Orbital stability of systems of closely-spaced planets,II: configurations with coorbital planets

We numerically investigate the stability of systems of 1 \({{\rm M}_{\oplus}}\) planets orbiting a solar-mass star. The systems studied have either 2 or 42 planets per occupied semimajor axis, for a total of 6, 10, 126, or 210 planets, and the planets were started on coplanar, circular orbits with the semimajor axes of the innermost planets at 1 AU. For systems with two planets per occupied orbit, the longitudinal initial locations of planets on a given orbit were separated by either 60° (Trojan planets) or 180°. With 42 planets per semimajor axis, initial longitudes were uniformly spaced. The ratio of the semimajor axes of consecutive coorbital groups in each system was approximately uniform. The instability time for a system was taken to be the first time at which the orbits of two planets with different initial orbital distances crossed. Simulations spanned virtual times of up to 1 × 10⁸, 5 × 10⁵, and 2 × 10⁵ years for the 6- and 10-planet, 126-planet, and 210-planet systems, respectively. Our results show that, for a given class of system (e.g., five pairs of Trojan planets orbiting in the same direction), the relationship between orbit crossing times and planetary spacing is well fit by the functional form log(t _c /t ₀) = b β + c, where t _c is the crossing time, t ₀ = 1 year, β is the separation in initial orbital semimajor axis (in terms of the mutual Hill radii of the planets), and b and c are fitting constants. The same functional form was observed in the previous studies of single planets on nested orbits (Smith and Lissauer 2009). Pairs of Trojan planets are more stable than pairs initially separated by 180°. Systems with retrograde planets (i.e., some planets orbiting in the opposite sense from others) can be packed substantially more closely than can systems with all planets orbiting in the same sense. To have the same characteristic lifetime, systems with 2 or 42 planets per orbit typically need to have about 1.5 or 2 times the orbital separation as orbits occupied by single planets, respectively.     

Compositional variability on the surface of 1 Ceres revealed through GRaND measurements of high‐energy gamma rays

High‐energy gamma rays (HEGRs) from Ceres’s surface were measured using Dawn's Gamma Ray and Neutron Detector (GRaND). Models of cosmic‐ray‐initiated gamma ray production predict that the HEGR flux will inversely vary with single‐layer hydrogen concentrations for Ceres‐like compositions. The measured data confirm this prediction. The hydrogen‐induced variations in HEGR rates were decoupled from the measurements by detrending the HEGR data with Ceres single‐layer hydrogen concentrations determined by GRaND neutron measurements. Models indicate that hydrogen‐detrended HEGR counting rates correlate with water‐free average atomic mass, which is denoted as <A>*. HEGR variations across Ceres’s surface are consistent with <A>* variations of ±0.5 atomic mass units. Chemical variations in the CM and CI chondrites, our closest analogs to Ceres’s surface, suggest that <A>* variations on Ceres are primarily driven by variations in the concentration of Fe, although other elements such as Mg and S could contribute. Dawn observations have shown that Ceres’s interior structure and surface composition have been modified by some combination of physical (i.e., ice‐rock fractionation) and/or chemical (i.e., alteration) processes that has led to variations in bulk surface chemistry. Locations of the highest inferred <A>* values, and thus possibly the highest Fe and least altered materials, tend to be younger, less cratered surfaces that are broadly associated with the impact ejecta of Ceres’s largest craters.     

Tidal heating in Enceladus

The heating in Enceladus in an equilibrium resonant configuration with other saturnian satellites can be estimated independently of the physical properties of Enceladus. We find that equilibrium tidal heating cannot account for the heat that is observed to be coming from Enceladus. Equilibrium heating in possible past resonances likewise cannot explain prior resurfacing events.     

Obliquity variations of a moonless Earth

We numerically explore the obliquity (axial tilt) variations of a hypothetical moonless Earth. Previous work has shown that the Earth’s Moon stabilizes Earth’s obliquity such that it remains within a narrow range, between 22.1° and 24.5°. Without lunar influence, a frequency map analysis by Laskar et al. (Laskar, J., Joutel, F., Robutel, P. [1993]. Nature 361, 615–617) showed that the obliquity could vary between 0° and 85°. This has left an impression in the astrobiology community that a big moon is necessary to maintain a habitable climate on an Earth-like planet. Using a modified version of the orbital integrator mercury, we calculate the obliquity evolution for moonless Earths with various initial conditions for up to 4 Gyr. We find that while obliquity varies significantly more than that of the actual Earth over 100,000 year timescales, the obliquity remains within a constrained range, typically 20–25° in extent, for timescales of hundreds of millions of years. None of our Solar System integrations in which planetary orbits behave in a typical manner show obliquity accessing more than 65% of the full range allowed by frequency-map analysis. The obliquities of moonless Earths that rotate in the retrograde direction are more stable than those of prograde rotators. The total obliquity range explored for moonless Earths with rotation periods less than 12 h is much less than that for slower-rotating moonless Earths. A large moon thus does not seem to be needed to stabilize the obliquity of an Earth-like planet on timescales relevant to the development of advanced life.     

