The minimum gap-opening planet mass in an irradiated circumstellar accretion disc

We consider the minimum mass planet, as a function of radius, that is capable of opening a gap in an α-accretion disc. We estimate that a half-Jupiter mass planet can open a gap in a disc with accretion rate     for viscosity parameter  α= 0.01  , and solar mass and luminosity. The minimum mass is approximately proportional to     . This estimate can be used to rule out the presence of massive planets in gapless accretion discs. We identify two radii at which an inwardly migrating planet may become able to open a gap and so slow its migration; the radius at which the heating from viscous dissipation is similar to that from stellar radiation in a flared disc, and the radius at which the disc becomes optically thin in a self-shadowed disc. In the inner portions of the disc, we find that the minimum planet mass required to open a gap is only weakly dependent on radius. If a migrating planet is unable to open a gap by the time it reaches either of the transition radii, then it is likely to be lost on to the star. If a gap-opening planet cuts off disc accretion allowing the formation of a central hole or clearing in the disc then we would estimate that the clearing radius would approximately be proportional to the stellar mass.     

Travelling wave convection in a rotating layer

Abstract

Small amplitude two-dimensional Boussinesq convection in a plane layer with stress-free boundaries rotating uniformly about the vertical is studied. A horizontally unbounded layer is modelled by periodic boundary conditions. When the centrifugal force is balanced by an appropriate pressure gradient the resulting equations are translation invariant, and overstable convection can take the form of travelling waves. In the Prandtl number regime 0.53 < [sgrave] < 0.68 such solutions are preferred over the more usual standing waves. For [sgrave] < 0.53, travelling waves are stable provided the Taylor number is sufficiently large.     

Excess heat capacity and entropy of mixing in the high-structural state (K,Ca)-feldspar binary

Low- and high-temperature heat capacities were measured for a series of synthetic high-structural state (K,Ca)-feldspars (Or–An) using both a relaxation and a differential scanning calorimeter. The data were collected at temperatures between 5 and 800 K on polycrystalline samples that had been synthesised and characterised in a previous study. Below T = 300 K, Or₉₀An₁₀, and Or₈₀An₂₀ showed excess heat capacities of mixing with maximum values of ~3 J mol⁻¹ K⁻¹. The other members of this binary (An > 20 mol%) had lower excess heat capacity values of up to ~1 J mol⁻¹ K⁻¹. Above T = 300 K, some compositions exhibited negative excess heat capacities of mixing (with maximum values of −2 J mol⁻¹ K⁻¹). The vibrational entropy at 298.15 K for Or₉₀An₁₀ and Or₈₀An₂₀ deviated strongly from the behaviour of a mechanical mixture, with excess entropy values of ~3.5 J mol⁻¹ K⁻¹. More An-rich members had only small excess vibrational entropies at T = 298.15 K. The difference in behaviour between members with An > 20 mol% and those with An ≤ 20 mol% is probably a consequence of the structural state of the (K,Ca)-feldspars, i.e., (K,Ca)-feldspars with An ≤ 20 mol% have monoclinic symmetry, whereas those with An > 20 mol% are triclinic. At T = 800 K, the vibrational entropy values were found to scatter around the values expected for a mechanical mixture and, thus, correspond to a quasi-ideal behaviour. The solvus for the (K,Ca)-feldspar binary was calculated based on the entropy data from this study in combination with enthalpy and volume of mixing data from a previous study.     

Excess heat capacity and entropy of mixing along the chlorapatite–fluorapatite binary join

The heat capacity at constant pressure, C _p, of chlorapatite [Ca₅(PO₄)₃Cl – ClAp], and fluorapatite [Ca₅(PO₄)₃F – FAp], as well as of 12 compositions along the chlorapatite–fluorapatite join have been measured using relaxation calorimetry [heat capacity option of the physical properties measurement system (PPMS)] and differential scanning calorimetry (DSC) in the temperature range 5–764 K. The chlor-fluorapatites were synthesized at 1,375–1,220°C from Ca₃(PO₄)₂ using the CaF₂–CaCl₂ flux method. Most of the chlor-fluorapatite compositions could be measured directly as single crystals using the PPMS such that they were attached to the sample platform of the calorimeter by a crystal face. However, the crystals were too small for the crystal face to be polished. In such cases, where the sample coupling was not optimal, an empirical procedure was developed to smoothly connect the PPMS to the DSC heat capacities around ambient T. The heat capacity of the end-members above 298 K can be represented by the polynomials: C _p^ClAp = 613.21 − 2,313.90T ^−0.5 − 1.87964 × 10⁷ T ⁻² + 2.79925 × 10⁹ T ⁻³ and C _p^FAp = 681.24 − 4,621.73 × T ^−0.5 − 6.38134 × 10⁶ T ⁻² + 7.38088 × 10⁸ T ⁻³ (units, J mol⁻¹ K⁻¹). Their standard third-law entropy, derived from the low-temperature heat capacity measurements, is S° = 400.6 ± 1.6 J mol⁻¹ K⁻¹ for chlorapatite and S° = 383.2 ± 1.5 J mol⁻¹ K⁻¹ for fluorapatite. Positive excess heat capacities of mixing, ΔC _p^ex, occur in the chlorapatite–fluorapatite solid solution around 80 K (and to a lesser degree at 200 K) and are asymmetrically distributed over the join reaching a maximum of 1.3 ± 0.3 J mol⁻¹ K⁻¹ for F-rich compositions. They are significant at these conditions exceeding the 2σ-uncertainty of the data. The excess entropy of mixing, ΔS ^ex, at 298 K reaches positive values of 3–4 J mol⁻¹ K⁻¹ in the F-rich portion of the binary, is, however, not significantly different from zero across the join within its 2σ-uncertainty.     

