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The search for slow moving planets in the distant solar system Ashton, Edward James 2017

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The Search for Slow Moving Planetsin the Distant Solar System.byEdward James AshtonB.Sc. in Astronomy, University of Canterbury, New Zealand, 2012A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinThe Faculty of Graduate and Postdoctoral Studies(Astronomy)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)August 2017c© Edward James Ashton 2017AbstractOut beyond the giant planets is a collection of bodies left over from planet formation. Theobjects that are just beyond Neptune are well studied compared to those that journey hundredsof au away; all such objects have been observed inside 100 au. We use a deep narrow surveyand an uncommon technique to search for objects currently at large heliocentric distances.Using data from the Outer Solar System Origins Survey (OSSOS), which covered ∼160 squaredegrees down to r ∼ 25, we searched for objects beyond 300 au. To find such objects wecreated a catalogue of all of the objects that were stationary of the astronomical seeing in threeimages taken over 2 hours. We then examined the stationary objects that were no longer theredays/weeks/months before and after the three images. Although other astronomical phenomenalike supernovae where discovered, no slow moving solar system object was found. From the nulldetection and using a survey simulator we obtain a 95% upper limit to the number of dwarfplanets (-3 > H > 2) in the distant solar system, 1100+1700−800 . To our knowledge this is the firstpublished limit for dwarf planets beyond several hundred au.iiLay SummaryWe searched a small fraction of the sky for slow moving solar system objects out at a distancerarely looked at. Since these objects were slow enough that they appeared to be stationary overa few hours, we used an algorithm to look for objects that were stationary in three images thatwere taken over two hours but moved on timescales more than a day. No such objects werefound and that allowed us to estimate an upper limit on the number of dwarf planets in thedistant solar system, 1100+1700−800 .iiiPrefaceAll the images and catalogues, the validate software and the survey simulator were obtainedfrom OSSOS with some parts altered by JJ Kavelaars to fit this work. The general idea forthe technique used for finding slow moving solar system objects was the idea of my supervisor,Brett Gladman. I created the code described in Chapter 3, implementing the idea and dealingwith unanticipated details. The results and analysis in Chapter 4 and 5 respectively are myoriginal work.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Planet Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The Structure of the Outer Solar System . . . . . . . . . . . . . . . . . . . . . . 21.3 The Origin of TNOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.3.1 Effects of an Extra Planet . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Undiscovered TNOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.1 TNO survey limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4.2 Distant TNO Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4.3 Improving Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 OSSOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1 Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Cadence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.1 Triples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.2 Nails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Catalogues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 In This Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 The Searching Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.1 Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.1.1 Streamlined Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.2 Creating the Stationary Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2.1 jmp and matt Stationary Catalogues . . . . . . . . . . . . . . . . . . . . 173.2.2 Final Stationary Catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.3 Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18v3.2.4 Crowding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2.5 Stationary Catalogue format . . . . . . . . . . . . . . . . . . . . . . . . . 193.3 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.4 Searching the Nails . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.1 On Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.4.2 Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.5 Creating the Master Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.6 Vetting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.6.1 Candidate List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.6.2 Candidate List format . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.6.3 Validate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1 False Positive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.1 Saturated Stars Halo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.2 Faint Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.3 Obscured Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.1.4 Inbetween Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.2 Optical Ghosts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284.3 Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 Possible Flare-Star Pheomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Constraints on Distant Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1 Survey Simulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1.1 Orbital Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.1.2 Size Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.2 Large Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345.3 Upper Limit of Dwarf Planets in the Outer Solar System. . . . . . . . . . . . . . 366 Conclusion and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41viList of Tables3.1 Example of a stationary catalogue file. . . . . . . . . . . . . . . . . . . . . . . . . 193.2 Example of a nailing parameters text file. . . . . . . . . . . . . . . . . . . . . . . 213.3 Example of a master table. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.4 Example of a candidate list file. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265.1 The simulated sample of 10,000 objects that OSSOS (extended by our analysisout to >1000 au) would detect, broken down into absolute magnitude bins . . . . 34viiList of Figures1.1 Known TNOs that have a pericentre greater than 25 au. . . . . . . . . . . . . . . 21.2 All (but one) of the known TNOs that have semi-major axes greater than 65 auand a pericentres greater than 29 au. . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 A comparison of how far, for a certain sized object, three surveys could detectout to. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 The cumulative distribution of the known TNOs down to a heliocentric absolutevisual magnitude of 8 (blue line). . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 The layout of MegaCams CCDs. . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Example of the image configuration for a block in the first half of OSSOS (left)and the second half (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 The RA pointings of all 8 OSSOS blocks. . . . . . . . . . . . . . . . . . . . . . . 133.1 An example of the inner/outer box method used. . . . . . . . . . . . . . . . . . . 203.2 The average number of founds for logirithmicaly spaced binned jmp flux values. . 244.1 The movement of an optical ghost in the triples and one nail (others not shown)to show the ghost is not in the vicinity in the nailing images. . . . . . . . . . . . 294.2 Images of a supernova event captured by OSSOS and labeled as a solar movingsolar system candidate by our code. . . . . . . . . . . . . . . . . . . . . . . . . . 304.3 Images of what is believed to be a flare star captured by OSSOS and labeled asa solar moving solar system candidate by our code. . . . . . . . . . . . . . . . . . 325.1 The cumulative fraction of the heliocentric distance the simulated objects wereat time of detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 The cumulative fraction of the r magnitude of the simulated objects at time ofdetection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.3 The fraction of objects with a certain fractional orbital distance for different Hmagnitude ranges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.4 A plot of the first 1000 objects in the simulated sample. . . . . . . . . . . . . . . 375.5 A histogram of the intrinsic population of simulated objects when the three ofthese objects are detected. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38viiiAcknowledgmentsI would like to acknowledge my supervisor Brett Gladman for giving me the opportunity towork on research, for his guidance and discussions, and for being patient when the writing wasslow.JJ Kavelaars for creating the source catalogues for all of the nailing image, adding the RAand Dec coordinates to all catalogues and the couple of hours he futilely tried to get validateworking on my laptop.Lynne Jones and Simon Kurghoff for allowing me to join their team and for their helpfulcomments.ix1. Introduction1.1 Planet FormationPlanet formation is a complex process. We know that there is dust in protoplanetary disks dueto the detection of infrared excess, and planets have been found around enough stars to saythat planets are common phenomena in the galaxy. What is not known is in what way doesdust come together to form planets.Currently there are a few theories on how planets come to be. One such theory follows theidea that planets formed the same way as stars, by gravitational collapse, where most of the gasand dust in a region of the protoplanetary disk collapses to form a planet (Boss, 1997). Thiscould be how the giant planets formed, although the metal abundence in Jupiter’s atmosphereis higher than that of the sun (Young et al., 1996), which should not be the case if Jupiter wasformed by gravitational collapse. The discrepancy in metal abundance could be remedied byJupiter being polluted by rocky objects. Gravitational collapse or ‘local instability’ is thus lessfavoured for the formation of giant planets in the Solar System.The leading theory of planet formation is known as ‘bottom up accretion’ or core accretion.This is where particles collide forming a collection of objects that slowly increase in averagemass until the most massive objects become planets. To form the gas envelopes around thegiant planets, once the most massive objects were big enough they were able to accrete gas(Lissauer et al., 2009). Bottom up accretion, too, has problems. In protoplanetary disks thepressure gradient causes gas to orbit at sub-keplerian speeds. The solid objects, which travelat the keplerian rate, will therefore feel a gas drag and drift towards the star. This drift hasthe highest effect on metre sized objects, since smaller objects are coupled to the gas and largerobjects have a small surface area to mass ratio. Therefore metre sized objects have to growquickly or else they will spiral into the star, a metre sized object at 10 au has a lifetime of ap-proximately a thousand years. This is known as the metre-size barrier (Weidenschilling, 1977).A way around the metre barrier is to have the dust clump into kilometre sized objects, knownas planetesimals, on a shorter timescale and then grow by colliding into one another.A problem with bottom up accretion is simulations suggests the time taken to form planetsmay be too long. A way to speed up accretion is to have ‘pebble’ sized objects (∼cm scale)accrete onto planetesimals when they get to 