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Relative magnetic helicity is commonly used in solar physics to avoid the well-known gauge ambiguity of standard magnetic helicity in magnetically open domains. However, its physical interpretation is challenging, owing to the invocation of a reference field. For the specific case of spherical-shell domains (with potential reference field), relative helicity may be written intrinsically in terms of the magnetic field alone, without the need to calculate the reference field or its vector potential. We use this intrinsic expression to prove that nonzero relative helicity implies lower bounds for both magnetic energy and free magnetic energy, generalizing the important Arnol’d inequality known for closed-field magnetic helicity. Further, we derive a stronger energy bound by spatially decomposing the relative helicity over a magnetic partition of the domain to obtain a new ideal invariant, which we call unsigned helicity. The bounds are illustrated with analytical linear force-free fields (that maximize relative helicity for given boundary conditions) as well as a nonpotential data-driven model of the solar corona. These bounds confirm that both relative helicity and the unsigned helicity can influence the dynamics in the solar corona.

We compare two candidate nonlinearities for regulating the solar cycle within the Babcock–Leighton paradigm: tilt quenching (whereby the tilt of active regions is reduced in stronger cycles) and latitude quenching (whereby flux emerges at higher latitudes in stronger solar cycles). Digitized historical observations are used to build a database of individual magnetic plage regions from 1923 to 1985. The regions are selected by thresholding in Ca ii K synoptic maps, with polarities constrained using Mount Wilson Observatory sunspot measurements. The resulting data show weak evidence for tilt quenching, but much stronger evidence for latitude quenching. Further, we use proxy observations of the polar field from faculae to construct a best-fit surface flux transport model driven by our database of emerging regions. A better fit is obtained when the sunspot measurements are used, compared to a reference model where all polarities are filled using Hale's Law. The optimization suggests clearly that the “dynamo effectivity range” of the Sun during this period should be less than 10°; this is also consistent with latitude quenching being dominant over tilt quenching.

We expand upon our 2021 paper that introduced “outflow fields”: alternatives to the widely used potential field source surface (PFSS) extrapolations of the Sun’s coronal magnetic field that 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 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. These include 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.”

Simulations of solar phenomena play a vital role in space-weather prediction. A critical computational question for automating research workflows in the context of data-driven solar coronal magnetic field simulations is quantifying a simulation's burn-in time, after which a solar quantity has evolved away from an arbitrary initial condition to a physically more realistic state. A challenge to quantifying simulation burn-in is that the underlying solar processes and data, like many physical phenomena, are non-Markovian and exhibit long memory or persistence and, therefore, their analysis evades standard statistical approaches. In this work, we provide evidence of long memory in the nonperiodic variations of solar quantities (including over timescales significantly shorter than previously identified) and demonstrate that magnetofrictional simulations capture the memory structure present in magnetogram data. We also provide an algorithm for the quantitative assessment of simulation burn-in time that can be applied to nonstationary time series with long memory. Our approach is based on time-delayed mutual information, an information-theoretic quantity, and includes a small-sample bias correction.

We investigate which scalar quantity or quantities can best predict the loss of equilibrium and subsequent eruption of magnetic flux ropes in the solar corona. Our models are initialized with a potential magnetic arcade, which is then evolved by means of two effects on the lower boundary: first, a gradual shearing of the arcade, modeling differential rotation on the solar surface; and second, supergranular diffusion. These result in flux cancellation at the polarity inversion line and the formation of a twisted flux rope. We use three model setups: full magnetohydrodynamics (MHD) in cartesian coordinates, and the magnetofrictional (MF) model in both cartesian and polar coordinates. The flux ropes are translationally invariant, allowing for very fast computational times and thus a comprehensive parameter study, comprising hundreds of simulations and thousands of eruptions. Similar flux rope behavior is observed using either magnetofriction or MHD, and there are several scalar criteria that could be used as proxies for eruptivity. The most consistent predictor of eruptions in either model is the squared current in the axial direction of the rope, normalized by the relative helicity, although a variation on the previously proposed eruptivity index is also found to perform well in both the MF and MHD simulations.

The Sun’s open–closed flux boundary (OCB) separates closed and open magnetic field lines, and is the site for interchange magnetic reconnection processes thought to be linked to the origin of the slow solar wind (SSW). We analyze the global magnetic field structure and OCB from 2010 December to 2019 December using three coronal magnetic field models: a potential-field source-surface (PFSS) model, a static equilibrium magnetofrictional model, and a time-dependent magnetofrictional model. We analyze the model and cycle dependence of the OCB length on the photosphere, as well as the magnetic flux in the vicinity of the OCB. Near solar maximum, the coronal magnetic field for each model consists predominantly of long, narrow coronal holes, and nearly all the open flux lies within 1 supergranule diameter (25 Mm) of the OCB. By comparing to interplanetary scintillation measurements of SSW speeds, we argue that the fraction of open flux within this 25 Mm band is a good predictor of the amount of SSW in the heliosphere. Importantly, despite its simplicity, we show that the PFSS model estimates this fraction as well as the time-dependent model. We discuss the implications of our results for understanding SSW origins and interchange reconnection at the OCB.

