system objects for many epochs (interval of 10 days), which were issued from the Astorb table. As of April 2007, Skybot does the calculations for over 360,000 asteroids. Calculations for one frame typically take about 15 seconds. Calculated topocentric or geocentric ephemerides by Skybot include the object name and number, the astrometric J2000 equatorial coordinates, the asteroid class, the apparent visual magnitude, the error on the position, the apparent angular size, the motion on the celestial sphere (velocity in arcsec per hour plus direction) among other properties. 10

11 For the 1380 frames, topocentric asteroid ephemerides were calculated in less than 6 hours or 15 seconds per frame. The fact that many frames had the same date and time was ignored, as this made the routines for requesting and storing asteroid ephemerides much easier to develop. 819 occurrences of asteroids were predicted on the 1380 frames. This value is within the range of expected occurrences of 500 to The occurrences were of 265 different asteroids (of which 91 have an official number) and were distributed over 514 of the 1380 frames. So on 37% of the frames, one or more asteroids were predicted. At this stage, two interesting properties of the predicted asteroids are their track length and apparent visual magnitude distributions. These properties say something about the probability of detecting and recognising asteroids on the frames as very faint asteroids are likely to remain undetected and slow asteroids could not be separated from stars. Figure 1: Histogram of the expected track lengths (in arcsec) of 819 asteroid occurrences during the integration times of the studied frames. The expected track length of the asteroids can be calculated using their expected motion in arcsec per hour and the integration time of the frames they are on. A histogram of the expected track length is shown in figure 1. Of the 819 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 measure compared to seeing effects (see section 4.6) and we keep 798 occurrences of 261 different asteroids (of which 91 have an official number), distributed over 503 frames. The frames on which no asteroids were predicted were no longer interesting. They were excluded from further processing steps. So on continuing steps, 503 frames were processed containing 798 predicted occurrences of asteroids. Of the occurrences, 170 were of asteroids which have no official number. These 11

12 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 positions more than asteroids which do have an official number. Figure 2: Histogram of the expected visual magnitudes of 798 asteroid occurrences. The predicted visual magnitudes of the asteroid occurrences are between 15 and 24, as visible in figure 2. The majority of visual magnitudes are between 18.5 and A fraction of the fainter asteroids are expected to be invisible on the frames as you will need a lot of integration time if you want to detect such faint objects. 4.3 Step 3: Extracting imaged sources near the predicted positions To search for sources on the frames the Sextractor module can be used, which is integrated inside the Astro-WISE environment. When a source is found by Sextractor, lots of properties are given for the source like the luminosity, the position, the shape and the position angle (which is the direction of movement in case of a moving object). When searching for sources around a predicted asteroid position, a maximum distance for selected sources had to be chosen. This distance should be big enough that not well known asteroids still get selected. Inspection of the errors in position given by Skybot showed that this error was of little value: the found deviation of asteroids when visually inspecting frames was very often in contradiction with the error given by Skybot. So the maximum distance had to be found in a different way. To choose this maximum distance the number of sources for different distances was studied (see figure 3). 12

13 Figure 3: Histogram of the radial distances of the 2269 found sources within 15 arcsec from the expected asteroid positions. When studying the area around an expected asteroid position, two types of sources are expected to be found: asteroids and randomly positioned objects (stars, galaxies, bad pixels, cosmic rays, etc.). The number of randomly positioned objects within a thin ring is expected to be proportional to the ring radius, because the surface of a thin ring is the thickness of the ring times two times pi times the radius of the ring. In the histogram the randomly positioned objects are visible as the linearly increasing number of objects between 4 and 15 arcsec away from the expected asteroid position. A line trough these values reaches zero for 0 arcsec position deviation as expected. In the histogram also a high peak of non random objects are visible between 0 and 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 conclude that the majority of asteroids will be less than 3 arcsec away from the expected position. Nevertheless, to avoid that not well known asteroids are excluded from our selection of sources, all sources having a distance of 15 arcsec or less were selected. In later steps this distance could be lowered if needed. Searching for sources within 15 arcsec of the 798 predicted asteroid occurrences resulted in 2269 sources distributed over 649 of the asteroid occurrences. So for 149 asteroid occurrences no sources were found within 15 arcsec and for 649 asteroid occurrences about 3 objects per asteroid occurrence were found. Inspection of the images showed that the Sextractor module on some occasions split highly elliptical asteroid sources into two sources. This will to be corrected in step 5 (section 4.5). Also a lot of sources seemed to be derived from bad sources of the frames (bad pixels, bad columns, cosmic rays). These had to be excluded from our set of sources first. 13