100s of kilometres in diameter. In this regimethe size of the planetesimals collection area results in a high accretion rate (Lambrechts andJohansen, 2012). This theory, known as pebble accretion, can form planets in a timescale thatagrees with observations. It is plausible that there is not just one planet formation mechanismbut multiple process depending on the environment.1Figure 1.1: Known TNOs that have a pericentre greater than 25 au. The semi-major axisthat correspond to certain MMR are given as dashed lines. The two largest TNOs have beencoloured differently with Pluto in red and Eris in Black. Data obtained from the Minor PlanetCenter and are osculating heliocentric orbits.1.2 The Structure of the Outer Solar SystemWhatever the mechanism of planet formation, there are planets and minor bodies, both in theSolar System and in other stellar system. The outer Solar System (Jupiter and beyond) con-tains four giant planets1, and a size distribution of smaller objects up to ∼1000 km in radius.Almost all of these smaller objects have semi-major axis beyond that of Neptune. These objectsare known as Trans-Neptunian Objects (TNOs).There is a swarm of icy debris just outside the orbit of Neptune known as the Kuiper Beltanalogous to the asteroid belt. The Kuiper belt objects (KBOs) can be split up into resonantand non-resonant. The resonant KBOs have periods that are near integer ratios of the period ofNeptune. The time it takes for a resonant KBO to complete N integer orbits is the same as thetime Neptune takes to complete M integer orbits. This phenomena is known as mean motionresonance (MMR). Non-resonant KBOs are simply those that are not in MMR with Neptune.There might be another separation in KBOs. There is evidence of two different inclination distri-butions in the Kuiper Belt. The distribution of objects that have, on average, lower inclinations(∼3◦) are known as cold KBOs. Similarly the higher inclination distribution (>5◦) objects are1There might have been a fifth giant planet in the giant planet region in the past that had a close encounterwith one of the other giant planets and was ejected from the Solar System (Nesvorny´, 2011).2Figure 1.2: All (but one) of the known TNOs that have semi-major axes greater than 65 auand a pericentres greater than 29 au. The missing object is 2014 FE72, with a semi-major axisof 2055 au, far greater than the next highest. Eris, with a = 67.6 au, has been coloured black.Data obtained from the Minor Planet Center and are osculating heliocentric orbits.known as hot KBOs(Brown, 2001). An observation that supports this (dynamical) division isthat cold KBOs have, on average, redder optical colours than hot KBOs. The non-resonantKuiper Belt is made up of hot and cold KBOs, whereas the resonant appear to be all hot KBOs.The close proximity of Neptune to the Kuiper belt results in gravitational interactions be-tween Neptune and KBOs but the dynamical lifetimes of KBOs are gigayears. There is apopulation of objects that have dynamical stability timescales that are much less that KBOsknown as the scattering objects (SOs). Named as they are readily scattering off Neptune, andas such usually have high eccentricities and pericentre near Neptune’s orbit. If a SO is scatteredto a semi-major axis less than that of Neptune then the object is called a Centaur.There are TNOs that are no longer interacting with Neptune. If a TNO’s pericenter isgreater than about 37 au. and it is not in a MMR with Neptune, it is said to be detached fromNeptune and are thus named Detached Objects (Dos). They are believed to be SOs at onepoint in time and, after an interaction with another body, had their pericenters raised.Far beyond the Kuiper Belt is the theorised Oort Cloud, which is the reservoir of isotropiccomets that have near parabolic orbits. The Oort cloud consists of an inner and outer re-gion. The inner Oort cloud, which starts about 2,000 au, is more of a disk shape. Whereas3the outer Oort cloud is nearly spherical, and it might extend out to hundreds of thousands of au.The TNOs that have been discovered so far are shown in Figure 1.1. The grouping of theresonant Kuiper Belt around MMR can be clearly seen with the 3:2 (3 Neptune orbits for 2 ofthe KBOs orbits) being the most populated. Also seen is a large grouping of TNOs betweenthe 3:2 and 2:1 MMR populations, this is where the vast majority of the cold KBOs lie. Outbeyond 50 au there is a trend of increased eccentricity with increased semi-major axis. Theseobjects are mostly SOs or DOs.Known TNOs with high semi-major axis, where almost all are SOs and DOs, are shown inFigure 1.2. The only TNO which has a semi-major axis greater than 65 and is not Neptunecrossing that is not shown in the figure is 2014 FE72, with a semi-major axis of 2055 au andpericentre of 36 au. Due to its incredibly large semi-major axis and the fact its not Neptunecross, 2014 FE72 could be the first inner Oort cloud object discovered. No outer Oort cloudobject with a pericentre beyond Neptune has been found yet.The higher the semi-major axis is, the further away a TNO generally is from the Earth,the fainter it is. Therefore we are biased towards objects with low semi-major axis. Looking atthe high semi-major axis (a>150 au) TNOs in Figure 1.2 the bias is clearly evident, the higherthe semi-major axis, the less detected TNOs there are. Simulatoins suggest the real distribu-tion of high semi-major axis TNO might be uniform(Lawler et al., 2017). Similarly the higherthe pericentre is, the further away a TNO generally is from the Earth, the fainter it is. There-fore there is a bias towards objects with low pericentres, and again this can be seen in Figure 1.2.So far, the largest TNOs found are Pluto sized. There are three of these objects; Pluto,Eris and Triton. Triton, which is now a moon of Neptune, is believed to have been part of theKuiper Belt due to its retrograde orbit around Neptune. The main theorised capture methodis Triton used to be part of a binary system with another KBO before they came too closeto Neptune and Triton’s companion was exchanged for Neptune (Agnor and Hamilton, 2006).Both Eris and Pluto are plausibly formed closer to the Sun and then planted into their currenthot-population detached and 3:2 resonant orbits respectively.1.3 The Origin of TNOsTNOs are believed to be left over planetesimals from planet formation, although there couldbe some collisional evolution since then. The cores of the giant planets are significantly moremassive compared to the largest TNO (∼10Me compared to 0.02Me), so the giant planet coreswere likely formed by runaway accretion. Runaway accretion happens when the larger plane-tary embryos that became the giant planets were able to accrete at a much faster rate than therest of the smaller planetesimals. This results in a few discreet outliers (Giant planets) and acontinuous distribution of smaller objects (TNOs).During planet formation, when the giant planets were massive enough, they were able tokick out all of the remaining planetesimals from the giant planet region. Most of the planetes-imals were ejected from the Solar System but small fraction were relocated to the Kuiper belt,scattered disk and Oort cloud. Most of the retained planetesimals are in the Oort cloud with4the Kuiper Belt receiving the least, perhaps ∼0.1%. This ejection event caused accretion ofplanetesimals in the outer solar system to cease, and along with the infrequency of collisionsdue to low number density, resulted in the size distribution of planetesimals ‘freezing out’.Therefore the size distribution of objects in the Kuiper belt and scattered disk today is thesame as the size distribution of planetesimals in the early Solar System.1.3.1 Effects of an Extra PlanetIf Batygin and Brown (2016) are correct in their prediction of a 10ME planet with a ∼600au, then this extra planet will effect the dynamics of the SOs. This prophesied ninth planetwould affect the number of scattered objects that are ejected, and modify the current orbitaldistribution in the a = 200 - 1000 au range(Lawler et al., 2017).1.4 Undiscovered TNOsIn terms of searching for another giant planet, NASA’s Wide-Field Infrared Survey Explorer(WISE) space telescope has search the sky in the infrared for distant objects in the Solar Sys-tem. WISE has ruled out a Saturn sized object or larger out to 28,000 au and a Jupiter sizedobject or larger to 82,000 au (Luhman, 2014).If there was another Pluto sized object in the Solar System where could it be? Anotherobject that lies in the planet region would have been discovered by now. If the object waswithin a couple of hundred au it had a ∼66% chance of being found by the Schwamb et al.(2009) search of the ecliptic, unless it was highly inclined or in the galactic plane. That leavesout beyond a couple of hundred au. If any Pluto sized object is out there they would likely bea SO or DO near apocentre of a large eccentricity orbit.If 100-1000 Pluto sized objects were formed initially, then 10s could still remain in KB andSD today. So there could be enough large objects in the scattered disk to warrant a searchbeyond a few 100 au.1.4.1 TNO survey limitsThe major problem with detecting objects out beyond a ∼200 au is the amount of light re-ceived from them. The flux from an object drops off as the distance squared but since thelight from bodies in the Solar System is reflected sunlight there is another factor of distancesquared, resulting in the flux of a distant solar system object being proportional to 1/d4. Thismeans distant TNOs are incredibly faint. If Pluto was moved from where it currently is at 30au out to 300 au, the increase in distance by a factor of 10 would result in a decrease in fluxby a factor of 10,000, corresponding to a change in magnitude of 10, dropping it from ∼14thto ∼24th magnitude, fainter than the flux limits of the very large-field surveys (the Schwambet al. (2009) limit was mag 21).Another, but not as severe, problem is the on-sky motion of distant objects. Objects inthe Kuiper Belt and beyond are far enough away that their on-sky motion is dominated by the5Figure 1.3: A comparison of how far, for a certain sized object, three surveys could detect outto. The three surveys Schwamb and Brown (blue), Sheppard and Trujillo (red), and this work(black). The solid lines represent the limit of the region of phase space which an object can bedetected by the surveys. The diagonal lines are caused by the limiting R band magnitude, thesevalues are displayed above each line and were created by scaling Pluto apparent magnitude.The shaded green area is the region of phase space that this work is sensitive to, with darkgreen only this work and light green if there is overlap with other surveys.6Earths orbital velocity. Therefore a TNO at opposition would have a retrograde on sky-velocity,in arcseconds per hour, approximated byrate =150d′′/hour (1.1)where d is the object’s heliocentric distance in au. The further away an object the slowerits sky motion. Conventional KPO surveys have ≈1 hour cadences that are optimal for KPOspeeds, therefore usually are only able to detect objects within a ∼300 au.1.4.2 Distant TNO SurveysAt the beginning of this work, the only known survey that could search for distant Pluto-sizedTNOs was the Schwamb et al. (2009) survey, which will be referred to as Schwamb and Brown.They covered a sky area of ∼12,000 square degrees and stated that they were able to detectobjects out to 1000 au, which was achieved by having a multi night discovery baseline. Theirstated limiting magnitude is R = 21.3, this corresponds to Pluto at 165 au.After this project started a paper detailing another TNO survey was release. Sheppardand Trujillo (2016), which will be referred to as Sheppard and Trujillo, searched a thousandsquared degrees and, according to the