Stability Limits in Resonant Planetary Systems

The relationship between the boundaries for Hill and Lagrange stability in orbital element space is modified in the case of resonantly interacting planets. Hill stability requires the ordering of the planets to remain constant while Lagrange stability also requires all planets to remain bound to the central star. The Hill stability boundary is defined analytically, but no equations exist to define the Lagrange boundary, so we perform numerical experiments to estimate the location of this boundary. To explore the effect of resonances, we consider orbital element space near the conditions in the HD 82943 and 55 Cnc systems. Previous studies have shown that, for non-resonant systems, the two stability boundaries are nearly coincident. However the Hill stability formula are not applicable to resonant systems, and our investigation shows how the two boundaries diverge in the presence of a mean-motion resonance, while confirming that the Hill and Lagrange boundaries are similar otherwise. In resonance the region of stability is larger than the domain defined by the analytic formula for Hill stability. We find that nearly all known resonant interactions currently lie in this extra stable region, i.e. where the orbits would be unstable according to the non-resonant Hill stability formula. This result bears on the dynamical packing of planetary systems, showing how quantifying planetary systems' dynamical interactions (such as proximity to the Hill-stability boundary) provides new constraints on planet formation models.Comment: 13 pages, 3 figures, 2 tables, accepted for publication in ApJ Letters. A version with full resolution figures is available at http://www.lpl.arizona.edu/~rory/research/xsp/resstab.pd

The Abundance of Low-luminosity Lyman alpha Emitters at High Redshift

We derive the luminosity function of high-redshift Lyman alpha emitting sources from a deep, blind, spectroscopic survey that utilized strong-lensing magnification by intermediate-redshift clusters of galaxies. We observed carefully selected regions near 9 clusters, consistent with magnification factors generally greater than 10 for the redshift range 4.5<z<6.7. Eleven emission-line candidates were located in the range 2.2<z<5.6 whose identification we justify as Lyman alpha, in most cases via further spectroscopic observations. The selection function we constructed for our survey takes into account our varying intrinsic Lyman alpha line sensitivity as a function of wavelength and sky position. By virtue of the strong magnification factor, we provide constraints on the Lyman alpha luminosity function to unprecedented limits of 10^40 erg/s, corresponding to a star-formation rate of 0.01 Msun/yr. Our cumulative z=5 Lyman alpha luminosity function is consistent with a power law form, n(>L) proportional to L^-1 over 10^41 to 10^42.5 erg/s. When combined with the results of other surveys, limited at higher luminosities, our results suggest evidence for the suppression of star formation in low-mass halos, as predicted in popular models of galaxy formation.Comment: 22 pages, 14 figures, submitted to Ap

Explicit diversification of event aspects for temporal summarization

During major events, such as emergencies and disasters, a large volume of information is reported on newswire and social media platforms. Temporal summarization (TS) approaches are used to automatically produce concise overviews of such events by extracting text snippets from related articles over time. Current TS approaches rely on a combination of event relevance and textual novelty for snippet selection. However, for events that span multiple days, textual novelty is often a poor criterion for selecting snippets, since many snippets are textually unique but are semantically redundant or non-informative. In this article, we propose a framework for the diversification of snippets using explicit event aspects, building on recent works in search result diversification. In particular, we first propose two techniques to identify explicit aspects that a user might want to see covered in a summary for different types of event. We then extend a state-of-the-art explicit diversification framework to maximize the coverage of these aspects when selecting summary snippets for unseen events. Through experimentation over the TREC TS 2013, 2014, and 2015 datasets, we show that explicit diversification for temporal summarization significantly outperforms classical novelty-based diversification, as the use of explicit event aspects reduces the amount of redundant and off-topic snippets returned, while also increasing summary timeliness

Stochastic Description of Agglomeration and Growth Processes in Glasses

We show how growth by agglomeration can be described by means of algebraic or differential equations which determine the evolution of probabilities of various local configurations. The minimal fluctuation condition is used to define vitrification. Our methods have been successfully used for the description of glass formation.Comment: 9 pages, 1 figure, LaTeX 2e, uses ws-ijmpb.cls ; submitted to International Journal of Modern Physics

A Faint Star-Forming System Viewed Through the Lensing Cluster Abell 2218: First Light at z~5.6?

We discuss the physical nature of a remarkably faint pair of Lyman alpha-emitting images discovered close to the giant cD galaxy in the lensing cluster Abell 2218 (z=0.18) during a systematic survey for highly-magnified star-forming galaxies beyond z=5. A well-constrained mass model suggests the pair arises via a gravitationally-lensed source viewed at high magnification. Keck spectroscopy confirms the lensing hypothesis and implies the unlensed source is a very faint (I~30) compact (<150 pc) and isolated object at z=5.576 whose optical emission is substantially contained within the Lyman alpha emission line; no stellar continuum is detectable. The available data suggest the source is a promising candidate for an isolated ~10^6 solar mass system seen producing its first generation of stars close to the epoch of reionization.Comment: 11 pages, 3 figures, to appear in Ap J Lett, minor revision following referee's repor

Sustaining interaction in a mathematical community of practice

This paper focuses on an activity in which students explore sequences through a game, using ToonTalk programming and a web-based collaboration system. Our analytical framework combines theory of communities of practice with domain epistemology. We note three factors which influence the length and quality of interactions: facilitation, reciprocation and audience-awareness