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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 degrees; this is also consistent with latitude quenching being dominant over tilt quenching., Comment: 19 pages, 14 figures, accepted for publication in ApJ

The global magnetic field in the solar corona is known to contain free magnetic energy and magnetic helicity above that of a current-free (potential) state. But the strength of this non-potentiality and its evolution over the solar cycle remain uncertain. Here we model the corona over Solar Cycle 24 using a simplified magneto-frictional model that retains the magnetohydrodynamic induction equation but assumes relaxation towards force-free equilibrium, driven by solar surface motions and flux emergence. The model is relatively conservative compared to some others in the literature, with free energy approximately 20-25% of the potential field energy. We find that unsigned helicity is about a factor 10 higher at Maximum than Minimum, while free magnetic energy shows an even greater increase. The cycle averages of these two quantities are linearly correlated, extending a result found previously for active regions. Also, we propose a practical measure of eruptivity for these simulations, and show that this increases concurrently with the sunspot number, in accordance with observed coronal mass ejection rates. Whilst shearing by surface motions generates 50% or more of the free energy and helicity in the corona, we show that active regions must emerge with their own internal helicity otherwise the eruptivity is substantially reduced and follows the wrong pattern over time., Comment: 28 pages, 14 figures, accepted for publication in Solar Physics

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: firstly a gradual shearing of the arcade, modelling differential rotation on the solar surface, and secondly 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 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, normalised by the relative helicity, although a variation on the previously proposed 'eruptivity index' is also found to perform well in both the magnetofrictional and MHD simulations., Comment: 20 pages, 11 figures, 1 table. Accepted to the Astrophysical Journal on 13th August 2023

We review the surface flux transport model for the evolution of magnetic flux patterns on the Sun's surface. Our underlying motivation is to understand the model's prediction of the polar field (or axial dipole) strength at the end of the solar cycle. The main focus is on the "classical" model: namely, steady axisymmetric profiles for differential rotation and meridional flow, and uniform supergranular diffusion. Nevertheless, the review concentrates on recent advances, notably in understanding the roles of transport parameters and - in particular - the source term. We also discuss the physical justification for the surface flux transport model, along with efforts to incorporate radial diffusion, and conclude by summarizing the main directions where researchers have moved beyond the classical model., Comment: 35 pages, 11 figures, accepted for publication in Space Science Reviews

The input of the Solar wind models plays a significant role in accurate solar wind predictions at 1 AU. This work introduces a synthetic magnetogram produced from a dynamo model as an input for Magnetohydrodynamics (MHD) simulations. We perform a quantitative study that compares the Space Weather Modeling Framework (SWMF) results for the observed and the synthetic solar magnetogram input. For each case, we compare the results for Extreme Ultra-Violet (EUV) images and extract the simulation data along the earth trajectory to compare with in-situ observations. We initialize SWMF using the real and synthetic magnetogram for a set of Carrington Rotations (CR)s within the solar cycle 23 and 24. Our results help quantify the ability of dynamo models to be used as input to solar wind models and thus, provide predictions for the solar wind at 1 AU.

We apply the magneto-frictional approach to investigate which quantity or quantities can best predict the loss of equilibrium of a translationally-invariant magnetic flux rope. The flux rope is produced self-consistently by flux cancellation combined with gradual footpoint shearing of a coronal arcade which is open at the outer boundary. This models the magnetic field in decaying active regions on the Sun. Such a model permits two types of eruption: episodic small events caused by shearing and relaxation of the overlying arcade, and major eruptions of the main low-lying coronal flux rope. Through a parameter study, we find that the major eruptions are best predicted not by individual quantities but by thresholds in the ratios of squared rope current to either magnetic energy or relative magnetic helicity. We show how to appropriately define the latter quantity for translationally-invariant magnetic fields, along with a related eruptivity index that has recently been introduced for three-dimensional magnetic fields. In contrast to previous configurations studied, we find that the eruptivity index has only a weak predictive skill, and in fact is lower prior to eruption, rather than higher. This is because the overlying background magnetic field has the same direction as the arcade itself. Thus we propose that there are a whole class of solar eruptions that cannot be predicted by a high eruptivity index., Comment: 25 pages, 11 figures. To be published in 'Frontiers in Astronomy and Space Sciences', accepted for publication 8th March 2022