Authors: Valentin Aslanyan1, David MacTaggart1,2, Roger B. Scott3, Chloe P. Wilkins4, David I. Pontin4, Anthony R. Yeates5, Peter F. Wyper5, Karen A. Meyer6, and Spiro K. Antiochos7
Affiliations:
1School of Mathematics & Statistics, University of Glasgow, Glasgow, G12 8QQ, UK
2Department of Physics, University of Trento, Povo, 38123, Italy
3Montana State University, Bozeman, MT 59715, USA
4School of Science, University of Newcastle, University Drive, Callaghan, NSW 2308, Australia
5Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK
6Division of Mathematics, School of Science and Engineering, University of Dundee, Dundee, DD1 4HN, UK
7University of Michigan, Department of Climate and Space Sciences and Engineering, Ann Arbor, MI 48109, USA
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Introduction:
In coining the term magnetohydrodynamics, Hannes Alfvén proved that in the limit of vanishing resistivity, the field lines are frozen into the plasma flow. This is often a reasonable approximation for the solar corona. However, finite resistivities lead the field lines to “slip”, or appear to move relative to the fluid velocity, which leads to magnetic reconnection and changes in magnetic topology. In the above-named article, we present a numerical tool to quantify the rate of such slippage we label Σ. Figure 1 is an illustration of this concept in the solar corona; suppose that the footpoint of a field line moves, while a blob of plasma to which it is attached higher up is stationary; in the limit of ideal MHD, it would be connected to that same blob continuously, but in the presence of a resistive region the field line would begin to slip along its length and become connected to a different fluid parcel.
We present the Universal Slippage calculator (USlip), which computes the rate of non-ideal motion of magnetic field lines from an input magnetic field defined by the user, as an array in Python, or directly from the Lare3d, ARMS, or DUMFRIC codes. To this end, we make use of a theoretical framework from previous studies[1,2,3] and our existing tool for squashing factor calculations, the Universal Fieldline Tracer (UFiT)[4]. This is synergistic, as the squashing factor is also a key tool in identifying reconnection sites.
Figure 1. Illustration of how magnetic field line slippage Σ (deviation from ideal MHD due to resistivity) may arise in the corona.
Model:
Derived from the equations of resistive MHD, an expression for the slippage rate requires only the 3D vector magnetic field and (optionally) the scalar local resistivity to be known. Furthermore, there is a related force-free slippage rate, which is also calculated. The difference in these quantities can elucidate whether the magnetic field is close to force-free in the domain.
Results:
To demonstrate the technical and scientific capabilities of this tool, we have post-processed three previous simulations. We have previously used the ARMS code to study interchange reconnection between open and closed field lines at a coronal hole boundary[5]. Such a process must involve field line slippage, and indeed we find that it does. The study assumed that the footpoints of field lines were transported at the photosphere by supergranules, conceptually as in Figure 1. Computationally, this was achieved by imposing a known velocity profile and a strictly frozen-in magnetic field as boundary conditions; these two facts allowed us to identify which field lines had undergone reconnection from open to closed and vice versa.
Figure 2. Field line slippage during an MHD simulation with the ARMS code. (a) Isosurface of Σ, (b) sample field lines colored by Σ and a slice at constant radius; the coloring is consistent across all panels. (d) Signed logarithm of the squashing factor positive/red corresponds to closed and negative/blue to open field lines.
The new analysis allows us to localize the nonideal effects more narrowly, as shown in Figure 2. In panel (a) we show an isosurface of constant slippage, inside which the effect is strongest; it extends above the driving supergranules. In panel (b) we color the field lines by the magnitude of slippage along them, showing which segments contribute most strongly to changes in connectivity. We furthermore plot a slice of Σ at constant radius in panel (c) and the squashing factor, another key diagnostic for reconnection, in panels (b) and (d). The ARMS code admits purely numerical resistivity, so we were not able to get an absolute value for the slippage, but instead have successfully used the relative rate (denoted Σ*, normalized by the resistivity) in the analysis presented here.
Figure 3. Field line slippage during a magnetofrictional simulation with the DUMFRIC code. (a) Isosurface of Σ, (b) sample field lines colored by Σ and a slice at constant radius; the colouring is consistent across all panels. (d) Signed logarithm of the squashing factor (positive/red corresponds to closed and negative/blue to open field lines.
Secondly, we have post-processed part of a continuous 47-year simulation of the entire corona [6] performed with the DUMFRIC code. This is a magnetofrictional code which begins with a purely potential field and evolves it subject to a changing imposed magnetic field at the photosphere. This time-dependent boundary condition is a combination of emerging active regions taken from observations and surface flows. We show the same diagnostics applied to the rapid reconfiguration of the magnetic field following a new active region in Figure 3: an isosurface in panel (a), field lines colored by Σ in panel (b), and two slices in panels (c) and (d). We observe an expanding “bubble” of slippage, which suggests a mechanism for the field line rearrangement.
Figure 4. Projection of the slippage vectors (Σα denoting the force-free slippage rate) along a field line in a Lare3d simulation in the (a) x-z and (b) x-y planes. (c) Absolute magnitude of Σ as a function of height along the field line.
Finally, we have repeated the above analysis for a simulation of a moving patch of parasitic flux[7] performed with the Lare3d code. A hemispherical region of closed field is shifted by an imposed surface flow. We have adapted the code to allow us to track the frozen-in footpoints of field lines as they are moved. As Lare3d has a constant imposed resistivity, we can obtain an absolute value (in units of 1/s) for the slippage rate, as shown for one example field line in Figure 4. We estimate that a 6.3Mm-long field line might slip 1.4Mm over the course of the simulation.
Conclusion:
We have explained the theoretical concept of a magnetic field line slippage rate, and applied it to previous coronal simulations using a new numerical tool. It is available from Github[8] and we hope that the community can apply this framework to future simulations of coronal and other magnetised plasmas.
Publication link:
https://doi.org/10.3847/1538-4357/ae9948
References:
[1] Eyink, G. L. 2015, ApJ, 807, 137
[2] MacTaggart, D. 2025, SoPh, 300, 48
[3] Stanish, S., & MacTaggart, D. 2026, MNRAS, 549, 5167
[4] Aslanyan, V., Scott, R. B., Wilkins, C. P., et al. 2024, ApJ, 971, 137
[5] Aslanyan, V., Pontin, D. I., Wyper, P. F., et al. 2021, ApJ, 909, 10
[6] Aslanyan, V., Meyer, K. A., Scott, R. B., & Yeates, A. R. 2024, ApJL, 961, L3
[7] Pontin, D. I., Priest, E. R., Chitta, L. P., & Titov, V. S. 2024, ApJ, 960, 51
[8] Aslanyan, V. 2024, UFiT, GitHub, https://github.com/Valentin-Aslanyan/UFiT