3D Radiative-hydrodynamics Research Articles

The potential of 3D radiation-hydrodynamics models for white dwarf asteroseismology

White dwarfs with hydrogen-rich atmospheres (DA) are the most abundant of all degenerate objects. In recent years work has been dedicated to increase the accuracy of their model atmospheres. Most notably, convective motions are now treated with 3D radiation-hydrodynamics instead of the standard mixing-length theory. We present and describe selected 3D model atmospheres close and within the instability strip of the pulsating ZZ Ceti white dwarfs. Our 3D simulations depend only weakly on numerical parameters and compared to 1D models, they provide more realistic determinations of the depth of the convective zone. The 3D structures can then be adopted as input for asteroseismology.

MIGRATION OF GAS GIANT PLANETS IN GRAVITATIONALLY UNSTABLE DISKS

Characterization of migration in gravitationally unstable disks is necessary to understand the fate of protoplanets formed by disk instability. As part of a larger study, we are using a 3D radiative hydrodynamics code to investigate how an embedded gas giant planet interacts with a gas disk that undergoes gravitational instabilities (GIs). This Letter presents results from simulations with a Jupiter-mass planet placed in orbit at 25 AU within a 0.14 $M_{\odot}$ disk. The disk spans 5 to 40 AU around a 1 $M_{\odot}$ star and is initially marginally unstable. In one simulation, the planet is inserted prior to the eruption of GIs; in another, it is inserted only after the disk has settled into a quasi-steady GI-active state, where heating by GIs roughly balances radiative cooling. When the planet is present from the beginning, its own wake stimulates growth of a particular global mode with which it strongly interacts, and the planet plunges inward six AU in about 10$^3$ years. In both cases with embedded planets, there are times when the planet's radial motion is slow and varies in direction. At other times, when the planet appears to be interacting with strong spiral modes, migration both inward and outward can be relatively rapid, covering several AUs over hundreds of years. Migration in both cases appears to stall near the inner Lindblad resonance of a dominant low-order mode. Planet orbit eccentricities fluctuate rapidly between about 0.02 to 0.1 throughout the GI-active phases of the simulations.

RADIAL STELLAR PULSATION AND THREE-DIMENSIONAL CONVECTION. I. NUMERICAL METHODS AND ADIABATIC TEST CASES

We are developing a 3D radiation hydrodynamics code to simulate the interaction of convection and pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with observed light and velocity curves. Previous 2D calculations were prevented from doing this because of drift in the radial coordinate system, due to the algorithm defining radial movement of the coordinate system during the pulsation cycle. We remove this difficulty by defining our coordinate system flow algorithm to require that the mass in a spherical shell remain constant throughout the pulsation cycle. We perform adiabatic test calculations to show that large amplitude solutions repeat over more than 150 pulsation periods. We also verify that the computational method conserves the peak kinetic energy per period, as must be true for adiabatic pulsation models.

Radiative hydrodynamic simulations of red supergiant stars

Context. It has been shown that convection in red supergiant stars gives rise to large granules causing surface inhomogeneities together with shock waves in the photosphere. The resulting motion of the photocenter (on time scales ranging from months to years) could possibly have adverse effects on the parallax determination with Gaia. Aims. We explore the impact of the granulation on the photocentric and photometric variability. We quantify these effects in order to better characterize the error possibly altering the parallax. Methods. We use 3D radiative-hydrodynamics simulations of convection with CO5BOLD and the post-processing radiative transfer code OPTIM3D to compute intensity maps and spectra in the Gaia G band [325-1030 nm]. Results. We provide astrometric and photometric predictions from 3D simulations of RSGs that are used to evaluate the degradation of the astrometric parameters of evolved stars derived by Gaia. We show from RHD simulations that a supergiant like Betelgeuse exhibits a photocentric noise characterised by a standard deviation of the order of 0.1 AU. The number of bright giant and supergiant stars whose Gaia parallaxes will be altered by the photocentric noise ranges from a few tens to several thousandths. The degradation of the astrometric fit due to the presence of this photocentric noise will be noticeable up to about 5 kpc for the brightest supergiants. Moreover, parallaxes of supergiants are affected by a error of the order of a few percents. We show that the photocentric noise, as predicted by the 3D simulation, does account for a substantial part of the supplementary 'cosmic noise' that affects Hipparcos measurements of Betelgeuse and Antares.

