Paintings on Paper

The process of drawing, mark making, and layering results in a highly personal calligraphy

The effects of numerical resolution on hydrodynamical surface convection simulations and spectral line formation

The computationally demanding nature of radiative-hydrodynamical simulations of stellar surface convection warrants an investigation of the sensitivity of the convective structure and spectral synthesis to the numerical resolution and dimension of the simulations, which is presented here. With too coarse a resolution the predicted spectral lines tend to be too narrow, reflecting insufficient Doppler broadening from the convective motions, while at the currently highest affordable resolution the line shapes have converged essentially perfectly to the observed profiles. Similar conclusions are drawn from the line asymmetries and shifts. In terms of abundances, weak FeI and FeII lines show a very small dependence (~0.02 dex) while for intermediate strong lines with significant non-thermal broadening the sensitivity increases (~0.10 dex). Problems arise when using 2D convection simulations to describe an inherent 3D phenomenon, which translates to inaccurate atmospheric velocity fields and temperature and pressure structures. In 2D the theoretical line profiles tend to be too shallow and broad compared with the 3D calculations and observations, in particular for intermediate strong lines. In terms of abundances, the 2D results are systematically about 0.1 dex lower than for the 3D case for FeI lines. Furthermore, the predicted line asymmetries and shifts are much inferior in 2D. Given these shortcomings and computing time considerations it is better to use 3D simulations of even modest resolution than high-resolution 2D simulations.Comment: Accepted for A&

Line formation in convective stellar atmospheres. I. Granulation corrections for solar photospheric abundances

In an effort to estimate the largely unknown effects of photospheric temperature fluctuations on spectroscopic abundance determinations, we have studied the problem of LTE line formation in the inhomogeneous solar photosphere based on detailed 2-dimensional radiation hydrodynamics simulations of the convective surface layers of the Sun. By means of a strictly differential 1D/2D comparison of the emergent equivalent widths, we have derived "granulation abundance corrections" for individual lines, which have to be applied to standard abundance determinations based on homogeneous 1D model atmospheres in order to correct for the influence of the photospheric temperature fluctuations. In general, we find a line strengthening in the presence of temperature inhomogeneities as a consequence of the non-linear temperature dependence of the line opacity. For many lines of practical relevance, the magnitude of the abundance correction may be estimated from interpolation in the tables and graphs provided with this paper. The application of abundance corrections may often be an acceptable alternative to a detailed fitting of individual line profiles based on hydrodynamical simulations. The present study should be helpful in providing upper bounds for possible errors of spectroscopic abundance analyses, and for identifying spectral lines which are least sensitive to the influence of photospheric temperature inhomogeneities.Comment: Accepted by A&

A simulation of solar convection at supergranulation scale

We present here numerical simulations of surface solar convection which cover a box of 30$\times30\times$3.2 Mm$^3$ with a resolution of 315$\times315\times$82, which is used to investigate the dynamics of scales larger than granulation. No structure resembling supergranulation is present; possibly higher Reynolds numbers (i.e. higher numerical resolution), or magnetic fields, or greater depth are necessary. The results also show interesting aspects of granular dynamics which are briefly presented, like extensive p-mode ridges in the k-$\omega$ diagram and a ringlike distribution of horizontal vorticity around granules. At large scales, the horizontal velocity is much larger than the vertical velocity and the vertical motion is dominated by p-mode oscillations.Comment: Contribution to the proceedings of the workshop entitled "THEMIS and the new frontiers of solar atmosphere dynamics" (March 2001), 6 pages, to appear in Nuovo Cimento

