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

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

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 $\sim 0.4 R_H$ (where $R_H$ is the Hill Radius) as opposed to $\sim 0.5 R_H$ 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 $a\sim 0.65 R_H$. 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

The precession of SS433's radio ruff on long timescales

Roughly perpendicular to SS433's famous precessing jets is an outflowing "ruff" of radio-emitting plasma, revealed by direct imaging on milli-arcsecond scales. Over the last decade, images of the ruff reveal that its orientation changes over time with respect to a fixed sky co-ordinate grid. For example, during two months of daily observations with the VLBA by Mioduszewski et al. (2004), a steady rotation through ~10 degrees is observed whilst the jet angle changes by ~20 degrees. The ruff reorientation is not coupled with the well-known precession of SS433's radio jets, as the ruff orientation varies across a range of 69 degrees whilst the jet angle varies across 40 degrees, and on greatly differing and non-commensurate timescales. It has been proposed that the ruff is fed by SS433's circumbinary disk, discovered by a sequence of optical spectroscopy by Blundell et al. (2008), and so we present the results of 3D numerical simulations of circumbinary orbits. These simulations show precession in the longitude of the ascending node of all inclined circumbinary orbits - an effect which would be manifested as the observed ruff reorientation. Matching the rate of ruff precession is possible if circumbinary components are sufficiently close to the binary system, but only if the binary mass fraction is close to equality and the binary eccentricity is non-zero.Comment: 4 pages, 5 figures, to be published in ApJ Le

Planet Hunters VII. Discovery of a New Low-Mass, Low-Density Planet (PH3 c) Orbiting Kepler-289 with Mass Measurements of Two Additional Planets (PH3 b and d)

We report the discovery of one newly confirmed planet ($P=66.06$ days, $R_{\rm{P}}=2.68\pm0.17R_\oplus$) and mass determinations of two previously validated Kepler planets, Kepler-289 b ($P=34.55$ days, $R_{\rm{P}}=2.15\pm0.10R_\oplus$) and Kepler-289-c ($P=125.85$ days, $R_{\rm{P}}=11.59\pm0.10R_\oplus$), through their transit timing variations (TTVs). We also exclude the possibility that these three planets reside in a $1:2:4$ Laplace resonance. The outer planet has very deep ($\sim1.3$), high signal-to-noise transits, which puts extremely tight constraints on its host star's stellar properties via Kepler's Third Law. The star PH3 is a young ($\sim1$ Gyr as determined by isochrones and gyrochronology), Sun-like star with $M_*=1.08\pm0.02M_\odot$, $R_*=1.00\pm0.02R_\odot$, and $T_{\rm{eff}}=5990\pm38$ K. The middle planet's large TTV amplitude ($\sim5$ hours) resulted either in non-detections or inaccurate detections in previous searches. A strong chopping signal, a shorter period sinusoid in the TTVs, allows us to break the mass-eccentricity degeneracy and uniquely determine the masses of the inner, middle, and outer planets to be $M=7.3\pm6.8M_\oplus$, $4.0\pm0.9M_\oplus$, and $M=132\pm17M_\oplus$, which we designate PH3 b, c, and d, respectively. Furthermore, the middle planet, PH3 c, has a relatively low density, $\rho=1.2\pm0.3$ g/cm$^3$ for a planet of its mass, requiring a substantial H/He atmosphere of $2.1^{+0.8}_{-0.3}$ by mass, and joins a growing population of low-mass, low-density planets.Comment: 21 pages, 10 figures, 5 tables, accepted into Ap

The Dynamics and Stability of Circumbinary Orbits

We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a nodal libration mechanism in the longitude of the ascending node and in the inclination to the plane of the binary. We (i) analyse and quantify the behaviour of these orbits with reference to analytical work performed by Farago & Laskar (2010) and (ii) investigate the stability of these orbits over time. This work is the first dynamically aware analysis of the stability of circumbinary orbits across both binary mass fraction and binary eccentricity. This work also has implications for exoplanetary astronomy in the existence and determination of stable orbits around binary systems.Comment: Monthly Notices of the Royal Astronomical Society. in pres

Development of a treatment selection algorithm for SGLT2 and DPP-4 inhibitor therapies in people with type 2 diabetes:a retrospective cohort study

