Vector magnetic fields, subsurface stresses and evolution of magnetic helicity

Observations of the strength and spatial distribution of vector magnetic fields in active regions have revealed several fundamental properties of the twist of their magnetic fields. First, the handedness of this twist obeys a hemispheric rule: left-handed in the northern hemisphere, right-handed in the southern. Second, the rule is weak; active regions often disobey it. It is statistically valid only in a large ensemble. Third, the rule itself, and the amplitude of the scatter about the rule, are quantitatively consistent with twisting of fields by turbulence as flux tubes buoy up through the convection zone. Fourth, there is considerable spatial variation of twist within active regions. However, relaxation to a linear force-free state, which has been documented amply in laboratory plasmas, is not observed.     

Modeling the Global Coronal Field with Simulated Synoptic Magnetograms from Earth and the Lagrange Points $L_{3}$, L4$L_{4}$, and L5$L_{5}$

The solar photospheric magnetic flux distribution is key to structuring the global solar corona and heliosphere. Regular full-disk photospheric magnetogram data are therefore essential to our ability to model and forecast heliospheric phenomena such as space weather. However, our spatio-temporal coverage of the photospheric field is currently limited by our single vantage point at/near Earth. In particular, the polar fields play a leading role in structuring the large-scale corona and heliosphere, but each pole is unobservable for \({>}\,6\) months per year. Here we model the possible effect of full-disk magnetogram data from the Lagrange points \(L_{4}\) and \(L_{5}\), each extending longitude coverage by \(60^{\circ}\). Adding data also from the more distant point \(L_{3}\) extends the longitudinal coverage much further. The additional vantage points also improve the visibility of the globally influential polar fields. Using a flux-transport model for the solar photospheric field, we model full-disk observations from Earth/\(L_{1}\), \(L_{3}\), \(L_{4}\), and \(L_{5}\) over a solar cycle, construct synoptic maps using a novel weighting scheme adapted for merging magnetogram data from multiple viewpoints, and compute potential-field models for the global coronal field. Each additional viewpoint brings the maps and models into closer agreement with the reference field from the flux-transport simulation, with particular improvement at polar latitudes, the main source of the fast solar wind.     

Tilt of Sunspot Bipoles in Solar Cycles 15 to 24

We use recently digitized sunspot drawings from Mount Wilson Observatory to investigate the latitudinal dependence of tilt angles of active regions and its change with solar cycle. The drawings cover the period from 1917 to present and contain information as regards polarity and strength of magnetic field in sunspots. We identified clusters of sunspots of same polarity, and used these clusters to form “bipole pairs”. The orientation of these bipole pairs was used to measure their tilts. We find that the latitudinal profile of tilts does not monotonically increase with latitude as most previous studies assumed, but instead, it shows a clear maximum at about 25?–?30 degree latitudes. Functional dependence of tilt (\(\gamma\)) on latitude (\(\varphi\)) was found to be \(\gamma= (0.20\pm0.08) \sin(2.80 \varphi) + (-0.00\pm0.06)\). We also find that latitudinal dependence of tilts varies from one solar cycle to another, but larger tilts do not seem to result in stronger solar cycles. Finally, we find the presence of a systematic offset in tilt of active regions (non-zero tilts at the equator), with odd cycles exhibiting negative offset and even cycles showing the positive offset.     

An Overview of Existing Algorithms for Resolving the 180° Ambiguity in Vector Magnetic Fields: Quantitative Tests with Synthetic Data

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, 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.     

Helicity Measurements from Two Magnetographs

We use 270 pairs of vector magnetograms observed by Haleakala Stokes Polarimeter (HSP) and Solar Magnetic Field Telescope (SMFT) of Huairou Solar Observing Station from 1997 to 2000 to compare current helicity derived by these two instruments. We apply the same approach to both data sets to resolve 180^∘ azimuth ambiguity and compute α coefficient of linear force-free field. After careful consideration of various aspects of both data sets, we find that in ≈80% of cases SMFT and HSP data result in the same sign of α, and the Pearson linear correlation coefficient between two data sets is r_p = 0.64. Operated by the Association of Universities for Research in Astronomy (AURA, Inc) under cooperative agreement with the National Science Foundation (NSF).     

Coronal Magnetography of Solar Active Region 8365 with the SSRT and NoRH Radio Heliographs

Microwave maps of solar active region NOAA 8365 are used to derive the coronal magnetograms of this region. The technique is based on the fact that the circular polarization of a radio source is modified when microwaves pass through the coronal magnetic field transverse to the line of sight. The observations were taken with the Siberian Solar Radio Telescope (SSRT) on October 21 – 23 and with the Nobeyama Radio Heliograph (NoRH) on October 22 – 24, 1998. The known theory of wave mode coupling in quasi-transverse (QT) region is employed to evaluate the coronal magnetograms in the range of 10 – 30 G at the wavelength 5.2 cm and 50 – 110 G at 1.76 cm, taking the product of electron density and the scale of coronal field divergence to be constant of 10¹⁸ cm^–2. The height of the QT-region is estimated from the force-free field extrapolations as 6.2 × 10⁹ cm for the 20 G and 2.3 × 10⁹ cm for 85 G levels. We find that on large spatial scale, the coronal magnetograms derived from the radio observations show similarity with the magnetic fields extrapolated from the photosphere.     

