Pencil-Beam Surveys for Trans-Neptunian Objects: Novel Methods for Optimization and Characterization

Digital co-addition of astronomical images is a common technique for increasing signal-to-noise and image depth. A modification of this simple technique has been applied to the detection of minor bodies in the Solar System: first stationary objects are removed through the subtraction of a high-SN template image, then the sky motion of the Solar System bodies of interest is predicted and compensated for by shifting pixels in software prior to the co-addition step. This "shift-and-stack" approach has been applied with great success in directed surveys for minor Solar System bodies. In these surveys, the shifts have been parameterized in a variety of ways. However, these parameterizations have not been optimized and in most cases cannot be effectively applied to data sets with long observation arcs due to objects' real trajectories diverging from linear tracks on the sky. This paper presents two novel probabilistic approaches for determining a near-optimum set of shift-vectors to apply to any image set given a desired region of orbital space to search. The first method is designed for short observational arcs, and the second for observational arcs long enough to require non-linear shift-vectors. Using these techniques and other optimizations, we derive optimized grids for previous surveys that have used "shift-and-stack" approaches to illustrate the improvements that can be made with our method, and at the same time derive new limits on the range of orbital parameters these surveys searched. We conclude with a simulation of a future applications for this approach with LSST, and show that combining multiple nights of data from such next-generation facilities is within the realm of computational feasibility.Comment: Accepted for publication in PASP March 1, 2010

Trans-Neptunian Space and the Post-Pluto Paradigm

The Pluto system is an archetype for the multitude of icy dwarf planets and accompanying satellite systems that populate the vast volume of the solar system beyond Neptune. New Horizons' exploration of Pluto and its five moons gave us a glimpse into the range of properties that their kin may host. Furthermore, the surfaces of Pluto and Charon record eons of bombardment by small trans-Neptunian objects, and by treating them as witness plates we can infer a few key properties of the trans-Neptunian population at sizes far below current direct-detection limits. This chapter summarizes what we have learned from the Pluto system about the origins and properties of the trans-Neptunian populations, the processes that have acted upon those members over the age of the solar system, and the processes likely to remain active today. Included in this summary is an inference of the properties of the size distribution of small trans-Neptunian objects and estimates on the fraction of binary systems present at small sizes. Further, this chapter compares the extant properties of the satellites of trans-Neptunian dwarf planets and their implications for the processes of satellite formation and the early evolution of planetesimals in the outer solar system. Finally, this chapter concludes with a discussion of near-term theoretical, observational, and laboratory efforts that can further ground our understanding of the Pluto system and how its properties can guide future exploration of trans-Neptunian space.Comment: Review chapter in "The Pluto System After New Horizons" University of Arizona Press, 2021. https://uapress.arizona.edu/book/the-pluto-system-after-new-horizon

Pencil-Beam Surveys for Trans-Neptunian Objects: Limits on Distant Populations

Two populations of minor bodies in the outer Solar System remain particularly elusive: Scattered Disk objects and Sedna-like objects. These populations are important dynamical tracers, and understanding the details of their spatial- and size-distributions will enhance our understanding of the formation and on-going evolution of the Solar System. By using newly-derived limits on the maximum heliocentric distances that recent pencil-beam surveys for Trans-Neptunian Objects were sensitive to, we determine new upper limits on the total numbers of distant SDOs and Sedna-like objects. While generally consistent with populations estimated from wide-area surveys, we show that for magnitude-distribution slopes of {\alpha} > 0.7-1.0, these pencil-beam surveys provide stronger upper limits than current estimates in literature.Comment: Submitted to Icaru

New Horizons: Long-Range Kuiper Belt Targets Observed by the Hubble Space Telescope

We report on Hubble Space Telescope (HST) observations of three Kuiper Belt Objects (KBOs), discovered in our dedicated ground-based search campaign, that are candidates for long-range observations from the New Horizons spacecraft: 2011 JY31, 2011 HZ102, and 2013 LU35. Astrometry with HST enables both current and future critical accuracy improvements for orbit precision, required for possible New Horizons observations, beyond what can be obtained from the ground. Photometric colors of all three objects are red, typical of the Cold Classical dynamical population within which they reside; they are also the faintest KBOs to have had their colors measured. None are observed to be binary with HST above separations of ~0.02 arcsec (~700 km at 44 AU) and {\Delta}m less than or equal to 0.5.Comment: Pages: 11, Figures: 2, Tables: 3, Icarus, available online May 2014 (http://dx.doi.org/10.1016/j.icarus.2014.04.014

Extinction in Lotka-Volterra model

Competitive birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.Comment: 11 pages, 17 figure

OSSOS: XXVII. Population Estimates for Theoretically Stable Centaurs Between Uranus and Neptune

We calculate the upper bounds of the population of theoretically stable Centaur orbits between Uranus and Neptune. These small bodies are on low-eccentricity, low-inclination orbits in two specific bands of semi-major axis, centred at $\sim$24.6 au and $\sim$25.6 au. They exhibit unusually long Gyr-stable lifetimes in previously published numerical integrations, orders of magnitude longer than that of a typical Centaur. Despite the increased breadth and depth of recent solar system surveys, no such objects have been found. Using the Outer Solar System Origins Survey (OSSOS) survey simulator to calculate the detection efficiency for these objects in an ensemble of fully characterised surveys, we determine that a population of 72 stable Centaurs with absolute magnitude $H_{r}\leq10$ ($95\%$ confidence upper limit) could remain undetected. The upcoming Legacy Survey of Space and Time (LSST) will be able to detect this entire intrinsic population due to its complete coverage of the ecliptic plane. If detected, these objects will be interesting dynamically-accessible mission targets -- especially as comparison of the stable Centaur orbital phase space to the outcomes of several modern planetary migration simulations suggests that these objects could be close to primordial in nature.Comment: Accepted to PSJ. 8 pages, 3 figures. Comments welcom