Stability Boundaries for Resonant Migrating Planet Pairs

Convergent migration allows pairs of planet to become trapped into mean motion resonances. Once in resonance, the planets' eccentricities grow to an equilibrium value that depends on the ratio of migration time scale to the eccentricity damping timescale, $K=\tau_a/\tau_e$, with higher values of equilibrium eccentricity for lower values of $K$. For low equilibrium eccentricities, $e_{eq}\propto K^{-1/2}$. The stability of a planet pair depends on eccentricity so the system can become unstable before it reaches its equilibrium eccentricity. Using a resonant overlap criterion that takes into account the role of first and second order resonances and depends on eccentricity, we find a function $K_{min}(\mu_p, j)$ that defines the lowest value for $K$, as a function of the ratio of total planet mass to stellar mass ($\mu_p$) and the period ratio of the resonance defined as $P_1/P_2=j/(j+k)$, that allows two convergently migrating planets to remain stable in resonance at their equilibrium eccentricities. We scaled the functions $K_{min}$ for each resonance of the same order into a single function $K_c$. The function $K_{c}$ for planet pairs in first order resonances is linear with increasing planet mass and quadratic for pairs in second order resonances with a coefficient depending on the relative migration rate and strongly on the planet to planet mass ratio. The linear relation continues until the mass approaches a critical mass defined by the 2/7 resonance overlap instability law and $K_c \to \infty$. We compared our analytic boundary with an observed sample of resonant two planet systems. All but one of the first order resonant planet pair systems found by radial velocity measurements are well inside the stability region estimated by this model. We calculated $K_c$ for Kepler systems without well-constrained eccentricities and found only weak constraints on $K$.Comment: 11 pages, 7 figure

MANAGING THE INCONCEIVABLE: PARTICIPATORY ASSESSMENTS OF IMPACTS AND RESPONSES TO EXTREME CLIMATE CHANGE

A comprehensive understanding of the implications of extreme climate change requires an in-depth exploration of the perceptions and reactions of the affected stakeholder groups and the lay public. The project on “Atlantic sea level rise: Adaptation to imaginable worst-case climate change” (Atlantis) has studied one such case, the collapse of the West Antarctic Ice Sheet and a subsequent 5-6 meter sea-level rise. Possible methods are presented for assessing the societal consequences of impacts and adaptation options in selected European regions by involving representatives of pertinent stakeholders. Results of a comprehensive review of participatory integrated assessment methods with a view to their applicability in climate impact studies are summarized including Simulation-Gaming techniques, the Policy Exercise method, and the Focus Group technique. Succinct presentations of these three methods are provided together with short summaries of relevant earlier applications to gain insights into the possible design options. Building on these insights, four basic versions of design procedures suitable for use in the Atlantis project are presented. They draw on design elements of several methods and combine them to fit the characteristics and fulfill the needs of addressing the problem of extreme sea-level rise. The selected participatory techniques and the procedure designs might well be useful in other studies assessing climate change impacts and exploring adaptation options.sea level rise, West Antarctic ice sheet, climate change

Purveyors of fine halos: Re-assessing globular cluster contributions to the Milky Way halo build-up with SDSS-IV

There is ample evidence in the Milky Way for globular cluster (GC) disruption. Hence one may expect that also part of the Galactic halo field stars may once have formed in GCs. We quantify the fraction of halo stars donated by GCs by searching for stars that bear the unique chemical fingerprints typical for a subset of GC stars often dubbed `second-generation stars'. These are stars showing light element abundance anomalies such as a pronounced CN-band strength accompanied by weak CH-bands. Based on this indicator, past studies have placed the fraction of halo stars with a GC origin between a few to up to 50%. Using low-resolution spectra from the most recent data release of the latest extension of the Sloan Digital Sky Survey (SDSS-IV), we were able to identify 118 metal-poor ($-1.8\le$[Fe/H]$\le -1.3$) CN-strong stars in a sample of 4470 halo giant stars out to 50 kpc. This results in an observed fraction of these stars of 2.6$\pm$0.2%. Using an updated formalism to account for the fraction of stars lost early on in the GCs' evolution we estimate the fraction of the halo that stems from disrupted clusters to be 11$\pm$1%. This number represents the case that stars lost from GCs were entirely from the first generation and is thus merely an upper limit. Our conclusions are sensitive to our assumptions of the mass lost early on from the first generation formed in the GCs, the ratio of first-to-second generation stars, and other GC parameters. We carefully test the influence of varying these parameters on the final result and find that, under realistic scenarios, the above fraction depends on the main assumptions at less than 10%. We further recover a flat trend in this fraction with Galactocentric radius, with a marginal indication of a rise beyond 30 kpc that could reflect the ex-situ origin of the outer halo. (abridged)Comment: 13 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Cyanoacetylene in IC 342: An Evolving Dense Gas Component with Starburst Age

