Collisions Between Gravity-Dominated Bodies: 1. Outcome Regimes and Scaling Laws

Collisions are the core agent of planet formation. In this work, we derive an analytic description of the dynamical outcome for any collision between gravity-dominated bodies. We conduct high-resolution simulations of collisions between planetesimals; the results are used to isolate the effects of different impact parameters on collision outcome. During growth from planetesimals to planets, collision outcomes span multiple regimes: cratering, merging, disruption, super-catastrophic disruption, and hit-and-run events. We derive equations (scaling laws) to demarcate the transition between collision regimes and to describe the size and velocity distributions of the post-collision bodies. The scaling laws are used to calculate maps of collision outcomes as a function of mass ratio, impact angle, and impact velocity, and we discuss the implications of the probability of each collision regime during planet formation. The analytic collision model presented in this work will significantly improve the physics of collisions in numerical simulations of planet formation and collisional evolution. (abstract abridged)Comment: Version 3, accepted to ApJ in Nov. 2011 published online Dec. 2011. Abstract abridge

Erosive Hit-and-Run Impact Events: Debris Unbound

Erosive collisions among planetary embryos in the inner solar system can lead to multiple remnant bodies, varied in mass, composition and residual velocity. Some of the smaller, unbound debris may become available to seed the main asteroid belt. The makeup of these collisionally produced bodies is different from the canonical chondritic composition, in terms of rock/iron ratio and may contain further shock-processed material. Having some of the material in the asteroid belt owe its origin from collisions of larger planetary bodies may help in explaining some of the diversity and oddities in composition of different asteroid groups.Comment: 7 pages, 3 figure

Collisional stripping of planetary crusts

Geochemical studies of planetary accretion and evolution have invoked various degrees of collisional erosion to explain differences in bulk composition between planets and chondrites. Here we undertake a full, dynamical evaluation of 'crustal stripping' during accretion and its key geochemical consequences. We present smoothed particle hydrodynamics simulations of collisions between differentiated rocky planetesimals and planetary embryos. We find that the crust is preferentially lost relative to the mantle during impacts, and we have developed a scaling law that approximates the mass of crust that remains in the largest remnant. Using this scaling law and a recent set of N-body simulations, we have estimated the maximum effect of crustal stripping on incompatible element abundances during the accretion of planetary embryos. We find that on average one third of the initial crust is stripped from embryos as they accrete, which leads to a reduction of ~20% in the budgets of the heat producing elements if the stripped crust does not reaccrete. Erosion of crusts can lead to non-chondritic ratios of incompatible elements, but the magnitude of this effect depends sensitively on the details of the crust-forming melting process. The Lu/Hf system is fractionated for a wide range of crustal formation scenarios. Using eucrites (the products of planetesimal silicate melting, thought to represent the crust of Vesta) as a guide to the Lu/Hf of planetesimal crust partially lost during accretion, we predict the Earth could evolve to a superchondritic 176-Hf/177-Hf (3-5 parts per ten thousand) at present day. Such values are in keeping with compositional estimates of the bulk Earth. Stripping of planetary crusts during accretion can lead to detectable changes in bulk composition of lithophile elements, but the fractionation is relatively subtle, and sensitive to the efficiency of reaccretion.Comment: 15 pages, 9 figures. Accepted for publication in EPSL. Abstract shortened. Accompanying animations can be found at http://www.star.bris.ac.uk/pcarter/crust_strip

Major health-related behaviours and mental well-being in the general population : the health survey for England

