Constraining the orbits of sub-stellar companions imaged over short orbital arcs

Imaging a star's companion at multiple epochs over a short orbital arc provides only four of the six coordinates required for a unique orbital solution. Probability distributions of possible solutions are commonly generated by Monte Carlo (MCMC) analysis, but these are biased by priors and may not probe the full parameter space. We suggest alternative methods to characterise possible orbits, which compliment the MCMC technique. Firstly the allowed ranges of orbital elements are prior-independent, and we provide means to calculate these ranges without numerical analyses. Hence several interesting constraints (including whether a companion even can be bound, its minimum possible semi-major axis and its minimum eccentricity) may be quickly computed using our relations as soon as orbital motion is detected. We also suggest an alternative to posterior probability distributions as a means to present possible orbital elements, namely contour plots of elements as functions of line of sight coordinates. These plots are prior-independent, readily show degeneracies between elements and allow readers to extract orbital solutions themselves. This approach is particularly useful when there are other constraints on the geometry, for example if a companion's orbit is assumed to be aligned with a disc. As examples we apply our methods to several imaged sub-stellar companions including Fomalhaut b, and for the latter object we show how different origin hypotheses affect its possible orbital solutions. We also examine visual companions of A- and G-type main sequence stars in the Washington Double Star Catalogue, and show that $\gtrsim50$ per cent must be unbound.Comment: Accepted for publication in MNRA

Search for long lived charged massive particles in pp collisions at s-hat = 1.8TeV

We report a search for the production of long-lived charged massive particles in a data sample of 90   pb-1 of √s=1.8   TeV pp̅ collisions recorded by the Collider Detector at Fermilab. The search uses the muonlike penetration and anomalously high ionization energy loss signature expected for such a particle to discriminate it from backgrounds. The data are found to agree with background expectations, and cross section limits of O(1) pb are derived using two reference models, a stable quark and a stable scalar lepton

Predicting the frequencies of diverse exo-planetary systems

Extrasolar planetary systems range from hot Jupiters out to icy comet belts more distant than Pluto. We explain this diversity in a model where the mass of solids in the primordial circumstellar disk dictates the outcome. The star retains measures of the initial heavy-element (metal) abundance that can be used to map solid masses onto outcomes, and the frequencies of all classes are correctly predicted. The differing dependences on metallicity for forming massive planets and low-mass cometary bodies are also explained. By extrapolation, around two-thirds of stars have enough solids to form Earth-like planets, and a high rate is supported by the first detections of low-mass exo-planets.Comment: 5 pages, 2 figures; accepted by MNRA

Multi-Epoch Observations of HD69830: High Resolution Spectroscopy and Limits to Variability

The main-sequence solar-type star HD69830 has an unusually large amount of dusty debris orbiting close to three planets found via the radial velocity technique. In order to explore the dynamical interaction between the dust and planets, we have performed multi-epoch photometry and spectroscopy of the system over several orbits of the outer dust. We find no evidence for changes in either the dust amount or its composition, with upper limits of 5-7% (1 $\sigma$ per spectral element) on the variability of the {\it dust spectrum} over 1 year, 3.3% (1 $\sigma$) on the broad-band disk emission over 4 years, and 33% (1 $\sigma$) on the broad-band disk emission over 24 years. Detailed modeling of the spectrum of the emitting dust indicates that the dust is located outside of the orbits of the three planets and has a composition similar to main-belt, C-type asteroids asteroids in our solar system. Additionally, we find no evidence for a wide variety of gas species associated with the dust. Our new higher SNR spectra do not confirm our previously claimed detection of H$_2$O ice leading to a firm conclusion that the debris can be associated with the break-up of one or more C-type asteroids formed in the dry, inner regions of the protoplanetary disk of the HD69830 system. The modeling of the spectral energy distribution and high spatial resolution observations in the mid-infrared are consistent with a $\sim$ 1 AU location for the emitting material

Eight billion asteroids in the Oort cloud

The Oort cloud is usually thought of as a collection of icy comets inhabiting the outer reaches of the Solar system, but this picture is incomplete. We use simulations of the formation of the Oort cloud to show that ∼4 per cent of the small bodies in the Oort cloud should have formed within 2.5 au of the Sun, and hence be ice-free rock-iron bodies. If we assume that these Oort cloud asteroids have the same size distribution as their cometary counterparts, the Large Synoptic Survey Telescope should find roughly a dozen Oort cloud asteroids during 10 years of operations. Measurement of the asteroid fraction within the Oort cloud can serve as an excellent test of the Solar system's formation and dynamical history. Oort cloud asteroids could be of particular concern as impact hazards as their high mass density, high impact velocity, and low visibility make them both hard to detect and hard to divert or destroy. However, they should be a rare class of object, and we estimate globally catastrophic collisions should only occur about once per billion years.AS andMWare supported by the European Union through ERC grant number 279973. DV is supported by the European Union through ERC grant number 320964.This is the final published version. It first appeared at http://mnras.oxfordjournals.org/content/446/2/2059

Evolution of local scour downstream of Type A PK weir in non-cohesive sediments

Abstract A large-scale piano key weir laboratory study was conducted to investigate the evolution of the scour process occurring in the downstream basin for two non-cohesive granular bed materials, including the analysis of scour-hole geometry and patterns at equilibrium. It was observed that hydraulic conditions, particularly tailwater level, significantly affect the scour mechanisms and equilibrium morphology, eventually resulting in scour depths that exceeded the weir height. Unprecedented insights on the scour dynamics are also provided, along with tools to estimate the time evolution and maximum scour depth, its location in the streamwise direction, and the maximum scour length

Debris disk size distributions: steady state collisional evolution with P-R drag and other loss processes

We present a new scheme for determining the shape of the size distribution, and its evolution, for collisional cascades of planetesimals undergoing destructive collisions and loss processes like Poynting-Robertson drag. The scheme treats the steady state portion of the cascade by equating mass loss and gain in each size bin; the smallest particles are expected to reach steady state on their collision timescale, while larger particles retain their primordial distribution. For collision-dominated disks, steady state means that mass loss rates in logarithmic size bins are independent of size. This prescription reproduces the expected two phase size distribution, with ripples above the blow-out size, and above the transition to gravity-dominated planetesimal strength. The scheme also reproduces the expected evolution of disk mass, and of dust mass, but is computationally much faster than evolving distributions forward in time. For low-mass disks, P-R drag causes a turnover at small sizes to a size distribution that is set by the redistribution function (the mass distribution of fragments produced in collisions). Thus information about the redistribution function may be recovered by measuring the size distribution of particles undergoing loss by P-R drag, such as that traced by particles accreted onto Earth. Although cross-sectional area drops with 1/age^2 in the PR-dominated regime, dust mass falls as 1/age^2.8, underlining the importance of understanding which particle sizes contribute to an observation when considering how disk detectability evolves. Other loss processes are readily incorporated; we also discuss generalised power law loss rates, dynamical depletion, realistic radiation forces and stellar wind drag.Comment: Accepted for publication by Celestial Mechanics and Dynamical Astronomy (special issue on EXOPLANETS