High-precision interpolation of stellar atmospheres with a deep neural network using a 1D convolutional auto encoder for feature extraction

Given the widespread availability of grids of models for stellar atmospheres, it is necessary to recover intermediate atmospheric models by means of accurate techniques that go beyond simple linear interpolation and capture the intricacies of the data. Our goal is to establish a reliable, precise, lightweight, and fast method for recovering stellar model atmospheres, that is to say the stratification of mass column, temperature, gas pressure, and electronic density with optical depth given any combination of the defining atmospheric specific parameters: metallicity, effective temperature, and surface gravity, as well as the abundances of other key chemical elements. We employed a fully connected deep neural network which in turn uses a 1D convolutional auto-encoder to extract the nonlinearities of a grid using the ATLAS9 and MARCS model atmospheres. This new method we call iNNterpol effectively takes into account the nonlinearities in the relationships of the data as opposed to traditional machine-learning methods, such as the light gradient boosting method (LightGBM), that are repeatedly used for their speed in well-known competitions with reduced datasets. We show a higher precision with a convolutional auto-encoder than using principal component analysis as a feature extractor.We believe it constitutes a useful tool for generating fast and precise stellar model atmospheres, mitigating convergence issues, as well as a framework for future developments. The code and data for both training and direct interpolation are available online at https://github.com/cwestend/iNNterpol for full reproducibility and to serve as a practical starting point for other continuous 1D data in the field and elsewhere.Comment: Accepted for publication in Astronomy and Astrophysics, 11 pages, 27 figures, 3 table

Temporal evolution of the Evershed flow in sunspots. II. Physical properties and nature of Evershed clouds

Context: Evershed clouds (ECs) represent the most conspicuous variation of the Evershed flow in sunspot penumbrae. Aims: We determine the physical properties of ECs from high spatial and temporal resolution spectropolarimetric measurements. Methods: The Stokes profiles of four visible and three infrared spectral lines are subject to inversions based on simple one-component models as well as more sophisticated realizations of penumbral flux tubes embedded in a static ambient field (uncombed models). Results: According to the one-component inversions, the EC phenomenon can be understood as a perturbation of the magnetic and dynamic configuration of the penumbral filaments along which these structures move. The uncombed inversions, on the other hand, suggest that ECs are the result of enhancements in the visibility of penumbral flux tubes. We conjecture that the enhancements are caused by a perturbation of the thermodynamic properties of the tubes, rather than by changes in the vector magnetic field. The feasibility of this mechanism is investigated performing numerical experiments of thick penumbral tubes in mechanical equilibrium with a background field. Conclusions: While the one-component inversions confirm many of the properties indicated by a simple line parameter analysis (Paper I of this series), we tend to give more credit to the results of the uncombed inversions because they take into account, at least in an approximate manner, the fine structure of the penumbra.Comment: Accepted for publication in A&

Downward pumping of magnetic flux as the cause of filamentary structures in sunspot penumbrae

The structure of a sunspot is determined by the local interaction between magnetic fields and convection near the Sun's surface. The dark central umbra is surrounded by a filamentary penumbra, whose complicated fine structure has only recently been revealed by high-resolution observations. The penumbral magnetic field has an intricate and unexpected interlocking-comb structure and some field lines, with associated outflows of gas, dive back down below the solar surface at the outer edge of the spot. These field lines might be expected to float quickly back to the surface because of magnetic buoyancy, but they remain submerged. Here we show that the field lines are kept submerged outside the spot by turbulent, compressible convection, which is dominated by strong, coherent, descending plumes. Moreover, this downward pumping of magnetic flux explains the origin of the interlocking-comb structure of the penumbral magnetic field, and the behaviour of other magnetic features near the sunspot

Resolving the Azimuthal Ambiguity in Vector Magnetogram Data with the Divergence-Free Condition: Application to Discrete Data

We investigate how the divergence-free property of magnetic fields can be exploited to resolve the azimuthal ambiguity present in solar vector magnetogram data, by using line-of-sight and horizontal heliographic derivative information as approximated from discrete measurements. Using synthetic data we test several methods that each make different assumptions about how the divergence-free property can be used to resolve the ambiguity. We find that the most robust algorithm involves the minimisation of the absolute value of the divergence summed over the entire field of view. Away from disk centre this method requires the sign and magnitude of the line-of-sight derivatives of all three components of the magnetic field vector.Comment: Solar Physics, in press, 20 pages, 11 figure

Milne-Eddington inversion of the Fe I line pair at 630~nm

The iron lines at 630.15 and 630.25 nm are often used to determine the physical conditions of the solar photosphere. A common approach is to invert them simultaneously under the Milne-Eddington approximation. The same thermodynamic parameters are employed for the two lines, except for their opacities, which are assumed to have a constant ratio. We aim at investigating the validity of this assumption, since the two lines are not exactly the same. We use magnetohydrodynamic simulations of the quiet Sun to examine the behavior of the ME thermodynamic parameters and their influence on the retrieval of vector magnetic fields and flow velocities. Our analysis shows that the two lines can be coupled and inverted simultaneously using the same thermodynamic parameters and a constant opacity ratio. The inversion of two lines is significantly more accurate than single-line inversions because of the larger number of observables.Comment: Accepted for publication in Astronomy and Astrophysics (Research Note