A ternary feldspar-mixing model based on calorimetric data: development and application

A mixing model for high structural state ternary feldspars in the NaAlSi₃O₈–KAlSi₃O₈–CaAl₂Si₂O₈ system is presented based exclusively on calorimetric and volumetric measurements. Comparisons with existing mixing models, which are based on phase-equilibrium experiments, reveal distinct differences. The incorporation of K into Ca-rich plagioclase and of Ca into K-rich alkali feldspar is more strongly limited by our calorimetry-based model, whereas the stability field of Na-rich feldspars is broadened. Natural feldspar assemblages from well-studied magmatic and high-grade metamorphic rocks (i.e. a teschenite sill in Scotland, the Klokken syenogabbro in Greenland, and a granulite-facies metapelite in Sri Lanka) were used to test the mixing models. It was found that the new model largely eliminates discrepancies between observed and predicted feldspar compositions that were present in earlier attempts. The reasons for the problems associated with phase-equilibrium based mixing models are discussed.     

Identifying Nonstationarity in Turbulence Series

Because of rapid forcing by varying cloud and sky conditions, turbulence time series collected in the atmospheric surface layer over land may often be nonstationary. The meteorological community, however, has no consensus definition of what nonstationarity is and, thus, no consensus method for how to identify it. This study, therefore, adopts definitions for first-order and second-order stationarity taken from the time series analysis literature and implements new analysis techniques and probabilistic tests to quantify first-order and second-order nonstationarity. First-order nonstationarity manifests as a change in the series mean; second-order nonstationarity, as a change in the variance. The analysis identifies nonstationarity in surface-level turbulent temperature and water vapour series collected during two sample days with solar forcing influenced by cirrus and cirrostratus clouds, but that nonstationarity is not as severe as expected despite the rapid thermal forcing by these clouds. On the other hand, even with negligible cloud forcing, both sample days exhibited severe nonstationarity at night.     

On wavelet analysis of nonstationary turbulence

Wavelets are new tools for turbulence analysis that are yielding important insights into boundary-layer processes. Wavelet analysis, however, has some as yet undiscussed limitations: failure to recognize these can lead to misinterpretation of wavelet analysis results. Here we discuss some limitations of wavelet analysis when applied to nonstationary turbulence. Our main point is that the analysis wavelet must be carefully matched to the phenomenon of interest, because wavelet coefficients obscure significant information in the signal being analyzed. For example, a wavelet that is a second-difference operator can provide no information on the linear trend in a turbulence signal. Wavelet analysis also yields no meaningful information about nonlinear behavior in a signal — contrary to claims in the literature — because, at any instant, a wavelet is a single-scale operator, while nonlinearity involves instantaneous interactions among many scales.     

Proton energy deposition in molecular and atomic oxygen and applications to the polar cap

We extend the microscopic approach developed for proton energy deposition in N₂ to the general case of proton bombardment of a polar atmosphere composed of N₂, O₂ and O. We calculate the volume emission rates of various N₂⁺, O₂, O₂⁺ and OI emissions that would be encountered in a typical PCA event. Our results demonstrate that the ratios of $\text{I}\text{(5577)}\text{I}\text{(3914)}$ and $\text{I}\text{(6300)}\text{I}\text{(3914)}$ are strongly depe spectra considered.     

A simple boom assembly for the shipboard deployment of air-sea interaction instruments

We have developed a simple boom for use in measuring meteorological variables from a ship. The main structural member of the boom, a triangular communications tower with rollers attached along its bottom side, is deployed horizontally from a long, flat deck, such as a helicopter deck, and will support a 100-kg payload at its outboard end. The boom is easy to deploy, requires minimal ship modifications, and provides ready access to the instruments mounted on it. And because it is designed for use with the ship crosswind, oceanographic work can go on at the same time as the air-sea interaction measurements.We describe our use of the boom on the Mikhail Somov during a cruise into the Antarctic sea ice and present some representative measurements made with instruments mounted on it. Theory, experiment, and our data all imply that instruments deployed windward from a rear helicopter deck can reach air undisturbed by the ship. Such an instrument site has clear advantages over the more customary mast, bow, or buoy locations.