Context.Recently, new solar model atmospheres have been developed to replace classical 1D local thermodynamical equilibrium (LTE) hydrostatic models and used to for example derive the solar chemical composition. Aims. We aim to test various models against key observational constraints. In particular, a 3D model used to derive the solar abundances, a 3D magnetohydrodynamical (MHD) model (with an imposed 10 mT vertical magnetic field), 1D NLTE and LTE models from the PHOENIX project, the 1D MARCS model, and the 1D semi-empirical model of Holweger & Müller. Methods. We confronted the models with observational diagnostics of the temperature profile: continuum centre-to-limb variations (CLVs), absolute continuum fluxes, and the wings of hydrogen lines. We also tested the 3D models for the intensity distribution of the granulation and spectral line shapes. Results. The predictions from the 3D model are in excellent agreement with the continuum CLV observations, performing even better than the Holweger & Müller model (constructed largely to fulfil such observations). The predictions of the 1D theoretical models are worse, given their steeper temperature gradients. For the continuum fluxes, predictions for most models agree well with the observations. No model fits all hydrogen lines perfectly, but again the 3D model comes ahead. The 3D model also reproduces the observed continuum intensity fluctuations and spectral line shapes very well. Conclusions. The excellent agreement of the 3D model with the observables reinforces the view that its temperature structure is realistic. It outperforms the MHD simulation in all diagnostics, implying that recent claims for revised abundances based on MHD modelling are premature. Several weaknesses in the 1D hydrostatic models (theoretical and semi-empirical) are exposed. The differences between the PHOENIX LTE and NLTE models are small. We conclude that the 3D hydrodynamical model is superior to any of the tested 1D models, which gives further confidence in the solar abundance analyses based on it.

Context. In the solar atmosphere, the acoustic cutoff frequency is a local quantity which depends on the atmospheric height. It separates the low-frequency evanescent waves from the high-frequency propagating waves. Aims. We measure the cutoff frequency of slow magnetoacoustic waves at various heights of a sunspot umbra and compare the results with the estimations from several analytical formulae. Methods. We analyzed the oscillations in the umbra of a sunspot belonging to active region NOAA 12662 observed in the 10830 Å spectral region with the GREGOR Infrared Spectrograph and in the Fe i 5435 Å line with the GREGOR Fabry-Pérot Interferometer. Both instrumets are attached to the GREGOR telescope at the Observatorio del Teide, Tenerife, Spain. We have computed the phase and amplification spectra between the velocity measured from different pairs of lines that sample various heights of the solar atmosphere. The cutoff frequency and its height variation have been estimated from the inspection of the spectra. Results. At the deep umbral photosphere the cutoff frequency is around 5 mHz and it increases to 6 mHz at higher photospheric layers. At the chromosphere the cutoff is ∼ 3.1 mHz. The comparison of the observationally determined cutoff with the theoretically predicted values reveals an agreement in the general trend and a reasonable match at the chromosphere, but also significant quantitative differences at the photosphere. Conclusions. Our analyses show strong evidence of the variation of the cutoff frequency with height in a sunspot umbra, which is not fully accounted for by current analytical estimations. This result has implications for our understanding of wave propagation, the seismology of active regions, and the evaluation of heating mechanisms based on compressible waves.

The question of possible small-scale dynamo action in the surface layers of the Sun is revisited with realistic 3D MHD simulations. As in other MHD problems, dynamo action is found to be a sensitive function of the magnetic Prandtl number P m = ν/η; it disappears below a critical value P c which is a function of the numerical resolution. At a grid spacing of 3.5 km, P c based on the hyperdiffusivities implemented in the code (STAGGER) is ≈1, increasing with increasing grid spacing. As in other settings, it remains uncertain whether small scale dynamo action is present in the astrophysical limit where P m 1 and magnetic Reynolds number R m 1. The question is discussed in the context of the strong effect that external stray fields are observed to have in generating and maintaining dynamo action in other numerical and laboratory systems, and in connection with the type-II hypertransient behavior of dynamo action observed in the absence of such external fields.