The Effect of Scattering on the Temperature Stratification of 3D Model Atmospheres of Metal-Poor Red Giants

AbstractWe study the effects of different approximations of scattering in 3D radiation-hydrodynamics simulations on the photospheric temperature stratification of metal-poor red giant stars. We find that assuming a Planckian source function and neglecting the contribution of scattering to extinction in optically thin layers provides a good approximation of the effects of coherent scattering on the photospheric temperature balance.

Radiative hydrodynamics simulations of red supergiant stars

Context. The red supergiant (RSG) Betelgeuse is an irregular variable star. Convection may play an important role in understanding this variability. Interferometric observations can be interpreted using sophisticated simulations of stellar convection. Aims. We compare the visibility curves and closure phases obtained from our 3D simulation of RSG convection with CO5BOLD to various interferometric observations of Betelgeuse from the optical to the H band in order to characterize and measure the convection pattern on this star. Methods. We use 3D radiative-hydrodynamics (RHD) simulation to compute intensity maps in different filters and we thus derive interferometric observables using the post-processing radiative transfer code OPTIM3D. The synthetic visibility curves and closure phases are compared to observations. Results. We provide a robust detection of the granulation pattern on the surface of Betelgeuse in the optical and in the H band based on excellent fits to the observed visibility points and closure phases. Moreover, we determine that the Betelgeuse surface in the H band is covered by small to medium scale (5-15 mas) convection-related surface structures and a large (30 mas) convective cell. In this spectral region, H2O molecules are the main absorbers and contribute to the small structures and to the position of the first null of the visibility curve (i.e. the apparent stellar radius).

The role of convection, overshoot, and gravity waves for the transport of dust in M dwarf and brown dwarf atmospheres

Observationally, spectra of brown dwarfs indicate the presence of dust in their atmospheres while theoretically it is not clear what prevents the dust from settling and disappearing from the regions of spectrum formation. Consequently, standard models have to rely on ad hoc assumptions about the mechanism that keeps dust grains aloft in the atmosphere. We apply hydrodynamical simulations to develop an improved physical understanding of the mixing properties of macroscopic flows in M dwarf and brown dwarf atmospheres, in particular of the influence of the underlying convection zone. We performed 2D radiation hydrodynamics simulations including a description of dust grain formation and transport with the CO5BOLD code. The simulations cover the very top of the convection zone and the photosphere including the dust layers for effective temperatures between 900K and 2800K, all with logg=5 assuming solar chemical composition. Convective overshoot occurs in the form of exponentially declining velocities with small scale heights, so that it affects only the region immediately above the almost adiabatic convective layers. From there on, mixing is provided by gravity waves that are strong enough to maintain thin dust clouds in the hotter models. With decreasing effective temperature, the amplitudes of the waves become smaller but the clouds become thicker and develop internal convective flows that are more efficient in mixing material than gravity waves. The presence of clouds leads to a highly structured appearance of the stellar surface on short temporal and small spatial scales. We identify convectively excited gravity waves as an essential mixing process in M dwarf and brown dwarf atmospheres. Under conditions of strong cloud formation, dust convection is the dominant self-sustaining mixing component.

3D simulations of M star atmosphere velocities and their influence on molecular FeH lines

