Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of Hot Jupiters

(abbreviated) We extend the theory of close encounters of a planet on a parabolic orbit with a star to include the effects of tides induced on the central rotating star. Orbits with arbitrary inclination to the stellar rotation axis are considered. We obtain results both from an analytic treatment and numerical one that are in satisfactory agreement. These results are applied to the initial phase of the tidal circularisation problem. We find that both tides induced in the star and planet can lead to a significant decrease of the orbital semi-major axis for orbits having periastron distances smaller than 5-6 stellar radii (corresponding to periods $\sim 4-5$ days after the circularisation has been completed) with tides in the star being much stronger for retrograde orbits compared to prograde orbits. We use the simple Skumanich law for the stellar rotation with its rotational period equal to one month at the age of 5Gyr. The strength of tidal interactions is characterised by circularisation time scale, $t_{ev}$ defined as a time scale of evolution of the planet's semi-major axis due to tides considered as a function of orbital period $P_{obs}$ after the process of tidal circularisation has been completed. We find that the ratio of the initial circularisation time scales corresponding to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter mass and $P_{obs}\sim$ four days. It grows with the mass of the planet, being of order five for a five Jupiter mass planet with the same $P_{orb}$. Thus, the effect of stellar rotation may provide a bias in the formation of planetary systems having planets on close orbits around their host stars, as a consequence of planet-planet scattering, favouring systems with retrograde orbits. The results may also be applied to the problem of tidal capture of stars in young stellar clusters.Comment: to be published in Celestial Mechanics and Dynamical Astronom

Association between somatic cell count and serial locomotion score assessments in UK dairy cows

This research investigated the effect of lameness, measured by locomotion score (LS) on the somatic cell count (SCC) of UK dairy cows. The data set consisted of 11,141 records of SCC and LS collected monthly on 12 occasions from 1,397 cows kept on 7 farms. The data were analyzed to account for the correlation of repeated measures of SCC within cow. Results were controlled for farm of origin, stage of lactation, parity, season, and test-day milk yield. Compared with the geometric mean SCC for cows with LS 1 on each farm, cows on farm 3 with LS 2 produced milk with 28,000 fewer somatic cells/mL, and cows with LS 2 on farm 6 produced milk with 30,000 fewer somatic cells/mL at a test day within 10 d. Cows that would have LS 3 six months later produced milk with 16,000 fewer somatic cells/mL compared with the geometric mean SCC for cows that would have LS 1 in 6 mo time. These results illustrate differences in disease dynamics between farms, highlight potential conflict between lameness and mastitis control measures, and emphasize the importance of developing farm-specific estimates of disease costs, and hence, health management plans in clinical practice

Association between milk yield and serial locomotion score assessments in UK dairy cows

This study investigated the effect of lameness, measured by serial locomotion scoring over a 12-mo period, on the milk yield of UK dairy cows. The data set consisted of 11,735 records of test-day yield and locomotion scores collected monthly from 1,400 cows kept on 7 farms. The data were analyzed in a multilevel linear regression model to account for the correlation of repeated measures of milk yield within cow. Factors affecting milk yield included farm of origin, stage of lactation, parity, season, and whether cows were ever lame or ever severely lame during the study period. Cows that had been severely lame 4, 6, and 8 mo previously gave 0.51 kg/d, 0.66 kg/d, and 1.55 kg/d less milk, respectively. A severe case of lameness in the first month of lactation reduced 305-d milk yield by 350 kg; this loss may be avoidable by prompt, effective treatment. Larger reductions can be expected when cases persist or recur. Evidence-based control plans are needed to reduce the incidence and prevalence of lameness in high yielding cows to improve welfare and productivity

A Simple Model of Liquid-liquid Phase Transitions

In recent years, a second fluid-fluid phase transition has been reported in several materials at pressures far above the usual liquid-gas phase transition. In this paper, we introduce a new model of this behavior based on the Lennard-Jones interaction with a modification to mimic the different kinds of short-range orientational order in complex materials. We have done Monte Carlo studies of this model that clearly demonstrate the existence of a second first-order fluid-fluid phase transition between high- and low-density liquid phases

The contribution of previous lameness events and body condition score to the occurrence of lameness in dairy herds: a study of 2 herds

It has been demonstrated that low body condition and previous occurrence of lameness increase the risk of future lameness in dairy cows. To date the population attributable fraction (PAF), which provides an estimate of the contribution that a risk factor makes toward the total number of disease events in a population, has not been explored for lameness using longitudinal data with repeated measures. Estimation of PAF helps to identify control measures that could lead to the largest improvements on-farm. The aim of this study was to use longitudinal data to evaluate the proportion of lameness that could be avoided in 2 separate herds (2 populations) through (1) reduced recurrence of previous lameness events, (2) and moving body condition score (BCS) into more optimal ranges. Data were obtained from 2 UK dairy herds: herd A, a 200-cow herd with 8 yr of data from a total of 724 cows where lameness events were based on weekly locomotion scores (LS; 1 to 5 scale), and herd B, a 600-cow herd with data recorded over 44 mo from a total of 1,040 cows where treatment of clinical cases was used to identify lameness events. The PAF for categories of BCS were estimated using a closed equation appropriate for multiple exposure categories. Simulation models were used to explore theoretical scenarios to reflect changes in BCS and recurrence of previous lameness events in each herd. For herd A, 21.5% of the total risk periods (cow-weeks) contained a lameness event (LS 3, 4, or 5), 96% of which were repeat events and 19% were recorded with BCS 16 wk before a risk period. The median PAF estimated for changes in BCS were in the region of 4 to 11%, depending on severity of lameness. Repeated bouts of lameness made a very large contribution to the total number of lameness events. This could either be because certain cows are initially susceptible and remain susceptible, due to the increased risk associated with previous lameness events, or due to interactions with environmental factors. This area requires further research

