First order resonance overlap and the stability of close two planet systems

Motivated by the population of multi-planet systems with orbital period ratios 1<P2/P1<2, we study the long-term stability of packed two planet systems. The Hamiltonian for two massive planets on nearly circular and nearly coplanar orbits near a first order mean motion resonance can be reduced to a one degree of freedom problem (Sessin & Ferraz Mello (1984), Wisdom (1986), Henrard et al. (1986)). Using this analytically tractable Hamiltonian, we apply the resonance overlap criterion to predict the onset of large scale chaotic motion in close two planet systems. The reduced Hamiltonian has only a weak dependence on the planetary mass ratio, and hence the overlap criterion is independent of the planetary mass ratio at lowest order. Numerical integrations confirm that the planetary mass ratio has little effect on the structure of the chaotic phase space for close orbits in the low eccentricity (e <~0.1) regime. We show numerically that orbits in the chaotic web produced primarily by first order resonance overlap eventually experience large scale erratic variation in semimajor axes and are Lagrange unstable. This is also true of the orbits in this overlap region which are Hill stable. As a result, we can use the first order resonance overlap criterion as an effective stability criterion for pairs of observed planets. We show that for low mass (<~10 M_Earth) planetary systems with initially circular orbits the period ratio at which complete overlap occurs and widespread chaos results lies in a region of parameter space which is Hill stable. Our work indicates that a resonance overlap criterion which would apply for initially eccentric orbits needs to take into account second order resonances. Finally, we address the connection found in previous work between the Hill stability criterion and numerically determined Lagrange instability boundaries in the context of resonance overlap.Comment: Accepted for publication in Ap

Keeping a Clean Reputation: More Evidence on the Perverse Effects of Disclosure

When a principal relies on an agent, a conflict of interest can encourage the agent to provide biased advice. Conventional wisdom suggests that such behavior can be reduced through disclosure requirements. However, disclosure has been shown to exacerbate self-serving bias and can actually lead to greater harm for the principal in one-shot interactions. But in many naturally occurring settings, agents form reputations, a mechanism that could diminish the incentive to provide biased advice. We test for bias in the advice agents provide when faced with reputation concerns, and examine the impact of disclosure in such an environment. In controlled laboratory experiments, we find little evidence of self-serving bias in the absence of disclosure when (3) agents form reputations and (4) principals use that information in selecting agents. However, we find the introduction of disclosure leads to self-serving biased advice that is difficult for principals to detect. When the conflict of interest is endogenous, we find that agents overwhelmingly put themselves in the position of having a conflict of interest, but principals neither avoid conflicted agents nor differentially discount the advice such agents provide

Auction Markets for Evaluations

When the value of a product or service is uncertain, outcomes can be inefficient. A market for evaluations can theoretically increase efficiency by voluntarily eliciting an evaluation that would otherwise not be provided. This paper uses a controlled laboratory experiment to test the performance of four market mechanisms to provide product evaluations. The mechanisms considered are derived from the oft studied uniform price sealed bid, discriminatory price sealed bid, English clock auction, and Dutch clock auction. Our results indicate for this nonrivalrous product that (i) each of these institutions improves social welfare and (ii) the performances of the four mechanisms are equivalent. This second point is particularly noteworthy given that differing behavior is routinely observed in traditional private value auctions

Experimental Gasoline Markets

Zone pricing in wholesale gasoline markets is a contentious topic in the public policy debate. With a controlled laboratory experiment, we investigate the competitive effects of zone pricing on consumers, retail stations, and refiners vis-à-vis the proposed policy prescription of uniform wholesale pricing to retailers. We also examine the issue of divorcement and the “rockets and feathers” phenomenon. The former is the legal restriction that refiners and retailers cannot be vertically integrated, and the latter is the perception that retail gasoline prices rise faster than they fall in response to random walk movements in the world price for oil

Triple-Star Candidates Among the Kepler Binaries

We present the results of a search through the photometric database of eclipsing Kepler binaries (Prsa et al. 2011; Slawson et al. 2011) looking for evidence of hierarchical triple star systems. The presence of a third star orbiting the binary can be inferred from eclipse timing variations. We apply a simple algorithm in an automated determination of the eclipse times for all 2157 binaries. The "calculated" eclipse times, based on a constant period model, are subtracted from those observed. The resulting O-C (observed minus calculated times) curves are then visually inspected for periodicities in order to find triple-star candidates. After eliminating false positives due to the beat frequency between the ~1/2-hour Kepler cadence and the binary period, 39 candidate triple systems were identified. The periodic O-C curves for these candidates were then fit for contributions from both the classical Roemer delay and so-called "physical" delay, in an attempt to extract a number of the system parameters of the triple. We discuss the limitations of the information that can be inferred from these O-C curves without further supplemental input, e.g., ground-based spectroscopy. Based on the limited range of orbital periods for the triple star systems to which this search is sensitive, we can extrapolate to estimate that at least 20% of all close binaries have tertiary companions.Comment: 19 pages, 13 figures, 3 tables; ApJ, 2013, 768, 33; corrected Fig. 7, updated references, minor fixes to tex

Effects of mental imagery use on anxiety, confidence, mental well-being, and performance in track and field athletes

Background: Student athletes can experience a number of stressors above and beyond those of their classmates, one being competition anxiety in their specific sport, which is common among varsity athletes (Storch, Storch, Killiany, & Roberti, 2005). Unfortunately, the tools to help with the demands of their sport mentally are often overlooked by not only the athletes, but their coaches, teammates, and supporters. The purpose of the present study was to introduce imagery as a tool to help deal with competition anxiety (i.e., fear of failure), and to improve confidence, mental well-being, and performance. Methods: Two female varsity level throwers (Mage = 20) met individually with the researcher twice a week during the competitive season. Athletes were first introduced to breathing and relaxation techniques, followed by basic imagery scripts. For each session, the imagery scripts were changed and adjusted based on the needs and feedback from the athletes to focus on different elements (e.g., anxiety, technique, recovering from a bad throw). Results: Both athletes decreased their anxiety levels, while increasing their self-confidence, mental well-being, and performance. Discussion & Conclusion: The results highlight the positive effect of employing imagery in sport life. Interdisciplinary Reflection: Imagery use can be also applied in other aspects of athletes’ lives

Holocene carbon-cycle dynamics based on CO2 trapped in ice at Taylor Dome, Antarctica

A high-resolution ice-core record of atmospheric CO2 concentration over the Holocene epoch shows that the global carbon cycle has not been in steady state during the past 11,000 years. Analysis of the CO2 concentration and carbon stable-isotope records, using a one-dimensional carbon-cycle model,uggests that changes in terrestrial biomass and sea surface temperature were largely responsible for the observed millennial-scale changes of atmospheric CO2 concentrations

An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES velocities. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We find that a four-planet model is preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses and orbits using an n-body model in three-dimensional space. Based on the radial velocities alone, we find that a 99% credible interval provides upper limits on the mutual inclinations for the three resonant planets ($\Phi_{cb}<6.20^\circ$ for the "c" and "b" pair and $\Phi_{be}<28.5^\circ$ for the "b" and "e" pair). Subsequent dynamical integrations of our posterior sample find that the GJ 876 planets must be roughly coplanar ($\Phi_{cb}<2.60^\circ$ and $\Phi_{be}<7.87^\circ$), suggesting the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model supports the idea of the outer-three planets having undergone significant past disk migration.Comment: 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples available at https://github.com/benelson/GJ87