paper, could detect motion down to 0.3 arcseconds perhour. Using Eq. 1.1, that speed corresponds to an object at 500 au. This survey used multipletelescopes so there is a large range of limiting magnitudes. A majority of the images were takenwith Chile where the limiting magnitude ranges from about 24 to 24.6. Less than 10% of theSurvey was taken with Magellan and Subaru telescopes, where the limit magnitude went downto ∼25.5.For a better understanding of the limits of these two surveys, the distance to an object, ofa particular size, that each survey can detect out to is plotted in Figure 1.3. The region whichthis work covers is also plotted. In regards to detecting Pluto sized objects at these distances,Schwamb and Brown are not sensitive enough (they could only just see Mars sized objects at300 au). Sheppard and Trujillo, on the other hand, are able to see Pluto sized objects out toalmost 500 au, only for a small fraction of survey. Most of the survey could not see objectsfainter than 24.6, which is Pluto at ∼350 au. It should also be noted that almost all of the skypatches that Sheppard and Trujillo observed are below the ecliptic and therefore do not overlapwith the area observed for this work.1.4.3 Improving SurveysThere are two ways a survey can increase the number of discovered objects, increase the skycoverage or increase the depth of the images. If the sky has uniform surface density of objects(for TNOs near the ecliptic this is approximately true) then one would expect the fractionalincrease in sky coverage to be the same as the fractional increase in detected objects. It is alittle more complicated for the case of increasing the image depth, for it depends on the absoluteH magnitude distribution2. If the slope of the H mag distribution of objects that are just too2H magnitude is defined as the magnitude of an object if it was 1 au away from both the Sun and Earth andit is was at opposition7faint to be detected was shallow there would be little justification for increasing the depth. Thecumulative H mag distribution appears to obey the followingdN(< H)dH∝ 10αH (1.2)where N(<H) is the number of object that have a H mag of ’H’ or less and α is logarithmicslope. The cumulative H mag distribution for the brightest TNOs is shown in Figure 1.4. Thereappears to be two different slopes. The size distribution is shallower at lower H, with α ∼ 0.14,and steeper at higher H, with α ∼ 0.6. The knee between the two slopes is at H ∼ 3. This is anincomplete sample of bright TNO. It is believed that there are few more undiscovered brighterthan H ∼ 3 within a couple of hundred au. Therefore the slope of the real distribution mightbe slightly different to the current slope but two distinct slopes is believed to be a real feature.A clear sign of the incompleteness is the fact that at H ∼ 6 the slope slowly shallows off. Ataround H = -0.5 the data diverges from the trend, this is due to low number statistics, thereare only two objects brighter than -0.5.At 300 au a TNO that has an apparent magnitude 25.5 will have an H magnitude of about1.4. Since this TNO would be the smallest object these surveys could find, at distances beyond300 au, we only have to worry about the shallow region of the H mag distribution. Therefore anincrease in limiting magnitude would not produce a large increase in objects found, or in thiscase not significantly increase the chance of finding an object. This means this survey is notideal for finding distant objects. A survey with a larger sky coverage and a magnitude shallowerwould have a better chance of finding a distant object. Although this survey is probing a uniqueregion of parameter space.1.5 Thesis OutlineThe structure of the rest of this thesis is as follows; information about the survey used in thiswork is detailed in Chapter 2. Chapter 3 explains the way we searched the data set for slowmoving object, including the algorithm that aided us. We detail the findings of the search inChapter 4. The upper limit for Dwarf planets and how it was obtained can be found in Chapter5. Finally, we give concluding remarks in Chapter 6.8Figure 1.4: The cumulative distribution of the known TNOs down to a heliocentric absolutevisual magnitude of 8 (blue line). Two exponential functions are plotted (dashed lines) to matchthe slope of the data. The logarithmic slope, α, of each exponential function is displayed aboveeach line. The rollover beyond H ∼ 6 is likely the increasing observational incompleteness.Note: these are not lines of best fit for the data. Data obtained from the Minor Planets Center.92. OSSOSThe data used for the search for the slow moving Solar System objects comes from the OuterSolar System Origins Survey (OSSOS). The original goal of OSSOS was to discover TNOs usingthe common method of searching for objects that move linearly in 3 images taken with 1-hourspacings, which allows detection out to about 300 au. Once found, these objects were then alltracked over months to years to measure their orbital elements with high precision. From 2013to 2016 the images that makes up OSSOS was acquired using the Canadian France HawaiianTelescope (CFHT), a 3.6 m telescope at Mauna Kea. For a more complete understanding ofOSSOS please refer to Bannister et al. (2016).The most distant OSSOS detection was found at a distance of 83 au (although there are33 OSSOS TNOs with a ¿ 83 au whose orbits taken them out well beyond 200 au; with fourhaving apocentre, Q=a(1+e), greater than 500 au. These large-a detections are discussed inShankman et al. (2017).OSSOS images were captured using MegaCam, a wide-field optical mosaic camera. Initially,MegaCam was able to capture 0.9 square degrees of sky area in one image using 36 charge coupledevices (CCDs). Even though MegaCam was installed will 40 CCDs, with a total sky area ofone square degree, the filter that was used at the time meant two CCDs on each side, known asthe ‘ears’, could not be used. See Figure 2.1 for how the CCDs are arranged. When the filterswere upgraded in 2015 the other four CCDs were able to be used. This resulted in the imageshaving 36 CCDs for the first half of OSSOS and 40 CCDs in the second half. The first half wastaken from 2013-2014 and the second half from 2015-2016. A single CCD is 2048 x 4612 pixels,giving MegaCam a resolution of 0.187 arcseconds per pixel.2.1 BlocksThe sky area that OSSOS covers is split up into multiple blocks, where a block is a groupof tightly packed images that creates an almost uninterrupted sky patch. Since the camerasfootprint on the sky is different for the first half of OSSOS compared with the second, imagesare arranged differently in blocks in the first half compared with the second. The blocks in thefirst half contain 21 images arranged three high (along the Dec axis) and seven long (along theRA axis). The three high by one long ‘columns’ are offset from one another so that block runsparallel to the ecliptic. The blocks in the second half contain 20 images arranged four high andfive long. The images are positioned such that the ‘ears’ are interlocking. Figure 2.2 containsthe image layout of both the first and second half blocks.A vast majority of the images in the first half blocks were taken in 2013/14 and a majorityof the images in the second half blocks in 2015/16. Each half contains 4 blocks. The namesof the first half blocks are E, O, L and H. The second half blocks are referred to as M, P Dand S. The RA pointings of all the blocks are shown in Figure 2.3. Each block covers about10Figure 2.1: The layout of MegaCams CCDs. Each rectangle is the border of a single CCD andthe CCD number is in the middle of the CCD. The blue CCDs make up the original layout andthe red CCDs are the add on ’ears’.Figure 2.2: Example of the image configuration for a block in the first half of OSSOS (left) andthe second half (right). The first half block is O Block and the second half block is D Block.The images that are coloured blue are from the first night of the block acquisition and red forthe second.1121 square degrees3, except L Block, which covers 20 square degrees. Giving OSSOS a total skyarea of about 167 square degrees. All the blocks lie within 15 degrees of the ecliptic, and mostare within 5 deg of the ecliptic4.The blocks were not stationary, they slowly moved parallel to the ecliptic at a speed thata typical KBO would move at. This is to minimise the number of TNOs that move out of thesky area, which goes back to the main purpose of OSSOS; to discover and track Kuiper Beltobjects. This slow advance of the blocks over a semester amounts to about 0.7 degrees of thetotal east-west motion, meaning that only a small fraction of the block at the RA extremitieshave only partial repeat coverage and may have fewer observations over the course of a semester,but even there nearly all RA/Dec locations on the triples (see below) have coverage for at leasthalf the 5-month semester.2.2 CadenceThe cadence is split up into two parts: the triple images and the nailing images. The tripleimages are described in Section 2.2.1 and the nailing images are described in Section2.2.2. Formuch more detail about the OSSOS cadence planning, see Bannister et al. (2016).2.2.1 TriplesThree images taken in roughly hourly intervals make up the triple. Since the exposure time ofeach image is five minutes, and the readout time is a minute, only 10 images can be taken inan hour. To have hourly spacings between two images of the same field, the triples for a blockhas to be done in two chunks of 10-11 triples each, which can be seen in Figure 2.2.The original purpose of the triple was to discover the TNOs by looking for linear motionobjects across the three images. Due to the importance of the triple, they were taken on nightsthat had better than average seeing. At CFHT this results in the triples often having FullWidth Haft Maximums (FWHMs) in the range of 0.5-0.75′′. Because OSSOS and the work inthis thesis require a TNO to be detected in all three triple images, it is the worst of the threeimages that determines the depth for moving object detection. Luckily image quality acrossthe OSSOS triples was very uniform (rarely more than 0.15′′ change between the 3 images ofthe triples).2.2.2 NailsThe nails, or nailing images, were taken at certain time differences before and after the tripleimages. For almost all the blocks there is at least one nail that is taken within ± 2 days of thetriple, at least one ± a week, one ± a month, two ± two months. In some cases there is a nailthat is ± three months from the triple. There are also nails that were taken ± a year from thetriples, during the previous/next opposition.3Because images with the ‘ears’ were slightly more than one square degree, only 20 images were needed forsecond half blocks to get to 21 square degrees4O, H, and M blocks were placed more than 5 degrees from the ecliptic to probe the TNO inclinationdistribution.120h2h4h6h8h10h12h14h16h18h20h22h20 au40 au60 au80 auEOLHPMSDSaturnUranusNeptunePlutoFigure 2.3: The RA pointings of all 8 OSSOS blocks. The blue dots represent the positionwhere a TNO was discovered by OSSOS. The most distant detection, which was in D block,was at 82 au although in principle OSSOS could detect motions to at least 200 au (and 300 auin the better-seeing blocks).13The original purpose of the nailing images was to track the TNOs discovered in the triple,to be able to constrain the TNOs orbits to a high precision. Once detected in the triples themotion of the TNO could be predicted with good precision for the few nights duration out tothe ±2 days nailing image, and be unambiguously identified by comparing that nail with thetriple images. Once nailed to that image, successive prediction in an iterative manner to theweek and months time scale was performed. For the purposes of this project, the nailing imageswill be