Temporal evolution of the Evershed flow in sunspots. I. Observational characterization of Evershed clouds

[Abridged] The magnetic and kinematic properties of the photospheric Evershed flow are relatively well known, but we are still far from a complete understanding of its nature. The evolution of the flow with time, which is mainly due to appearance of velocity packets called Evershed clouds (ECs), may provide information to further constrain its origin. Here we undertake a detailed analysis of the evolution of the Evershed flow by studying the properties of ECs. In this first paper we determine the sizes, proper motions, location in the penumbra, and frequency of appearance of ECs, as well as their typical Doppler velocities, linear and circular polarization signals, Stokes V area asymmetries, and continuum intensities. High-cadence, high-resolution, full vector spectropolarimetric measurements in visible and infrared lines are used to derive these parameters. We find that ECs appear in the mid penumbra and propage outward along filaments with large linear polarization signals and enhanced Evershed flows. The frequency of appearance of ECs varies between 15 and 40 minutes in different filaments. ECs exhibit the largest Doppler velocities and linear-to-circular polarization ratios of the whole penumbra. In addition, lines formed deeper in the atmosphere show larger Doppler velocities, much in the same way as the ''quiescent'' Evershed flow. According to our observations, ECs can be classified in two groups: type I ECs, which vanish in the outer penumbra, and type II ECs, which cross the outer penumbral boundary and enter the sunspot moat. Most of the observed ECs belong to type I. On average, type II ECs can be detected as velocity structures outside of the spot for only about 14 min. Their proper motions in the moat are significantly reduced with respect to the ones they had in the penumbra.Comment: Accepted for publication in A&

Theoretical Models of Sunspot Structure and Dynamics

Recent progress in theoretical modeling of a sunspot is reviewed. The observed properties of umbral dots are well reproduced by realistic simulations of magnetoconvection in a vertical, monolithic magnetic field. To understand the penumbra, it is useful to distinguish between the inner penumbra, dominated by bright filaments containing slender dark cores, and the outer penumbra, made up of dark and bright filaments of comparable width with corresponding magnetic fields differing in inclination by some 30 degrees and strong Evershed flows in the dark filaments along nearly horizontal or downward-plunging magnetic fields. The role of magnetic flux pumping in submerging magnetic flux in the outer penumbra is examined through numerical experiments, and different geometric models of the penumbral magnetic field are discussed in the light of high-resolution observations. Recent, realistic numerical MHD simulations of an entire sunspot have succeeded in reproducing the salient features of the convective pattern in the umbra and the inner penumbra. The siphon-flow mechanism still provides the best explanation of the Evershed flow, particularly in the outer penumbra where it often consists of cool, supersonic downflows.Comment: To appear in "Magnetic Coupling between the Interior and the Atmosphere of the Sun", eds. S.S. Hasan and R.J. Rutten, Astrophysics and Space Science Proceedings, Springer-Verlag, Heidelberg, Berlin, 200

Applicability of Milne-Eddington inversions to high spatial resolution observations of the quiet Sun

The physical conditions of the solar photosphere change on very small spatial scales both horizontally and vertically. Such a complexity may pose a serious obstacle to the accurate determination of solar magnetic fields. We examine the applicability of Milne-Eddington (ME) inversions to high spatial resolution observations of the quiet Sun. Our aim is to understand the connection between the ME inferences and the actual stratifications of the atmospheric parameters. We use magnetoconvection simulations of the solar surface to synthesize asymmetric Stokes profiles such as those observed in the quiet Sun. We then invert the profiles with the ME approximation. We perform an empirical analysis of the heights of formation of ME measurements and analyze the uncertainties brought about by the ME approximation. We also investigate the quality of the fits and their relationship with the model stratifications. The atmospheric parameters derived from ME inversions of high-spatial resolution profiles are reasonably accurate and can be used for statistical analyses of solar magnetic fields, even if the fit is not always good. We also show that the ME inferences cannot be assigned to a specific atmospheric layer: different parameters sample different ranges of optical depths, and even the same parameter may trace different layers depending on the physical conditions of the atmosphere. Despite this variability, ME inversions tend to probe deeper layers in granules as compared with intergranular lanes.Comment: Accepted for publication in Astronomy and Astrophysic

VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager

In this paper we describe in detail the implementation and main properties of a new inversion code for the polarized radiative transfer equation (VFISV: Very Fast inversion of the Stokes vector). VFISV will routinely analyze pipeline data from the Helioseismic and Magnetic Imager (HMI) on-board of the Solar Dynamics Observatory (SDO). It will provide full-disk maps (4096$\times$4096 pixels) of the magnetic field vector on the Solar Photosphere every 10 minutes. For this reason VFISV is optimized to achieve an inversion speed that will allow it to invert 16 million pixels every 10 minutes with a modest number (approx. 50) of CPUs. Here we focus on describing a number of important details, simplifications and tweaks that have allowed us to significantly speed up the inversion process. We also give details on tests performed with data from the spectropolarimeter on-board of the Hinode spacecraft.Comment: 23 pages, 9 figures (2 color). Submitted for publication to Solar Physic