One-dimensional, geometrically stratified semi-empirical models of the quiet-Sun photosphere and lower chromosphere^⋆

¹ Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany
e-mail: borrero@leibniz-kis.de
² Institute for Solar Physics, Department of Astronomy, Stockholm University, AlbaNova University, Centre, 10691 Stockholm, Sweden

Received: 19 December 2023
Accepted: 23 March 2024

Abstract

Context. One-dimensional, semi-empirical models of the solar atmosphere are widely employed in numerous contexts within solar physics, ranging from the determination of element abundances and atomic parameters to studies of the solar irradiance and from Stokes inversions to coronal extrapolations. These models provide the physical parameters (i.e. temperature, gas pressure, etc.) in the solar atmosphere as a function of the continuum optical depth τ_c. The transformation to the geometrical z scale (i.e. vertical coordinate) is provided via vertical hydrostatic equilibrium.

Aims. Our aim is to provide updated, one-dimensional, semi-empirical models of the solar atmosphere as a function of z, but employing the more general case of three-dimensional magneto-hydrostatic equilibrium (MHS) instead of vertical hydrostatic equilibrium (HE).

Methods. We employed a recently developed Stokes inversion code that, along with non-local thermodynamic equilibrium effects, considers MHS instead of HE. This code is applied to spatially and temporally resolved spectropolarimetric observations of the quiet Sun obtained with the CRISP instrument attached to the Swedish Solar Telescope.

Results. We provide average models for granules, intergranules, dark magnetic elements, and overall quiet-Sun as a function of both τ_c and z from the photosphere to the lower chromosphere.

Conclusions. We demonstrate that, in these quiet-Sun models, the effect of considering MHS instead of HE is negligible. However, employing MHS increases the consistency of the inversion results before averaging. We surmise that in regions with stronger magnetic fields (i.e. pores, sunspots, network) the benefits of employing the magneto-hydrostatic approximation will be much more palpable.