Global Coronal Equilibria with Solar Wind Outflow II -- Optimizing the Outflow Model

Abstract

We expand upon our paper (Rice and Yeates, 2021) which introduced `Outflow Fields': alternatives to the widely-used potential field source surface (PFSS) extrapolations of the Sun's coronal magnetic field which take into account the effect of the solar Wind. We showed that our fields have several advantages over PFSS, namely more accurate measurements of the Open Solar Flux (OSF) relative to observations, more realistic streamer shapes and less dependence on the arbitrary source-surface height. In this paper we seek to quantify these improvements. This includes comparison of magnetic field line angles with eclipse photography, an improved solar wind solution model and the introduction of data from a wider range of observations. We use these comparisons to determine the optimum parameters for our model using an evolutionary algorithm, in addition to the creation of synthetic eclipse images. We find that our Outflow Fields can accurately capture the overall topology of the magnetic field, and reduce the well-known discrepancy with in-situ magnetic field measurements by a significant margin relative to PFSS. Specifically, over the period between 2000 and 2022 for a typical source-surface height we find that optimized Outflow fields reduce this discrepancy from around 45% to 24% while also matching the field line topology seen during eclipse photography. Our model is presented for wider use by the community as a new python package "outflowpy".

Figures (12)

• Figure 1: Outflow speeds $V(r)$ as a function of altitude $r$, shown up to five solar radii and for a variety of coronal sound speeds $c_s$, calculated using the implicit formula \ref{['eqn:parker_implicit']} and a magnetofrictional constant $\nu_0 = 5 \times 10 ^ { -17} \rm s \, cm ^{-2}$.
• Figure 2: Magnetic field data from the HMI synoptic map series, for the 2017 August 21. The upper panel shows the raw input data (a weighted combination of the synoptic maps for CR2193 and CR2194), and the lower panel shows this same data after our smoothing and interpolation process, ready to be used as a lower boundary condition for an Outflow Field.
• Figure 3: Plots of the OSF on 2017 August 21 as a function of altitude, for both the PFSS model and Outflow Fields at both $110\,\mathrm{km}\,\mathrm{s}^{-1}$ and $150\,\mathrm{km}\,\mathrm{s}^{-1}$, with source surface heights $r_{ss}$ varying between $1.5 R_\odot$ and $5.0 R_\odot$. The source surface height for each result is indicated by the black-outlined circles at the end of each plotted line. The OSF is measured in Maxwells ($\mathrm{Mx}\equiv\mathrm{G}\,\mathrm{cm}^{-2}$), and the magnetofrictional constant used to generate the Outflow Fields is $\nu_0 = 5 \times 10 ^ { -17} \rm s \, cm ^{-2}$.
• Figure 4: Qualitative comparison of the magnetic field structures of PFSS fields and Outflow Fields (with $c_s = 150 \,\mathrm{km}\,\mathrm{s}^{-1}$) for two source-surface heights. The input magnetic field data is centered on the HMI measurements from 2017 August 21. The magnetofrictional constant used to generate the Outflow Fields is $\nu_0 = 5 \times 10 ^ { -17} \rm s \, cm ^{-2}$.
• Figure 5: Comparison between PFSS, Outflow Field extrapolations and in-situ measurements of the OSF at 1AU. The in-situ data is taken from 2022SoPh..297...82F. The extrapolated data are presented as 27-day moving averages, with the plotted error being a 99% confidence interval. The magnetofrictional constant in the Outflow Fields is $\nu_0 = 5 \times 10 ^ { -17} \rm s \, cm ^{-2}$ and the source surface height is $r_{ss} = 2.5R_\odot$.