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

Mentally disordered offenders : an evaluation of the "open doors" programme at HM Prison, Barlinnie

This study was designed to evaluate the effectiveness of a programme which aims to support and manage mentally disordered offenders in HM Prison, Barlinnie. The following hypotheses were tested: 1. Significant levels of psychiatric morbidity would be found in a prison setting. 2. The 'Open Doors' participants had more mental health problems than controls. 3. Participation in the programme improved their mental health. METHODOLOGY: To assess psychiatric morbidity in the prison all the admissions over a one week period were interviewed. The questionnaires recorded demographic and health information and psychological morbidity was assessed using the Clinical Interview Schedule-Revised (CIS-R) and the Schedules for Clinical Assessment in Neuropsychiatry (SCAN). This cohort was followed up after 5 months to identify which services had been used. Programme participants were interviewed at the beginning and at the end of their involvement with the "Open Doors" programme. The first questionnaire included demographic and health information, the structured clinical interview for DSM-lli-R non patient (SCID), the General Health Questionnaire (GHQ 30), the Holmes and Rahe Social Readjustment Scale examining life events (LE) and the Health of the Nation Outcome scales (HoNOS). The follow up questionnaires included some demographic information and repeated the SCID, the GHQ 30, LE and HoNOS. A participant satisfaction scale was also used on follow up. A control group matched for age, time into imprisonment, length of sentence and charge/conviction were interviewed. Interviews were carried out with programme staff and managers. Interviews were held with other staff groups within the prison and in the community. Group sessions were directly observed. Programme literature and paperwork was examined. RESULTS: The survey of psychological morbidity in the prison population found a 5% incidence of psychosis, 20% depression and 9.2% anxiety disorders. Sixty six percent abused drugs, 16% abused or were dependent on alcohol and 2% used both. Two were referred to 'Open Doors' and less than 10% to other prison mental health services including drug and alcohol workers.Twenty percent of "Open Doors" subjects had a psychotic illness, 30% had a non psychotic depression and 22% an anxiety disorder. They had significantly more mental health problems than the controls. Forty five percent fulfilled criteria for drug abuse or dependence, 35% for alcohol and 5% for both. Over 65% had used drugs intravenously. At follow up interview "Open Doors" participants showed significant improvements in their mental health. CONCLUSIONS: There is a very high incidence of mental ill health in the prison population. Existing services are not able to identify or treat this high volume of mental disorder. The programme was identifying and working with prisoners with significant mental health problems. Those individuals who do become involved in the programme improve following participation and there are high levels of participant satisfaction. However the number of prisoners who do become involved in the programme is small and the impact on the prison population is therefore low

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

A Prograde, Low-Inclination Orbit for the Very Hot Jupiter WASP-3b

We present new spectroscopic and photometric observations of the transiting exoplanetary system WASP-3. Spectra obtained during two separate transits exhibit the Rossiter-McLaughlin (RM) effect and allow us to estimate the sky-projected angle between the planetary orbital axis and the stellar rotation axis, lambda = 3.3^{+2.5}_{-4.4} degrees. This alignment between the axes suggests that WASP-3b has a low orbital inclination relative to the equatorial plane of its parent star. During our first night of spectroscopic measurements, we observed an unexpected redshift briefly exceeding the expected sum of the orbital and RM velocities by 140 m/s. This anomaly could represent the occultation of material erupting from the stellar photosphere, although it is more likely to be an artifact caused by moonlight scattered into the spectrograph.Comment: 23 pages, 4 figures, Accepted for publication in The Astrophysical Journal, Replacement includes revised citation

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

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