Structure of the solar photosphere studied from the radiation hydrodynamics code ANTARES

Astrophys Space Sci (2017) 362:181 DOI 10.1007/s10509-017-3151-7 O R I G I N A L A RT I C L E Structure of the solar photosphere studied from the radiation hydrodynamics code ANTARES P. Leitner1 · B. Lemmerer1 · A. Hanslmeier1 · T. Zaqarashvili1,2,3 · A. Veronig1 · H. Grimm-Strele4,5 · H.J. Muthsam4 Received: 16 June 2017 / Accepted: 2 August 2017 © The Author(s) 2017. This article is published with open access at Springerlink.com Abstract The ANTARES radiation hydrodynamics code is capable of simulating the solar granulation in detail unequaled by direct observation. We introduce a state-ofthe-art numerical tool to the solar physics community and demonstrate its applicability to model the solar granulation. The code is based on the weighted essentially nonoscillatory finite volume method and by its implementation of local mesh refinement is also capable of simulating turbulent fluids. While the ANTARES code already provides promising insights into small-scale dynamical processes occurring in the quiet-Sun photosphere, it will soon be capable of modeling the latter in the scope of radiation magnetohydrodynamics. In this first preliminary study we focus on the vertical photospheric stratification by examining a 3-D model photosphere with an evolution time much larger than the dynamical timescales of the solar granulation and of particular large horizontal extent corresponding to 25 × 25 on the solar surface to smooth out horizontal spatial inhomogeneities separately for up- and downflows. The highly resolved Cartesian grid thereby covers ∼ 4 Mm of the upper convection zone and the adjacent photosphere. Correlation analysis, both local and two-point, provides a suitable means to probe the photospheric structure and thereby to identify B P. Leitner 1 University of Graz, Universitätsplatz 5, 8010 Graz, Austria 2 Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, 8042 Graz, Austria 3 Abastumani Astrophysical Observatory at Ilia State University, 3/5 Cholokashvili avenue, 0162 Tbilisi, Georgia 4 Faculty of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Wien, Austria 5 Max-Planck Institute for Astrophysics, Karl-Schwarzschild-Strasse 1, 85741 Garching, Germany several layers of characteristic dynamics: The thermal convection zone is found to reach some ten kilometers above the solar surface, while convectively overshooting gas penetrates even higher into the low photosphere. An ≈ 145 km wide transition layer separates the convective from the oscillatory layers in the higher photosphere. Keywords Sun: photosphere · Sun: granulation · Methods: radiation hydrodynamics modeling · Methods: data analysis 1 Introduction The structure and dynamics of the solar photosphere is crucially determined by the mass and energy transport processes taking place across the solar surface. For the study of the solar convection and its phenomenological manifestation on the visible surface of the Sun, the solar granulation, numerical simulations not only complement observational data but also serve as a means of their own by providing complete and almost continuous information in 3-D of the physical state and the dynamics which otherwise often has to be drawn indirectly from observations. The physics of the layers surrounding the solar surface is rather involved; below the surface the opacity is sufficiently large so that the local adiabatic gradient is exceeded by the temperature gradient needed for radiative-diffusive energy transport, turning the fluid convectively unstable. This process is primarily described by mixing length theory (e.g. Cox and Giuli 1968; Spruit 1974) that proved to be successful at determining the average energy transport (Cattaneo et al. 1991), while neglecting e.g. the dynamical modifications to the hydrostatic equilibrium near the surface (MacGregor 1991). At the solar surface and above, along with a rapid decrease of the opacity, radiation becomes the primary energy 181 Page 2 of 13 P. Leitner et al. Fig. 1 Left: Vertical profile of horizontally averaged pressure, density, and temperature for a given model time step as a function of geometric depth x as obtained from the ANTARES model based on the ATLAS 9 package (Kurucz 1970). Error-bars indicate the quantities’ variation at a given geometric depth. Right: Comparison to data from the energy- balance model atmosphere No. C of the quiet Sun of Fontenla et al. (1993). The steep temperature gradient at the surface that is visible in both model atmospheres is due to the large temperature sensitivity of the dominant H− opacity (e.g. Stein and Nordlund 1998) transport mechanism, although a continuing mass flow overshooting into convectively stable regions still characterizes the lower photosphere. Ionization and molecular dissociation processes taking place in the near surface layers considerably affect the internal energy and the equation of state. The extent to which numerical models reflect reality has improved significantly with increasing numerical accuracy and level of physical detail since the 1970s, one such enhancement being the consideration of non-gray radiative transport. The photosphere and the subjacent thin 4 Mm wide layer of the upper convection zone that are covered in the simulation studied here constitute a region of almost negligible radial extent, accounting for no more than 0.64% of the solar radius. Yet it is these layers that feature remarkably rich dynamical processes driven by steep vertical gradients of temperature, pressure, and density, the latter falling off by 5 and 4 orders of magnitude, respectively, see Fig. 1. We present the state-of-the-art radiation hydrodynamics (RHD) code ANTARES (A Numerical Tool for Astrophysical RESearch), applied to the study of the near surface convection and the photosphere of the Sun. In spite of the broad range of applicability, ranging from the modeling of photospheric turbulence (Muthsam et al. 2007) to Cepheid pulsation (Muthsam et al. 2011), the code has not received much attention in the solar physics community so far. While, for the time being, the code is restricted to the modeling of the quiet Sun, an MHD upgrade is foreseen in the near future that will allow us to study the modifications to the dynamics and to the energy transport due to the photospheric magnetic field and to extend its applicability to magnetoactive regions at the solar surface. Further recent developments of the code are summarized in Blies et al. (2015) and include the consid- eration of two-component flows (Zaussinger 2010), a parallel multigrid solver for the 2-D non-linear Helmholtz equation (Happenhofer et al. 2013), and a generalization to solve the Navier-Stokes equations on curvilinear grids (GrimmStrele et al. 2014). While the over many years of development fully matured ANTARES code is characterized by its elaborate numerical schemes and its stability, it is by far not the only simulation project of similar s (...truncated)