14 4.4 Step 4: Excluding bad sources When studying sources found by the Sextractor module, a lot of them turned out to be bad sources like bad pixels, bad columns and cosmic rays. Fortunately most of them were easily distinguished from other sources: on the WFI frames they are very small (less than 1 arcsec). We performed a visual inspection to ensure that these sources are indeed not astronomical sources: no PSF profile appeared for these sources. Removing sources smaller than 1 arcsec hopefully removed most bad sources. Figure 4: Histogram of the minor axes in arcsec of the 2269 found sources within 15 arcsec from the expected asteroid position. 14

15 Figure 5: Cut-outs centered on 50 of the 1310 sources which were removed by the 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 the selection criterion, because their minor axes were bigger than 1 arcsec. Nonrandom positioned objects appear within 3 arcsec. 15

16 In figure 4 the high number of small sources is clearly visible of the 2269 sources were removed in this process. They are shown in figure sources survived the new selection criterion. They were found for 532 of the 649 asteroid occurrences. 117 asteroid occurrences lost their sources during this selection criterion. Visual inspection of the remaining sources showed that the process did not remove all bad columns from the set of sources. They are of little 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 objects are removed from our set of sources. The histogram of position deviations in figure 6 shows that this is the case. As before, the remaining random objects are visible as the linearly increasing number of objects between 3 and 15 arcsec away from the expected asteroid position. A line trough these values reaches zero for 0 arcsec position deviation as expected. Fluctuations from the linear behaviour is caused by asteroids which were imaged many times in order to determine their colour information. 4.5 Step 5: combining split up sources During retrieving sources from the frames by the Sextractor module, a number of highly elliptical sources (asteroids?) were split into two sources. A routine for combining these sources (obliging the position angles of two sources and the line connecting the two to be within 10 degrees from each other and obliging the sum of the major axes of the sources to be at least half the length of the calculated major axis of the combined source) found 54 sources which could be combined to 27 combined sources. After combining the 54 split up sources 932 remain in the set of sources for the 532 asteroid occurrences. Two of the combined sources are bad columns. As before, this is of little concern here. The bad column will be removed in proceeding steps. 4.6 Step 6: Searching for asteroids by using the expected track 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 comparing the differences between the expected track length of the to be found asteroid and measured track lengths of the sources. The measured track lengths of the sources (from now called source length ) can be calculated by subtracting the source 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 the horizontal axis, the source lengths of the sources are shown. On the vertical axis, the track length differences are shown. 16

17 Figure 7: Scatter of the absolute track length deviations (arcsec) and the source length (arcsec) of 932 sources having minor axes bigger than 1 arcsec. Sources with absolute track length deviations bigger than 2 arcsec will be excluded by the selection criterion as well as sources with source lengths smaller than 0.5 arcsec 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 is smaller than about 2 arcsec, independent of the (expected) source lengths. Their source length range from 0 to 12 arcsec. These objects are asteroid candidates. 2) A vertical group of objects for which their source length is smaller than about 0.5 arcsec, independent of the track length difference. Their track length difference range from 0 to 11 arcsec. These objects are more or less circular objects, for example stars and QSO s. 3) A group of objects having both a source length bigger than 0.5 arcsec and a track length deviation bigger than 2 arcsec. These objects are elliptically shaped were the asteroid is suspected to be differently shaped. So they are elliptically shaped objects, but not the predicted asteroid. So for example galaxies. 17