40Ar-39Ar ages of Dellen,Jänisjärvi,and Sääksjärvi impact craters

Abstract— ⁴⁰Ar-³⁹Ar age measurements were made for three whole rock melt samples produced during impact events which formed the Dellen, Jänisjärvi, and Sääksjärvi craters on the Baltic Shield. An age of 109.6 ± 1.0 Ma was obtained for the Dellen sample based on an age spectrum plateau. The age spectrum shows a small (7%) loss of radiogenic ⁴⁰Ar from low temperature fractions. Ages of 698 ± 22 Ma and 560 ± 12 Ma were obtained from isochrons for the Jänisjärvi and Sääksjärvi samples, respectively. Data obtained by laser degassing support the Sääksjärvi result. The presence of excess ⁴⁰Ar is indicated in lower temperature fractions for both samples and is correlated with K concentrations in the Sääksjärvi sample. Models explaining these results may require a change in the local “atmospheric” Ar isotopic composition as cooling of melt rocks proceeded. However, it cannot be excluded that devitrification and/or alteration changed the Ar budget. A crater production rate on the Baltic Shield based on measured ages of 6 craters is (0.3 ± 0.2) · 10^?14 20-km-and-larger craters per km² per year, in satisfactory agreement with previous estimates.     

Size Matters to Lesbians,Too: Queer Feminist Interventions into the Scale of Big Data

How can we recognize those whose lives and data become attached to the far-from-groundbreaking framework of “small data”? Specifically, how can marginalized people who do not have the resources to produce, self-categorize, analyze, or store “big data” claim their place in the big data debates? I examine the place of lesbians and queer women in the big data debates through the Lesbian Herstory Archive's not “big” enough lesbian, gay, bisexual, trans, and queer (LGBTQ) organizing history data set—perhaps the largest data set known to exist on LGBTQ activist history—as one such alternative. In a contribution to critical data studies, I take a queer feminist approach to the scale of big data by reading for the imbricated scales and situated knowledge of data.     

Geoarchaeology of stratified paleoindian deposits at the Big Eddy site,Southwest Missouri,U.S.A.

The Big Eddy site (23CE426) in the Sac River valley of southwest Missouri is a rare recorded example of distinctly stratified Early through Late Paleoindian cultural deposits. Early point types recovered from the site include Gainey, Sedgwick, Dalton (fluted and unfluted), San Patrice, Wilson, and Packard. The Paleoindian record at Big Eddy represents only a fraction of the site's prehistoric cultural record; stratified cultural deposits in alluvium above the Paleoindian components span the entire known prehistoric sequence, and terminal Pleistocene alluvium may contain pre‐Early Paleoindian cultural deposits. This study focused on the paleogeomorphic setting, stratigraphy, depositional environments, pedology, geochronology, and history of landscape evolution of the late Pleistocene and early Holocene alluvium at the site. The Paleoindian sequence is associated with a complex buried soil 2.85 m below the modern surface (T1a) of the first terrace of the Sac River valley in the site vicinity. This soil formed at the top of the early submember of the Rodgers Shelter Member (underlying the T1c paleogeomorphic surface) and contains at least 70 cm of stratified Paleoindian cultural deposits, all in floodplain and upper point‐bar facies. A suite of 36 radiocarbon ages indicates that the alluvium hosting the Paleoindian sequence aggraded between ca. 13,250 and 11,870 cal yr B.P. (11,380 and 10,180 14C yr B.P.). Underlying deposits accumulated between ca. 15,300 and 13,250 cal yr B.P. (12,950 and 11,380 14C yr B.P.). By ca. 11,250 cal yr B.P. (9,840 14C yr B.P.) the T1c paleogeomorphic surface was buried by the earliest increment of a thick sequence of overbank sheetflood facies, ultimately resulting in deep burial and preservation of the Paleoindian record. The landform‐sediment assemblage that hosts the Paleoindian and possibly earlier cultural deposits at Big Eddy is both widespread and well preserved in the lower Sac River valley. Moreover, the terminal Pleistocene and early Holocene depositional environments were favorable for the preservation of the archaeological record. © 2007 Wiley Periodicals, Inc.     

