arXiv subjects

F. Hersant

Publications and source records attributed to F. Hersant.

34 records · Page 2Linked to original sources

arXiv2011

Thermal phase curves of non-transiting terrestrial exoplanets 2. Characterizing airless planets

Context. The photometric signal we receive from a star hosting a planet is modulated by the variation of the planet signal with its orbital phase. Such phase variations are observed for transiting hot Jupiters with current instrumentation, and have also been measured for one transiting terrestrial planet (Kepler 10 b) and one non-transiting gas giant (Ups A b). Future telescopes (JWST and EChO) will have the capability to measure thermal phase curves of exoplanets including hot rocky planets in transiting and non-transiting configurations, and at different wavelengths. Short-period planets with a mass below 10 R_EARTH are indeed frequent and nearby targets (within 10 pc) are already known and more are to be found. Aims. To test the possibility to use multi-wavelengths infrared phase curves to constrain the radius, the albedo and the orbital inclination of a non-transiting planet with no atmosphere and on a 1:1 spin orbit resonance. Methods. We model the thermal emission of a synchronous rocky planet with no atmosphere and its apparent variation with the orbital phase for a given orbital inclination. We assume that the planet is detected by radial velocity so its orbital period and minimum mass are known. We simulate observed noisy phase curves and then apply a procedure to retrieve the radius and albedo of the planet and the inclination of the orbit. Results. Airless planets can be distinguished from planets having a dense atmosphere and their radius, albedo and inclination (and therefore true mass) can be retrieved from multiband observations with MIRI-JWST and EChO in the 5-15 μm range. [...] As inclination above 60° represents half of randomly oriented orbits, the growing population of short-period terrestrial-sized planets detected by radial velocity surveys and transits should offer several nearby promising targets for this method [...]. See full abstract in the paper.

astro-ph.EP↗

arXiv2011

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 $G=T/ν^2L$, where $L$ is the cylinder length, scales with Reynolds number $R$ and gap width $η$, $G=1.46 η^{3/2} (1-η)^{-7/4}R^{3/2}$. 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: $$ G=0.50\frac{η^{2}}{(1-η)^{3/2}}\frac{R^{2}}{\ln[η^2(1-η)R^ 2/10^4]^{3/2}}.$$ These predictions are found to be in excellent agreement with available experimental data. Predictions for scaling of velocity fluctuations are also provided.

physics.flu-dyn↗

arXiv2011

Oxygen depletion in dense molecular clouds: a clue to a low O2 abundance?

Context: Dark cloud chemical models usually predict large amounts of O2, often above observational limits. Aims: We investigate the reason for this discrepancy from a theoretical point of view, inspired by the studies of Jenkins and Whittet on oxygen depletion. Methods: We use the gas-grain code Nautilus with an up-to-date gas-phase network to study the sensitivity of the molecular oxygen abundance to the oxygen elemental abundance. We use the rate coefficient for the reaction O + OH at 10 K recommended by the KIDA (KInetic Database for Astrochemistry) experts. Results: The updates of rate coefficients and branching ratios of the reactions of our gas-phase chemical network, especially N + CN and H3+ + O, have changed the model sensitivity to the oxygen elemental abundance. In addition, the gas-phase abundances calculated with our gas-grain model are less sensitive to the elemental C/O ratio than those computed with a pure gas-phase model. The grain surface chemistry plays the role of a buffer absorbing most of the extra carbon. Finally, to reproduce the low abundance of molecular oxygen observed in dark clouds at all times, we need an oxygen elemental abundance smaller than 1.6E-4. Conclusion: The chemistry of molecular oxygen in dense clouds is quite sensitive to model parameters that are not necessarily well constrained. That O2 abundance may be sensitive to nitrogen chemistry is an indication of the complexity of interstellar chemistry.

astro-ph.SR↗

arXiv2011

On the dynamics of resonant super-Earths in disks with turbulence driven by stochastic forcing

We investigate the evolution of a system of two super-Earths with masses < 4 Earth masses embedded in a turbulent protoplanetary disk. The aim is to examine whether or not resonant trapping can occur and be maintained in presence of turbulence and how this depends on the amplitude of the stochastic density fluctuations in the disk. We have performed 2D numerical simulations using a grid-based hydrodynamical code in which turbulence is modelled as stochastic forcing. We assume that the outermost planet is initially located just outside the position of the 3:2 mean motion resonance (MMR) with the inner one and we study the dependance of the resonance stability with the amplitude of the stochastic forcing. For systems of two equal-mass planets we find that in disk models with an effective viscous stress parameter α 10^{-3}, damping effects due to type I migration can counteract the effects of diffusion of the resonant angles, in such a way that the 3:2 MMR can possibly remain stable over the disk lifetime. For systems of super-Earths with mass ratio q=m_i/m_o < 1/2, where m_i (m_o) is the mass of the innermost (outermost) planet, the 3:2 MMR is broken in turbulent disks with effective viscous stresses 2x10^{-4}< α< 10^{-3} but the planets become locked in stronger p+1:p resonances, with p increasing as the value for α increases. For α> 2x10^{-3}, the evolution can eventually involve temporary capture in a 8:7 commensurability but no stable MMR is formed. Our results suggest that for values of the viscous stress parameter typical to those generated by MHD turbulence, MMRs between two super-Earths are likely to be disrupted by stochastic density fluctuations. For lower levels of turbulence however, as is the case in presence of a dead-zone, resonant trapping can be maintained in systems with moderate values of the planet mass ratio.

