Higher-order in time “quasi-unconditionally stable” ADI solvers for the compressible Navier–Stokes equations in 2D and 3D curvilinear domains

This paper introduces alternating-direction implicit (ADI) solvers of higher order of time-accuracy (orders two to six) for the compressible Navier–Stokes equations in two- and three-dimensional curvilinear domains. The higher-order accuracy in time results from 1) An application of the backward differentiation formulae time-stepping algorithm (BDF) in conjunction with 2) A BDF-like extrapolation technique for certain components of the nonlinear terms (which makes use of nonlinear solves unnecessary), as well as 3) A novel application of the Douglas–Gunn splitting (which greatly facilitates handling of boundary conditions while preserving higher-order accuracy in time). As suggested by our theoretical analysis of the algorithms for a variety of special cases, an extensive set of numerical experiments clearly indicate that all of the BDF-based ADI algorithms proposed in this paper are “quasi-unconditionally stable” in the following sense: each algorithm is stable for all couples (h,Δt)of spatial and temporal mesh sizes in a problem-dependent rectangular neighborhood of the form (0,M_h)×(0,M_t). In other words, for each fixed value of Δt below a certain threshold, the Navier–Stokes solvers presented in this paper are stable for arbitrarily small spatial mesh-sizes. The second-order formulation has further been rigorously shown to be unconditionally stable for linear hyperbolic and parabolic equations in two-dimensional space. Although implicit ADI solvers for the Navier–Stokes equations with nominal second-order of temporal accuracy have been proposed in the past, the algorithms presented in this paper are the first ADI-based Navier–Stokes solvers for which second-order or better accuracy has been verified in practice under non-trivial (non-periodic) boundary conditions

Signs of strong Na and K absorption in the transmission spectrum of WASP-103b

Context: Transmission spectroscopy has become a prominent tool for characterizing the atmospheric properties on close-in transiting planets. Recent observations have revealed a remarkable diversity in exoplanet spectra, which show absorption signatures of Na, K and $\mathrm{H_2O}$, in some cases partially or fully attenuated by atmospheric aerosols. Aerosols (clouds and hazes) themselves have been detected in the transmission spectra of several planets thanks to wavelength-dependent slopes caused by the particles' scattering properties. Aims: We present an optical 550 - 960 nm transmission spectrum of the extremely irradiated hot Jupiter WASP-103b, one of the hottest (2500 K) and most massive (1.5 $M_J$) planets yet to be studied with this technique. WASP-103b orbits its star at a separation of less than 1.2 times the Roche limit and is predicted to be strongly tidally distorted. Methods: We have used Gemini/GMOS to obtain multi-object spectroscopy hroughout three transits of WASP-103b. We used relative spectrophotometry and bin sizes between 20 and 2 nm to infer the planet's transmission spectrum. Results: We find that WASP-103b shows increased absorption in the cores of the alkali (Na, K) line features. We do not confirm the presence of any strong scattering slope as previously suggested, pointing towards a clear atmosphere for the highly irradiated, massive exoplanet WASP-103b. We constrain the upper boundary of any potential cloud deck to reside at pressure levels above 0.01 bar. This finding is in line with previous studies on cloud occurrence on exoplanets which find that clouds dominate the transmission spectra of cool, low surface gravity planets while hot, high surface gravity planets are either cloud-free, or possess clouds located below the altitudes probed by transmission spectra.Comment: Accepted for publication in A&

Young planets under extreme UV irradiation. I. Upper atmosphere modelling of the young exoplanet K2-33b

The K2-33 planetary system hosts one transiting ~5 R_E planet orbiting the young M-type host star. The planet's mass is still unknown, with an estimated upper limit of 5.4 M_J. The extreme youth of the system (<20 Myr) gives the unprecedented opportunity to study the earliest phases of planetary evolution, at a stage when the planet is exposed to an extremely high level of high-energy radiation emitted by the host star. We perform a series of 1D hydrodynamic simulations of the planet's upper atmosphere considering a range of possible planetary masses, from 2 to 40 M_E, and equilibrium temperatures, from 850 to 1300 K, to account for internal heating as a result of contraction. We obtain temperature profiles mostly controlled by the planet's mass, while the equilibrium temperature has a secondary effect. For planetary masses below 7-10 M_E, the atmosphere is subject to extremely high escape rates, driven by the planet's weak gravity and high thermal energy, which increase with decreasing mass and/or increasing temperature. For higher masses, the escape is instead driven by the absorption of the high-energy stellar radiation. A rough comparison of the timescales for complete atmospheric escape and age of the system indicates that the planet is more massive than 10 M_E.Comment: 11 pages, 7 figure

A grid of upper atmosphere models for 1--40 MEARTH planets: application to CoRoT-7 b and HD219134 b,c