18 So a first criterion for searching candidate asteroids is having a track length difference smaller than 2 arcsec. Unfortunately, when visually inspecting the sources with a bigger track length difference, 3 combined sources (which seem to be asteroids) from the previous step have this property. This was caused by uncertain determinations of the source lengths of the combined sources in the previous step. When for combined sources the track length differences are kept smaller than 5 arcsec, these 3 combined sources survive the criterion. From the three groups of objects, the first two overlap. The overlapping region contains both asteroids and non asteroid objects. They are objects with both a small 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 0.5 arcsec, a lot of non-random positioned objects (asteroids?) would get excluded. To prevent this, the criterion was expanded by only excluding objects with a source length smaller than 0.5 arcsec if their position deviation is more than 2 arcsec (non-random appearing sources in figure 6). In figure 7 groups of sources with a slope of -1 are visible. These groups are sources from different frames belonging to the same asteroid (in order to get colour information for those asteroids). After the criterion was run on the set of sources, 468 sources were excluded and 464 of the 932 sources remained for 401 of the 532 asteroid occurrences. 131 asteroid occurrences lost their sources during this selection criterion. The excluded sources are shown in figure 8. 18

19 Figure 8: Cut-outs centered on 50 of the 932 sources which were removed by the selection criterion, because their source lengths were incomparable with the expected track lengths of the asteroids. 4.7 Step 7: Searching for asteroids by using the expected direction of movement Asteroids move on the sky with a certain direction. For all the predicted asteroids this direction of movement was delivered by Skybot. As the direction of movement is a direct function of the orbit of the asteroid, the value delivered by Skybot can be assumed to be very precise. Figure 9 shows a histogram of the difference between the predicted directions of movement and the measured directions of movement for the 464 sources. The majority of sources in the histogram has a deviation of less than 12 degrees. These sources are asteroid candidates and insisting that the deviation is less than 12 degrees seems to be a good criterion. 19

20 Figure 9: Histogram of the absolute angle deviations in degrees of 464 sources. Non-randomly oriented sources have measured directions of movement deviating less than 12 degrees from the expected directions of movement of the asteroids. Figure 10: Scatter of the absolute angle deviations (in degrees) and the source lengths (in arcsec) of 464 sources. Increasing absolute angle deviations with decreasing source lengths are visible. It is interesting to study how the deviation in direction of movement is related to the source length of the sources. This is shown in figure 10. You can expect that with decreasing source length the deviation in direction of movement get 20

21 higher. This is caused by an increasing uncertainty in measuring the direction of movement from the frame by the Sextractor module. In the figure this effect is well visible. The figure shows that for sources with source lengths of more than 2 arcsec, the direction of movement can be measured within 5 degree uncertainty. When the source length gets lower than 2 arcsec, the deviation in direction of movement increases dramatically. In the previous step, objects with a measured track length of less than 0.5 arcsec 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 be measured accurately, the direction of movement criterion was not executed on these objects. After the criterion was run on the set of sources, 98 sources were excluded and 366 of the 464 remained for 360 of the 401 asteroid occurrences. 41 asteroid occurrences lost their sources during this selection criterion. The excluded sources are shown in figure 11. Figure 11: Cut-outs centered on 50 of the 98 sources which were removed by the selection criterion, because their their directions of movement were incomparable with the expected directions of movement of the asteroids. 21

22 4.8 Step 8: Excluding asteroid occurrences with multiple candidates After the previous steps only 6 (or 2%) of the 360 asteroid occurrences have two possible candidates. All other 354 different asteroid occurrences have just one possible candidate. As the processing steps were quite strict, most of these candidates will in fact be the asteroid. More selection criteria (like searching for objects in star catalogues and insisting certain magnitude deviations) can be done in future. For the 6 asteroid occurrences with multiple candidates the candidates simply were removed from the set of sources. So 354 (or 44%) of the 798 asteroid occurrences we started with remain with an asteroid candidate. These candidates are studied in chapter 5. This chapter is concluded with an overview of the processes done during this chapter for retrieving source candidates for the asteroid occurrences. This overview is shown in table 1. Table 1: Processes done for retrieving source candidates Process Passed Asteroid occurrences Passed Sources Step 2: Predicting asteroids Step 3: Extracting sources Step 4: Excluding bad sources Step 5: Combining split sources Step 6: Excluding bad lengths Step 7: Excluding bad angles Step 8: Excluding multiple sources

