Chromosphere of the quiet sun -- I. Shock and current-sheet dynamics and heating

TL;DR

This study tackles the longstanding problem of quiet-Sun chromospheric heating by using a high-resolution 3D radiation-MHD simulation with Bifrost to separate the roles of shocks and current sheets. By applying physics-based criteria, the authors quantify how shocks dominate the lower chromosphere while current sheets dominate the upper chromosphere, with shocks and CS together accounting for a majority of the mechanical heating ($66\%$) and a notable $13\%$ overlap, and show that compressive heating is a major local contributor. The results support a multi-process heating paradigm, where intermittently generated shocks and reconnection-driven CS events, modulated by local plasma $\beta$ and Mach number, shape the chromospheric energy balance. The work underscores the need for next-generation, high-resolution observations to resolve these small-scale dynamics and to constrain energy transport and coupling between the chromosphere, transition region, and corona.

Abstract

The solar chromosphere is a crucial interface between the solar interior and its interplanetary environment, regulating how energy is locally deposited into heat and transported into the upper atmospheric layers. Despite significant progress, the dominant processes responsible for chromospheric heating remain debated, particularly under quiet-Sun (QS) conditions. We aim to disentangle and quantify the respective roles of shocks and current sheets (CS) in QS chromospheric modeling. We use a simulation performed with the radiation-magnetohydrodynamics code Bifrost. In order to identify shocks and CS events across space and time, we develop and apply physics-based criteria, allowing us to describe their dynamics and evaluate their contributions to both dissipative (viscous and ohmic) and mechanical (including compressive work) heating. Shocks are found to dominate the energy deposition in the lower chromosphere (up to $59\%$ of the mechanical heating), while CS become the primary contributor in the upper chromosphere, as both plasma $β$ and Mach number $Ma$ drop. Overall, $66\%$ of the mechanical chromospheric heating is powered by the combined action of shocks and CS. These results support a multi-process view of the chromospheric heating in the QS, dominated by shocks, CS, and non-steep gradient dynamics. In addition to viscous and ohmic dissipation, compressive heating can play a major role locally in the model, particularly in chromospheric shock structures, where it offsets non-reversibly cooling from expansion and radiation, and therefore constitutes a key heating contribution to consider in the energy budget. This study further highlights the need for next-generation observations to resolve the intermittent and small-scale nature of chromospheric dynamics, in order to bring new constraints on the coupling between the different layers of the solar atmosphere.

Figures (13)

• Figure 1: 3D visualization of ch012023. The horizontal and corrugated slice represents the $\tau_{500}=1$ surface, coloured with the photospheric vertical magnetic field $B_z$. Vertical convective velocities $v_z$ are illustrated on the side of the upper-convection zone, and magnetic field lines are coloured with temperatures. 15x15 seeds have been uniformly distributed horizontally at 3 Mm to trace magnetic field lines. These lines connect to different structures, and preferentially to magnetic concentration located in intergranular lanes at the photosphere. Magnetic field lines are coloured by temperature, ranging from pink in the temperature minimum region of the chromosphere ($\sim4000$ K), to white in the transition region ($\sim40~000$ K), and finally green when reaching the low corona at the top of our box ($\sim500~000$ K). Note the vortex-like pink feature at the middle of the box, known as a magnetic tornado. An animation is available at (To be decided with AA) and covers 12 s, which corresponds to 30 solar minutes.
• Figure 2: Temperature distribution. Left: Probability density function (PDF) of the temperature as a function of height. The horizontally-averaged mean temperature profile is shown with a dotted line. Note the logarithmic temperature scale. Right: Vertical cut in the middle of the domain of the temperature map. Note the 2d cut of the vortex-like structure highlighted in Fig. \ref{['fig:3DglobRend']} between $x=3$ and 7 Mm, along with spicular structures, notably at $x=8$ Mm, propagating chromospheric temperatures into the transition region. An animation is available at (To be decided with AA) and covers 71 s, which correspond here to 2 solar hours.
• Figure 3: Shock locations. Top-left: The compression frequency $-\mathbf{\nabla}\cdot\mathbf{v}$ taken at Y = 6 Mm. Red and green areas correspond to compression and expansion, respectively, and the magnetic polarity is illustrated along magnetic field lines (grey) with arrows. A zoom of the blue-dashed square is proposed in the bottom panels to highlight shock features (purple). Dark and blue arrows are used to highlight particular compression locations due to wave propagation and rising over-density, respectively. The $\beta=1$ surface is illustrated with a dashed black line. An animation is available at (To be decided with AA) and covers 13 s, which corresponds to 21 solar minutes. Top-right: 3D rendering of the shock fronts in the simulation domain at t = 274 min. Similar to Fig. \ref{['fig:3DglobRend']}, but we do not colour magnetic field lines for the sake of clarity. Note that we use an orange dashed line along with a dark arrow to highlight the dome-like shape of a shock's front. The locations of the magneto-acoustic shocks are highlighted in magenta for both panels, identified with large values of compression ($-\mathbf{\nabla}\cdot\mathbf{v}>c_s/(6.ds)$, see Eq. \ref{['eq:cs_crit']}). An animation is available at (To be decided with AA) and covers 11 s, which corresponds to 18 solar minutes. Bottom: A zoom on shock features, showing from left to right the temperature, density, vertical and horizontal velocity along x, respectively. We note that the purple contours overlay the strong gradients of the different quantities. Indicative purple arrows are shown to illustrate the shock motions.
• Figure 4: CS location. Top-left: The normalized-parallel current $|\mathbf{\nabla}\times B\cdot B|/B^2$ taken at $y=6$ Mm. Note that this quantity has the dimension of a spatial frequency, with white areas corresponding to high amplitudes. The magnetic polarity is illustrated along magnetic field lines (yellow) with arrows. A zoom of the yellow-dashed square is proposed in the bottom panels to highlight a CS feature. The $\beta=1$ surface is illustrated with a red dashed line. Blue arrows are used to highlight particular locations of weaker and broader current layers, not labelled as CS following Eq. \ref{['eq:alpha_crit']}, and likely due to wave propagation, magnetic field braiding, and phase mixing. The $\beta=1$ surface is illustrated with a dashed red line. An animation is available at (To be decided with AA) and covers 12 s, which corresponds to 20 solar minutes. Top-right: 3D rendering of CS in the simulation domain at t = 224 min. The locations of CS are highlighted in green for both panels, identified with large values of the normalized-parallel current ($|(\mathbf{\nabla}\times B)\cdot B|/B^2>1/(6.ds)$, see Eq. \ref{['eq:alpha_crit']}). Bottom: A zoom on CS features, showing from left to right the temperature, vertical velocity, horizontal velocity, and magnetic field component along x, respectively. We note that the green contours overlay the strong gradients in $B_x$ and bipolar velocity patterns. Indicative arrows are shown in cyan and dark red to illustrate these motions.
• Figure 5: Fractional number of grid cells labelled as shocks (purple line) or CS (green line), as a function of height. An indicative dotted vertical line shows the position $z=0$ Mm (bottom of the photosphere), and a zoom is proposed to catch the small peak of shocks filling factor at this location. These curves are averaged over one hour in time and horizontally in space.