We present a new code for the tracing of magnetic field lines and calculation of related quantities such as the squashing factor in the solar corona. The Universal Fieldline Tracer (UFiT) is an open-source package that can currently take inputs directly from four well-established coronal models, with additional models planned to be made directly accessible in the future. This package contains tools to make use of large-scale three-dimensional field line maps to calculate volumetric quantities, such as the total volume of the open corona, or the fraction that maps to regions on the solar surface within some distance of a coronal hole boundary, which may be relevant to phenomenological models of solar wind speed such as the Wang–Sheeley–Arge model. Synthetic coronagraphs can also be produced rapidly by this package. We have postprocessed long-term magnetofrictional simulations to demonstrate that the separatrix web occupies a larger fraction of the corona during solar maximum than solar minimum.

An important element of 3D data-driven simulations of solar magnetic fields is the determination of the horizontal electric field at the solar photosphere. This electric field is used to drive the 3D simulations and inject energy and helicity into the solar corona. One outstanding problem is the localisation of the horizontal electric field such that it is consistent with Ohm’s law. Yeates ( Astrophys. J. 836 (1), 131, 2017 ) put forward a new “sparse” technique for computing the horizontal electric field from normal-component magnetograms that minimises the number of non-zero values. This aims to produce a better representation of Ohm’s law compared to previously used “non-sparse” techniques. To test this new approach we apply it to active region (AR) 10977, along with the previously developed non-sparse technique of Mackay, Green, and van Ballegooijen ( Astrophys. J. 729 (2), 97, 2011 ). A detailed comparison of the two techniques with coronal observations is used to determine which is the most successful. Results show that the non-sparse technique of Mackay, Green, and van Ballegooijen ( 2011 ) produces the best representation for the formation and structure of the sigmoid above AR 10977. In contrast, the Yeates ( 2017 ) approach injects strong horizontal fields between spatially separated, evolving magnetic polarities. This injection produces highly twisted unphysical field lines with significantly higher magnetic energy and helicity. It is also demonstrated that the Yeates ( 2017 ) approach produces significantly different results that can be inconsistent with the observations depending on whether the horizontal electric field is solved directly or indirectly through the magnetic vector potential. In contrast, the Mackay, Green, and van Ballegooijen ( 2011 ) method produces consistent results using either approach. The sparse technique of Yeates ( 2017 ) has significant pitfalls when applied to spatially resolved solar data, where future studies need to investigate why these problems arise.

We investigate how representing active regions with bipolar magnetic regions (BMRs) affects the end-of-cycle polar field predicted by the surface flux transport model. Our study is based on a new database of BMRs derived from the SDO/HMI active region patch data between 2010 and 2020. An automated code is developed for fitting each active region patch with a BMR, matching both the magnetic flux and axial dipole moment of the region and removing repeat observations of the same region. By comparing the predicted evolution of each of the 1090 BMRs with the predicted evolution of their original active region patches, we show that the bipolar approximation leads to a 24% overestimate of the net axial dipole moment, given the same flow parameters. This is caused by neglecting the more complex multipolar and/or asymmetric magnetic structures of many of the real active regions, and may explain why previous flux transport models had to reduce BMR tilt angles to obtain realistic polar fields. Our BMR database and the Python code to extract it are freely available.

3D magnetic reconnection is a fundamental plasma process crucial for heating the solar corona and generating the solar wind, but resolving and characterizing it for the Sun remain challenging. Using high-quality data from the Chinese New Vacuum Solar Telescope, the Solar Dynamics Observatory, and the Interface Region Imaging Spectrograph, this work presents highly suggestive direct imaging evidence of magnetic reconnection during the untangling of braided magnetic structures above a sunspot. These magnetic structures, visible as bright superpenumbral threads in extreme-ultraviolet passbands, initially bridge opposite-polarity magnetic fluxes and then gradually tangle in their middle section. Magnetic extrapolation reveals the fibrils to form a small flux rope that is twisted and braided, possibly created by persistent and complex photospheric motions. During untangling, repetitive reconnection events occur inside the flux rope, accompanied by transient plasma heating, bidirectional outflowing blobs, and signatures of nanojets. An emission analysis reveals that the outflowing blobs are multithermal structures with temperatures well below 1 MK, undergoing rapid cooling and leaving emission imprints in Hα images. The measured reconnection angles indicate that 16%–22% of the magnetic field along each thread is antiparallel, with the remaining field acting as a guide field. The estimated energy released during these reconnection events is comparable to nanoflares, which can be powered by up to 6% of the magnetic energy stored in the antiparallel field. This work presents a textbook example of magnetic flux rope reconnection in the solar atmosphere, providing new insights into fine-scale energy release processes within sunspot superpenumbral fibrils.