Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow v.s. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque $G=T/\nu^2L$, where $L$ is the cylinder length, scales with Reynolds number $R$ and gap width $\eta$, $G=1.46 \eta^{3/2} (1-\eta)^{-7/4}R^{3/2}$. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: $$G=0.50\frac{\eta^{2}}{(1-\eta)^{3/2}}\frac{R^{2}}{\ln[\eta^2(1-\eta)R^ 2/10^4]^{3/2}}.$$ These predictions are found to be in excellent agreement with available experimental data. Predictions for scaling of velocity fluctuations are also provided.Comment: revTex, 6 Figure

Sulfur chemistry: 1D modeling in massive dense cores

The main sulfur-bearing molecules OCS, H2S, SO, SO2, and CS have been observed in four high mass dense cores (W43-MM1, IRAS 18264, IRAS 05358, and IRAS 18162). Our goal is to put some constraints on the relative evolutionary stage of these sources by comparing these observations with time-dependent chemical modeling. We used the chemical model Nahoon, which computes the gas-phase chemistry and gas-grain interactions of depletion and evaporation. Mixing of the different chemical compositions shells in a 1D structure through protostellar envelope has been included since observed lines suggest nonthermal supersonic broadening. Observed radial profiles of the temperature and density are used to compute the chemistry as a function of time. With our model, we underproduce CS by several orders of magnitude compared to the other S-bearing molecules, which seems to contradict observations, although some uncertainties in the CS abundance observed at high temperature remain. The OCS/SO2, SO/SO2, and H2S/SO2 abundance ratios could in theory be used to trace the age of these massive protostars since they show a strong dependence with time, but the sources are too close in age compared to the accuracy of chemical models and observations. Our comparison between observations and modeling may, however, indicate that W43-MM1 could be chemically younger than the three other sources. Turbulent diffusivity through the protostellar envelopes has to be less efficient than 2e14 cm2s-1. Otherwise, it would have smoothed out the abundance profiles, and this would have been observed. The sulfur chemistry depends strongly on the 1D physical conditions. In our case, no conclusion can be given on the relative age of IRAS 18264, IRAS 18162 and IRAS 05358 except that they are very close. W43-MM1 seems younger than the other sources.Comment: Accepted for publication to A&

A new equation for the mid-plane potential of power law disks

We show that the gravitational potential in the plane of an axisymmetrical flat disk where the surface density varies as a power of the radius obeys an inhomogeneous first-order Ordinary Differential Equation (ODE) solvable by standard techniques. The potential being exactly known at the origin for any power index (and at infinity as well), the search for solutions consists of a Two-point Boundary Value Problem (TBVP) with Dirichlet conditions. The computating time is then linear with the number of grid points, instead of quadratic from direct summation methods. Complex mass distributions which can be decomposed into a mixture of power law surface density profiles are easily accessible through the superposition principle. This ODE definitively takes the place of the untractable bidimensional Poisson equation for planar calculations. It opens new horizons to investigate various aspects related to self-gravity in astrophysical disks (force calculations, stability analysis, etc.).Comment: 5 pages, 1 figure, accepted for publication in A&

The effect of rotation and tidal heating on the thermal lightcurves of Super Mercuries

Short period (<50 days) low-mass (<10Mearth) exoplanets are abundant and the few of them whose radius and mass have been measured already reveal a diversity in composition. Some of these exoplanets are found on eccentric orbits and are subjected to strong tides affecting their rotation and resulting in significant tidal heating. Within this population, some planets are likely to be depleted in volatiles and have no atmosphere. We model the thermal emission of these "Super Mercuries" to study the signatures of rotation and tidal dissipation on their infrared light curve. We compute the time-dependent temperature map at the surface and in the subsurface of the planet and the resulting disk-integrated emission spectrum received by a distant observer for any observation geometry. We calculate the illumination of the planetary surface for any Keplerian orbit and rotation. We include the internal tidal heat flow, vertical heat diffusion in the subsurface and generate synthetic light curves. We show that the different rotation periods predicted by tidal models (spin-orbit resonances, pseudo-synchronization) produce different photometric signatures, which are observable provided that the thermal inertia of the surface is high, like that of solid or melted rocks (but not regolith). Tidal dissipation can also directly affect the light curves and make the inference of the rotation more difficult or easier depending on the existence of hot spots on the surface. Infrared light curve measurement with the James Webb Space Telescope and EChO can be used to infer exoplanets' rotation periods and dissipation rates and thus to test tidal models. This data will also constrain the nature of the (sub)surface by constraining the thermal inertia.Comment: 15 pages, 13 figures, accepted for publication in Astronomy & Astrophysic

Self-gravity at the scale of the polar cell

We present the exact calculus of the gravitational potential and acceleration along the symmetry axis of a plane, homogeneous, polar cell as a function of mean radius a, radial extension e, and opening angle f. Accurate approximations are derived in the limit of high numerical resolution at the geometrical mean of the inner and outer radii (a key-position in current FFT-based Poisson solvers). Our results are the full extension of the approximate formula given in the textbook of Binney & Tremaine to all resolutions. We also clarify definitely the question about the existence (or not) of self-forces in polar cells. We find that there is always a self-force at radius except if the shape factor a.f/e reaches ~ 3.531, asymptotically. Such cells are therefore well suited to build a polar mesh for high resolution simulations of self-gravitating media in two dimensions. A by-product of this study is a newly discovered indefinite integral involving complete elliptic integral of the first kind over modulus.Comment: 4 pages, 4 figures, A&A accepte

