Revisiting the coronal current sheet model: Parameter range analysis and comparison with the potential field model

Abstract

Aims. We study the properties of the coronal magnetic field according to the current sheet source surface (CSSS) model in 1976–2017 for all physically reasonable values of the three model parameters (cusp surface radius Rcs, source surface radius Rss, and current parameter a), and compare the CSSS field with the potential field source surface (PFSS) model field. Methods. We used the synoptic maps of the photospheric magnetic field from the Wilcox Solar Observatory (WSO), National Solar Observatory/Kitt Peak (NSO/KP), and the NSO Synoptic Optical Long-term Investigations of the Sun Vector Spectromagnetograph (SOLIS/VSM) in order to calculate the coronal magnetic field according to the CSSS and PFSS models. We calculated the coronal field strength, its latitudinal variation and neutral line location, as well as its polarity match with the heliospheric magnetic field. Results. The CSSS model can correct the erroneous latitudinal variation of the PFSS model if the source surface is sufficiently far out with respect to the cusp surface (Rss ≥ 3 ⋅ Rcs). The topology of the neutral line only slightly depends on source surface radius or current parameter, but excludes very low values of the cusp surface (Rcs ≤ 1.5). A comparison of the polarities gives an optimum cusp surface radius that varies in time between 2 and 5; a stronger current yields a larger optimum Rcs. Interestingly, the optimum polarity match percentages and optimum radii vary very similarly in the two models over the four solar cycles we studied. Conclusions. The CSSS model can produce a stronger total coronal flux than the PFSS model and correct its latitudinal variation. However, the topology of the CSSS model is rather independent of horizontal currents and remains very similar to that of the PFSS model. Therefore, the CSSS model cannot improve the match of field polarities between corona and heliosphere.

Application of historic datasets to understanding open solar flux and the 20th-century grand solar maximum. 2. Solar observations

“…The modelled values are showing that at each sunspot minimum only half the OSF is in polar coronal holes, the other half being within the streamer belt (i.e at sunspot minima F CH ≈ F SB ≈ F S /2). PFSS modelling shows this fraction of OSF outside the polar coronal holes is not unreasonable (see Figure 5 of Koskela et al, 2019) but the total OSF derived is too small by roughly the factor two compared to the in-situ data (the open flux problem), even though the temporal variations are very similar (see Figure 8 Koskela et al, 2019).…”

“…To simplify solution of the equations, the coronal electric currents are only field-aligned and perpendicular to gravity (Low, 1991). Koskela et al (2019) show that increasing a fit parameter a from 0.01 to 1.0, introduced to allow for the radial length scale of the coronal currents (Mackay and Yeates, 2012), increases the total OSF predicted by magnetostatic equivalents of PFSS by 50% at all phases of the solar cycle. The magneto-frictional non-potential modelling by Yeates et al (2010) increased the OSF at solar minimum by only 25% and by 75-85% at solar maximum.…”

Reconstruction of Carrington Rotation means of Open Solar Flux over the past 154 years

“…However computation of the OSF from the integrated magnetic flux threading coronal holes detected this way (Lowder et al, 2014;Lowder, Qiu, and Leamon, 2017) leads to OSF estimates that are smaller than those derived from other methods by a factor of close to two (Linker et al, 2017;Wallace et al, 2019), probably because of open flux embedded in the streamer belt that is not detected as dark in the EUV or X-ray emissions. Those other methods have included: Potential Field Source Surface (PFSS) modelling of coronal fields from photospheric field measurements (Altschuler and Newkirk, 1969;Schatten, Wilcox, and Ness, 1969;Wang and Sheeley, 1992); developments of PFSS such as Current Sheet Source Surface (CSSS) modelling (Koskela, Virtanen, and Mursula, 2019); non-potential modelling using magnetic flux transport and magneto-frictional simulations, which can also allow for currents below the coronal source surface (Yeates et al, 2010); MHD simulations based on photospheric field observations (Riley, Linker, and Mikić, 2001;Riley et al, 2011); interplanetary and geomagnetic observations (discussed below); and, at sunspot minimum (when polar coronal holes dominate), polar faculae and streamer belt width (Muñoz-Jaramillo et al, 2012;Lockwood et al, 2022b).…”

A Near-half-century Simulation of the Solar Corona

“…Long-term studies of the solar corona typically approximate the magnetic field using the potential field source surface (PFSS) model (e.g., Wang et al 2000;Virtanen et al 2020;Luhmann et al 2022), or the current sheet source surface (CSSS) model (Zhao & Hoeksema 1995;Koskela et al 2019). PFSS assumes a current-free domain in which the field is at every time in a minimal-energy equilibrium.…”