predominantly used with the reverse intent: objects identified as stationary over the2-hour triplet time span will be verified as still present in the nails that are deep enough thatthe objects should be visible.2.3 FiltersInitially all of OSSOS images were taken in the r-band using the filter ‘r.MP9601’. r.MP9601has a central wavelength of 630 nm, a bandwidth of 124 nm and a mean transmission of 82.1%.As mentioned before, in 2015 MegaCams filters were upgraded. When the switch happenedOSSOS started using the new r-band filter ‘r.MP9602’. r.MP9602 has a central wavelength of640 nm, a bandwidth of 148 nm and a mean transmission of 97%. The large bandwidth andbetter transmission of r.MP9602 compared with r.MP9601 means that r.MP9602 can detectmore photons for a given exposure time and seeing, hence can see deeper.Three of the first half blocks used the r.MP9601 filter. The last first half block, H block,had most of the images taken using the r.MP9601 filter except a few of the nails at the end ofthe run. These last few nailing images used the r.MP9602 filter. Part way through the secondhalf the filter for the nails changed to the wide filter ‘gri.MP9605’. This wide filter is ∼3 timeswider than the r filters, so its images are deeper than the r filters. This greater depth greatlyaided object recovery in nailing images with seeing somewhat worse than that of the triplesobtained. Only a small fraction of the nails of M and P blocks were taken using the wide filter.A large minority of the S block nails and almost all the nails of D block were taken using thewide filter.2.4 CataloguesOSSOS uses two different methods to identity sources. This is to decrease the number of falsepositive point sources that are found in an image. The two methods are the S-Extractor method,which uses the counts of clusters of pixel to find sources, and the wavelet method, which useswavelet decomposition theory to find sources. For a detail explanation on how these methodswork please refer to Petit et al. (2004). The sources that were found using the S-Extractormethod are known as jmp sources. Named after Jean-Marc Petit, the person that wrote thecode using this method. Similarly, the sources that were found using the wavelet method areknown as matt sources, after the person that wrote the code using this method, Matt Holman.All of the sources found in an image gets put into a catalogue. Because there are two sourcefinding methods there are two catalogues for each image, the jmp and matt catalogue. A cat-alogue contains the x-y pixel and RA-Dec position ofthe centre of the source5 and the sourcesflux, maximum pixel value, elongation.5The RA-Dec position was not initially in the catalogue and had to be added later for this work14To find moving objects in the triple images, all of the sources that weren’t stationary needto be found. So OSSOS had to create catalogues for the triple images. For the nailing images,all that was needed was the RA and Dec plate solution6 to know where in the image the TNOis predicted to be. This meant that the catalogues for the nails were not initially created andhad to be made for this work.2.5 In This WorkThe further a solar system object is from, the Sun the slower it’s on-sky motion is (Equation1.1). Therefore distant solar system objects should appear (near) stationary in the triples butnot on the timescale of a few days to months. This means the conventional OSSOS searchcannot detect these objects. The strategy for this thesis was to create a catalogue of all thestationary objects that appear in the triples and then go through the nails to find them again.Stationary objects that do not show up in the nails are the examined to determine whetherthey are solar system objects moving less than 0.5′′/hr (and thus beyond 300 au from the Sun).6the plate solution is how the pixels in the image maps to the RA/Dec coordinate system.153. The Searching MethodThe method used to search for distant objects is broken up into three key parts. The firstpart is the creation of the stationary catalogue, where an algorithm identifies all the stationaryobjects in a mosaic image (Section 3.2). The second part is the searching for the stationarycatalogue objects in the nailing images (Section 3.4). The final part is creating a list of slowmoving candidates and examining images of each candidate (Section 3.6). Before getting intothe details of the searching method, a description of how we were able to identify an object ontwo different images is given in the next section.3.1 MatchingTo be able to say whether an object is real and stationary, and later to say whether it is stillthere or not, one must be able to match sources between different catalogues. An idealisticview would be to say if the Right Ascension (RA, δ) and Declination (Dec, δ) of two objectson different catalogues were the same then that is a match, so they are the same object.Unfortunately the real world involves uncertainty and natural variation, so the same objectwould have the slightly different RA and Dec in two different catalogues. Therefore a tolerancehas to be introduce and one would say two sources are the same object if the on sky separationis smaller than the tolerance. Using the general formula for angular distances on the celestialsphere, two sources would be matched if their coordinates obeyed the following inequalityT 2 > (δ1 − δ2)2 + ((α1 − α2) cos(δ1))2 (3.1)where T is the tolerance, it given value is explain in Section 3.2.3, and the subscript 1 and2 denote two different candidates matching sources in two images.3.1.1 Streamlined MatchingThe algorithm would have to do a significant number of matches between objects in two differ-ent catalogues if all the objects in the catalogue are checked, resulting in large computationaltime, going as N1*N2, with N being the number of sources in a catalogue. By only checkinga fraction of the catalogues we can drastically decrease the computational time. Although thisneeds to be done without the risk of missing a potential match. The term matcher, which willbe used below, will refer to the source in the first catalogue that sources in the second cataloguewill be tried to be matched to. Matchee will refer to a source in the second catalogue.By sorting a catalogue by increasing declination we can guess where in the catalogue thepossible matches are. The index, I, of where in the matchee catalogue the declination are similarto that of the matcher, assuming the increase in declination is constant, is found usingI =δ − δminδmax − δmin l (3.2)16where δ is the declination of the matcher, δmin and δmax are the minimum and maximumdeclination respectively in the matchee catalogue, and l is the length of the matchee catalogue.To find an appropriate starting position I is reduced by 0.01l (A hundredth of the length ofthe matchee catalogue) until the following inequality is trueδI < δ − T (3.3)where δI is the declination of the Ith object in the matchee catalogue and T is the appropriatetolerance (see Section 3.2.3). Once the inequality is satisfied the algorithm preforms a matchingcheck on all the objects in the catalogue sequentially from the Ith object until this inequalityis metδI > δ + T (3.4)Essentially the algorithm checks all the objects in the catalogue with a declination in therange of plus or minus the tolerance from the matchers declination. This streamlined matchingmethod is used for all the catalogue matches in the algorithm and results in more than an orderof magnitude faster execution.3.2 Creating the Stationary CatalogueThe stationary catalogue is a list of the objects that appear to be stationary, within tolerances,over the two hours in which the triple images were taken. First we find stationary objectsusing the jmp and matt catalogue separately: we create a jmp stationary catalogue and amatt stationary catalogue, see Section 3.2.1. Then we combine the jmp and matt stationarycatalogue to create a final stationary catalogue, see Section jmp and matt Stationary CataloguesAn algorithm is used to created the jmp/matt stationary catalogue using the following method.The algorithm goes through the first triple images catalougue, one source at a time, and triesto match it to sources in the other two triple image catalogues. First the second triple imagecatalogue (which will be known as catalogue two) is search for possible matches using the widetolerance, see Section 3.2.3. If there are more than one catalogue two matched object, thealgorithm redoes the match but with a tight tolerance, see Section 3.2.3 as well. If this tightsearch produces only one match, then the third triple image catalogue (which will be knownas catalogue three) is searched, also using the tight tolerance. If one match is again the result,the algorithm tries to match the catalogue two matched object to the catalogue three matchedobject, using the tight tolerance. If that match is successful then these three sources are consid-ered a stationary object and added to the stationary catalogue. These stationary objects foundwith the tight tolerance are given the status of ’immune’, which is useful later, see Section 3.2.4.If no stationary object was found using the tight tolerance or if there was only one cataloguetwo matched object using the wide tolerance, then the algorithm searches catalogue three usingthe wide tolerance. If one or more catalogue three matched objects were found, the algorithmtries to match the catalogue two matched object (the ones that were found using the widetolerance) to the catalogue three matched object, using the wide tolerance.173.2.2 Final Stationary CatalogueThe final stationary catalogue is the intersection of the jmp and matt stationary catalogues.Therefore to make it into the stationary catalogue we require it to be found in both the jmpand matt catalogue on all three triple images. This is to cut down on non-real objects gettingin the final stationary catalogue. To create the final stationary catalogue we matched the jmpstationary catalogue with the matt stationary catalogue using tolerances given in Section 3.2.3.The average position in all three triple images is used as the position of a jmp/matt stationarycatalogue object in the matching. This final stationary catalogue will, from now on, be knownas the stationary catalogue.3.2.3 TolerancesThe tolerances we want to use needs to take into account two factors. The first factor is theuncertainty in the position of sources due to the source being blurred by the atmosphere. Thesecond factor is the movements of our targets. If we want to search for objects as close as300 au then distance traveled by the objects at the inner edge becomes non-negligible in thetime frame of the triple. The wide tolerance for stationary catalogue creation is calculated bysumming the angular distance a body traveling at 0.5 arcseconds per hour would cover betweenthe two images and the average of the image seeingsTw = β√S2Tx + S2Ty + 0.5txy (3.5)where STx and STy are the seeings of the two triple images, β is a tolerance coefficient andtxy is the time between the two triple images. The difference in Julian date between two images,in units of hours, is used as txy. If the two seeing were the same, we wanted the seeing part ofthe wide tolerance to be equal to the seeing. So we decided on a beta value of 1√2. Just theseeing part of the wide tolerance is used for the cases where a tighter tolerance is neededTt = β√S2Tx + S2Ty (3.6)The same β value used for the wide tolerance is also used for the tight tolerance.When matching the jmp and matt stationary catalogue, to created the stationary catalogue,the worst seeing of the triple images is used as the tolerance. We don’t have to worry aboutthe motion of slow moving objects in the tolerance since the objects position is averaged overthe three images.3.2.4 CrowdingIf there are a, b and c sources that are all within the tolerance from each other in first, secondand third triple image respectively, then the code will a · b · c stationary objects. One of theways were tried to fix this multiplicity problem was to do the tight search. This helped whenthere was a real object in the sources, but not if it is just a bunch of rubbish sources.The next way we tried to solve the multiplicity problem was to remove the duplicates in thestationary catalogue. We went through each object in the stationary catalogue, from lowestto highest Dec, and tried to match it with other objects in the stationary catalogue. The sumof the worst seeing of the three triple images and the angular distance a body traveling at 0.5arcseconds per hour would cover between the two images was used as the tolerance1848.1314007699 14.8073824444 48.1314006186 48.1314047704 48.1313985996 48.1314010704 48.1314031354 48.1313964252 .... 