<i>Context. <i/>The measurement of line broadening in cool stars is in general a difficult task. In order to detect slow rotation or weak magnetic fields, an accuracy of 1 km s<sup>-1<sup/> is needed. In this regime the broadening from convective motion becomes important. We present an investigation of the velocity fields in early to late M-type star hydrodynamic models, and we simulate their influence on molecular line shapes. The M star model parameters range between of and effective temperatures from 2500 K to 4000 K.<i>Aims. <i/>Our aim is to characterize the - and -dependence of the velocity fields and express them in terms of micro- and macro-turbulent velocities in the one dimensional sense. We present a direct comparison between 3D hydrodynamical velocity fields and 1D turbulent velocities. The velocity fields strongly affect the line shapes of , and it is our goal to give a rough estimate of the and parameter range in which 3D spectral synthesis is necessary and where 1D synthesis suffices. We want to distinguish between the velocity-broadening from convective motion and the rotational- or Zeeman-broadening in M-type stars we are planning to measure. For the latter, lines are an important indicator.<i>Methods. <i/>In order to calculate M-star structure models, we employ the 3D radiative-hydrodynamics (RHD) code CO<sup>5<sup/>BOLD. The spectral synthesis in these models is performed with the line synthesis code LINFOR3D. We describe the 3D velocity fields in terms of a Gaussian standard deviations and project them onto the line of sight to include geometrical and limb-darkening effects. The micro- and macro-turbulent velocities are determined with the “curve of growth” method and convolution with a Gaussian velocity profile, respectively. To characterize the and dependence of lines, the equivalent width, line width, and line depth are examined.<i>Results. <i/>The velocity fields in M-stars strongly depend on and . They become stronger with decreasing and increasing . The projected velocities from the 3D models agree within ~100 m s<sup>-1<sup/> with the 1D micro- and macro-turbulent velocities. The line quantities systematically depend on and .<i>Conclusions. <i/>The influence of hydrodynamic velocity fields on line shapes of M-type stars can well be reproduced with 1D broadening methods. lines turn out to provide a means to measure and in M-type stars. Since different lines all behave in a similar manner, they provide an ideal measure for rotational and magnetic broadening.

Absolute dimensions of solar-type eclipsing binaries

The influence of stellar activity on the fundamental properties of stars around and below 1 Msun is not well understood. We aim to determine absolute dimensions and abundances for the solar-type detached eclipsing binary V636 Cen. The results are based on uvby light curves, uvby-beta standard photometry, radial velocity observations, and high-resolution spectra. Masses and radii that are precise to 0.5% have been established for the components of V636 Cen. The 0.85 Msun secondary component is moderately active with starspots and CaII H and K emission, and the 1.05 Msun primary shows signs of activity as well, but at a much lower level. We derive a [Fe/H] abundance of -0.20+/-0.08 and similar abundances for Si, Ca, Ti, V, Cr, Co, and Ni. Corresponding solar-scaled stellar models are unable to reproduce V636 Cen, especially its secondary component, which is ~10% larger and ~400 K cooler than predicted. Models adopting significantly lower mixing-length parameters l/H_p remove these discrepancies, seen also for other solar-type binary components. For the observed [Fe/H], Claret models for l/H_p = 1.4 (primary) and 1.0 (secondary) reproduce the components of V636 Cen at a common age of 1.35 Gyr. V636 Cen and 10 other well-studied inactive and active solar-type binaries suggest that chromospheric activity, and its effect on envelope convection, is likely to cause radius and temperature discrepancies, which can be removed by adjusting the model mixing length parameters downwards. Noting this, the sample may also lend support to theoretical 2D radiation hydrodynamics studies, which predict a slight decrease of the mixing length parameter with increasing temperature/mass for inactive main sequence stars.

The Solar Photospheric Nitrogen Abundance: Determination with 3D and 1D Model Atmospheres

AbstractWe present a new determination of the solar nitrogen abundance making use of 3D hydrodynamical modelling of the solar photosphere, which is more physically motivated than traditional static 1D models. We selected suitable atomic spectral lines, relying on equivalent width measurements already existing in the literature. For atmospheric modelling we used the co5bold 3D radiation hydrodynamics code. We investigated the influence of both deviations from local thermodynamic equilibrium (non-LTE effects) and photospheric inhomogeneities (granulation effects) on the resulting abundance. We also compared several atlases of solar flux and centre-disc intensity presently available. As a result of our analysis, the photospheric solar nitrogen abundance is A(N) = 7.86 ± 0.12.

