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We report here on the present state-of-the-art in algorithms used for resolving the 180 • ambiguity in solar vector magnetic field measurements. With present observations and techniques, 268 T.R. METCALF ET AL. some assumption must be made about the solar magnetic field in order to resolve this ambiguity. Our focus is the application of numerous existing algorithms to test data for which the correct answer is known. In this context, we compare the algorithms quantitatively and seek to understand where each succeeds, where it fails, and why. We have considered five basic approaches: comparing the observed field to a reference field or direction, minimizing the vertical gradient of the magnetic pressure, minimizing the vertical current density, minimizing some approximation to the total current density, and minimizing some approximation to the field's divergence. Of the automated methods requiring no human intervention, those which minimize the square of the vertical current density in conjunction with an approximation for the vanishing divergence of the magnetic field show the most promise.

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Recent observational studies suggest that active region magnetic ux emerges in a twisted state, and that the sense of twist depends weakly on solar hemisphere. We propose that this twist is imparted to the ux through its interaction with turbulent velocities in the convection zone. This process, designated the-e ect, operates on isolated magnetic ux tubes subjected to bu eting by turbulence with a non-vanishing kinetic helicity hu r ui. The-e ect leads to twist of the same sense inferred from observation, and opposite to that predicted by the-e ect. A series of numerical calculations are performed to estimate the magnitude of the-e ect in the solar convective zone. The results compare favorably with observation in both mean value and statistical dispersion. We nd a further relationship with total magnetic ux which can be tested in future observations. The model also predicts that twist is uncorrelated with the tilt angle of the active region.

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We compare patterns of variation for the Sun and 72 Sun-like stars by combining total and spectral solar irradiance measurements between 2003 and 2017 from the SORCE satellite, Strömgren b, y stellar photometry between 1993 and 2017 from Fairborn Observatory, and solar and stellar chromospheric Ca ii H+K emission observations between 1992 and 2016 from Lowell Observatory. The new data and their analysis strengthen the relationships found previously between chromospheric and brightness variability on the decadal timescale of the solar activity cycle. Both chromospheric H+K and photometric b, y variability among Sun-like stars are related to average chromospheric activity by power laws on this timescale. Young active stars become fainter as their H+K emission increases, and older, less active, more Sun-age stars tend to show a pattern of direct correlation between photometric and chromospheric emission variations. The directly correlated pattern between total solar irradiance and chromospheric Ca ii emission variations shown by the Sun appears to extend also to variations in the Strömgren b, y portion of the solar spectrum. Although the Sun does not differ strongly from its stellar age and spectral class mates in the activity and variability characteristics that we have now studied for over three decades, it may be somewhat unusual in two respects: (1) its comparatively smooth, regular activity cycle, and (2) its rather low photometric brightness variation relative to its chromospheric activity level and variation, perhaps indicating that facular emission and sunspot darkening are especially well-balanced on the Sun.

The most commonly used index of stellar magnetic activity is the instrumental flux scale of singlyionized calcium H & K line core emission, S, developed by the Mount Wilson Observatory (MWO) HK Project, or the derivative index R HK . Accurately placing the Sun on the S scale is important for comparing solar activity to that of the Sun-like stars. We present previously unpublished measurements of the reflected sunlight from the Moon using the second-generation MWO HK photometer during solar cycle 23 and determine cycle minimum S 23,min = 0.1634 ± 0.0008, amplitude ∆S 23 = 0.0143 ± 0.0012, and mean S 23 = 0.1701 ± 0.0005. By establishing a proxy relationship with the closely related National Solar Observatory Sacramento Peak calcium K emission index, itself well-correlated with the Kodaikanal Observatory plage index, we extend the MWO S time series to cover cycles 15-24 and find on average S min = 0.1621 ± 0.0008, ∆S cyc = 0.0145 ± 0.0012, S cyc = 0.1694 ± 0.0005. Our measurements represent an improvement over previous estimates which relied on stellar measurements or solar proxies with non-overlapping time series. We find good agreement from these results with measurements by the Solar-Stellar Spectrograph at Lowell Observatory, an independently calibrated instrument, which gives us additional confidence that we have accurately placed the Sun on the S-index flux scale.