arXiv subjects

Robert F. Stein

Publications and source records attributed to Robert F. Stein.

18 recordsLinked to original sources

arXiv2024

The Stagger Code for Accurate and Efficient, Radiation-Coupled MHD Simulations

We describe the Stagger Code for simulations of magneto-hydrodynamic (MHD) systems. This is a modular code with a variety of physics modules that will let the user run simulations of deep stellar atmospheres, sunspot formation, stellar chromospheres and coronae, proto-stellar disks, star formation from giant molecular clouds and even galaxy formation. The Stagger Code is efficiently and highly parallelizable, enabling such simulations with large ranges of both spatial and temporal scales. We, describe the methodology of the code, and present the most important of the physics modules, as well as its input and output variables. We show results of a number of standard MHD tests to enable comparison with other, similar codes. In addition, we provide an overview of tests that have been carried out against solar observations, ranging from spectral line shapes, spectral flux distribution, limb darkening, intensity and velocity distributions of granulation, to seismic power-spectra and the excitation of p modes. The Stagger Code has proven to be a high fidelity code with a large range of uses.

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arXiv2016

The asteroseismic surface effect from a grid of 3D convection simulations. I. Frequency shifts from convective expansion of stellar atmospheres

We analyse the effect on adiabatic stellar oscillation frequencies of replacing the near-surface layers in 1D stellar structure models with averaged 3D stellar surface convection simulations. The main difference is an expansion of the atmosphere by 3D convection, expected to explain a major part of the asteroseismic surface effect; a systematic overestimation of p-mode frequencies due to inadequate surface physics. We employ pairs of 1D stellar envelope models and 3D simulations from a previous calibration of the mixing-length parameter, alpha. That calibration constitutes the hitherto most consistent matching of 1D models to 3D simulations, ensuring that their differences are not spurious, but entirely due to the 3D nature of convection. The resulting frequency shift is identified as the structural part of the surface effect. The important, typically non-adiabatic, modal components of the surface effect are not included in the present analysis, but relegated to future papers. Evaluating the structural surface effect at the frequency of maximum mode amplitude, $ν_{\rm max}$, we find shifts from $δν$=-0.8 microHz for giants at $\log g$=2.2 to -35 microHz for a ($T_{\rm eff}=6901$ K, $\log g$=4.29) dwarf. The fractional effect $δν(ν_{\rm max})/ν_{\rm max}$, ranges from -0.1% for a cool dwarf (4185 K, 4.74) to -6% for a warm giant (4962 K, 2.20).

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arXiv2014

Improvements to stellar structure models, based on a grid of 3D convection simulations. II. Calibrating the mixing-length formulation

We perform a calibration of the mixing length of convection in stellar structure models against realistic 3D radiation-coupled hydrodynamics (RHD) simulations of convection in stellar surface layers, determining the adiabat deep in convective stellar envelopes. The mixing-length parameter $α$ is calibrated by matching averages of the 3D simulations to 1D stellar envelope models, ensuring identical atomic physics in the two cases. This is done for a previously published grid of solar-metallicity convection simulations, covering from 4200 K to 6900 K on the main sequence, and 4300-5000 K for giants with logg=2.2. Our calibration results in an $α$ varying from 1.6 for the warmest dwarf, which is just cool enough to admit a convective envelope, and up to 2.05 for the coolest dwarfs in our grid. In between these is a triangular plateau of $α$ ~ 1.76. The Sun is located on this plateau and has seen little change during its evolution so far. When stars ascend the giant branch, they largely do so along tracks of constant $α$, with $α$ decreasing with increasing mass.

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arXiv2014

Improvements to Stellar Structure Models, Based on a Grid of 3D Convection Simulations. I. $T(τ)$-Relations

Relations between temperature, T, and optical depth, tau, are often used for describing the photospheric transition from optically thick to optically thin in stellar structure models. We show that this is well justified, but also that currently used T(tau) relations are often inconsistent with their implementation. As an outer boundary condition on the system of stellar structure equations, T(tau) relations have an undue effect on the overall structure of stars. In this age of precision asteroseismology, we need to re-assess both the method for computing and for implementing T(tau) relations, and the assumptions they rest on. We develop a formulation for proper and consistent evaluation of T(tau) relations from arbitrary 1D or 3D stellar atmospheres, and for their implementation in stellar structure and evolution models. We extract radiative T(tau) relations, as described by our new formulation, from 3D simulations of convection in deep stellar atmospheres of late-type stars from dwarfs to giants. These simulations employ realistic opacities and equation of state, and account for line-blanketing. For comparison, we also extract T(tau) relations from 1D MARCS model atmospheres using the same formulation. T(tau)-relations from our grid of 3D convection simulations display a larger range of behaviours with surface gravity, compared with those of conventional theoretical 1D hydrostatic atmosphere models. Based on this, we recommend no longer to use scaled solar T(tau) relations. Files with T(tau) relations for our grid of simulations are made available to the community, together with routines for interpolating in this irregular grid. We also provide matching tables of atmospheric opacity, for consistent implementation in stellar structure models.

