Ambipolar diffusion in smoothed particle magnetohydrodynamics

In partially ionised plasmas, the magnetic field can become decoupled from the neutral gas and diffuse through it in a process known as ambipolar diffusion. Although ambipolar diffusion has been implemented in several grid codes, we here provide an implementation in smoothed particle magnetohydrodynamics (SPMHD). We use the strong coupling approximation in which the ion density is negligible, allowing a single fluid approach. The equations are derived to conserve energy, and to provide a positive definite contribution to the entropy. We test the implementation in both a simple 1D SPMHD code and the fully 3D code PHANTOM. The wave damping test yields agreement within 0.03-2 per cent of the analytical result, depending on the value of the collisional coupling constant. The oblique C-shocks test yields results that typically agree within 4 per cent of the semi-analytical result. Our algorithm is therefore suitable for exploring the effect ambipolar diffusion has on physical processes, such as the formation of stars from molecular clouds.Comment: Accepted for publication by MNRA

The growth and hydrodynamic collapse of a protoplanet envelope

We have conducted three-dimensional self-gravitating radiation hydrodynamical models of gas accretion onto high mass cores (15-33 Earth masses) over hundreds of orbits. Of these models, one case accretes more than a third of a Jupiter mass of gas, before eventually undergoing a hydrodynamic collapse. This collapse causes the density near the core to increase by more than an order of magnitude, and the outer envelope to evolve into a circumplanetary disc. A small reduction in the mass within the Hill radius (R_H) accompanies this collapse as a shock propagates outwards. This collapse leads to a new hydrostatic equilibrium for the protoplanetary envelope, at which point 97 per cent of the mass contained within the Hill radius is within the inner 0.03 R_H which had previously contained less than 40 per cent. Following this collapse the protoplanet resumes accretion at its prior rate. The net flow of mass towards this dense protoplanet is predominantly from high latitudes, whilst at the outer edge of the circumplanetary disc there is net outflow of gas along the midplane. We also find a turnover of gas deep within the bound envelope that may be caused by the establishment of convection cells.Comment: 16 pages, 16 figures. Accepted for publication in MNRA

On the relative motions of dense cores and envelopes in star-forming molecular clouds

Hydrodynamical simulations of star formation indicate that the motions of protostars through their natal molecular clouds may be crucial in determining the properties of stars through competitive accretion and dynamical interactions. Walsh, Myers & Burton recently investigated whether such motions might be observable in the earliest stages of star formation by measuring the relative shifts of line-centre velocities of low- and high-density tracers of low-mass star-forming cores. They found very small (~0.1 km/s) relative motions. In this paper, we analyse the hydrodynamical simulation of Bate, Bonnell & Bromm and find that it also gives small relative velocities between high-density cores and low-density envelopes, despite the fact that competitive accretion and dynamical interactions occur between protostars in the simulation. Thus, the simulation is consistent with the observations in this respect. However, we also find some differences between the simulation and the observations. Overall, we find that the high-density gas has a higher velocity dispersion than that observed by Walsh et al. We explore this by examining the dependence of the gas velocity dispersion on density and its evolution with time during the simulation. We find that early in the simulation the gas velocity dispersion decreases monotonically with increasing density, while later in the simulation, when the dense cores have formed multiple objects, the velocity dispersion of the high-density gas increases. Thus, the simulation is in best agreement with the observations early on, before many objects have formed in each dense core.Comment: 8 pages, 7 figures. Accepted for publication in MNRA

Gas accretion by planetary cores

We present accretion rates obtained from three-dimensional self-gravitating radiation hydrodynamical models of giant planet growth. We investigate the dependence of accretion rates upon grain opacity and core/protoplanet mass. The accretion rates found for low mass cores are inline with the results of previous one-dimensional models that include radiative transfer.Comment: To be published in American Institute of Physics; Conference proceedings - Exoplanets and Disks: Their Formation and Diversity. 4 pages, 3 figure

On the accumulation of planetesimals near disc gaps created by protoplanets

We have performed three-dimensional two-fluid (gas-dust) hydrodynamical models of circumstellar discs with embedded protoplanets (3 - 333 M\oplu) and small solid bodies (radii 10cm to 10m). We find that high mass planets (\gtrsim Saturn mass) open sufficiently deep gaps in the gas disc such that the density maximum at the outer edge of the gap can very efficiently trap metre-sized solid bodies. This allows the accumulation of solids at the outer edge of the gap as solids from large radii spiral inwards to the trapping region. This process of accumulation occurs fastest for those bodies that spiral inwards most rapidly, typically metre-sized boulders, whilst smaller and larger objects will not migrate sufficiently rapidly in the discs lifetime to benefit from the process. Around a Jupiter mass planet we find that bound clumps of solid material, as large as several Earth masses, may form, potentially collapsing under self-gravity to form planets or planetesimals. These results are in agreement with Lyra et al. (2009), supporting their finding that the formation of a second generation of planetesimals or of terrestrial mass planets may be triggered by the presence of a high mass planet.Comment: 14 pages, 10 figures. Accepted for publication in MNRA

Planet migration: self-gravitating radiation hydrodynamical models of protoplanets with surfaces