Three-dimensional simulations of the atmosphere of an AGB star

Context. Winds of asymptotic giant branch stars are assumed to be driven by radiation pressure on dust. Previously, this process has been modeled with detailed time-dependent simulations of atmospheres and winds assuming spherically symmetric flows. In such models kinetic energy is injected by a variable inner boundary (“piston”) simulating the effects of stellar pulsation. However, the dynamical processes in these atmospheres – convection and pulsations – are actually three-dimensional. Aims. We present and analyze first 3D radiation hydrodynamics simulations of the convective interior and the atmosphere of a typical AGB star. In particular, we check whether the piston description in the 1D wind models is compatible with the 3D results. Methods. We used two different RHD codes, one (CO5BOLD) to produce 3D models of the outer convective envelope and the inner atmosphere of an AGB star, the other to describe the atmosphere and the wind acceleration region, including dust formation and non-grey radiative transfer, but assuming spherically symmetric flows. From the movements of stellar surface layers in the 3D models, we derived a description for the variable inner boundary in the 1D models. Results. The 3D models show large convection cells and pulsations that give rise to roughly spherically expanding shock waves in the atmosphere, levitating material into regions which are cool enough to allow for dust formation. The atmospheric velocity fields have amplitudes and time scales close to the values that are necessary to start dust formation in the 1D wind models. Conclusions. The convection cells in the 3D simulations are so large that the associated shock fronts appear almost spherical, justifying the assumption of spherical symmetry and the use of a piston boundary condition in the context of wind models. Nevertheless, certain non-radial structures exist in the dust shell developing in the 3D simulations which should be detectable with current interferometric techniques.

Creation of hot dense matter in short-pulse laser-plasma interaction with tamped titanium foils

Dense titanium plasma has been heated to an electron temperature up to 1300eV with a 100TW, high intensity short-pulse laser. The experiments were conducted using Ti foils (5μm thick) sandwiched between layers of either aluminum (1 or 2μm thick) or plastic (2μm thick) to prevent the effects of prepulse. Targets of two different sizes, i.e., 250×250μm2 and 1×1mm2 were used. Spectral measurements of the Ti inner-shell emission, in the region between 4and5keV, were taken from the front-side (i.e., the laser illuminated side) of the target. The data show large shifts in the Kα emission from open-shell ions, suggesting bulk heating of the sample at near solid density, which was largest for reduced mass targets. Comparison with collisional radiative and 2D radiation hydrodynamics codes indicates a peak temperature of Te,peak=1300eV of solid titanium plasma in ∼0.2μm thin layer. Higher bulk temperature (Te,bulk=100eV) for aluminum tamped compared to CH tamped targets (Te,bulk=40eV) was observed. A possible explanation for this difference is described whereby scattering due to the nuclear charge of the tamping material leads to modified electron transport behavior.

DOT tomography of the solar atmosphere

We compare high-quality image sequences from the Dutch Open Telescope (DOT) with synthetic image sequences obtained from 3D radiation-hydrodynamics simulations of the solar granulation. In particular, we study the subsonic brightness pattern observed in the wings of H & K. The simulations reproduce the observed intensity contrast, time scales, and Fourier behaviour rather well. Most differences can be attributed to the resolution difference between the observations and the simulation and the small geometrical extent of the simulation. We conclude that magnetic fields play no major role in the formation of reversed granulation.

Massive Stars and the Energy Balance of the Interstellar Medium. I. The Impact of an Isolated 60M⊙Star

We present results of numerical simulations carried out with a 2D radiation hydrodynamics code in order to study the impact of massive stars on their surrounding interstellar medium. This first paper deals with the evolution of the circumstellar gas around an isolated 60 M star.

3D radiation hydrodynamics: Interacting photo-evaporating clumps

We present the results of a new radiation hydrodynamics code called Maartje. This code describes the evolution of a flow in three spatial dimensions using an adaptive mesh, and contains a combination of a ray tracer and an atomic physics module to describe the effects of ionizing radiation. The code is parallelized using a custom threadpool library. We present an application in which we follow the ionization of two dense spherical clumps which are exposed to an ionizing radiation field from a 50 000 K black body. We study various configurations in which one of the clumps shields the other from the ionizing photons. We find that relatively long-lived filamentary structures with narrow tails are formed. This raises the possibility that cometary knots (such as are found in the Helix Nebula) may be the result of the interaction of an ionizing radiation field with an ensemble of clumps, as opposed to the identification of a single knot with a single clump.