CID: Chemistry In Disks VII. First detection of HC3N in protoplanetary disks

Molecular line emission from protoplanetary disks is a powerful tool to constrain their physical and chemical structure. Nevertheless, only a few molecules have been detected in disks so far. We take advantage of the enhanced capabilities of the IRAM 30m telescope by using the new broad band correlator (FTS) to search for so far undetected molecules in the protoplanetary disks surrounding the TTauri stars DM Tau, GO Tau, LkCa 15 and the Herbig Ae star MWC 480. We report the first detection of HC3N at 5 sigma in the GO Tau and MWC 480 disks with the IRAM 30-m, and in the LkCa 15 disk (5 sigma), using the IRAM array, with derived column densities of the order of 10^{12}cm^{-2}. We also obtain stringent upper limits on CCS (N < 1.5 x 10^{12} cm^{-3}). We discuss the observational results by comparing them to column densities derived from existing chemical disk models (computed using the chemical code Nautilus) and based on previous nitrogen and sulfur-bearing molecule observations. The observed column densities of HC3N are typically two orders of magnitude lower than the existing predictions and appear to be lower in the presence of strong UV flux, suggesting that the molecular chemistry is sensitive to the UV penetration through the disk. The CCS upper limits reinforce our model with low elemental abundance of sulfur derived from other sulfur-bearing molecules (CS, H2S and SO).Comment: 8 pages, 4 figures, 3 tables, Accepted for publication in Ap

On the pressure of collisionless particle fluids. The case of solids settling in disks

Aims. Collections of dust, grains, and planetesimals are often treated as a pressureless fluid. We study the validity of neglecting the pressure of such a fluid by computing it exactly for the case of particles settling in a disk. Methods. We solve a modified collisionless Boltzmann equation for the particles and compute the corresponding moments of the phase space distribution: density, momentum, and pressure. Results. We find that whenever the Stokes number, defined as the ratio of the gas drag timescale to the orbital timescale, is more than 1/2, the particle fluid cannot be considered as pressureless. While we show it only in the simple case of particles settling in a laminar disk, this property is likely to remain true for most flows, including turbulent flows.Comment: Accepted for publication as a research note in Astronomy and Astrophysics. Language edite

The impact of atmospheric circulation on the chemistry of the hot Jupiter HD 209458b

This is the author accepted manuscript. The final version is available from EDP Sciences via the DOI in this record.We investigate the effects of atmospheric circulation on the chemistry of the hot Jupiter HD 209458b. We use a simplified dynamical model and a robust chemical network, as opposed to previous studies which have used a three dimensional circulation model coupled to a simple chemical kinetics scheme. The temperature structure and distribution of the main atmospheric constituents are calculated in the limit of an atmosphere that rotates as a solid body with an equatorial rotation rate of 1 km/s. Such motion mimics a uniform zonal wind which resembles the equatorial superrotation structure found by three dimensional circulation models. The uneven heating of this tidally locked planet causes, even in the presence of such a strong zonal wind, large temperature contrasts between the dayside and nightside, of up to 800 K. This would result in important longitudinal variations of some molecular abundances if the atmosphere were at chemical equilibrium. The zonal wind, however, acts as a powerful disequilibrium process. We identify the existence of a pressure level of transition between two regimes, which may be located between 100 and 0.1 mbar depending on the molecule. Below this transition layer, chemical equilibrium holds, while above it, the zonal wind tends to homogenize the chemical composition of the atmosphere, bringing molecular abundances in the limb and nightside regions close to chemical equilibrium values characteristic of the dayside, i.e. producing an horizontal quenching effect in the abundances. Reasoning based on timescales arguments indicates that horizontal and vertical mixing are likely to compete in HD 209458b's atmosphere, producing a complex distribution where molecular abundances are quenched horizontally to dayside values and vertically to chemical equilibrium values characteristic of deep layers.M.A., O.V., F.S., and E.H. acknowledge support from the European Research Council (ERC Grant 209622: E3ARTHs). Computer time for this study was provided by the computing facilities MCIA (Mésocentre de Calcul Intensif Aquitain) of the Université de Bordeaux and of the Université de Pau et des Pays de l’Adour. We thank the anonymous referee for a constructive report that helped to improve this manuscript

The Newtonian potential of thin disks

The one-dimensional, ordinary differential equation (ODE) by Hur\'e & Hersant (2007) that satisfies the midplane gravitational potential of truncated, flat power-law disks is extended to the whole physical space. It is shown that thickness effects (i.e. non-flatness) can be easily accounted for by implementing an appropriate "softening length" $\lambda$. The solution of this "softened ODE" has the following properties: i) it is regular at the edges (finite radial accelerations), ii) it possesses the correct long-range properties, iii) it matches the Newtonian potential of a geometrically thin disk very well, and iv) it tends continuously to the flat disk solution in the limit $\lambda \rightarrow 0$. As illustrated by many examples, the ODE, subject to exact Dirichlet conditions, can be solved numerically with efficiency for any given colatitude at second-order from center to infinity using radial mapping. This approach is therefore particularly well-suited to generating grids of gravitational forces in order to study particles moving under the field of a gravitating disk as found in various contexts (active nuclei, stellar systems, young stellar objects). Extension to non-power-law surface density profiles is straightforward through superposition. Grids can be produced upon request.Comment: Accepted for publication in A&