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arXiv2013

Models of solar surface dynamics: impact on eigenfrequencies and radius

We study the effects of different descriptions of the solar surface convection on the eigenfrequencies of p-modes. 1-D evolution calculations of the whole Sun and 3-D hydrodynamic and magnetohydrodynamic simulations of the current surface are performed. These calculations rely on realistic physics. Averaged stratifications of the 3-D simulations are introduced in the 1-D solar evolution or in the structure models. The eigenfrequencies obtained are compared to those of 1-D models relying on the usual phenomenologies of convection and to observations of the MDI instrument aboard SoHO. We also investigate how the magnetic activity could change the eigenfrequencies and the solar radius, assuming that, 3 Mm below the surface, the upgoing plasma advects a 1.2 kG horizontal field. All models and observed eigenfrequencies are fairly close below 3 mHz. Above 3 mHz the eigenfrequencies of the phenomenological convection models are above the observed eigenfrequencies. The frequencies of the models based on the 3-D simulations are slightly below the observed frequencies. Their maximum deviation is ~ 3 μHz at 3 mHz but drops below 1 μHz at 4 mHz. Replacing the hydrodynamic by the magnetohydrodynamic simulation increases the eigenfrequencies. The shift is negligible below 2.2 mHz and then increases linearly with frequency to reach ~ 1.7 μHz at 4 mHz. The impact of the simulated activity is a 14 milliarcsecond shrinking of the solar layers near the optical depth unity.

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arXiv2013

A Grid of 3D Stellar Atmosphere Models of Solar Metallicity: I. General Properties, Granulation and Atmospheric Expansion

Present grids of stellar atmosphere models are the workhorses in interpreting stellar observations, and determining their fundamental parameters. These models rely on greatly simplified models of convection, however, lending less predictive power to such models of late type stars. We present a grid of improved and more reliable stellar atmosphere models of late type stars, based on deep, 3D, convective, stellar atmosphere simulations. This grid is to be used in general for interpreting observations, and improve stellar and asteroseismic modeling. We solve the Navier Stokes equations in 3D and concurrent with the radiative transfer equation, for a range of atmospheric parameters, covering most of stellar evolution with convection at the surface. We emphasize use of the best available atomic physics for quantitative predictions and comparisons with observations. We present granulation size, convective expansion of the acoustic cavity, asymptotic adiabat, as function of atmospheric parameters. These and other results are also available in electronic form.

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arXiv2012

On the Formation of Active Regions

Magneto-convection can produce an active region without an initial coherent flux tube. A simulation was performed where uniform, untwisted, horizontal magnetic field of 1 kG strenght was advected into the bottom of a computational domain 48 Mm wide by 20 Mm deep. The up and down convective motions produce a hierarchy of magnetic loops with a wide range of scales, with smaller loops riding "piggy back" in a serpentine fashion on larger loops. When a large loop approaches the surface it produces an small active region with a compact leading spot and more diffuse following spots.

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arXiv2011

Emerging Flux Simulations and Proto-Active Regions

The emergence of minimally structured (uniform and horizontal) magnetic field from a depth of 20 Mm has been simulated. The field emerges first in a mixed polarity pepper and salt pattern, but then collects into separate, unipolar concentrations and produces pores. The field strength was then artificially increased to produce spot-like structures. The field strength at continuum optical depth unity peaks at 1 kG, with a maximum of 4 kG. Where the vertical field is strong, the spots persist (at present an hour of solar time has been simulated). Where the field is weak, the spot gets filled in and disappears. Stokes profiles have been calculated and processed with the Hinode annular mtf, the slit diffraction and frequency smoothing. These data are available at steinr.pa.msu.edu/~bob/stokes.