14.8073975145 14.8073712102 14.8073695923 14.8074052414 14.8073758476 14.8073752605 687.73 613.91 492.11 23294.4 .... 27957.02 26740.37 3805.0 2287.72 1.16 048.1143399616 14.8082718238 48.1143388131 48.1143432284 48.1143445087 48.1143387823 48.1143368908 48.1143375459 .... 14.8082694455 14.8082719547 14.808270203 14.8082725373 14.8082693815 14.808277421 136.27 127.11 109.45 5586.02 .... 5632.82 5234.16 1973.0 456.51 1.22 048.1727496004 14.8086946687 48.1727493395 48.1727473581 48.1727507883 48.1727466923 48.1727478864 48.1727555377 .... 14.8086948694 14.8086945154 14.808694109 14.8086953876 14.8086945146 14.8086946161 33777.65 32575.2 33308.2 .... 2441686.0 2475728.0 2492010.0 65097.0 63253.8 1.06 048.1393181221 14.8088762082 48.1393133338 48.1393078427 48.1393303148 48.1392989591 48.139324379 48.1393339032 .... 14.8088817573 14.8088797403 14.8088635259 14.8088894937 14.8088673644 14.8088753675 82.25 78.65 70.85 5891.88 .... 4966.62 3925.74 1709.0 182.2 1.39 0...Table 3.1: Example of a stationary catalogue file.T = STw + 0.5txy (3.7)where STw is the worst seeing of the three triple images. If there is a match, the objectwith the higher declination is removed from stationary catalogue, unless it is ’immune’. Sinceobjects found using the tight tolerance are most likely real objects, we do not remove them. If anobject gets matched to an ’immune’ object, nothing happens. Later when that ’immune’ objectgets rematched with the first object, then the first object gets removed from the stationarycatalogue. Each object in the stationary catalogue gets a number called ’multi’, which is thenumber of other objects it removed. Even though this value is recorded it is not used.3.2.5 Stationary Catalogue formatThe stationary catalogue is a text file were each line represents a stationary object. The firstcolumn is the averaged RA value of all six catalogues, and the second column is the averageDEC value. The next six columns are the six RA values from each catalogue, the first threeare from the jmp catalogues and the last three are from the matt catalogues. Each set of threeis in chronological order. Similarly the next six columns are the Dec values, and the six afterthat are the flux values. The next column is the median jmp ’Max Int’ value and the columnafter is the median matt value. The next column is the median jmp elongation, and the lastcolumn is the multi which is described in Section 3.2.4. See Table 3.1 for an example of thestationary catalogue file.3.3 ParametersBefore the nailing catalogues can be searched, some information about the nails and the triplehas to be obtained. An important piece of information about the nails is the RA and Decrange that each CCD covers, so we know which nailing catalogues we need to search in sincethe nailing images are at constantly moving pointing each night. Unfortunately the area of skythat the CCD cover are not rectangles with sides being constant in either RA or Dec, so itis difficult to know the exact sky area of a CCD. To solve this problem we use two boxes todescribe each CCD: An inner box and an outer box. The sides of the boxes are constant ineither RA or Dec. All of the inner box is in the CCD sky area and all of the CCD sky area iswithin the outer box, see Figure 3.1. Therefore if an object is within the inner box then it isdefinitely in the CCD sky area. If an object is outside the inner box but inside the outer boxthen the object might be in the CCD sky area, and a further check is required. Lastly, if the19Figure 3.1: An example of the inner/outer box method used. The blue box represents the areacovered by the CCD, the green box is the inner box and the red box is the outer box. This isnot a real area covered by a CCD, the amount of rotation of the CCD sky area is accentuated.object is outside the outer box then the object is not in the CCDs sky area.The boxes are created by first finding the RA and DEC of CCDs corner pixels. The largerof the bottom two corners Dec is the Dec of the bottom side of the inner box, and the smallerDec is the Dec of the bottom side of the outer box. Similarly, the smaller/larger of the top twocorners DEC is the Dec of the top side of the inner/outer box. This process is repeated to findthe RA of the left and right sides of the boxes.For a particular nailing mosaic image, the largest and smallest RA and DEC values obtainedfrom the sky areas of the mosaics CCDs are recorded to create a box containing all the sky areaof the mosaic image. This box will be known as the nailing box.Other information that is required is the seeing and zero point of each CCD, the exposuretime of the image, the filter used, and the date which the image was taken. All of these areextracted from the image headers.All of these nailing image parameters are put into a single text file. The file is formattedsuch that each nailing image has its own line with the first column being the images odometernumber. The next four columns are the minimum and maximum, RA and Dec that describesthe nailing box coordinates (min RA, max RA, min Dec, max Dec). The following two columnsare the filter used and the exposure time of the image. The last column is the Julian date ofwhen the image was taken rounded down to the nearest day.Below each nailing image line in the file is a line for each of the CCDs of that image. Thefirst column of a CCD line is the ccd number. The next four columns are the minimum and201828172 49.087339 50.335460 15.787888 16.789221 gri.MP9605 300.133000 57245ccd00 50.111982 50.218112 16.552550 16.788323 50.109115 50.221323 16.552491 16.788899 3700 5183 4.48 33.608000ccd01 49.998254 50.105395 16.552437 16.788828 49.995716 50.108274 16.552305 16.789083 3638 5128 4.46 33.604000ccd02 49.884006 49.991984 16.552367 16.789159 49.881861 49.994467 16.552079 16.789190 3631 5596 4.40 33.610000ccd03 49.769556 49.878051 16.552127 16.788773 49.767662 49.880281 16.551551 16.789221 3773 5545 4.34 33.558000ccd04 49.654921 49.763975 16.551453 16.788007 49.653473 49.765759 16.550777 16.788685 3850 5532 4.23 33.624000ccd05 49.540504 49.649637 16.550663 16.786874 49.539230 49.651250 16.549775 16.787895 4162 5829 4.05 33.548000ccd06 49.426179 49.535508 16.549741 16.785452 49.425382 49.536647 16.548616 16.786840 4110 5997 4.17 33.589000ccd07 49.312483 49.421649 16.548466 16.783615 49.311985 49.422494 16.547197 16.785277 4296 6062 4.06 33.625000ccd08 49.199419 49.308266 16.547289 16.781659 49.199301 49.308736 16.545802 16.783667 3915 5895 4.26 33.535000...Table 3.2: Example of a nailing parameters text file.maximum, RA and Dec that describes the outer box coordinates (min RA, max RA, min Dec,max Dec). Similarly the following four columns are for the inner box. The next two columnsis the length of the jmp and matt catalogue respectively. The final two columns is the CCDsseeing and zero point respectively. For an example of a nailing parameter file see Table 3.2.Some additional information about the triples is also needed, To if a nail overlaps with thetriple, the sky area of each triple is calculated the same way as the nails. A box, known as thetriple box, that spans the lowest to highest RA and DEC of the triple mosaic images is created.3.4 Searching the NailsOnce the nailing parameters file is created, the nailing images can be searched for the ap-pearances of each object in the stationary catalogue. Initially the code loaded all the nailingcatalogues for the block in question. When it was time to run the code on blocks with a highernumber of nailing images the code failed due to memory issues. This was remedied by onlyloading the nailing catalogues of use for the stationary catalogue being examined. A nailingcatalogue was consider useful if the sky area of the image it belonged to overlapped with thesky area of the triple image being examined. The nailing box, see Section 3.3, is used as theboundary of the nails sky area and likewise the triple box is used as the boundary of the triplessky area.3.4.1 On PixelsThe algorithm goes through each nailing image to see if the stationary catalogue object is inone of its nailing catalogues. To start with the algorithm checks to see if the sky position of thestationary object might be on a nailing image. If the stationary object lies within the imagebox, the object might be on one of the CCDs, so it looks at each individual CCD of the im-age. If the stationary object does not lie within the image box, the next nailing image is checked.A CCDs inner and outer box is used to determine if the sky position of the stationary objectis on the CCD. If the coordinate position lies in the inner box then the stationary object isconsidered on pixels. If the coordinate position lies outside the inner box but inside the outerbox then the RA and Dec position is converted into x and y pixel position of the nailing image.If the xy pixel position corresponds an actual pixel on the image then the stationary object isconsidered on pixels. If the coordinate position lies outside the outer box then the stationaryobject is not on pixels.21When the algorithm finds that the stationary object is on pixels on a nailing image it searchesthrough the catalogue of that nailing image to find if a source is present at the expected RAand Dec. The searching method is outlined in Section 3.1 and the matching tolerance used isoutlined below.3.4.2 ToleranceWhen matching between the stationary catalogue and a nailing catalogue the following toleranceis usedT = β√S2T + S2N (3.8)where ST is the seeing of the worst triple image, SN is the seeing of the nailing image andβ is the tolerance coefficient. Just like in Section 3.2.3, a value of 1√2is used for β.If there is a match then the stationary object is considered found in that nail. Once a matchhas been found the algorithm stops searching through that catalogue and searches for the nextnail. Both the jmp and matt catalogues are searched.3.5 Creating the Master TableOnce the nails have been searched, the information is recorded in a text file known as the mastertable. The master table contains all the stationary catalogue of a single image, along with all thenailing images each stationary object should be on pixels and whether they were found on a par-ticular nail. Below is a description of exactly what is in the master table and how it is organised.Each stationary object has one line in the master table that contains information aboutthe triple images that they are in. These lines are called the stationary object lines. Thefirst column of the stationary object lines is the objects unique identifier. The identifier is theodometer number of the first triple image the stationary catalogue object appears on followedby a dot, then the CCD number and finally the objects position in the stationary catalogue.For example, if stationary catalogue object is on CCD05 of the triple image 1755517 and is the234th image on the stationary catalogue then its identifier would be 175517.050234.The next six columns is the objects six RA values in the triple images. Then followed bythe six DEC values, the six flux values. The next two columns are the median jmp and matt’max int’ values respectively. The ’max int’ values are to do with the maximum pixel value ofthe source. The jmp elongation value is the following column7 The next two columns are themaximum seeing and zero point of the triple images. The last two columns contain the exposertime and the filter used.Below each stationary catalogue line is information about the nailing images that they areon pixels. There is one line for each nailing image that the object is considered on pixels. Allnailing lines contain the following information: the nails odometer number, which CCD theobject is/should be on, filter used, exposure time, seeing, and the zero point. If the objectwas found in the jmp and/or matt catalogue, then there is additional information. The first7The ’max int’ and elongation values were, at one point, going to be used. We decided that they were notneeded but they were kept in the master table.221846160.111542 47.953081 47.953143 47.953212 47.953096 47.953151 47.953187 14.709081 14.709001 14.709043 14.709083 .... 