[Paper Review] The Stagger-grid: A Grid of 3D Stellar Atmosphere Models - I. Methods and General Properties

Z. Magic, R. Collet+6 more|Feb 11, 2013

Stellar, planetary, and galactic studiesPhysics and Astronomy76 references138 citations

TL;DR

The Stagger-grid presents a comprehensive, publicly available grid of 3D hydrodynamic stellar atmosphere models for late-type stars, computed using the Stagger-code with realistic equation of state and opacity treatments. Key findings include a tight scaling relation between vertical velocity and surface entropy jump, and significant 3D vs. 1D model differences—especially in metal-poor stars—highlighting the limitations of 1D mixing-length theory in stellar atmosphere modeling.

ABSTRACT

We present the Stagger-grid, a comprehensive grid of time-dependent, 3D hydrodynamic model atmospheres for late-type stars with realistic treatment of radiative transfer, covering a wide range in stellar parameters. This grid of 3D models is intended for various applications like stellar spectroscopy, asteroseismology and the study of stellar convection. In this introductory paper, we describe the methods used for the computation of the grid and discuss the general properties of the 3D models as well as their temporal and spatial averages (<3D>). All our models were generated with the Stagger-code, using realistic input physics for the equation of state (EOS) and for continuous and line opacities. Our ~220 grid models range in Teff from 4000 to 7000K in steps of 500K, in log g from 1.5 to 5.0 in steps of 0.5 dex, and [Fe/H] from -4.0 to +0.5 in steps of 0.5 and 1.0 dex. We find a tight scaling relation between the vertical velocity and the surface entropy jump, which itself correlates with the constant entropy value of the adiabatic convection zone. The range in intensity contrast is enhanced at lower metallicity. The granule size correlates closely with the pressure scale height sampled at the depth of maximum velocity. We compare the <3D> models with widely applied 1D models, as well as with theoretical 1D hydrostatic models generated with the same EOS and opacity tables as the 3D models, in order to isolate the effects of using self-consistent and hydrodynamic modeling of convection, rather than the classical mixing length theory approach. For the first time, we are able to quantify systematically over a broad range of stellar parameters the uncertainties of 1D models arising from the simplified treatment of physics, in particular convective energy transport. In agreement with previous findings, we find that the differences can be significant, especially for metal-poor stars.

Motivation & Objective

• To develop a systematic, self-consistent grid of 3D stellar atmosphere models for late-type stars with realistic physics.
• To quantify the systematic errors introduced by 1D models that rely on mixing-length theory (MLT) for convective energy transport.
• To provide a reference dataset for improving stellar parameter determination, spectroscopy, and stellar evolution modeling.
• To enable future applications such as limb-darkening calibration, photometric color prediction, and microturbulence calibration in 3D.
• To establish a foundation for 1.5D and full 3D spectral synthesis by providing interpolated and averaged models.

Proposed method

• The grid was computed using the Stagger-code, solving the time-dependent, compressible Navier-Stokes equations with radiative transfer in 3D.
• Radiative transfer was implemented via the opacity binning method to reduce computational cost while preserving spectral energy distribution accuracy.
• Models span 220 combinations of T_eff (4000–7000 K in 500 K steps), log g (1.5–5.0 in 0.5 dex steps), and [Fe/H] (−4.0 to +0.5 in 0.5 and 1.0 dex steps).
• The equation of state and opacity tables were based on first-principles physical data, ensuring consistency with 1D models for comparison.
• Temporal and spatial averages (⟨3D⟩ models) were computed to enable direct comparison with standard 1D atmosphere models.
• Numerical diffusion was minimized and kept constant across simulations to ensure stability and consistency in flow properties.

Experimental results

Research questions

• RQ1 How do 3D hydrodynamic models differ from 1D models in their temperature structure and emergent spectra, particularly in metal-poor stars?
• RQ2 What is the quantitative impact of using 3D convection instead of MLT on stellar atmospheric parameters and spectral synthesis?
• RQ3 Is there a universal scaling relation between convective velocity and atmospheric stratification properties such as entropy jump?
• RQ4 How do granule size and intensity contrast vary with stellar parameters like T_eff, log g, and metallicity?
• RQ5 To what extent can ⟨3D⟩ models improve the accuracy of stellar parameter determination and abundance analysis compared to 1D models?

Key findings

• A tight scaling relation was found between the vertical velocity and the surface entropy jump, which correlates with the adiabatic convection zone's constant entropy value.
• The intensity contrast in 3D models increases significantly at lower metallicities, indicating stronger granulation in metal-poor stars.
• Granule size correlates closely with the pressure scale height at the depth of maximum velocity, supporting a physical scaling relation.
• The 3D models show substantial deviations from 1D models, especially in metal-poor stars, with differences in temperature structure and emergent flux that cannot be captured by MLT.
• The ⟨3D⟩ models systematically differ from 1D models in temperature stratification and line formation, demonstrating that MLT-based 1D models introduce significant systematic errors in stellar parameter estimation.
• The grid enables direct calibration of 1D model free parameters (e.g., α_MLT, micro/macro-turbulence) using 3D simulations, improving consistency with first-principles physics.