Structure and dynamics of the internetwork solar chromosphere: results of a small-scale dynamo simulation

TL;DR

This work addresses how quiet-Sun chromospheric heating and structure arise when magnetic fields are generated purely by a small-scale dynamo (SSD) in a 3D radiative MHD framework with NLTE hydrogen ionisation. It employs the MURaM code with NLTE radiative transfer, a non-LTE equation of state, and a high-resolution domain (12×12×18 Mm) to self-consistently model the SSD-driven chromosphere, including shock–field interactions and energy transport via Poynting flux and enthalpy flux. The results show a dynamically rich, magnetically dominated mid-to-upper chromosphere, with a base Poynting flux around $$, and a total energy input capable of powering chromospheric losses, though the simulated corona remains transient and not in a steady million-degree state due to domain limitations and missing non-ideal processes. This implies SSD-generated internetwork fields can plausibly account for quiet-Sun chromospheric heating and upper-atmosphere dynamics, motivating larger-domain simulations with non-ideal effects to fully capture coronal heating and canopy formation.

Abstract

The heating and structure of the solar chromosphere depends on the underlying magnetic field, among other parameters. The lowest magnetic flux of the solar atmosphere is found in the quiet Sun internetwork and is thought to be provided by the small-scale dynamo (SSD) process. We aim to understand the chromospheric structure and dynamics in a simulation with purely SSD generated magnetic fields. We perform a 3D radiation-magnetohydrodynamic (rMHD) simulation of the solar atmosphere, including the necessary physics to simulate the solar chromosphere. No magnetic field is imposed beyond that generated by an SSD process. We analyse the magnetic field in the chromosphere, and the resulting energy balance. Plasma at chromospheric temperatures reaches high into the atmosphere, with small, transient regions reaching coronal temperatures. An average Poynting flux of $5\times10^6~\mathrm{erg\;cm}^{-3}$\;s$^{-1}$ is found at the base of the chromosphere. The magnetic field in the chromosphere falls off more slowly with height than predicted by a potential field extrapolation from the radial component of the photospheric field. Starting in the middle chromosphere, the magnetic energy density is an order of magnitude larger than the kinetic energy density and, in the upper chromosphere, also larger than the thermal energy density. Nonetheless, even in the high chromosphere, the plasma beta in shock fronts and low-field regions can locally reach values above unity. The interactions between shocks and the magnetic field are essential to understanding the dynamics of the internetwork chromosphere. The SSD generated magnetic fields are strong enough to dominate the energy balance in the mid-to-upper chromosphere. The energy flux into the chromosphere is $8.16\times 10^{6}~\mathrm{erg\;cm^{-2}\;s^{-1}}$, larger than the canonical values required to heat the quiet sun chromosphere and corona.

Figures (12)

• Figure 1: A snapshot of the simulation, panel a) The intensity in the continuum (1st) band of the multigroup scheme, panel b) the vertical velocity at $\tau_{500} = 1$, panel c) the intensity in the low-chromospheric (4th) band of the multi-group scheme, and panel d) the vertical magnetic field strength at $\tau_{500} = 1$. The maximum field strength has been saturated to better illustrate the salt-and-pepper field concentrations. The dashed line represents the slice shown in Fig. \ref{['fig:slice_atmosphere']}& \ref{['fig:Eslice']}. https://datashare.mpcdf.mpg.de/s/cdBaEXnLoWpl0o9, the image represents $t=0$ of the animation.
• Figure 2: A vertical slice through the simulation taken in the xz plane at $y=6~\mathrm{Mm}$. The figure includes; panel a) Temperature, b) vertical velocity and c) vertical magnetic field, and d) the plasma density. We use an arcsinh norm for the magnetic field, and limit all panels to highlight the chromosphere. The horizontal dashed lines represent the photosphere $\tau_{500}=0$ and base of the chromosphere $z=0.8~\mathrm{Mm}$. https://datashare.mpcdf.mpg.de/s/flU0hJhAJUmPKlh, the image represents $t=0$ of the animation.
• Figure 3: Horizontally and temporally averaged thermodynamic properties of the simulated chromosphere. Top: the hydrogen ionisation fraction and chromospheric filling factor, which is the area fraction at each height with a temperature below 20kK. Middle: the temperature (red) and density (black). The shaded areas cover two standard-deviations around the mean. Additionally the density which is recovered from hydrostatic equilibrium is included in the middle panel. This is calculated including only the gas pressure (dash-dotted), the gas and turbulent pressures (dash-dotted), and the gas pressure, turbulent pressure and magnetic term (indistinguishable from the averaged density). Bottom: the error of the density calculated recovered with the hydrostatic equilibrium approximation. The vertical dashed lines represent the photosphere ($z=0~\mathrm{Mm}$) and the base of the chromosphere ($z=0.8~\mathrm{Mm}$).
• Figure 4: Horizontally and temporally averaged values of unsigned vertical field $|B_z|$ and the horizontal field $B_h = \left( B_x^2 + B_y^2 \right)^{0.5}$ through the atmosphere. The shaded regions cover two standard deviations. The dash-dotted lines illustrate the magnetic energy assuming a potential field extrapolation from z=0.
• Figure 5: Horizontally and temporally averaged values of $\log_{10}\beta$. The shaded region covers two standard deviations. The vertical dashed lines represent the photosphere $(z=0)$ and the base of the chromosphere $(z=800~\mathrm{km})$.