astro-ph.EP↗

arXiv2011

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.

astro-ph.GA↗

arXiv2010

Chemistry in Disks. IV. Benchmarking gas-grain chemical models with surface reactions

Abridged: We detail and benchmark two sophisticated chemical models developed by the Heidelberg and Bordeaux astrochemistry groups. The main goal of this study is to elaborate on a few well-described tests for state-of-the-art astrochemical codes covering a range of physical conditions and chemical processes, in particular those aimed at constraining current and future interferometric observations of protoplanetary disks. We consider three physical models: a cold molecular cloud core, a hot core, and an outer region of a T Tauri disk. Our chemical network (for both models) is based on the original gas-phase osu_03_2008 ratefile and includes gas-grain interactions and a set of surface reactions for the H-, O-, C-, S-, and N-bearing molecules. The benchmarking is performed with the increasing complexity of the considered processes: (1) the pure gas-phase chemistry, (2) the gas-phase chemistry with accretion and desorption, and (3) the full gas-grain model with surface reactions. Using atomic initial abundances with heavily depleted metals and hydrogen in its molecular form, the chemical evolution is modeled within 10^9 years. The time-dependent abundances calculated with the two chemical models are essentially the same for all considered physical cases and for all species, including the most complex polyatomic ions and organic molecules. This result however required a lot of efforts to make all necessary details consistent through the model runs, e.g. definition of the gas particle density, density of grain surface sites, the strength and shape of the UV radiation field, etc. The reference models and the benchmark setup, along with the two chemical codes and resulting time-dependent abundances are made publicly available in the Internet: http://www.mpia.de/homes/semenov/Chemistry_benchmark/home.html

astro-ph.GA↗

arXiv2010

Sensitivity analyses of dense cloud chemical models

Because of new telescopes that will dramatically improve our knowledge of the interstellar medium, chemical models will have to be used to simulate the chemistry of many regions with diverse properties. To make these models more robust, it is important to understand their sensitivity to a variety of parameters. In this article, we report a study of the sensitivity of a chemical model of a cold dense core, with homogeneous and time-independent physical conditions, to variations in the following parameters: initial chemical inventory, gas temperature and density, cosmic-ray ionization rate, chemical reaction rate coefficients, and elemental abundances. From the results of the parameter variations, we can quantify the sensitivity of the model to each parameter as a function of time. Our results can be used in principle with observations to constrain some parameters for different cold clouds. We also attempted to use the Monte Carlo approach with all parameters varied collectively. Within the parameter ranges studied, the most critical parameters turn out to be the reaction rate coefficients at times up to 4e5 yr and elemental abundances at later times. At typical times of best agreement with observation, models are sensitive to both of these parameters. The models are less sensitive to other parameters such as the gas density and temperature. The improvement of models will require that the uncertainties in rate coefficients of important reactions be reduced. As the chemistry becomes better understood and more robust, it should be possible to use model sensitivities concerning other parameters, such as the elemental abundances and the cosmic ray ionization rate, to yield detailed information on cloud properties and history. Nevertheless, at the current stage, we cannot determine the best values of all the parameters simultaneously based on purely observational constraints.

astro-ph.GA↗

arXiv2010

Chemistry in Disks. III. -- Photochemistry and X-ray driven chemistry probed by the ethynyl radical (CCH) in DM Tau, LkCa 15, and MWC 480

We studied several representative circumstellar disks surrounding the Herbig Ae star MWC 480 and the T Tauri stars LkCa 15 and DM Tau at (sub-)millimeter wavelengths in lines of CCH. Our aim is to characterize photochemistry in the heavily UV-irradiated MWC 480 disk and compare the results to the disks around cooler T Tauri stars. We detected and mapped CCH in these disks with the IRAM Plateau de Bure Interferome- ter in the C- and D-configurations in the (1-0) and (2-1) transitions. Using an iterative minimization technique, the CCH column densities and excitation conditions are con- strained. Very low excitation temperatures are derived for the T Tauri stars. These values are compared with the results of advanced chemical modeling, which is based on a steady-state flared disk structure with a vertical temperature gradient, and a gas- grain chemical network with surface reactions. Both model and observations suggest that CCH is a sensitive tracer of the X-ray and UV irradiation. The predicted radial dependency and source to source variations of CCH column densities qualitatively agree with the observed values, but the predicted column densities are too low by a factor of several. The chemical model fails to reproduce high concentrations of CCH in very cold disk midplane as derived from the observed low excitation condition for both the (1-0) and (2-1) transitions.

astro-ph.GA↗

arXiv2009

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.

astro-ph.IM↗

arXiv2009

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.

astro-ph.IM↗

arXiv2009

Cold CO in circumstellar disks: On the effects of photodesorption and vertical mixing