We present the first images of the J=5-4 and J=16-15 lines of the dense gas tracer, cyanoacetylene, HC_3N, in an external galaxy. The central 200 pc of the nearby star-forming spiral galaxy, IC 342, was mapped using the VLA and the Plateau de Bure Interferometer. HC_3N(5-4) line emission is found across the nuclear mini-spiral, but is very weak towards the starburst site, the location of the strongest mid-IR and radio emission. The J=16-15 and 10-9 lines are also faint near the large HII region complex, but are brighter relative to the 5-4 line, consistent with higher excitation. The brightest HC_3N emission is located in the northern arm of the nuclear minispiral, 100 pc away from the radio/IR source to the southwest of the nucleus. This location appears less affected by ultraviolet radiation, and may represent a more embedded, earlier stage of star formation. HC_3N excitation temperatures are consistent with those determined from C^{18}O; the gas is dense, 10^{4-5}/cc, and cool, T_K ~< 40 K. So as to not violate limits on the total H_2 mass determined from C^{18}O, at least two dense components are required to model IC 342's giant molecular clouds. These observations suggest that HC_3N(5-4) is an excellent probe of the dense, quiescent gas in galaxies. The high excitation combined with faint emission towards the dense molecular gas at the starburst indicates that it currently lacks large masses of very dense gas. We propose a scenario where the starburst is being caught in the act of dispersing or destroying its dense gas in the presence of the large HII region. This explains the high star formation efficiency seen in the dense component. The little remaining dense gas appears to be in pressure equilibrium with the starburst HII region.Comment: Accepted, AJ. 12 pages, 5 figure

Retrofitting O'Raifeartaigh Models with Dynamical Scales

We provide a method for obtaining simple models of supersymmetry breaking, with all small mass scales generated dynamically, and illustrate it with explicit examples. We start from models of perturbative supersymmetry breaking, such as O'Raifeartaigh and Fayet models, that would respect an $R$ symmetry if their small input parameters transformed as the superpotential does. By coupling the system to a pure supersymmetric Yang-Mills theory (or a more general supersymmetric gauge theory with dynamically small vacuum expectation values), these parameters are replaced by powers of its dynamical scale in a way that is naturally enforced by the symmetry. We show that supersymmetry breaking in these models may be straightforwardly mediated to the supersymmetric Standard Model, obtain complete models of direct gauge mediation, and comment on related model building strategies that arise in this simple framework.Comment: 15 pages, harvmac bi

A note on non-homogeneous deformations with homogeneous Cauchy stress for a strictly rank-one convex energy in isotropic hyperelasticity

It has recently been shown that for a Cauchy stress response induced by a strictly rank-one convex hyperelastic energy potential, a homogeneous Cauchy stress tensor field cannot correspond to a non-homogeneous deformation if the deformation gradient has discrete values, i.e. if the deformation is piecewise affine linear and satisfies the Hadamard jump condition. In this note, we expand upon these results and show that they do not hold for arbitrary deformations by explicitly giving an example of a strictly rank-one convex energy and a non-homogeneous deformation such that the induced Cauchy stress tensor is constant. In the planar case, our example is related to another previous result concerning criteria for generalized convexity properties of conformally invariant energy functions, which we extend to the case of strict rank-one convexity