New insights on measured and calculated vitrinite reflectance

Measurement of dispersed vitrinite reflectance in organic sediments is one of the few regional data sets used for placing bounds on the thermal history of a sedimentary basin. Reflectance data are important when access to complementary information such as high‐quality seismic data is unavailable to place bounds on subsidence history and in locations where uplift is an important part of the basin history. Attributes which make vitrinite reflectance measurements a useful data set are the relative ease of making the measurement, and the availability of archived well cores and cuttings in state, provincial, and federal facilities. In order to fully utilize vitrinite data for estimating the temperature history in a basin, physically based methods are required to calibrate an equivalent reflectance from a modelled temperature history with measured data. The most common method for calculating a numerical vitrinite reflectance from temperature history is the EASY%R_o method which we show systematically underestimates measured data. We present a new calculated reflectance model and an adjustment to EASY%R_o which makes the correlation between measured vitrinite values and calculated vitrinite values a physical relationship and more useful for constraining thermal models. We then show that calibrating the thermal history to vitrinite on a constant age date surface (e.g., top Cretaceous) instead of calibrating the thermal history in depth removes the heating rate component from the reflectance calculation and makes thermal history calibration easier to understand and more directly related to heat flow. Finally, we use bounds on the vitrinite–temperature relationships on a constant age date surface to show that significant uncertainty exists in the vitrinite data reported in most data sets.     

Remote sensing analysis of physical complexity of North Pacific Rim rivers to assist wild salmon conservation

Salmon populations are highly variable in both space and time. Accurate forecasting of the productivity of salmon stocks makes effective management and conservation of the resource extremely challenging. Furthermore, widespread and consistent data on the productivity of species‐specific and total salmon stocks in a river are almost nonexistent. Ranking rivers based on physical complexity derived from remote sensing allows rivers to be objectively compared. Our approach considered rivers with great geomorphic complexity (e.g. having expansive, multichanneled floodplains and/or on‐channel lakes) as likely to have greater productivity of salmon than rivers flowing in constrained or canyon‐bound channels. Our objective was to develop a database of landscape metrics that could be used to rank the rivers in relation to potential salmon productivity. We then examined the rankings in relation to existing empirical (monitoring) data describing productivity of salmon stocks. To extract the metrics for each river basin we used a digital elevation model and multispectral satellite imagery. We developed procedures to extract channel networks, floodplains, on‐channel lakes and other catchment features; variables such as catchment area, channel elevation, main channel length, floodplain area, and density of hydrojunctions (nodes) were measured. We processed 1509 catchments in the North Pacific Rim including the Kamchatka Peninsula in Russia and western North America. Overall, catchments were most physically complex in western Kamchatka and western Alaska, and particularly on the Arctic North Slope of Alaska. We could not directly examine coherence between potential and measured productivity except for a few rivers, but the expected relationship generally held. The resulting database and systematic ranking are objective tools that can be used to address questions about landscape structure and biological productivity at regional to continental extents, and provide a way to begin to efficiently prioritize the allocation of funding and resources towards salmon management and conservation. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of210Pb dating in lake sediments using stable Pb,Ambrosia pollen,and137Cs

We used sediment chronology data from fourteen published studies of lake cores across much of North America and Scandinavia in order to make a large scale comparison of the different dating techniques. The uncertainty of²¹⁰Pb derived dates was determined using common sediment event markers: the stable Pb rise, the¹³⁷Cs rise, and theAmbrosia pollen rise. For all data combined, the 95% confidence intervals for the stable Pb rise and theAmbrosia rise, were approximately 30 years. These 95% confidence intervals are slightly higher than those derived by First-Order Error analysis performed by others on²¹⁰Pb derived dates. When comparing the concordance of two²¹⁰Pb models (CRS and CIC) against markers of known history, we found that the CRS model dates (constant rate of supply) had consistently better agreement than the CIC model dates (constant initial concentration). Major discrepancies between¹³⁷Cs and²¹⁰Pb were common, but were consistently more severe in sediments of soft water lakes pointing to an inability of sediments with low mineral content to immobilize Cs.This is the ninth of a series of papers to be published by this journal following the 20 ^th anniversary of the first application of²¹⁰Pb dating of lake sediments, Dr. P. G. Appleby is guest editing this series.