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arXiv2011

The Mass Mixing Length in Convective Stellar Envelopes

The scale length over which convection mixes mass in a star can be calculated as the inverse of the vertical derivative of the unidirectional (up or down) mass flux. This is related to the mixing length in the mixing length theory of stellar convection. We give the ratio of mass mixing length to pressure scale height for a grid of 3D surface convection simulations, covering from 4300\,K to 6900\,K on the main-sequence, and up to giants at $\log g = 2.2$, all for solar composition. These simulations also confirm what is already known from solar simulations, that convection doesn't proceed by discrete convective elements, but rather as a continuous, slow, smooth, warm upflow and turbulent, entropy deficient, fast down drafts. This convective topology also results in mixing on a scale as that of the classic mixing length formulation, and is simply a consequence of mass conservation on flows in a stratified atmosphere.

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arXiv2007

Local helioseismology and correlation tracking analysis of surface structures in realistic simulations of solar convection

We apply time-distance helioseismology, local correlation tracking and Fourier spatial-temporal filtering methods to realistic supergranule scale simulations of solar convection and compare the results with high-resolution observations from the SOHO Michelson Doppler Imager (MDI). Our objective is to investigate the surface and sub-surface convective structures and test helioseismic measurements. The size and grid of the computational domain are sufficient to resolve various convective scales from granulation to supergranulation. The spatial velocity spectrum is approximately a power law for scales larger than granules, with a continuous decrease in velocity amplitude with increasing size. Aside from granulation no special scales exist, although a small enhancement in power at supergranulation scales can be seen. We calculate the time-distance diagram for f- and p-modes and show that it is consistent with the SOHO/MDI observations. From the simulation data we calculate travel time maps for surface gravity waves (f-mode). We also apply correlation tracking to the simulated vertical velocity in the photosphere to calculate the corresponding horizontal flows. We compare both of these to the actual large-scale (filtered) simulation velocities. All three methods reveal similar large scale convective patterns and provide an initial test of time-distance methods.

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arXiv2006

Validation of Time-Distance Helioseismology by Use of Realistic Simulations of Solar Convection

Recent progress in realistic simulations of solar convection have given us an unprecedented opportunity to evaluate the robustness of solar interior structures and dynamics obtained by methods of local helioseismology. We present results of testing the time-distance method using realistic simulations. By computing acoustic wave propagation time and distance relations for different depths of the simulated data, we confirm that acoustic waves propagate into the interior and then turn back to the photosphere. This demonstrates that in the numerical simulations properties of acoustic waves (p-modes) are similar to the solar conditions, and that these properties can be analyzed by the time-distance technique. For the surface gravity waves (f-mode), we calculate perturbations of their travel times, caused by localized downdrafts, and demonstrate that the spatial pattern of these perturbations (representing so-called sensitivity kernels) is similar to the patterns obtained from the real Sun, displaying characteristic hyperbolic structures. We then test the time-distance measurements and inversions by calculating acoustic travel times from a sequence of vertical velocities at the photosphere of the simulated data, and inferring a mean 3D flow fields by performing inversion based on the ray approximation. The inverted horizontal flow fields agree very well with the simulated data in subsurface areas up to 3 Mm deep, but differ in deeper areas. Due to the cross-talk effects between the horizontal divergence and downward flows, the inverted vertical velocities are significantly different from the mean convection velocities of the simulation dataset.

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arXiv2004

Observational manifestations of solar magneto-convection -- center-to-limb variation

We present the first center-to-limb G-band images synthesized from high resolution simulations of solar magneto-convection. Towards the limb the simulations show "hilly" granulation with dark bands on the far side, bright granulation walls and striated faculae, similar to observations. At disk center G-band bright points are flanked by dark lanes. The increased brightness in magnetic elements is due to their lower density compared with the surrounding intergranular medium. One thus sees deeper layers where the temperature is higher. At a given geometric height, the magnetic elements are cooler than the surrounding medium. In the G-band, the contrast is further increased by the destruction of CH in the low density magnetic elements. The optical depth unity surface is very corrugated. Bright granules have their continuum optical depth unity 80 km above the mean surface, the magnetic elements 200-300 km below. The horizontal temperature gradient is especially large next to flux concentrations. When viewed at an angle, the deep magnetic elements optical surface is hidden by the granules and the bright points are no longer visible, except where the "magnetic valleys" are aligned with the line of sight. Towards the limb, the low density in the strong magnetic elements causes unit line-of-sight optical depth to occur deeper in the granule walls behind than for rays not going through magnetic elements and variations in the field strength produce a striated appearance in the bright granule walls.