14.709043 14.709058 50.30 54.65 54.93 1858.34 1270.47 1141.97 1595.00 78.10 1.51 0 3.06 32.740 400.32 r.MP96021828216 ccd00 gri.MP9605 300.18 5.39 33.519 matt 47.953133 14.7090481828217 ccd00 gri.MP9605 300.17 5.41 33.5621831712 ccd00 gri.MP9605 300.12 3.90 33.540 jmp 47.953091 14.7090211832621 ccd39 gri.MP9605 300.14 3.26 33.424 jmp 47.953140 14.709042 matt 47.953144 14.7089601836410 ccd25 gri.MP9605 450.15 3.86 33.973 jmp 47.953148 14.709024 matt 47.953136 14.7090101836589 ccd15 gri.MP9605 450.17 4.46 34.054 matt 47.953106 14.7090051846610 ccd10 gri.MP9605 450.32 3.53 33.890 jmp 47.953259 14.7090671847469 ccd09 gri.MP9605 450.19 3.22 33.969 jmp 47.953167 14.709029 matt 47.953175 14.7090361847477 ccd09 gri.MP9605 450.18 3.36 33.987 jmp 47.953194 14.709087 matt 47.953167 14.7090851850927 ccd25 gri.MP9605 450.16 3.29 33.943 jmp 47.953163 14.709047 matt 47.953156 14.7090621850964 ccd25 gri.MP9605 450.08 7.25 33.8641852577 ccd23 gri.MP9605 450.17 3.08 34.060 jmp 47.953125 14.709010 matt 47.953129 14.7090161852587 ccd23 gri.MP9605 450.17 3.09 34.062 jmp 47.953152 14.709094 matt 47.953148 14.709089Table 3.3: Example of a master table.additional column is either ’jmp’ or ’matt’. Indicating which catalogue the object was foundon. Followed by the RA and DEC of the object on the nail. There could be up to two of thesesets of additional columns, one for jmp and one for matt. For an example of a master table seeTable VettingA decision has to be made which stationary catalogue objects could be slow moving solarsystem objects by how many nails they reappear in. Section 3.6.1 below details the criterion astationary catalogue object has to meet in order to be slow moving candidate. The format forthe candidate list is contained in Section 3.6.2. Section 3.6.3 explains how the candidates areexamined further to determine whether they are slow moving objects.3.6.1 Candidate ListAs mentioned in Section 2.2.1 the triple images have, on average, better seeing than the nailingimages. Therefore an object that is at the limit of detectability in the triple images might betoo faint to be seen in the worst seeing nails. This may cause some of the faint stationaryobjects that are actually stars and are to faint to be seen in the nails to be incorrectly labeledas a slow moving candidate.The way we determine the flux that separate bright and faint objects is by looking at theaverage number of founds for binned jmp flux values. Assuming that a majority of objectsin the stationary catalogue are real, the average number of founds for a particular flux binshould not depend on flux if the objects are bright enough to be seen on all the nails. Theconsistency of the average number of founds for bright flux is evident in Figure 3.2. Whenlooking at the low flux end, the objects are too faint to be seen in all the nails. The averagenumber of founds for the low flux bins should, therefore, be less than the average number offounds of the high flux bins, which can also be seen in Figure 3.2. The flux at which the aver-age number of founds starts to drop is used as the dividing line between bright and faint objects.If an object was too faint to be seen in a nail then that nail should not be counted as beingon pixels for that nail. Therefore a way to determine the quality of the nailing image compared23Figure 3.2: The average number of founds for logirithmicaly spaced binned jmp flux values.The drop off at low fluxes is due to these objects being to faint to be seen on the worst nails.The point at which the fluxes start to drop off is used as the dividing line between faint andbright objects. This figure was created using data form P block.24to the triple images was devised. If a faint object was not found on the nail, in either the jmpor matt catalogue, then an image quality check is performed. The first check is to see whetherthe seeing of the nail is worse than that of the tripleSN > ST + 0.25 (3.9)The seeings are in number of pixels. As can be seen by the equation above, the nails seeingwas allowed to be slightly worse than that of the triple. If the nail does pass the first check,Equation 3.9, then a second check is performed. This time to use the zero pointsSN >√2.5∆ZpST (3.10)where ∆Zp is the difference between the zero point of the nail and the triple. If the secondinequality is also satisfied, then the nail is deemed not deep enough to see the faint object inquestion and the nail is not counted as being on pixels for that object.Generally a wider band will means more photons from the source being detected, resultingin the image being deeper. The cut above does not take this into account, this cut only works ifthe filters used for both the triple and the nail have the same band. The two red filters have thesame band, but the wide filter doesn’t, therefore a different cut is needed when the dealing withnails using the wide filter (since the triples are always using one of the two r band filters). Thewide filter is three times wider than the r band filter, so if an objects colour is approximatedto being grey then the wide filter will receive three times as many photons per second from theobject compared with the red filters. If the nailing image was taken using the wide filter thenthe following inequalitySN >√3tNtTST (3.11)is used to determine whether the nail should be considered, where tN is the exposure timeof the nailing image and tT is the exposure time of a single triple image. If the inequality ismet then the nail is deemed not deep enough to see the faint object in question and the nail isnot counted as being on pixels for that object. Since it is assumed that bright objects shouldbe seen on all the nails, they do not undergo a quality check.Ideally a slow moving object would be a stationary catalogue object that doesn’t have anyfounds. There is a chance that an asteroid, a cosmic ray, noise etc. could happen to createa source where the slow moving object was, resulting in a false found. Therefore stationarycatalogue objects with a couple of founds should be looked at as well. We decided that faintobjects that have two or less founds should be considered a candidate. Since there are less ofthem and, if they are really stars, they have a higher chance of being found, bright objects thathave three or less founds should be considered a candidate.Due to the shifting of the nails night by night, some stationary objects on the edge of theblock may only have only a couple of nails which they are on pixels. Therefore if criteria forbeing a candidate only depends on the number of founds, there will be objects that only havea few on pixel nails and are found on all/most of them that make it to the candidate list. Tostop these kind of objects getting into the candidate list, the on pixel count must be 5 or moreto be considered a candidate.2531845955.000699 47.008786 14.439502 1845955p00 1845967p00 1845993p00 1828216p08 1828217p08 1831712p08 1832625p08 .... 1836414p05 1846188p00 1847469p07 1847477p07 1850931p05 1852581p03 1852591p031845955.001150 47.057304 14.510514 1845955p00 1845967p00 1845993p00 1828216p08 1828217p08 1831712p08 1832625p07 .... 1836414p06 1846188p00 1846610p10 1847469p07 1847477p07 1850931p05 1852581p02 1852591p021845955.010761 46.900652 14.451291 1845955p01 1845967p01 1845993p01 1828216p08 1828217p08 1831712p08 1832625p08 .... 1836414p06 1846188p01 1847469p10 1847477p10 1850931p06 1852581p05 1852591p051845955.020016 46.850212 14.321343 1845955p02 1845967p02 1845993p02 1831712p08 1832625p08 1836414p06 1836583p06 .... 1836593p06 1836595p06 1836597p06 1847446p00 1847461p00 1850931p05 1852581p03 1852591p031845955.020194 46.850105 14.351472 1845955p02 1845967p02 1845993p02 1831712p08 1832625p08 1836414p06 1836583p06 .... 1836593p06 1836595p06 1836597p06 1847446p00 1847461p00 1850931p05 1852581p03 1852591p03..Table 3.4: Example of a candidate list file.By examining objects that have on pixel count of 5 or more, we exclude a few percent ofthe total object. To reduce the number of objects excluded we make some exceptions. If anobject has an on pixel count of 4 and is found on 1 or fewer of them or on pixel count of 3 andno founds then that object is a candidate. This means that, by also examining objects thatonly have 4 or 3 on pixel nails, less than a percent of objects are excluded from examination.3.6.2 Candidate List formatThe candidate list contains the stationary sources unique identifier followed by its average RAand DEC position. The next three columns are the image names of the three triple images(in chronological order). An image name is the odometer number of the image followed by a pthen the CCD number. The remaining columns contain the image names of all the nails thatthe candidate is on pixels. The first row only has the number 3 in it (which is explained in thesection below). The candidate list filename is the odometer of the first triple image followed by’.vetting’. For an example of a candidate list see Table ValidateTo determine whether or not the objects in the candidate list are slow moving objects theimages were viewed. This was achieved using a programme called validate8. Validate uses theinformation in the candidate list file to display cut outs of given images centred on inputtedcoordinates. The RA and Dec (second and third column respectively) of the file is used as theinput coordinates and following image names are the given images. Validate displays one cutout at a time and a button has to be clicked in order to view the next (or previous) cut out inthe sequence. There is also an accept and a reject button. Once the candidate is accepted orrejected then images of next candidate pop up. If a candidate is accepted a comment can beadded.There are two rounds of image viewing. The first round only the triple images are viewed.This is to quickly remove all the candidates that are not point sources, like artifacts from brightstar halos. The 3 in the first row of the candidate list is to tell the software that only the firstthree images (triples) should be viewed. The candidates that were accepted in the first roundof vetting were placed into another candidate file. This new candidate list didn’t have a 3 in itsfirst line, therefore allowing all images to be viewed. From viewing the nails, one can determinewhether the object is slow moving in the outer solar system.8validate was written by JJ Kavelaars at the Hertzberg Research Institute264. ResultsAfter applying the method described in Chapter 3 to each image in each block, we found nodistant solar system object. The number of candidates for each square degree ranged from 10sto a couple of