1,194 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
Context matters : a multilevel analysis of patterns of mobility to non-poor neighborhoods for poor renter households.
The goal of this longitudinal, multilevel study was to develop a better understanding of poor renter households\u27 mobility patterns by identifying the relative importance of individual and contextual variables. Variability in neighborhood poverty rates (NPR) was analyzed for 1564 poor, renter households living in 179 metropolitan statistical areas (MSAs) across the continental U.S. during the 1990s. Household heads were typically black (73%), middle age (mean=37 years) females (59%) who had 12 or fewer years of education (77%). Each household completed three to nine Panel Study of Income Dynamics (PSID) surveys. Using geocodes, census data were linked with survey data to provide information about the NPR and metropolitan opportunity structure at each survey occasion. Multilevel modeling was used to analyze this hierarchically-structured data (measurement occasions nested within households nested within MSAs). While 58% of variability in outcomes was due to between-household differences, 15% was due to between-MSA differences (the remainder was between-measurement occasion variability). Each of the three blocks of predictors significantly improved the model: individual decisions (work, housing, fertility and marriage), personal characteristics (race, age, gender and education) and MSA characteristics (segregation, housing, labor market and area poverty conditions). Controlling for other predictors, race was the most important predictor, increasing a black household\u27s NPR by over ten points and interacting with several other predictors. Being black amplified the negative effect of having more children, weakened positive effects of increased income and a better MSA opportunity structure, and interacted with MSA segregation to the disadvantage of black households. Increased education lowered the NPR. Across income levels, the average white household lived in a non-poor neighborhood while the average black household had an NPR nearly twice as high. Living in public housing was associated with a 4.7 percentage point differential in NPR (compared to no assistance). Other forms of government-assisted housing also increased the NPR, but by less than one percentage point. Mobility lowered the NPR, as did becoming a homeowner. Individual choices made a difference, but characteristics individuals were born with amplified or diminished effects of their efforts. The NPR was further influenced by housing type, tenure and mobility. Most importantly, metropolitan context mattered
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
String Branchings on Complex Tori and Algebraic Representations of Generalized Krichever-Novikov Algebras
The propagation differential for bosonic strings on a complex torus with
three symmetric punctures is investigated. We study deformation aspects between
two point and three point differentials as well as the behaviour of the
corresponding Krichever-Novikov algebras. The structure constants are
calculated and from this we derive a central extension of the Krichever-Novikov
algebras by means of b-c systems. The defining cocycle for this central
extension deforms to the well known Virasoro cocycle for certain kinds of
degenerations of the torus.
AMS subject classification (1991): 17B66, 17B90, 14H52, 30F30, 81T40Comment: 11 pages, amste
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
Transit timing variations for planets near eccentricity-type mean motion resonances
We derive the transit timing variations (TTVs) of two planets near a second-order mean motion resonance (MMR) on nearly circular orbits. We show that the TTVs of each planet are given by sinusoids with a frequency of jn_2 -(j-2){n_1, where j ≥ 3 is an integer characterizing the resonance and n2 and n1 are the mean motions of the outer and inner planets, respectively. The amplitude of the TTV depends on the mass of the perturbing planet, relative to the mass of the star, and on both the eccentricities and longitudes of pericenter of each planet. The TTVs of the two planets are approximated anti-correlated, with phases of φ and ≈φ + π, where the phase φ also depends on the eccentricities and longitudes of pericenter. Therefore, the TTVs caused by proximity to a second-order MMR do not in general uniquely determine both planet masses, eccentricities, and pericenters. This is completely analogous to the case of TTVs induced by two planets near a first-order MMR. We explore how other TTV signals, such as the short-period synodic TTV or a first-order resonant TTV, in combination with the second-order resonant TTV, can break degeneracies. Finally, we derive approximate formulae for the TTVs of planets near any order eccentricity-type MMR; this shows that the same basic sinusoidal TTV structure holds for all eccentricity-type resonances. Our general formula reduces to previously derived results near first-order MMRs
Measurement of planet masses with transit timing variations due to synodic "chopping" effects
Gravitational interactions between planets in transiting exoplanetary systems
lead to variations in the times of transit that are diagnostic of the planetary
masses and the dynamical state of the system. Here we show that synodic
"chopping" contributions to these transit timing variations (TTVs) can be used
to uniquely measure the masses of planets without full dynamical analyses
involving direct integration of the equations of motion. We present simple
analytic formulae for the chopping signal, which are valid (generally <10%
error) for modest eccentricities e <~ 0.1. Importantly, these formulae
primarily depend on the mass of the perturbing planet, and therefore the
chopping signal can be used to break the mass/free-eccentricity degeneracy
which can appear for systems near first order mean motion resonances. Using a
harmonic analysis, we apply these TTV formulae to a number of Kepler systems
which had been previously analyzed with full dynamical analyses. We show that
when chopping is measured, the masses of both planets can be determined
uniquely, in agreement with previous results, but without the need for
numerical orbit integrations. This demonstrates how mass measurements from TTVs
may primarily arise from an observable chopping signal. The formula for
chopping can also be used to predict the number of transits and timing
precision required for future observations, such as those made by TESS or
PLATO, in order to infer planetary masses through analysis of TTVs.Comment: submitted to ApJ, comments appreciate
Fight or Flight? Defending Against Sequential Attacks in the Game of Siege
This paper examines theory and behavior in a two-player game of siege, sequential attack and defense. The attacker’s objective is to successfully win at least one battle while the defender’s objective is to win every battle. Theoretically, the defender either folds immediately or, if his valuation is sufficiently high and the number of battles is sufficiently small, then he has a constant incentive to fight in each battle. Attackers respond to defense with diminishing assaults over time. Consistent with theoretical predictions, our experimental results indicate that the probability of successful defense increases in the defenders valuation and it decreases in the overall number of battles in the contest. However, the defender engages in the contest significantly more often than predicted and the aggregate expenditures by both parties exceed predicted levels. Moreover, both defenders and attackers actually increase the intensity of the fight as they approach the end of the contest
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