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arXiv2002

Solar Surface Magneto-Convection

Magneto-convection simulations on meso-granule and granule scales near the solar surface are used to study small scale dynamo activity, the emergence and disappearance of magnetic flux tubes, and the formation and evolution of micropores. From weak seed fields, convective motions produce highly intermittent magnetic fields in the intergranular lanes which collect over the boundaries of the underlying meso-granular scale cells. Instances of both emerging magnetic flux loops and magnetic flux disappearing from the surface occur in the simulations. We show an example of a flux tube collapsing to kG field strength and discuss how the nature of flux disappearance can be investigated. Observed stokes profiles of small magnetic structures are severely distorted by telescope diffraction and seeing. Because of the strong stratification, there is little recycling of plasma and field in the surface layers. Recycling instead occurs by exchange with the deep layers of the convection zone. Plasma and field from the surface descend through the convection zone and rise again toward the surface. Because only a tiny fraction of plasma rising up from deep in the convection zone reaches the surface due to mass conservation, little of the magnetic energy resides in the near surface layers. Thus the dynamo acting on weak incoherent fields is global, rather than a local surface dynamo.

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arXiv2002

What Causes P-mode Asymmetry Reversal?

The solar acoustic p-mode line profiles are asymmetric. Velocity spectra have more power on the low-frequency sides, whereas intensity profiles show the opposite sense of asymmetry. Numerical simulations of the upper convection zone have resonant p-modes with the same asymmetries and asymmetry reversal as the observed modes. The temperature and velocity power spectra at optical depth $τ_{\rm cont} = 1$ have the opposite asymmetry as is observed for the intensity and velocity spectra. At a fixed geometrical depth, corresponding to $<τ_{\rm cont}>=1$, however, the temperature and velocity spectra have the same asymmetry. This indicates that the asymmetry reversal is produced by radiative transfer effects and not by correlated noise.

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arXiv2002

Dynamic Hydrogen Ionization

We investigate the ionization of hydrogen in a dynamic Solar atmosphere. We show that the time scale for ionization/recombination can be estimated from the eigenvalues of a modified rate matrix where the optically thick Lyman transitions that are in detailed balance have been excluded. We find that the time scale for ionization/recombination is dominated by the slow collisional leakage from the ground state to the first excited state. Throughout the chromosphere the time scale is long ($10^3$-$10^5$ s), except in shocks where the increased temperature and density shorten the time scale for ionization/recombination, especially in the upper chromosphere. Because the relaxation time scale is much longer than dynamic time scales, hydrogen ionization does not have time to reach its equilibrium value and its fluctuations are much smaller than the variation of its statistical equilibrium value appropriate for the instantaneous conditions. The ionization state tends to represent the higher temperature of the shocks, and the mean electron density is up to a factor of six higher than the electron density calculated in statistical equilibrium from the mean atmosphere. The simulations show that a static picture and a dynamic picture of the chromosphere are fundamentally different and that time variations are crucial for our understanding of the chromosphere itself and the spectral features formed there.

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arXiv2001

Solar Convection and Magneto-Convection Simulations

Magneto-convection simulations with two scenarios have been performed: In one, horizontal magnetic field is advected into the computational domain by fluid entering at the bottom. In the other, an initially uniform vertical magnetic field is imposed on a snapshot of non-magnetic convection and allowed to evolve. In both cases, the field is swept into the intergranular lanes and the boundaries of the underlying mesogranules. The largest field concentrations at the surface reach pressure balance with the surrounding gas. They suppress both horizontal and vertical flows, which reduces the heat transport. They cool, become evacuated and their optical depth unity surface is depressed by several hundred kilometers. Micropores form, typically where a small granule disappears and surrounding flux tubes squeeze into its previous location.

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arXiv2000

The response of a turbulent accretion disc to an imposed epicyclic shearing motion

We excite an epicyclic motion, whose amplitude depends on the vertical position, $z$, in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays we can obtain information about the interaction between the warp and the disc turbulence. A high amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, $α_{\rm v}$, pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, $α_{\rm h}$, pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, $α_{\rm v}$ is approximately equal to $α_{\rm h}$ and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness ($\sim 0.01$) of $α_{\rm v}$ and $α_{\rm h}$ we conclude that for $β= p_{\rm gas}/p_{\rm mag} \sim 10$ the timescale for diffusion or damping of a warp is much shorter than the usual viscous timescale. Finally, we review the astrophysical implications.

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arXiv1994

Does a Non-Magnetic Solar Chromosphere Exist?

Enhanced chromospheric emission which corresponds to an outwardly increasing semiempirical temperature structure can be produced by wave motion without any increase in the mean gas temperture. Hence, the sun may not have a classical chromosphere in magnetic field free internetwork regions. Other significant differences between the properties of dynamic and static atmospheres should be considered when analyzing chromospheric observations.

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