Effects of Photospheric Temperature Inhomogeneities on Lithium abundance Determinations (2D)

Based on detailed 2D radiation hydrodynamics (RHD) simulations, we have investigated the effects of photospheric temperature inhomogeneities induced by convection on spectroscopic determinations of the lithium abundance. Computations have been performed both for the solar case and for a metal-poor dwarf. NLTE effects are taken into account, using a five-level atomic model for Li I. Comparisons are presented with traditional 1D models having the same effective temperature and gravity. The net result is that, while LTE results differ dramatically between 1D and 2D models, especially in the metal-poor case, this does not remain true when NLTE effects are included: 1D/2D differences in the inferred NLTE Li abundance are always well below 0.1 dex. The present computations still assume LTE in the continuum. New computations removing this assumption are planned for the near future.

Iterative Linear Solvers in a 2D Radiation–Hydrodynamics Code: Methods and Performance

Computer codes containing both hydrodynamics and radiation play a central role in simulating both astrophysical and inertial confinement fusion (ICF) phenomena. A crucial aspect of these codes is that they require an implicit solution of the radiation diffusion equations. We present in this paper the results of a comparison of five different linear solvers on a range of complex radiation and radiation–hydrodynamics problems. The linear solvers used are diagonally scaled conjugate gradient, GMRES with incomplete LU preconditioning, conjugate gradient with incomplete Cholesky preconditioning, multigrid, and multigrid-preconditioned conjugate gradient. These problems involve shock propagation, opacities varying over 5–6 orders of magnitude, tabular equations of state, and dynamic ALE (Arbitrary Lagrangian Eulerian) meshes. We perform a problem size scalability study by comparing linear solver performance over a wide range of problem sizes from 1000 to 100,000 zones. The fundamental question we address in this paper is: Is it more efficient to invert the matrix in many inexpensive steps (like diagonally scaled conjugate gradient) or in fewer expensive steps (like multigrid)? In addition, what is the answer to this question as a function of problem size and is the answer problem dependent? We find that the diagonally scaled conjugate gradient method performs poorly with the growth of problem size, increasing in both iteration count and overall CPU time with the size of the problem and also increasing for larger time steps. For all problems considered, the multigrid algorithms scale almost perfectly (i.e., the iteration count is approximately independent of problem size and problem time step). For pure radiation flow problems (i.e., no hydrodynamics), we see speedups in CPU time of factors of ≈15–30 for the largest problems, when comparing the multigrid solvers relative to diagonal scaled conjugate gradient. For the incomplete factorization preconditioners, we see a weak dependence of iteration count on problem size. The speedups observed for pure radiation flow are typically on the order of 10 relative to diagonal scaled conjugate gradient. For radiation–hydrodynamics problems, we again see multigrid scaling perfectly. However, for the problems considered, we see speedups relative to diagonal scaled conjugate gradient of no more than ≈10, with incomplete Cholesky in fact either equaling or outperforming multigrid. We trace these observations to the time step control and the feature of ALE to relax distorted zones.

Exploratory Simulation of Solar Granules: How Sharp is the Convection/Radiation Transition?

Currently, the most successful direct simulation of the solar granules (and the convection/radiation transition layer) is the three-dimensional (3D) model computed by Stein and Nordlund (1989). So far, there is no other similar 3D models available for comparison [however, see Ludwig et al. (1997) for a recent 2D calculation]. We are developing an alternative numerical approach to simulate the 3D radiation hydrodynamics of this layer. In this approach, the Eddington approximation is used to handle the radiation rather than solving the radiative transfer equations along rays, and the ADISM method (Chan and Wolff 1982) which solves the Navier Stokes equations in conservative forms is used to speed up the thermal relaxation of the fluid layer. We are in the process of testing the numerical accuracy of the codes. This paper summarizes the results of a test that illustrate the effects of vertical space resolution on the mean profiles of some important quantities.