We calculate radial migration rates of protoplanets in laminar minimum mass solar nebula discs using three-dimensional self-gravitating radiation hydrodynamical (RHD) models. The protoplanets are free to migrate, whereupon their migration rates are measured. For low mass protoplanets (10-50 M_\oplus) we find increases in the migration timescales of up to an order of magnitude between locally-isothermal and RHD models. In the high-mass regime the migration rates are changed very little. These results are arrived at by calculating migration rates in locally-isothermal models, before sequentially introducing self-gravity, and radiative transfer, allowing us to isolate the effects of the additional physics. We find that using a locally-isothermal equation of state, without self-gravity, we reproduce the migration rates obtained by previous analytic and numerical models. We explore the impact of different protoplanet models, and changes to their assumed radii, upon migration. The introduction of self-gravity gives a slight reduction of the migration rates, whilst the inertial mass problem, which has been proposed for high mass protoplanets with circumplanetary discs, is reproduced. Upon introducing radiative transfer to models of low mass protoplanets (\approx 10 M_\oplus), modelled as small radius accreting point masses, we find outward migration with a rate of approximately twice the analytic inward rate. However, when modelling such a protoplanet in a more realistic manner, with a surface which enables the formation of a deep envelope, this outward migration is not seen.Comment: 21 pages, 21 figure

Circumplanetary disc properties obtained from radiation hydrodynamical simulations of gas accretion by protoplanets

We investigate the properties of circumplanetary discs formed in three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by protoplanets. We determine disc sizes, scaleheights, and density and temperature profiles for different protoplanet masses, in solar nebulae of differing grain opacities. We find that the analytical prediction of circumplanetary disc radii in an evacuated gap (R_Hill/3) from Quillen & Trilling (1998) yields a good estimate for discs formed by high mass protoplanets. The radial density profiles of the circumplanetary discs may be described by power-laws between r^-2 and r^-3/2. We find no evidence for the ring-like density enhancements that have been found in some previous models of circumplanetary discs. Temperature profiles follow a ~r^-7/10 power-law regardless of protoplanet mass or nebula grain opacity. The discs invariably have large scaleheights (H/r > 0.2), making them thick in comparison with their encompassing circumstellar discs, and they show no flaring.Comment: 9 pages, 6 figures, accepted for publication in MNRA

Gas accretion onto planetary cores: three-dimensional self-gravitating radiation hydrodynamical calculations

We present results from three-dimensional, self-gravitating radiation hydrodynamical models of gas accretion by planetary cores. In some cases, the accretion flow is resolved down to the surface of the solid core -- the first time such simulations have been performed. We investigate the dependence of the gas accretion rate upon the planetary core mass, and the surface density and opacity of the encompassing protoplanetary disc. Accretion of planetesimals is neglected. We find that high-mass protoplanets are surrounded by thick circumplanetary discs during their gas accretion phase but, contrary to locally-isothermal calculations, discs do not form around accreting protoplanets with masses ~< 50M_Earth when radiation hydrodynamical simulations are performed, even if the grain opacity is reduced from interstellar values by a factor of 100. We find that the opacity of the gas plays a large role in determining the accretion rates for low-mass planetary cores. For example, reducing the opacities from interstellar values by a factor of 100 leads to roughly an order of magnitude increase in the accretion rates for 10-20M_Earth protoplanets. The dependence on opacity becomes less important in determining the accretion rate for more massive cores where gravity dominates the effects of thermal support and the protoplanet is essentially accreting at the runaway rate. Finally, for low-mass planetary cores (~< 20M_Earth), we obtain accretion rates that are in agreement with previous one-dimensional quasi-static models. This indicates that three-dimensional hydrodynamical effects may not significantly alter the gas accretion timescales that have been obtained from quasi-static models.Comment: 16 pages, 15 figures, accepted for publication in MNRAS. V2 includes small corrections to the radiation hydrodynamical accretion rates for a Jupiter mass core, including an updated figure 8; conclusions are unaffecte

Intrapopulation Variability Shaping Isotope Discrimination and Turnover: Experimental Evidence in Arctic Foxes

Tissue-specific stable isotope signatures can provide insights into the trophic ecology of consumers and their roles in food webs. Two parameters are central for making valid inferences based on stable isotopes, isotopic discrimination (difference in isotopic ratio between consumer and its diet) and turnover time (renewal process of molecules in a given tissue usually measured when half of the tissue composition has changed). We investigated simultaneously the effects of age, sex, and diet types on the variation of discrimination and half-life in nitrogen and carbon stable isotopes (δ15N and δ13C, respectively) in five tissues (blood cells, plasma, muscle, liver, nail, and hair) of a top predator, the arctic fox Vulpes lagopus. We fed 40 farmed foxes (equal numbers of adults and yearlings of both sexes) with diet capturing the range of resources used by their wild counterparts. We found that, for a single species, six tissues, and three diet types, the range of discrimination values can be almost as large as what is known at the scale of the whole mammalian or avian class. Discrimination varied depending on sex, age, tissue, and diet types, ranging from 0.3‰ to 5.3‰ (mean = 2.6‰) for δ15N and from 0.2‰ to 2.9‰ (mean = 0.9‰) for δ13C. We also found an impact of population structure on δ15N half-life in blood cells. Varying across individuals, δ15N half-life in plasma (6 to 10 days) was also shorter than for δ13C (14 to 22 days), though δ15N and δ13C half-lives are usually considered as equal. Overall, our multi-factorial experiment revealed that at least six levels of isotopic variations could co-occur in the same population. Our experimental analysis provides a framework for quantifying multiple sources of variation in isotopic discrimination and half-life that needs to be taken into account when designing and analysing ecological field studies