Background: Current treatment guidelines do not provide recommendations to support the selection of treatment for most people with type 2 diabetes. We aimed to develop and validate an algorithm to allow selection of optimal treatment based on glycaemic response, weight change, and tolerability outcomes when choosing between SGLT2 inhibitor or DPP-4 inhibitor therapies. Methods: In this retrospective cohort study, we identified patients initiating SGLT2 and DPP-4 inhibitor therapies after Jan 1, 2013, from the UK Clinical Practice Research Datalink (CPRD). We excluded those who received SGLT2 or DPP-4 inhibitors as first-line treatment or insulin at the same time, had estimated glomerular filtration rate (eGFR) of less than 45 mL/min per 1·73 m2, or did not have a valid baseline glycated haemoglobin (HbA1c) measure (&lt;53 or ≥120 mmol/mol). The primary efficacy outcome was the HbA1c value reached 6 months after drug initiation, adjusted for baseline HbA1c. Clinical features associated with differential HbA1c outcome on the two therapies were identified in CPRD (n=26 877), and replicated in reanalysis of 14 clinical trials (n=10 414). An algorithm to predict individual-level differential HbA1c outcome on the two therapies was developed in CPRD (derivation; n=14 069) and validated in head-to-head trials (n=2499) and CPRD (independent validation; n=9376). In CPRD, we further explored heterogeneity in 6-month weight change and treatment discontinuation. Findings: Among 10 253 patients initiating SGLT2 inhibitors and 16 624 patients initiating DPP-4 inhibitors in CPRD, baseline HbA1c, age, BMI, eGFR, and alanine aminotransferase were associated with differential HbA1c outcome with SGLT2 inhibitor and DPP-4 inhibitor therapies. The median age of participants was 62·0 years (IQR 55·0–70·0). 10 016 (37·3%) were women and 16 861 (62·7%) were men. An algorithm based on these five features identified a subgroup, representing around four in ten CPRD patients, with a 5 mmol/mol or greater observed benefit with SGLT2 inhibitors in all validation cohorts (CPRD 8·8 mmol/mol [95% CI 7·8–9·8]; CANTATA-D and CANTATA-D2 trials 5·8 mmol/mol [3·9–7·7]; BI1245.20 trial 6·6 mmol/mol [2·2–11·0]). In CPRD, predicted differential HbA1c response with SGLT2 inhibitor and DPP-4 inhibitor therapies was not associated with weight change. Overall treatment discontinuation within 6 months was similar in patients predicted to have an HbA1c benefit with SGLT2 inhibitors over DPP-4 inhibitors (median 15·2% [13·2–20·3] vs 14·4% [12·9–16·7]). A smaller subgroup predicted to have greater HbA1c reduction with DPP-4 inhibitors were twice as likely to discontinue SGLT2 inhibitors than DPP-4 inhibitors (median 26·8% [23·4–31·0] vs 14·8% [12·9–16·8]). Interpretation: A validated treatment selection algorithm for SGLT2 inhibitor and DPP-4 inhibitor therapies can support decisions on optimal treatment for people with type 2 diabetes. Funding: BHF-Turing Cardiovascular Data Science Award and the UK Medical Research Council

Lipid analysis of CO2-rich subsurface aquifers suggests an autotrophy-based deep biosphere with lysolipids enriched in CPR bacteria.

Sediment-hosted CO2-rich aquifers deep below the Colorado Plateau (USA) contain a remarkable diversity of uncultivated microorganisms, including Candidate Phyla Radiation (CPR) bacteria that are putative symbionts unable to synthesize membrane lipids. The origin of organic carbon in these ecosystems is unknown and the source of CPR membrane lipids remains elusive. We collected cells from deep groundwater brought to the surface by eruptions of Crystal Geyser, sequenced the community, and analyzed the whole community lipidome over time. Characteristic stable carbon isotopic compositions of microbial lipids suggest that bacterial and archaeal CO2 fixation ongoing in the deep subsurface provides organic carbon for the complex communities that reside there. Coupled lipidomic-metagenomic analysis indicates that CPR bacteria lack complete lipid biosynthesis pathways but still possess regular lipid membranes. These lipids may therefore originate from other community members, which also adapt to high in situ pressure by increasing fatty acid unsaturation. An unusually high abundance of lysolipids attributed to CPR bacteria may represent an adaptation to membrane curvature stress induced by their small cell sizes. Our findings provide new insights into the carbon cycle in the deep subsurface and suggest the redistribution of lipids into putative symbionts within this community

Rethinking the patient: using Burden of Treatment Theory to understand the changing dynamics of illness

&lt;b&gt;Background&lt;/b&gt; In this article we outline Burden of Treatment Theory, a new model of the relationship between sick people, their social networks, and healthcare services. Health services face the challenge of growing populations with long-term and life-limiting conditions, they have responded to this by delegating to sick people and their networks routine work aimed at managing symptoms, and at retarding - and sometimes preventing - disease progression. This is the new proactive work of patient-hood for which patients are increasingly accountable: founded on ideas about self-care, self-empowerment, and self-actualization, and on new technologies and treatment modalities which can be shifted from the clinic into the community. These place new demands on sick people, which they may experience as burdens of treatment.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Discussion&lt;/b&gt; As the burdens accumulate some patients are overwhelmed, and the consequences are likely to be poor healthcare outcomes for individual patients, increasing strain on caregivers, and rising demand and costs of healthcare services. In the face of these challenges we need to better understand the resources that patients draw upon as they respond to the demands of both burdens of illness and burdens of treatment, and the ways that resources interact with healthcare utilization.&lt;p&gt;&lt;/p&gt; &lt;b&gt;Summary&lt;/b&gt; Burden of Treatment Theory is oriented to understanding how capacity for action interacts with the work that stems from healthcare. Burden of Treatment Theory is a structural model that focuses on the work that patients and their networks do. It thus helps us understand variations in healthcare utilization and adherence in different healthcare settings and clinical contexts