23 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 which are 44% of the total. These objects are shown in figure 12. The 354 found occurrences 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 or 70% of 91 numbered asteroids were possibly found. Before studying the found candidates, we want to know how many of the objects are indeed the searched for asteroids. So we want to know how many non asteroids (could) have survived the previous selection criteria or how much pollution our data contains. This can be done by running the selection criteria on different parts of the frames we have used (so where no asteroids are likely to be found). When doing this a couple of times 2064 sources were lead through the 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 sources within 15 arcsec of the predicted asteroid positions, about 0.5% or 11 non asteroids 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. 23

24 144 or 55% of the 261 searched for asteroids were possibly found. This low fraction of found asteroids can have a number of causes: 1) Badly done position predictions caused by a big uncertainties in the orbital elements 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 frames we conclude that this option is unlikely. Badly done position predictions are a likely cause for not finding the asteroids. Juric et al, 2002 [1] did not find 34% of their predicted asteroid occurrences and their most plausible explanation for this was the big uncertainty in many of the predicted asteroid positions due to big uncertainties in their orbital elements. Asteroids being too faint to be detected is also a likely cause for not finding the asteroids. Of the 798 predicted asteroid occurrences 70 (see figure 2) or 9% are fainter than visual magnitude Of the 354 found candidates only 3 or 1% are fainter than magnitude So the big majority of the asteroids fainter than magnitude 22.0 no candidate was found. They were probably just too faint to be detected on the WFI during the integration times of the frames. Limiting ourselves to searching for asteroids brighter than magnitude 22.0 would have result in 798 minus 70 equals 728 predictions with 354 minus 3 equals 351 candidates. So the fraction of found asteroid occurrences would have been increased from 44 to 48% when limiting the brightness of the asteroids to magnitude Found asteroid positions Figure 13: Histogram of the radial distances from the expected asteroid positions of the 354 asteroid candidates. 24

25 When the position deviations are shown, 281 (or 79%) of the 354 asteroid candidates (or 35% of the 798 predicted asteroid occurrences) are within 3 arcsec from the expected position. This is visible in figure 13. These occurrences are of 127 or 88% of the 144 found asteroids. 243 (or 69%) of the 354 asteroid candidates (or 30% of the 798 predicted asteroid occurrences) are even within 1 arcsec from the expected position. It is most likely that the candidates are indeed the asteroids searched for as the 3 arcsec area is only 4% of the 15 arcsec area. So for the found asteroid occurrences, the majority of the expected positions seem to be calculated with very high precision. 79 (or 55%) of the 144 found unique asteroids are of asteroids which do not have an official number yet. 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 conclude that the initial search for sources within 15 arcsec from the expected position seems to be big enough. Only 12% of the candidates were found between 3 and 15 arcsec and it is expected that the fraction of candidates found between 15 and (for example) 30 arcsec is less. Increasing the search area will probably result in just a few percent of found asteroids and in extra pollution of wrong candidates as well. Nevertheless, as mentioned before, a big fraction of asteroids is not found which is caused by badly known orbits of many of the asteroids resulting in badly done position predictions. 5.2 Found asteroid magnitudes The magnitude predicted by Skybot is a visual magnitude, but does not equal the V-band magnitude. The frames studied for known asteroids were taken using 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 measured B and V band magnitudes and the predicted visual magnitudes is shown for the 354 asteroid candidates. For the V band frames, the measured luminosity is about 0.4 magnitudes weaker than the predicted visual magnitude. This is in agreement with the value found by Juric et al, 2002 [1] of 0.41 magnitude with a rms of For the B band frames, the measured luminosity is about 1.0 magnitudes weaker than the predicted visual magnitude. This higher value is caused by a lower luminosity of asteroids in the B band. 25