Numerical simulations of surface convection in a late M-dwarf

Based on detailed 2D and 3D numerical radiation-hydrodynamics (RHD) simulations of time-dependent compressible convection, we have studied the dynamics and thermal structure of the convective surface layers of a prototypical late-type M-dwarf (Teff~2800K log(g)=5.0, solar chemical composition). The RHD models predict stellar granulation qualitatively similar to the familiar solar pattern. Quantitatively, the granular cells show a convective turn-over time scale of ~100s, and a horizontal scale of 80km; the relative intensity contrast of the granular pattern amounts to 1.1%, and root-mean-square vertical velocities reach 240m/s at maximum. Deviations from radiative equilibrium in the higher, formally convectively stable atmospheric layers are found to be insignificant allowing a reliable modeling of the atmosphere with 1D standard model atmospheres. A mixing-length parameter of alpha=2.1 provides the best representation of the average thermal structure of the RHD model atmosphere while alternative values are found when fitting the asymptotic entropy encountered in deeper layers of the stellar envelope alpha=1.5, or when matching the vertical velocity field alpha=3.5. The close correspondence between RHD and standard model atmospheres implies that presently existing discrepancies between observed and predicted stellar colors in the M-dwarf regime cannot be traced back to an inadequate treatment of convection in the 1D standard models. The RHD models predict a modest extension of the convectively mixed region beyond the formal Schwarzschild stability boundary which provides hints for the distribution of dust grains in cooler (brown dwarf) atmospheres.Comment: 19 pages, 16 figures, accepted for publication in A&

Are granules good tracers of solar surface velocity fields?

Using a numerical simulation of compressible convection with radiative transfer mimicking the solar photosphere, we compare the velocity field derived from granule motions to the actual velocity field of the plasma. We thus test the idea that granules may be used to trace large-scale velocity fields at the sun's surface. Our results show that this is indeed the case provided the scale separation is sufficient. We thus estimate that neither velocity fields at scales less than 2500 km nor time evolution at scales shorter than 0.5 hr can be faithfully described by granules. At larger scales the granular motions correlate linearly with the underlying fluid motions with a slope of ~< 2 reaching correlation coefficients up to ~0.9.Comment: 4 pages - accepted in Astronomy and Astrophysic

High-resolution models of solar granulation: the 2D case

Using grid refinement, we have simulated solar granulation in 2D. The refined region measures 1.97*2.58 Mm (vertical*horizontal). Grid spacing there is 1.82*2.84 km. The downflows exhibit strong Kelvin-Helmholtz instabilities. Below the photosphere, acoustic pulses are generated. They proceed laterally (in some cases distances of at least the size of our refined domain) and may be enhanced when transversing downflows) as well as upwards where, in the photosphere they contribute significantly to 'turbulence' (velocity gradients, etc.) The acoustic pulses are ubiquitous in that at any time several of them are seen in our high-resolution domain. Their possible contributions to p-mode excitation or heating of the chromosphere needs to be investigated

A simulation of solar convection of supergranulation scale

We present here numerical simulations of surface solar convection which cover a box of 30×30×3.2 Mm3 with a resolutionof 315×315×82, which is used to investigate the dynamics of scales larger than granulation. No structure resembling supergranulation is present; possibly higher Reynolds numbers (i.e. higher numerical resolution), or magnetic fields, or greater depth are necessary. The results also show interesting aspects of granular dynamics which are briefly presented, like extensive p-mode ridges inthe k-ω diagram and a ringlike distribution of horizontal vorticity around granules. At large scales, the horizontal velocity is much larger than the vertical velocity and the vertical motion is dominated by p-mode oscillations

White dwarf envelopes: further results of a non-local model of convection

We present results of a fully non-local model of convection for white dwarf envelopes. We show that this model is able to reproduce the results of numerical simulations for convective efficiencies ranging from very inefficient to moderately efficient; this agreement is made more impressive given that no closure parameters have been adjusted in going from the previously reported case of A-stars to the present case of white dwarfs; for comparison, in order to match the peak convective flux found in numerical simulations for both the white dwarf envelopes discussed in this paper and the A-star envelopes discussed in our previous work requires changing the mixing length parameter of commonly used local models by a factor of 4. We also examine in detail the overshooting at the base of the convection zone, both in terms of the convective flux and in terms of the velocity field: we find that the flux overshoots by approximately 1.25 H_P and the velocity by approximately 2.5 H_P. Due to the large amount of overshooting found at the base of the convection zone the new model predicts the mixed region of white dwarf envelopes to contain at least 10 times more mass than local mixing length theory (MLT) models having similar photospheric temperature structures. This result is consistent with the upper limit given by numerical simulations which predict an even larger amount of mass to be mixed by convective overshooting. Finally, we attempt to parametrise some of our results in terms of local MLT-based models, insofar as is possible given the limitations of MLTComment: Accepted for publication in MNRAS; 11 pages, 5 figures, 3 table