Dynamics of deep submarine silicic explosive eruptions in the Kermadec arc, as reflected in pumice vesicularity textures

Despite increasing recognition of silicic pumice-bearing deposits in the deep marine environment, the processes involved in explosive silicic submarine eruptions remain in question. Here we present data on bubble sizes and number densities (number of bubbles per unit of melt matrix) for deep submarine-erupted pumices from three volcanoes (Healy, Raoul SW and Havre) along the Kermadec arc (SW Pacific) to investigate the effects of a significant (>~1 km) overlying water column and the associated increased hydrostatic pressure on magma vesiculation and fragmentation. We compare these textural data with those from chemically similar, subaerially erupted pyroclasts from nearby Raoul volcano as well as submarine-erupted ‘Tangaroan’ fragments derived by non-explosive, buoyant detachment of foaming magma from Macauley volcano, also along the Kermadec arc. Deep submarine-erupted pumices are macroscopically similar (colour, density, texture) to subaerial or shallow submarine-erupted pumices, but show contrasting microscopic bubble textures. Deep submarine-erupted pyroclasts have fewer small (<10 μm diameter) bubbles and narrower bubble size distributions (BSDs) when compared to subaerially erupted pyroclasts from Raoul (35-55 μm vs. 20-70 μm range in volume based median bubble size, respectively). Bubble number density (BND) values are consistently lower than subaerial-erupted pyroclasts and do not display the same trends of decreasing BND with increasing vesicularity. We interpret these textural differences to result from deep submarine eruptions entering the water column at higher pressures than subaerial eruptions entering the atmosphere (~10 MPa vs. 0.1 MPa for a vent at 1000 mbsl). The presence of an overlying water column acts to suppress rapid acceleration of magma, as occurs in the upper conduit of subaerial eruptions, therefore suppressing coalescence, permeability development and gas loss, amounting to closed-system degassing conditions. The higher confining pressure environment of deep submarine settings hinders extensive post-fragmentation clast expansion, coalescence of bubbles, and thinning of bubble walls, causing clasts to have similar BND values regardless of their vesicularity. Although deep submarine-erupted pyroclasts are closely similar to their subaerial counterparts on the basis of bulk vesicularities and macroscopic appearance, they differ markedly in their microscopic textures, allowing them to be fingerprinted in modern and ancient pumiceous marine sediments

Dynamic screening in solar and stellar nuclear reactions

In the hot, dense plasma of solar and stellar interiors, the Coulomb interaction is screened by the surrounding plasma. Although the standard Salpeter approximation for static screening is widely accepted and used in stellar modeling, the question of dynamic screening has been revisited. In particular, Shaviv and Shaviv apply the techniques of molecular dynamics to the conditions in the solar core in order to numerically determine the dynamic screening effect. By directly calculating the motion of ions and electrons due to Coulomb interactions, they compute the effect of screening without the mean-field assumption inherent in the Salpeter approximation. Here we reproduce their numerical analysis of the screening energy in the plasma of the solar core and conclude that the effects of dynamic screening are relevant and should be included in the treatment of the plasma, especially in the computation of stellar nuclear reaction rates.Comment: Astrophysics and Space Science, Special Issue Solar & Stellar Modelling Corrected sign error. Now consistent with final published versio

Unravelling the temporal association between lameness and body condition score in dairy cattle using a multistate modelling approach

Recent studies have reported associations between lameness and body condition score (BCS) in dairy cattle, however the impact of change in the dynamics of BCS on both lameness occurrence and recovery is currently unknown. The aim of this study was to investigate in a longitudinal study the effect of change in BCS on the transitions from the non-lame to lame, and lame to non-lame states. A total of 731 cows with 6889 observations from 4 UK herds were included in the study. Mobility score (MS) and body condition score (BCS) were recorded every 13-15 days from July 2010 until December 2011. A multilevel multistate discrete time event history model was built to investigate the transition of lameness over time. There were 1042 non-lame episodes and 593 lame episodes of which approximately 50% (519/1042) of the non-lame episodes transitioned to the lame state and 81% (483/593) of the lame episodes ended with a transition to the non-lame state. Cows with a lower BCS at calving (BCS Group 1 (1.00-1.75) and Group 2 (2.00-2.25)) had a higher probability of transition from non-lame to lame and a lower probability of transition from lame to non-lame compared to cows with BCS 2.50-2.75 i.e. they were more likely to become lame and if lame, they were less likely to recover. Similarly, cows who suffered a greater decrease in BCS (compared to their BCS at calving) had a higher probability of becoming lame and a lower probability of recovering in the next 15 days. An increase in BCS from calving was associated with the converse effect i.e. a lower probability of cows moving from the non-lame to the lame state and higher probability of transition from lame to non-lame. Days of lactation, months of calving and parity was associated with both lame and non-lame transitions and there was evidence of heterogeneity among cows in lameness occurrence and recovery. This study suggests loss of BCS and increase of BCS could influence the risk of becoming lame and the chance of recovery from lameness. Regular monitoring and maintenance of BCS on farms could be a key tool for reducing lameness. Further work is urgently needed in this area to allow a better understanding of the underlying mechanisms behind these relationships