Anthony Robinson Yeates

Solar wind science and forecasting relies on empirical relations between modeled coronal magnetic‐field structure—particularly flux‐tube expansion and distance to coronal hole boundary—and solar‐wind speed. There is lots of uncertainty in these relations, creating large uncertainties in the inner‐boundary conditions to heliospheric models. This uncertainty could potentially be sampled using ensemble techniques, but current functional forms and numbers of free parameters in empirical relations make this difficult. We present a simplified empirical solar‐wind speed equation that can be readily optimized for different configurations of a Potential Field Source Surface and Schatten Current Sheet (PFSS + SCS) coronal model, in‐lieu of the full Wang–Sheeley–Arge (WSA) equation. Optimization is performed using an 11‐year data set of in situ solar‐wind speed observations, reconstructed at 21.5 rS. We trial several functional forms and explore three linear‐regression techniques, highlighting challenges of fitting empirical relations to noisy data with large class imbalances. To minimize overfitting, we select a regression approach that fits directly to the distributions, rather than time series. Using k‐fold cross validation we find an equation candidate that successfully reproduces the distribution of observed solar‐wind speeds and performs comparably to WSA when coupled with the Heliospheric Upwind eXtrapolation with Time‐dependence (HUXt) model to generate hindcasts at 1AU. The new relation is not intended to replace WSA; the internal complexity remains a key element for WSA. Indeed, the simplified equation produces less variability on average. But this trade‐off is balanced by usability within ensemble frameworks, where now the equation can be easily perturbed to quantify uncertainty in solar‐wind speed.

We present the universal Slippage calculator ( USlip ), an extension of the universal Fieldline Tracer ( UFiT ), which computes magnetic field line slippage rates from an input magnetic field defined on a structured grid. The slippage rate provides a local, physically grounded diagnostic of nonideal evolution, directly quantifying departures from ideal frozen-in motion. We outline the theoretical formulation and describe an efficient numerical implementation. The method is validated against analytical solutions and applied to simulations using three coronal codes treating varying spatial scales, all of which are standard inputs for USlip . In all the examples considered, the slippage rate not only identifies where magnetic connectivity changes occur but also accurately reproduces the observed direction of field-line slippage. The consistency of the results across analytical tests and multiple simulation platforms demonstrates that USlip is a robust and versatile tool for diagnosing 3D reconnection in dynamically evolving systems.

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.”

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.

Relative magnetic helicity is commonly used in solar physics to avoid the well known gauge ambiguity of standard magnetic helicity in magnetically open domains. But its physical interpretation is difficult 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 non-zero 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 non-potential 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.

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 H α 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.

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.

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.