The sun‐as‐a‐star solar spectrum

The Sun is the only star for which individual surface features can be observed directly. For other stars, the properties of starspots, stellar rotation, stellar flares, etc, are derived indirectly via variation of star‐integrated spectral line profiles or their luminosity measurements. Solar disk‐integrated and disk‐resolved observations allow for investigations of the contribution of individual solar disk features to sun‐as‐a‐star spectra. Here, we provide a brief overview of three sun‐as‐a‐star programs, currently in operation, and describe recent improvements in observations and data reduction for the Integrated Sunlight Spectrometer (ISS), one of three instruments comprising the Synoptic Optical Long‐term Investigations of the Sun (SOLIS) system. Next, we discuss studies employing sun‐as‐a‐star observations (including Ca II K line as proxy for total unsigned magnetic flux and 2800 MHz radio flux) as well as the effects of flares on solar disk‐integrated spectra. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cyclic and Long-Term Variation of Sunspot Magnetic Fields

Measurements from the Mount Wilson Observatory (MWO) were used to study the long-term variations of sunspot field strengths from 1920 to 1958. Following a modified approach similar to that presented in Pevtsov et al. (Astrophys. J. Lett. 742, L36, 2011), we selected the sunspot with the strongest measured field strength for each observing week and computed monthly averages of these weekly maximum field strengths. The data show the solar cycle variation of the peak field strengths with an amplitude of about 500?–?700 gauss (G), but no statistically significant long-term trends. Next, we used the sunspot observations from the Royal Greenwich Observatory (RGO) to establish a relationship between the sunspot areas and the sunspot field strengths for cycles 15?–?19. This relationship was used to create a proxy of the peak magnetic field strength based on sunspot areas from the RGO and the USAF/NOAA network for the period from 1874 to early 2012. Over this interval, the magnetic field proxy shows a clear solar cycle variation with an amplitude of 500?–?700 G and a weaker long-term trend. From 1874 to around 1920, the mean value of magnetic field proxy increases by about 300?–?350 G, and, following a broad maximum in 1920?–?1960, it decreases by about 300 G. Using the proxy for the magnetic field strength as the reference, we scaled the MWO field measurements to the measurements of the magnetic fields in Pevtsov et al. (2011) to construct a combined data set of maximum sunspot field strengths extending from 1920 to early 2012. This combined data set shows strong solar cycle variations and no significant long-term trend (the linear fit to the data yields a slope of ??0.2±0.8 G?year^?1). On the other hand, the peak sunspot field strengths observed at the minimum of the solar cycle show a gradual decline over the last three minima (corresponding to cycles 21?–?23) with a mean downward trend of ≈?15 G?year^?1.     

Active Regions with Superpenumbral Whirls and Their Subsurface Kinetic Helicity

We search for a signature of helicity flow from the solar interior to the photosphere and chromosphere. For this purpose, we study two active regions, NOAA 11084 and 11092, that show a regular pattern of superpenumbral whirls in chromospheric and coronal images. These two regions are good candidates for comparing magnetic/current helicity with subsurface kinetic helicity because the patterns persist throughout the disk passage of both regions. We use photospheric vector magnetograms from SOLIS/VSM and SDO/HMI to determine a magnetic helicity proxy, the spatially averaged signed shear angle (SASSA). The SASSA parameter produces consistent results leading to positive values for NOAA 11084 and negative ones for NOAA 11092 consistent with the clockwise and counter-clockwise orientation of the whirls. We then derive the properties of the subsurface flows associated with these active regions. We measure subsurface flows using a ring-diagram analysis of GONG high-resolution Doppler data and derive their kinetic helicity, h _z . Since the patterns persist throughout the disk passage, we analyze synoptic maps of the subsurface kinetic helicity density. The sign of the subsurface kinetic helicity is negative for NOAA 11084 and positive for NOAA 11092; the sign of the kinetic helicity is thus anticorrelated with that of the SASSA parameter. As a control experiment, we study the subsurface flows of six active regions without a persistent whirl pattern. Four of the six regions show a mixture of positive and negative kinetic helicity resulting in small average values, while two regions are clearly dominated by kinetic helicity of one sign or the other, as in the case of regions with whirls. The regions without whirls follow overall the same hemispheric rule in their kinetic helicity as in their current helicity with positive values in the southern and negative values in the northern hemisphere.