1,239 research outputs found
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
Competing Alignments of Nematic Liquid Crystals on Square Patterned Substrates
A theoretical analysis is presented of a nematic liquid crystal confined
between substrates pat- terned with squares that promote vertical and planar
alignment. Two approaches are used to eluci- date the behavior across a wide
range of length scales: Monte Carlo simulation of hard particles and
Frank-Oseen continuum theory. Both approaches predict bistable degenerate
azimuthal alignment in the bulk along the edges of the squares; the continuum
calculation additionally reveals the possi- bility of an anchoring transition
to diagonal alignment if the polar anchoring energy associated with the pattern
is sufficiently weak. Unlike the striped systems previously analyzed, the Monte
Carlo simulations suggest that there is no "bridging" transition for
sufficiently thin cells. The extent to which these geometrically patterned
systems resemble topographically patterned substrates, such as square wells, is
also discussed.Comment: 11 pages, 12 figure
Stability of Satellites in Closely Packed Planetary Systems
We perform numerical integrations of four-body (star, planet, planet,
satellite) systems to investigate the stability of satellites in planetary
Systems with Tightly-packed Inner Planets (STIPs). We find that the majority of
closely-spaced stable two-planet systems can stably support satellites across a
range of parameter-space which is only slightly decreased compared to that seen
for the single-planet case. In particular, circular prograde satellites remain
stable out to (where is the Hill Radius) as opposed to
in the single-planet case. A similarly small restriction in the
stable parameter-space for retrograde satellites is observed, where planetary
close approaches in the range 2.5 to 4.5 mutual Hill radii destabilize most
satellites orbits only if . In very close planetary pairs (e.g.
the 12:11 resonance) the addition of a satellite frequently destabilizes the
entire system, causing extreme close-approaches and the loss of satellites over
a range of circumplanetary semi-major axes. The majority of systems
investigated stably harbored satellites over a wide parameter-space, suggesting
that STIPs can generally offer a dynamically stable home for satellites, albeit
with a slightly smaller stable parameter-space than the single-planet case. As
we demonstrate that multi-planet systems are not a priori poor candidates for
hosting satellites, future measurements of satellite occurrence rates in
multi-planet systems versus single-planet systems could be used to constrain
either satellite formation or past periods of strong dynamical interaction
between planets.Comment: 11 pages, 5 figures. Accepted for publication, ApJ
Ice core records of atmospheric CO2 around the last three glacial terminations
Air trapped in bubbles in polar ice cores constitutes an archive for the reconstruction of the global carbon cycle and the relation between greenhouse gases and climate in the past. High-resolution records from Antarctic ice cores show that carbon dioxide concentrations increased by 80 to 100 parts per million by volume 600 ± 400 years after the warming of the last three deglaciations. Despite strongly decreasing temperatures, high carbon dioxide concentrations can be sustained for thousands of years during glaciations; the size of this phase lag is probably connected to the duration of the preceding warm period, which controls the change in land ice coverage and the buildup of the terrestrial biosphere.</jats:p
TTVFast: An efficient and accurate code for transit timing inversion problems
Transit timing variations (TTVs) have proven to be a powerful technique for
confirming Kepler planet candidates, for detecting non-transiting planets, and
for constraining the masses and orbital elements of multi-planet systems. These
TTV applications often require the numerical integration of orbits for
computation of transit times (as well as impact parameters and durations);
frequently tens of millions to billions of simulations are required when
running statistical analyses of the planetary system properties. We have
created a fast code for transit timing computation, TTVFast, which uses a
symplectic integrator with a Keplerian interpolator for the calculation of
transit times (Nesvorny et al. 2013). The speed comes at the expense of
accuracy in the calculated times, but the accuracy lost is largely unnecessary,
as transit times do not need to be calculated to accuracies significantly
smaller than the measurement uncertainties on the times. The time step can be
tuned to give sufficient precision for any particular system. We find a
speed-up of at least an order of magnitude relative to dynamical integrations
with high precision using a Bulirsch-Stoer integrator.Comment: Submitted to ApJ. Our code is available in both C and Fortran at:
http://github.com/kdeck/TTVFast . If you download this version, please check
back after the referee process for a possibly updated versio
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
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