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Context: The evolution of the photospheric magnetic field can be simulated with surface flux transport (SFT) simulations, which allow for the study of the evolution of the entire field, including polar fields, solely using observations of the active regions. However, because only one side of the Sun is visible at a time, active regions that emerge and decay on the far-side are not observed and not included in the simulations. As a result, some flux is missed. Aims: We construct additional active regions and apply them to the far-side of the Sun in an SFT simulation to assess the possible effects and the magnitude of error that the missing far-side flux causes. We estimate how taking the missing far-side flux into account affects long-term SFT simulations. Methods: We identified active regions from synoptic maps of the photospheric magnetic field between 1975 and 2019. We divided them into solar cycle wings and determined their lifetimes. Using the properties of observed active regions with sufficiently short lifetimes, we constructed additional active regions and inserted them into an SFT simulation. Results: We find that adding active regions with short lifetimes to the far-side of the Sun results in significantly stronger polar fields in minimum times and slightly delayed polarity reversals. These results partly remedy the earlier results, which show overly weak polar fields and polarity reversals that are slightly too early when far-side emergence is not taken into account. The far-side active regions do not significantly affect poleward flux surges, which are mostly caused by larger long-living active regions. The far-side emergence leads to a weak continuous flow of flux, which affects polar fields over long periods of time.

Context: The axial dipole moments of emerging active regions control the evolution of the axial dipole moment of the whole photospheric magnetic field and the strength of polar fields. Hale’s and Joy’s laws of polarity and tilt orientation affect the sign of the axial dipole moment of an active region. If both laws are valid (or both violated), the sign of the axial moment is normal. However, for some active regions, only one of the two laws is violated, and the signs of these axial dipole moments are the opposite of normal. Those opposite-sign active regions can have a significant effect, for example, on the development of polar fields. Aims: Our aim is to determine the axial dipole moments of active regions identified from magnetographic observations and study how the axial dipole moments of normal and opposite signs are distributed in time and latitude in solar cycles 21−24. Methods: We identified active regions in the synoptic maps of the photospheric magnetic field measured at the National Solar Observatory (NSO) Kitt Peak (KP) observatory, the Synoptic Optical Long term Investigations of the Sun (SOLIS) vector spectromagnetograph (VSM), and the Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory (SDO), and determined their axial dipole moments. Results: We find that, typically, some 30% of active regions have opposite-sign axial moments in every cycle, often making more than 20% of the total axial dipole moment. Most opposite-signed moments are small, but occasional large moments, which can affect the evolution of polar fields on their own, are observed. Active regions with such a large opposite-sign moment may include only a moderate amount of total magnetic flux. We find that in cycles 21−23 the northern hemisphere activates first and shows emergence of magnetic flux over a wider latitude range, while the southern hemisphere activates later, and emergence is concentrated to lower latitudes. Cycle 24 differs from cycles 21−23 in many ways. Cycle 24 is the only cycle where the northern butterfly wing includes more active regions than the southern wing, and where axial dipole moment of normal sign emerges on average later than opposite-signed axial dipole moment. The total axial dipole moment and even the average axial moment of active regions is smaller in cycle 24 than in previous cycles.

Aims: Sunspot activity is often hemispherically asymmetric, and during the Maunder minimum, activity was almost completely limited to one hemisphere. In this work, we use surface flux simulation to study how magnetic activity limited only to the southern hemisphere affects the long-term evolution of the photospheric magnetic field in both hemispheres. The key question is whether sunspot activity in one hemisphere is enough to reverse the polarity of polar fields in both hemispheres. Methods: We simulated the evolution of the photospheric magnetic field from 1978 to 2016 using the observed active regions of the southern hemisphere as input. We studied the flow of magnetic flux across the equator and its subsequent motion towards the northern pole. We also tested how the simulated magnetic field is changed when the activity of the southern hemisphere is reduced. Results: We find that activity in the southern hemisphere is enough to reverse the polarity of polar fields in both hemispheres by the cross-equatorial transport of magnetic flux. About 1% of the flux emerging in the southern hemisphere is transported across the equator, but only 0.1%–0.2% reaches high latitudes to reverse and regenerate a weak polar field in the northern hemisphere. The polarity reversals in the northern hemisphere are delayed compared to the southern hemisphere, leading to a quadrupole Sun lasting for several years.

Aims: The heliospheric current sheet (HCS) has been observed to be southward shifted in the late declining to minimum phase of the solar cycle. Here we study the existence of a simultaneous shift in the heliosphere and in the corona using a robust new method. Methods: We use the synoptic maps of the photospheric field of the Wilcox Solar Observatory (WSO) and the Mount Wilson Observatory (MWO) together with the potential field source surface (PFSS) model to calculate the coronal magnetic field and compare it with the simultaneous heliospheric magnetic field of the NASA/NSSDC OMNI 2 dataset. We divide the magnetic field into the two sectors, towards (T) and away (A) from the Sun, and calculate how often the sector polarities at 1 AU and in the corona match each other. We divide the sectors both at 1 AU and in the corona. We also calculate the annual (T − A)/(T + A) ratios of sector occurrence both at 1 AU and in the corona. Results: We verify that the HCS/neutral line is southward shifted both in the corona and heliosphere. We find that the coronal shift is systematically larger than the simultaneous heliospheric shift. Conclusions: The fact that the southward shift of the coronal neutral line is larger than the simultaneous shift of the heliospheric current sheet at 1 AU implies that the radial evolution of the magnetic field between the two sites is different between the northern and southern hemispheres.

Here we use the PFSS model and photospheric data from Wilcox Solar Observatory, SOHO/MDI, SDO/HMI, and SOLIS to compare the coronal field with heliospheric magnetic field measured at 1 au, compiled in the NASA/NSSDC OMNI 2 data set. We calculate their mutual polarity match and the power of the radial decay, p, of the radial field using different source surface distances and different number of harmonic multipoles. We find the average polarity match of 82% for the declining phase, 78%–79% for maxima, 76%–78% for the ascending phase, and 74%–76% for minima. On an average, the source surface of 3.25 RS gives the best polarity match. We also find strong evidence for solar cycle variation of the optimal source surface distance, with highest values (3.3 RS) during solar minima and lowest values (2.6 RS–2.7 RS) during the other three solar cycle phases. Raising the number of harmonic terms beyond 2 rarely improves the polarity match, showing that the structure of the HMF at 1 au is most of the time rather simple. All four data sets yield fairly similar polarity matches. Thus, polarity comparison is not affected by photospheric field scaling, unlike comparisons of the field intensity.

Aims: We aim to use the surface flux transport model to simulate the long-term evolution of the photospheric magnetic field from historical observations. In this work we study the accuracy of the model and its sensitivity to uncertainties in its main parameters and the input data. Methods: We tested the model by running simulations with different values of meridional circulation and supergranular diffusion parameters, and studied how the flux distribution inside active regions and the initial magnetic field affected the simulation. We compared the results to assess how sensitive the simulation is to uncertainties in meridional circulation speed, supergranular diffusion, and input data. We also compared the simulated magnetic field with observations. Results: We find that there is generally good agreement between simulations and observations. Although the model is not capable of replicating fine details of the magnetic field, the long-term evolution of the polar field is very similar in simulations and observations. Simulations typically yield a smoother evolution of polar fields than observations, which often include artificial variations due to observational limitations. We also find that the simulated field is fairly insensitive to uncertainties in model parameters or the input data. Due to the decay term included in the model the effects of the uncertainties are somewhat minor or temporary, lasting typically one solar cycle.