There is growing observational and theoretical evidence suggesting that atmospheric escape is a key driver of planetary evolution. Commonly, planetary evolution models employ simple analytic formulae (e.g., energy limited escape) that are often inaccurate, and more detailed physical models of atmospheric loss usually only give snapshots of an atmosphere's structure and are difficult to use for evolutionary studies. To overcome this problem, we upgrade and employ an already existing upper atmosphere hydrodynamic code to produce a large grid of about 7000 models covering planets with masses 1 - 39 Earth mass with hydrogen-dominated atmospheres and orbiting late-type stars. The modeled planets have equilibrium temperatures ranging between 300 and 2000 K. For each considered stellar mass, we account for three different values of the high-energy stellar flux (i.e., low, moderate, and high activity). For each computed model, we derive the atmospheric temperature, number density, bulk velocity, X-ray and EUV (XUV) volume heating rates, and abundance of the considered species as a function of distance from the planetary center. From these quantities, we estimate the positions of the maximum dissociation and ionisation, the mass-loss rate, and the effective radius of the XUV absorption. We show that our results are in good agreement with previously published studies employing similar codes. We further present an interpolation routine capable to extract the modelling output parameters for any planet lying within the grid boundaries. We use the grid to identify the connection between the system parameters and the resulting atmospheric properties. We finally apply the grid and the interpolation routine to estimate atmospheric evolutionary tracks for the close-in, high-density planets CoRoT-7 b and HD219134 b,c...Comment: 21 pages, 4 Tables, 15 Figure

Higher-order implicit-explicit multi-domain compressible Navier-Stokes solvers

This paper presents a new class of solvers for the subsonic compressible Navier-Stokes equations in general two- and three-dimensional multi-domains. Building up on the recent single-domain ADI-based high-order Navier-Stokes solvers (Bruno and Cubillos, Journal of Computational Physics 307 (2016) 476-495) this article presents multi-domain implicit-explicit methods of high-order of temporal accuracy. The proposed methodology incorporates: 1) A novel linear-cost implicit solver based on use of high-order backward differentiation formulae (BDF) and an alternating direction implicit approach (ADI); 2) A fast explicit solver; 3) Nearly dispersionless spectral spatial discretizations; and 4) A domain decomposition strategy that negotiates the interactions between the implicit and explicit domains. In particular, the implicit methodology is quasi-unconditionally stable (it does not suffer from CFL constraints for adequately resolved flows), and it can deliver orders of time accuracy between two and six in the presence of general boundary conditions. As demonstrated via a variety of numerical experiments in two and three dimensions, further, the proposed multi-domain parallel implicit-explicit implementations exhibit high-order convergence in space and time, robust stability properties, limited dispersion, and high parallel efficiency

PyTranSpot\texttt{PyTranSpot} - A tool for multiband light curve modeling of planetary transits and stellar spots

Several studies have shown that stellar activity features, such as occulted and non-occulted starspots, can affect the measurement of transit parameters biasing studies of transit timing variations and transmission spectra. We present $\texttt{PyTranSpot}$, which we designed to model multiband transit light curves showing starspot anomalies, inferring both transit and spot parameters. The code follows a pixellation approach to model the star with its corresponding limb darkening, spots, and transiting planet on a two dimensional Cartesian coordinate grid. We combine $\texttt{PyTranSpot}$ with an MCMC framework to study and derive exoplanet transmission spectra, which provides statistically robust values for the physical properties and uncertainties of a transiting star-planet system. We validate $\texttt{PyTranSpot}$'s performance by analyzing eleven synthetic light curves of four different star-planet systems and 20 transit light curves of the well-studied WASP-41b system. We also investigate the impact of starspots on transit parameters and derive wavelength dependent transit depth values for WASP-41b covering a range of 6200-9200 $\AA$, indicating a flat transmission spectrum.Comment: 17 pages, 22 figures; accepted for publication in Astronomy & Astrophysic

Neutron Irradiation Tests of Calibrated Cryogenic Sensors at Low Temperatures

This paper presents the advancement of a program being carried out in view of selecting the cryogenic temperature sensors to be used in the LHC accelerator. About 10,000 sensors will be installed around the 26.6 km LHC ring, and most of them will be exposed to high radiation doses during the accelerator lifetime. The following thermometric sensors : carbon resistors, thin films, and platinum resistors, have been exposed to high neutron fluences (>10$^15$ n/cm$^2$) at the ISN (Grenoble, France) Cryogenic Irradiation Test Facility. A cryostat is placed in a shielded irradiation vault where a 20 MeV deuteron beam hits a Be target, resulting in a well collimated and intense neutron beam. The cryostat, the on-line acquisition system, the temperature references and the main characteristics of the irradiation facility are described. The main interest of this set-up is its ability to monitor online the evolution of the sensors by comparing its readout with temperature references that are in principle insensitive to the neutron radiation (i.e. Argon gas bulbs when working at about 84 K, and below 4.5 K, either helium gas bulbs or the saturation pressure of the superfluid helium bath). The resistance shifts of the different sensors at liquid helium temperatures are presented

Neutron Irradiation Tests in Superfluid Helium of LHC Cryogenic Thermometers

For control and monitoring purposes, about 10,000 individually calibrated cryogenic temperature sensors will be installed along the 26.7 km LHC. In order to reduce maintenance constraints these sensor s should be as immune as possible to the high neutron fluence environment. For selecting the sensor to be used, a radiation hardness evaluation program at cryogenic conditions is being performed in an irradiation vault of the ISN SARA Cyclotron (Grenoble, France). The set-up is capable of simulating the whole life of a LHC thermometer: same total neutron dose (1015 n.cm-2), irradiation at low tempe rature (1.8 K) and thermal cycles. Bath temperature and sensor resistance are monitored on-line. This paper presents the latest results of this program