Quantifying how Surface Complexity Influences Properties of the Solar Corona and Solar Wind

TL;DR

Addresses how photospheric boundary resolution affects the global coronal magnetic field and heating using a data-constrained MHD model MAS with WTD heating. Applies spherical harmonic decomposition to separate spatial scales across three effective resolutions, analyzing the magnetic field, squashing factor Q, and heating from the photosphere to the middle corona ($\le 3\,R_\odot$). Findings show small-scale photospheric flux boosts heating across scales; the best resolution yields about $40\%$ more heating than the base, and higher resolution fragments magnetic flux domains (higher-$\ell$ power in Q and heating) while large-scale structure converges by $3\,R_\odot$. Implications: low-resolution models may miss essential heating drivers and connectivity, guiding future modeling and subgrid parameterizations to account for unresolvable surface flux.

Abstract

The Sun's magnetic field is a key driver in coronal heating and consequently solar wind acceleration. Remote measurement of the photosphere provides the magnetic surface boundary condition necessary for data-constrained 3D global coronal models. With one such model, we explore how the spatial resolution of the surface boundary condition influences the global properties of the magnetic field and coronal heating. Using spherical harmonic decomposition, we quantify how three different resolution simulations vary in the low and middle corona. Through examination of the magnetic field, the squashing factor, and the heating rate, we demonstrate that small-scale photospheric magnetic flux enhances heating across spatial regimes. We calculate 40% more heating in our best resolution simulation as compared to our base resolution. We describe a strong correlation between the structure of the magnetic field and structure of the heating rate in the low corona across resolutions. These results provide key information as to what more efficient, low-resolution models might inherently miss. This can provide context to incorporate the effects of unresolvable features in future modeling efforts.

Figures (10)

• Figure 1: After applying SHD on the photospheric boundary condition synoptic map (left: medium, middle: high, right: super), the SHD is re-composed into data for logarithmic-spaced bins in $\ell$. Units are in Gauss and relative for each row. First row: Regridded data for $\ell = [0, 3]$, with identical features across resolution. Second row: Regridded data for $\ell = [4, 23]$, largely corresponding to the active region. Third row: Regridded data for $\ell = [24, 123]$, with diminishing magnetic field structures in the medium simulation. Fourth row: Regridded data for $\ell = [124, 627]$, where the magnetic structures in the super simulation are more prominent than both the high and medium resolutions. Fifth row: the SHD back to gridded data for the total range of $\ell$ values, which are visual matches to the three upper left panels of Figure \ref{['fig:br_combo_1']}.
• Figure 2: Three upper left panels: the photospheric radial magnetic field (Gauss) of each simulation (in Carrington longitude and latitude): medium (top, blue), high (middle, orange), and super (bottom, green). Upper right panels: similarly, the square root of the unsigned flux ($\sqrt{\mathrm{G}}$) of the photospheric radial magnetic field. Bottom panels: the associated total power spectra in units of the inputted data, squared. The power of the super simulation remains greater than the high and medium simulations at high $\ell$ values. This indicates more power in the super simulation at these smaller spatial scales. This is a quantification of the qualitative differences shown in the upper panels.
• Figure 3: As in Figure \ref{['fig:br_combo_1']}, the SHD and associated power spectra of the radial magnetic field (G) and square root of the unsigned flux (G$^{1/2}$), but now at 3 R$_\odot$. The overarching large-scale location of the HCS (i.e. the position of the inversion line where B$_r$ = 0) suggests that there should be similar structure across resolutions. Their similar power spectra confirms this.
• Figure 4: The power spectra of the square root of the unsigned radial magnetic field summed by logarithmic bins for each slice (1.0 R$_\odot$, 1.03 R$_\odot$, 1.51 R$_\odot$, 3 R$_\odot$) examined. There are noticeable magnitude difference in the lowest $\ell$ values in the photosphere (left, 1.0 R$_\odot$). In the low corona (center left, 1.03 R$_\odot$), the differences in the largest spatial scales have diminished while they have persisted in the smallest spatial scales. As the simulation approaches the heliospheric current sheet (center right, 1.51 R$_\odot$ and right, 3 R$_\odot$), the power of the structures at each spatial regime have become nearly identical.
• Figure 5: Constructed analogously to Figure \ref{['fig:br_combo_1']}, the visualization and total power spectra for all three resolutions of the photospheric log$_{10}$Q$_{\mathrm{avg}}$ (left) and $\sqrt{|\mathrm{log}_{10}\mathrm{Q}_{\mathrm{avg}}|}$ (right). For this scalar quantity, the structures remain nearly identical in the upper left and upper right panels. This is further shown in the similar shapes of the power spectra in the lower panels. The medium power spectrum having more power at low $\ell$ values is a reflection of the fractal nature of the squashing factor. A possible example of this effect is the band structures around $\pm 60 \degree$ latitude.