hundred. Almost all of the stationary objects that make it into the candidatelist are false positive. The main types of false positive candidates are described in Section 4.1.Even though no distant solar system object was found, we did find some objects that weren’tfalse positives. They include optical ghosts of very bright stars (Section 4.2), what we believeare faint flare stars (Section 4.4) and faint supernovae (Section 4.3).4.1 False PositiveThere are four main types of false positives. The two most common are cause by saturated starhalos (Section 4.1.1) and faint stars (Section 4.1.2). Other types of false positives that are lessfrequent, and thus not discussed, are chance alignment of noise, stars right next to galaxies,galaxies on the edge of a CCD.4.1.1 Saturated Stars HaloSaturated stars produce a ‘halo’ around themselves that produce enormous numbers of sourcesin each triple catalogue. Since the telescope comes back to nearly the same sky patch for thetriples, a saturated star appears on nearly the same part of the triple images, so its halo hasnearly the same shape. This results in chance alignments of halo-produced sources that thecode thinks is are stationary objects, because they are within tolerances of being at constantRA and Dec. In the nails, the saturated star will be in a different part of the image, so its halowill have a different shape. The halo-produced sources will not line up with the halo createdstationary objects. The halo-created stationary objects will have no founds and thus be labeledas a candidate.These kinds of false positives are easy to reject. By looking at just the triple images, onecan tell they are not point sources, hence cannot be solar system objects. Therefore they canbe quickly rejected in the first vetting pass.4.1.2 Faint StarsAs discussed earlier, stars that are near the flux limit in the triples may not be visible in theworst seeing nails. Therefore some of these faint stars may only have a couple of good seeingnails resulting in one or two on pixel nails and thus being placed in the candidate list. Theseare real object but are false in the sense that they are not moving.27We attempted to stop these faint stars from showing up in the candidate list by not countingthe nails that were ‘worse’ that the triples (see 3.6.1) but it apears to be not 100% successful.Identifying stationary objects as faint stars was the most time consuming part of examiningthe candidate lists, although the process was made easier, and occurred less often, when therewere nails taken using the wide filter.4.1.3 Obscured StarsSome bright stars also make it into the candidate list when a star is partly or fully coveredup by a diffraction spike from a saturated star almost all of the on pixel nailing images. Thiscovering up of the star causes the source finding software to be unable to detect it. So the star‘appears’ in only in a couple of nails. These false positives can be quickly rejected in the secondvetting pass.4.1.4 Inbetween StarsThere are a group of false positive that appear in the space between two close stars but thereis nothing at the given coordinates. They are believed to be created when two stars close toeach other are matched together and create a false stationary object between the two. Thesefalse positives only appeared in the second half blocks, for reasons unknown.For the first two blocks they were found, candidates that were this kind of false positivewere accepted in the first round of vetting then rejected in the second. To save time they wererejected in the first round of vetting for the remaining blocks. The order is irrelevant becausethe are clearly not moving objects.4.2 Optical GhostsOptical Ghosts are internal reflections of very bright stars that appear to be slowly movingin the triples. Since the block is slowly shifting, explained in Section 2.1, when the telescopecomes back for the next triple image the field has slightly shifted, resulting in the optical ghostmoving a tiny amount, but less that the stationary tolerance in the triples. When it comes tothe nails, the block has shifted enough that the optical ghost is no longer anywhere near itsposition in the triples. The movement of an optical ghost can be seen in Figure 4.1. The lastthree images make up the triple and the first image is a nail taken 2 months before.The total number of optical ghosts found was 26. Even though they are technically falsepositives, their similarities to slow moving solar system objects warrant a discussion aboutthem. The similarities were so close that the first optical ghost found was initially thought tobe a slow moving solar system object.The way to differentiate between an optical ghost and a slow moving solar system objectis to closely examine the object’s movement. On the timescale of a few hours, solar systemobjects have linear speeds. Optical ghosts, on the other hand, appear to have a slight changein direction and speed. Another telltale sign that an object is an optical ghost is the directionof the movement. Mentioned in Section 1.4.1, the on-sky motion of objects out beyond a fewhundred au are dominated by Earths orbital velocity. So much so that bound objects at that28(a) 2 months before. (b) First triple image. (c) Second triple image. (d) Third triple image.Figure 4.1: The movement of an optical ghost in the triples and one nail (others not shown) toshow the ghost is not in the vicinity in the nailing images. These images are from E Block.distance all have the same direction on the sky, parallel with the ecliptic. Therefore if an objectis not traveling in this direction it is not a (bound) solar system object.4.3 SupernovaeThe code was able to find distant supernovae. They were supernova that had their peak bright-ness around the time of the triples and were faint enough that they could only be spotted in afew of the nails. One of the supernova that was found is shown in Figure 4.2. It appears thebrightest in the triples images and the nail the day after with nothing in the nails before. In thenail a month later the supernova has dimmed but still visible but in the nail 8 months later itcan no longer be seen. A rapid rise time of less that a week and then fading over several weeksis typical of supernova light curves. Additionally, the supernovae were all seen in the outskirtsof galaxies, as one would expect. The total number supernovae found was 34.It is most likely that there are more supernovae in the data that didn’t make it into thecandidate list due supernovae reappearing on too many nails. If there is scientific interest thecode could be altered to extract additional supernovae, but without multi color follow-up whenthey were visible, there is little scientific value.4.4 Possible Flare-Star PheomenaA phenomena similar to supernova was also discovered in the list of candidates. They werepoint sources that were visible in all three triples and in the nails a few days either side of thetriple but nothing in any of the other nails. What differs these objects from supernovae is thatthere are no galaxies close by and nothing could be seen in the nails that were a week or amonth later. We suspect that they might be flare stars that are normally below the magnitudelimit and flare up around the time of the triples.The rise times of flares tend to be tens to hundreds and the decay times (from max luminosityto half of it) is minutes to hours. These timescales are correlated with the flare energy(Pettersen,1989). Thus, the presence of signal ‘days later but not weeks later’ is more in line with a flare9The two nailing images that the supernova was found on were the two nails that were taken the day afterthe triple. The supernova in the nail one month after was not detected even though it can be clearly seen.29(a) 2 months before. (b) 1 months before.(c) First triple image. (d) Second triple image. (e) Third triple image.(f) A day after. (g) 1 month after. (h) 8 months after.Figure 4.2: Images of a supernova event captured by OSSOS and labeled as a solar movingsolar system candidate by our code, because it was only detected by the code on two nailingimages9. The supernova occurs in the centre of the red circles with its host galaxy on its left.These images are from L Block.30star then with a supernovae, but most flare stars decay on time scales of hours rather thandays. Because these were never detected in the wings of galaxies it may be more likely to beenergetic flares from stars in the halo of our galaxy, but these events will be on the energeticend of known flare phenomena. While there may be interest in exploring this in future work,these are clearly not moving objects and thus were not pursued in this thesis. The total numberof these flare-stars-like objects found was 32.31(a) 3 months before. (b) 2 months before. (c) 1 months before.(d) First triple image. (e) Second triple image. (f) Third triple image.(g) A day after. (h) 3 days after. (i) 1 months after. (j) 3 months after.Figure 4.3: Images of what is believed to be a flare star captured by OSSOS and labeled as asolar moving solar system candidate by our code. These images are from P Block.325. Constraints on Distant PlanetsEven though no solar system object was discovered, we can use this null result to place an upperlimit on the number of the largest TNOs in the outer solar system. To get an upper limit weneed to make some assumptions. Firstly we assume that the code would have found a real solarsystem object if one was there since some of the objects that made it into the candidate list be-haved similarly to a slow moving solar system object, especially the optical ghosts (Section 4.2).Therefore no planting and finding of artificial objects was required to establish a magnitudedetection limit. Secondly we assume that the efficiency of the code to find a real solar sys-tem object of a certain r magnitude is the same as that established for OSSOS(Bannister et al.,2016). From this assumption the survey simulator used for OSSOS can be used for this work too.Section 5.1 details how the survey simulator works and the distributions used for this work.The statistics of the simulated objects we are able to detect is given in Section 5.2. Finally,Section 5.3 details how we use the survey simulator to produce an upper limit to the numberof the largest TNOs in the outer solar system.5.1 Survey SimulatorA survey simulator was created for OSSOS to bias a postulated orbital model to compare tothat found by OSSOS (see Kavelaars et al. (2009) for a description). The simulator works bycreating one object at a time from an input orbital and size distribution and assessing whetherthis object would have been found by OSSOS. For every OSSOS triple image the simulatorcalculates the objects sky position at the time the image was taken to see if the object is in theimages field of view. If the object is in an images field of view the simulator probabilisticallydetermines if it is found based on its calculated apparent magnitude and sky motion. Thesample of simulated detections from this model can be compared to those found by OSSOS.If they are not similar then the input distribution is not a correct representation of the actualdistribution. The simulator can also be used to estimate the number of intrinsic objects theremust be in order to acquire a certain number of detections.5.1.1 Orbital DistributionThe orbital distribution used for this work consists of a uniform a (see Section 1.2) ranging from150 au to 999 au. For the pericentre distribution we assume that it is also uniformly distributedstarting from 33 au, just outside the orbit of Neptune, out to 99 au. The eccentricities arecalculated using e = 1 - q/a. The inclination distribution we use is the typical sin i timesa Gaussian. Since SOs and DOs are part of the hot TNO population we use a width of13◦ with