Background: Major behavioural risk factors are known to adversely affect health outcomes and be strongly associated with mental illness. However, little is known about the association of these risk factors with mental well-being in the general population. We sought to examine behavioural correlates of high and low mental well-being in the Health Survey for England. Methods: Participants were 13 983 adults, aged 16 years and older (56% females), with valid responses for the combined 2010 and 2011 surveys. Mental well-being was assessed using the Warwick-Edinburgh Mental Well-being Scale (WEMWBS). ORs of low and high mental well-being, compared to the middle-range category, were estimated for body mass index (BMI), smoking, drinking habits, and fruit and vegetable intake. Results: ORs for low mental well-being were increased in obese individuals (up to 1.72, 95% CI 1.26 to 2.36 in BMI 40+ kg/m2). They increased in a linear fashion with increasing smoking (up to 1.98, 95% CI 1.55 to 2.53, >20 cigarettes/day) and with decreasing fruit and vegetable intake (up to 1.53, 95% CI 1.24 to 1.90, <1 portion/day); whereas ORs were reduced for sensible alcohol intake (0.78, 95% CI 0.66 to 0.91, ≤4 units/day in men, ≤3 units/day in women). ORs for high mental well-being were not correlated with categories of BMI or alcohol intake. ORs were reduced among ex-smokers (0.81, 95% CI 0.71 to 0.92), as well as with lower fruit and vegetable intake (up to 0.79, 95% CI 0.68 to 0.92, 1 to <3 portions/day). Conclusions; Along with smoking, fruit and vegetable consumption was the health-related behaviour most consistently associated with mental well-being in both sexes. Alcohol intake and obesity were associated with low, but not high mental well-being

The Formation of the Collisional Family around the Dwarf Planet Haumea

Haumea, a rapidly rotating elongated dwarf planet (~ 1500 km in diameter), has two satellites and is associated with a "family" of several smaller Kuiper Belt objects (KBOs) in similar orbits. All members of the Haumea system share a water ice spectral feature that is distinct from all other KBOs. The relative velocities between the Haumea family members are too small to have formed by catastrophic disruption of a large precursor body, which is the process that formed families around much smaller asteroids in the Main Belt. Here we show that all of the unusual characteristics of the Haumea system are explained by a novel type of giant collision: a graze-and-merge impact between two comparably sized bodies. The grazing encounter imparted the high angular momentum that spun off fragments from the icy crust of the elongated merged body. The fragments became satellites and family members. Giant collision outcomes are extremely sensitive to the impact parameters. Compared to the Main Belt, the largest bodies in the Kuiper Belt are more massive and experience slower velocity collisions; hence, outcomes of giant collisions are dramatically different between the inner and outer solar system. The dwarf planets in the Kuiper Belt record an unexpectedly large number of giant collisions, requiring a special dynamical event at the end of solar system formation.Comment: Accepted for publication in ApJ, 12 pages, 4 figures, 2 tables

Feasibility trial evaluation of a physical activity and screen-viewing course for parents of 6 to 8 year-old children : Teamplay

Background: Many children spend too much time screen-viewing (watching TV, surfing the internet and playing video games) and do not meet physical activity (PA) guidelines. Parents are important influences on children’s PA and screen-viewing (SV). There is a shortage of parent-focused interventions to change children’s PA and SV. Methods: Teamplay was a two arm individualized randomized controlled feasibility trial. Participants were parents of 6–8 year old children. Intervention participants were invited to attend an eight week parenting program with each session lasting 2 hours. Children and parents wore an accelerometer for seven days and minutes of moderate-to-vigorous intensity PA (MVPA) were derived. Parents were also asked to report the average number of hours per day that both they and the target child spent watching TV. Measures were assessed at baseline (time 0) at the end of the intervention (week 8) and 2 months after the intervention had ended (week 16). Results: There were 75 participants who provided consent and were randomized but 27 participants withdrew post-randomization. Children in the intervention group engaged in 2.6 fewer minutes of weekday MVPA at Time 1 but engaged in 11 more minutes of weekend MVPA. At Time 1 the intervention parents engaged in 9 more minutes of weekday MVPA and 13 more minutes of weekend MVPA. The proportion of children in the intervention group watching ≥ 2 hours per day of TV on weekend days decreased after the intervention (time 0 = 76%, time 1 = 39%, time 2 = 50%), while the control group proportion increased slightly (79%, 86% and 87%). Parental weekday TV watching decreased in both groups. In post-study interviews many mothers reported problems associated with wearing the accelerometers. In terms of a future full-scale trial, a sample of between 80 and 340 families would be needed to detect a mean difference of 10-minutes of weekend MVPA. Conclusions: Teamplay is a promising parenting program in an under-researched area. The intervention was acceptable to parents, and all elements of the study protocol were successfully completed. Simple changes to the trial protocol could result in more complete data collection and study engagement