Aims. We attempt to understand the presence of gas phase CO below its freezing temperature in circumstellar disks. We study two promising mechanisms to explain this phenomenon: turbulent mixing and photodesorption. Methods. We compute the chemical evolution of circumstellar disks including grain surface reactions with and without turbulent mixing and CO photodesorption. Results. We show that photodesorption significantly enhances the gas phase CO abundance, by extracting CO from the grains when the visual extinction remains below about 5 magnitudes. However the resulting dependence of column density on radial distance is not consistent with observations so far. We propose that this inconsistency could be the result of grain growth. On the other hand, the influence of turbulent mixing is not found to be straightforward. The efficiency of turbulent mixing depends upon a variety of parameters, including the disk structure. For the set of parameters we chose, turbulent mixing is not found to have any significant influence on the CO column density.

astro-ph↗

arXiv2008

A new equation for the mid-plane potential of power law discs. II. Exact solutions and approximate formulae

The first-order ordinary differential equation (ODE) that describes the mid-plane gravitational potential in flat finite size discs in which the surface density is a power-law function of the radius R with exponent s (Huré & Hersant 2007) is solved exactly in terms of infinite series. The formal solution of the ODE is derived and then converted into a series representation by expanding the elliptic integral of the first kind over its modulus before analytical integration. Inside the disc, the gravitational potential consists of three terms: a power law of radius R with index 1+s, and two infinite series of the variables R and 1/R. The convergence of the series can be accelerated, enabling the construction of reliable approximations. At the lowest-order, the potential inside large astrophysical discs (s ~ -1.5 +/- 1) is described by a very simple formula whose accuracy (a few percent typically) is easily increased by considering successive orders through a recurrence. A basic algorithm is given. Applications concern all theoretical models and numerical simulations where the influence of disc gravity must be checked and/or reliably taken into account.

astro-ph↗

arXiv2007

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.).

astro-ph↗

arXiv2004

An hydrodynamic shear instability in stratified disks

We discuss the possibility that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances with characteristic scales much smaller than the vertical scale height. The instability is studied using three methods: one based on the energy integral, which allows the determination of a sufficient condition of stability, one using a WKB approach, which allows the determination of the necessary and sufficient condition for instability and a last one by numerical solution. This linear instability occurs in any inviscid stably stratified differential rotating fluid for rigid, stress-free or periodic boundary conditions, provided the angular velocity $Ω$ decreases outwards with radius $r$. At not too small stratification, its growth rate is a fraction of $Ω$. The influence of viscous dissipation and thermal diffusivity on the instability is studied numerically, with emphasis on the case when $d \ln Ω/ d \ln r =-3/2$ (Keplerian case). Strong stratification and large diffusivity are found to have a stabilizing effect. The corresponding critical stratification and Reynolds number for the onset of the instability in a typical disk are derived. We propose that the spontaneous generation of these linear modes is the source of turbulence in disks, especially in weakly ionized disks.

astro-ph↗

arXiv2004

Turbulence in circumstellar disks

We investigate the analogy between circumstellar disks and the Taylor-Couette flow. Using the Reynolds similarity principle, the analogy results in a number of parameter-free predictions about stability of the disks, and their turbulent transport properties, provided the disk structure is available. We discuss how the latter can be deduced from interferometric observations of circumstellar material. We use the resulting disk structure to compute the molecular transport coefficients, including the effect of ionization by the central object. The resulting control parameter indicates that the disk is well into the turbulent regime. The analogy is also used to compute the effective accretion rate, as a function of the disk characteristic parameters (orbiting velocity, temperature and density). These values are in very good agreement with experimental, parameter-free predictions derived from the analogy. The turbulent viscosity is also computed and found to correspond to an $α$-parameter $2\times 10^{-4}<α<2\times 10^{-2}$. Predictions regarding fluctuations are also checked: luminosity fluctuations in disks do obey the same universal distribution as energy fluctuations observed in a laboratory turbulent flow. Radial velocity dispersion in the outer part of the disk is predicted to be of the order of 0.1 km/s, in agreement with available observations. All these issues provide a proof of the turbulent character of the circumstellar disks, as well as a parameter-free theoretical estimate of effective accretion rates.

astro-ph↗

arXiv2001

A powerful local shear instability in stratified disks

In this paper, we show that astrophysical accretion disks are dynamically unstable to non-axisymmetric disturbances. This instability is present in any stably stratified anticyclonically sheared flow as soon as the angular velocity decreases outwards. In the large Froude number limit, the maximal growth rate is proportional to the angular rotation velocity, and is independent of the stratification. In the low Froude number limit, it decreases like the inverse of the Froude number, thereby vanishing for unstratified, centrigugally stable flows. The instability is not sensitive to disk boundaries. We discuss the possible significance of our result, and its implications on the turbulent state achieved by the disks. We conclude that this linear instability is one of the best candidates for the source of turbulence in geometrically thin disks, and that magnetic fields can be safely ignored when studying their turbulent state. The relevance of the instability for thick disks or nearly neutrally stratified disks remains to be explored.

astro-ph↗