the minimum and maximum values being 0 and 180◦ respectively. All the otherparameters, longitude of the ascending node, the argument of pericentre and the mean anomaly,are uniformly distributed from 0 to 360◦.33Mag range No. of Objects Fraction with r < 21.3 Fraction with d < 300 au-3 < H < -2 1862 0.38 0.42-2 ≤ H < -1 1990 0.33 0.54-1 ≤ H < 0 2088 0.30 0.720 ≤ H < 1 2104 0.28 0.981 ≤ H < 2 1956 0.26 1.00Total sample 10000 0.30 0.72Table 5.1: The simulated sample of 10,000 objects that OSSOS (extended by our analysis outto >1000 au) would detect, broken down into absolute magnitude bins. See text for discussion.5.1.2 Size DistributionFor the simulated size distribution we wanted to examine objects ranging from smallest objectthat we would have been able to detected up to a Mars sized object. A Mars sized object (witha Pluto albedo) would have an absolute magnitude of -3. The smallest object that we can detectwould have an apparent mag of 25.5 at 300 au. This corresponds to an object with a Hr ≈ 0.7,which in the visual is Hv ≈ 1.2. The matching tolerance used in making the stationary catalogue(Section 3.2.3) allowed the algorithm to find objects moving slightly faster than 0.5′′/hour, dueto the seeing of the triples. The closest object the algorithm deployed in this thesis coulddetect was actually slightly closer than 300 au. Due to this, and the fact the range wouldbe a convenient 5 magnitudes, we decided to simulate down to H = 2 objects. ∆5 mags cor-responds to a change in radius by a factor of 10. Therefore the H mag range we used was -3 to 2.For the slope of the size distribution, we use the current size distribution of known TNOs(see Figure 1.4 as a reference). Since the largest H value in our range, H = 2, is lower than theapparent knee between slopes at H ∼ 3, the simulated sample will be situated in size regionwhere the size distribution slope is shallow, α = 0.14. Because of this, and that there is noreason to believe the slope changes for TNOs larger than Pluto, we used a logarithmic sizedistribution with a slope of α = 0.14 for the entire simulated population.5.2 Large SampleTo get a better understanding of the detectability of our synthetic distributions we ran thesurvey simulator was until 10,000 objects were detected from the orbital and H-magnitude dis-tributions just described. We split the simulated sample up into five groups of equal H magranges. The H mag ranges for each group can be seen in Table 5.1 along with the number ofobjects in each group. As can be seen there is rough the same number of objects in each group,due to the shallow absolute magnitude distribution which results in small objects not vastlyoutnumbering the larger ones.When looking at the cumulative fraction of the objects distance at detection, Figure 5.1,one can see that, even though all the objects come within 100 au, most of them are detectedat distances of > 100 au. Therefore a survey needs to be sensitive to sub arcsecond per hourspeeds to be able to detect a large portion of these objects. Another obvious feature is differ-ences between the different H mag groups. The groups with a lower H were detected at largerdistances. Almost all of the 1 ≤ H < 2 group being detected within 300 au, thus would not34Figure 5.1: The cumulative fraction of the heliocentric distance the simulated objects wereat time of detection. The black solid line represents the total sample of 10,000 objects. Thecoloured dashed lines represent different H magnitude range: red for -3 < H < -2, yellow for-2 ≤ H < -1, green for -1 ≤ H < 0, blue for 0 ≤ H < 1 and magenta for 1 ≤ H < 2. Even thesmallest objects are in majority detected beyond 100 au and thus require sensitivity to <1′′/hrrates.have been detected by this work but rather the original OSSOS reduction which was sensitiveto rates faster than 0.5′′/hr. In contrast, more than half of the -3 < H < -2 group (Mars scale)would be detected beyond 300 au. Table 5.1 contains the fraction of objects found within 300au for each group and the total sample. For the total sample 0.72 of the objects were detectedwithin 300 au. Therefore the main part of OSSOS had a better chance of finding high-a TNOscompared to this work.The cumulative distribution of ‘apparent magnitude at detection’ is shown in Figure 5.2.One can see that there is little difference between the different H mag groups. The higher Hmag groups have a slightly higher fraction for a given r mag compared with the lower H maggroups. If OSSOS had a r mag limit that was the same as the Schwamb and Brown survey limitof 21.3 (Section 1.4.2), only 0.3 of the simulated objects would have been detected. That valuegoes down to 0.26 for the smallest objects and up to 0.42 for the largest objects, see Table 5.1.Even though a Schwamb and Brown mag limit would have detected only 30% of the objectsOSSOS would have detected per unit area, Schwamb and Brown had ∼70 times more sky areathat OSSOS. Thus, as an overall search, that survey will outperform OSSOS, but is unable todetect faint and/or very distant objects.35Figure 5.2: The cumulative fraction of the r magnitude of the simulated objects at time ofdetection. The black solid line represents the total sample of 10,000 objects. The coloureddashed lines represent different H magnitude range: red for -3 < H < -2, yellow for -2 ≤ H <-1, green for -1 ≤ H < 0, blue for 0 ≤ H < 1 and magenta for 1 ≤ H < 2.To examine what part of the orbit, in terms of distance from the Sun, the objects were whendetected we create a quantity known as the fractional orbital distance, which is defined byF =d− qQ− q (5.1)where d is the heliocentric distance to the object when they would be detected, q is thepericentre and Q is the apocentre of the object. When d = q then F = 0 and when d = Q thenF = 1. We compared the distribution of F for 3 different magnitude ranges (-3 < H < -2, -1≤ H < 0, 1 ≤ H < 2) by putting F into 15 bins, seen in Figure 5.3. The smallest objects arepredominantly found at lower F values, near pericentre, whereas the largest objects were moreuniformly spread with a spike at apocentre. This makes sense since the larger objects can bedetected further out, see Figure 5.4. These further out objects will be closer to apocentre, whereKepler’s 2nd Law indicates they spend more time (and if detected there, they contribute a spikeof signal). In contrast, the fainter objects are in vast majority only visible near perihelion.5.3 Upper Limit of Dwarf Planets in the Outer Solar System.If we expect to get 3 detections then the Poisson likelihood of getting no detections is e−3 '5%.Therefore the OSSOS null detection allows us to say the number of intrinsic model objects thatmust be checked before obtaining 3 simulated detections thus serves as an estimate of the 95%upper limit on the true intrinsic population of these large objects. We ran the simulator untilwe got 100 values for the upper limit10. A histogram of the 100 trials of this calculation (using10since the simulator runs until 3 objects are tracked there were simulations where an object was detected andnot tracked. This resulted in the simulator stopping at the 4th detected object (3rd tracked object).36Figure 5.3: The fraction of objects with a certain fractional orbital distance for different Hmagnitude ranges: red for -3 < H < -2, green for -1 ≤ H < 0 and magenta for 1 ≤ H < 2. Eachgroup has around 2000 values which are split up into 15 bins. Note that all semi-major axesare represented here, allowing a few of the physically smallest objects (magenta-coded) objectsto be detectable near apocentre.Figure 5.4: A plot of the first 1000 objects in the simulated sample. Red represents an r magof less than 21.3 and blue represents a r mag of greater than 21.3.37Figure 5.5: A histogram of the intrinsic population of simulated objects when the three of theseobjects are detected.different random seeds for the object-generation algorithm) is shown in Figure 5.5. The samplehas a median value of 1145. The range that encompasses 95% of the values, centred on themedian, is 286 to 2876. Therefore we estimate that the 95% upper limit to the number of dwarfplanets in the outer solar system is 1100+1700−800 .386. Conclusion and Future WorkAfter searching through the ∼160 square degrees of OSSOS for a slow moving object beyond 300au, 34 supernovae, 32 possible flare stars and 26 optical ghost were found but no solar systemobjects. By simulating high semi-major axis SOs and DOs we obtained an understanding ofstatistics of the objects we were sensitive to. By finding the total number of simulated objectsneeded to get 3 detection we were able to state the 95% upper limit on the number of dwarfplanets (-3 > H > 2) in this scattering and detached orbit population, of 1100+1700−800 .Although this work is the first search sensitive to Mars-scale objects at 500-1000 au, theupper limit of ∼ 1000 objects from −3 < H < 2 is not very constraining. The half of thisdistribution (H < −0.5) corresponds to Pluto-scale and larger objects, and estimates based onthe fact the 3 such objects (Pluto, Eris, and Triton) are currently known have been used (e.g.Nesvorny´ and Vokrouhlicky´ (2016)) to estimate that ∼ 1000 − 4000 must have existed in thevery early Solar System during the planetary migration phase, given an estimated ‘retentionefficiency’ of order 10−3. Thus, a current upper limit of 1000 such bodies is not very constrain-ing to these late-stage planetary formation models as those models would indicate likely <10such objects remain in the outer reaches of our Solar System.When thinking about future surveys to find the largest members still lurking in the large-apopulation, the main factor is the slope of the size distribution. The fact that the slope in theregion of the largest TNOs is so shallow means that it is better to increase the sky coveragecompared to depth. Therefore to maximise the likelihood of finding a large distant object, afuture survey should reduce the magnitude limit to be all-sky. However because we are dealingwith such a small number of objects that are dwarf planet size, it may be that all the of thecurrently-exisiting objects are fainter than the all-sky magnitude limit, resulting in no detec-tions (like the Schwamb and Brown survey). If no there were no detections the next step wouldbe to increase the magnitude limit and look at patches of the sky, having in mind that theelusive object may simply be where one is not looking.A future survey that has the most promise of finding a distant solar system object is theupcoming Large Synoptic Survey Telescope (LSST). LSST is an 8.4m diameter all-sky surveytelescope that will search for transient objects like TNOs. It will be able to detect objectsdown to about magnitude 24.5, and have multi-night sensitivity allowing the lowest rates tobe detected. The main data flow will include hunting for outer solar system moving objects( Chapter 5 showed that given the OSSOS skycoverage and magnitude depth, it would detect of order 0.3% of the intrinsic population. Thesky coverage of LSST will be about 9000 square degrees, that is ∼60 times the size of OSSOS.Since LSST and OSSOS have a similar mag depth then LSST should have a sim20% chanceof finding a H < 2 distant outer solar system object. Thus, even if there remains only 10dwarf-planet and larger scale objects in the distant solar system, LSST should detect a couple.Because LSST will be nearly all-sky, doing much better after LSST’s survey will require all-sky39synoptic coverage to deeper than 25th or 26th magnitude; there are no current plans for anyfacilities with that capability.40BibliographyAgnor, C. B. and Hamilton, D. P. (2006). Neptune’s capture of its moon Triton in a binary-planet gravitational encounter. Nature, 441:192–194.Bannister, M. T., Kavelaars, J. 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