Parental modelling, media equipment and screen-viewing among young children : cross-sectional study

Objective: To examine whether parental screenviewing, parental attitudes or access to media equipment were associated with the screen-viewing of 6-year-old to 8-year-old children. Design: Cross-sectional survey. Setting: Online survey. Main outcome: Parental report of the number of hours per weekday that they and, separately, their 6- year-old to 8-year-old child spent watching TV, using a games console, a smart-phone and multiscreen viewing. Parental screen-viewing, parental attitudes and pieces of media equipment were exposures. Results: Over 75% of the parents and 62% of the children spent more than 2 h/weekday watching TV. Over two-thirds of the parents and almost 40% of the children spent more than an hour per day multiscreen viewing. The mean number of pieces of media equipment in the home was 5.9 items, with 1.3 items in the child’s bedroom. Children who had parents who spent more than 2 h/day watching TV were over 7.8 times more likely to exceed the 2 h threshold. Girls and boys who had a parent who spent an hour or more multiscreen viewing were 34 times more likely to also spend more than an hour per day multiscreen viewing. Media equipment in the child’s bedroom was associated with higher TV viewing, computer time and multiscreen viewing. Each increment in the parental agreement that watching TV was relaxing for their child was associated with a 49% increase in the likelihood that the child spent more than 2 h/day watching TV. Conclusions: Children who have parents who engage in high levels of screen-viewing are more likely to engage in high levels of screen-viewing. Access to media equipment, particularly in the child’s bedroom, was associated with higher levels of screen-viewing. Family-based strategies to reduce screen-viewing and limit media equipment access may be important ways to reduce child screen-viewing

Process evaluation of the Teamplay parenting intervention pilot : implications for recruitment, retention and course refinement

Background Parenting programs could provide effective routes to increasing children’s physical activity and reducing screen-viewing. Many studies have reported difficulties in recruiting and retaining families in group parenting interventions. This paper uses qualitative data from the Teamplay feasibility trial to examine parents’ views on recruitment, attendance and course refinement. Methods Semi-structured interviews were conducted with 16 intervention and 10 control group parents of 6–8 year old children. Topics discussed with the intervention group included parents’ views on the recruitment, structure, content and delivery of the course. Topics discussed with the control group included recruitment and randomization. Interviews were digitally recorded, transcribed and thematically analyzed. Results Many parents in both the intervention and control group reported that they joined the study because they had been thinking about ways to improve their parenting skills, getting ideas on how to change behavior, or had been actively looking for a parenting course but with little success in enrolling on one. Both intervention and control group parents reported that the initial promotional materials and indicative course topics resonated with their experiences and represented a possible solution to parenting challenges. Participants reported that the course leaders played an important role in helping them to feel comfortable during the first session, engaging anxious parents and putting parents at ease. The most commonly reported reason for parents returning to the course after an absence was because they wanted to learn new information. The majority of parents reported that they formed good relationships with the other parents in the group. An empathetic interaction style in which leaders accommodated parent’s busy lives appeared to impact positively on course attendance. Conclusions The data presented indicate that a face-to-face recruitment campaign which built trust and emphasized how the program was relevant to families positively affected recruitment in Teamplay. Parents found the parenting component of the intervention attractive and, once recruited, attendance was facilitated by enjoyable sessions, empathetic leaders and support from fellow participants. Overall, data suggest that the Teamplay recruitment and retention approaches were successful and with small refinements could be effectively used in a larger trial