Bimodal Distribution of Magnetic Fields and Areas of Sunspots

We applied automatic identification of sunspot umbrae and penumbrae to daily observations from the Helioseismic Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) to study their magnetic flux (B) and area (A). The results confirm a previously known logarithmic relationship between the area of sunspots and their maximum flux density. In addition, we find that the relation between average magnetic flux (Bavg) and sunspot area shows a bimodal distribution: for small sunspots and pores (A < 20 millionth of solar hemisphere, MSH), Bavg = 800 G (gauss), and for large sunspots (A > 100 MSH), Bavg is about 600 G. For intermediate sunspots, average flux density linearly decreases from about 800 G to 600 G. A similar bimodal distribution was found in several other integral parameters of sunspots. We show that this bimodality can be related to different stages of sunspot penumbra formation and can be explained by the difference in average inclination of magnetic fields at the periphery of small and large sunspots.Comment: 13 pages, 5 figures, accepted for publication in Solar Physic

Application of Mutual Information Methods in Time-Distance Helioseismology

We apply a new technique, the mutual information (MI) from information theory, to time-distance helioseismology, and demonstrate that it can successfully reproduce several classic results based on the widely used cross-covariance method. MI quantifies the deviation of two random variables from complete independence, and represents a more general method for detecting dependencies in time series than the cross-covariance function, which only detects linear relationships. We provide a brief description of the MI-based technique and discuss the results of the application of MI to derive the solar differential rotation profile, a travel-time deviation map for a sunspot and a time-distance diagram from quiet Sun measurements.Comment: 14 pages, 5 figures, accepted for publication in Solar Physic

Latitude of Ephemeral Regions as Indicator of Strength of Solar Cycles

Digitized images of full disk CaK spectroheliograms from two solar observatories were used to study cycle variation of ephemeral regions (ERs) over ten solar cycles 14-23. We calculate monthly averaged unsigned latitude of ERs and compare it with annual sunspot number. We find that average latitude of ERs can be used as a predictor for strength of solar cycle. For a short-term prediction (dT about 1-2 years), maximum latitude of ephemeral regions (in current cycle) defines the amplitude of that cycle (higher is the latitude of ERs, larger are the amplitudes of sunspot cycle). For a long-term prediction (dT about 1.5 solar cycles), latitude of ERs at declining phase of n-th cycle determines the amplitude of (n+2)-th sunspot cycle (lower is the latitude of ERs, stronger is the cycle). Using this latter dependency, we forecast the amplitude of sunspot cycle 24 at W=92 +/- 13 (in units of annual sunspot number).Comment: Memorie della Societ\`a Astronomica Italiana, in pres

Signature of Differential Rotation in Sun-as-a-Star Ca II K Measurements

The characterization of solar surface differential rotation (SDR) from disk-integrated chromospheric measurements has important implications for the study of differential rotation and dynamo processes in other stars. Some chromospheric lines, such as Ca II K, are very sensitive to the presence of activity on the disk and are an ideal choice for investigating SDR in Sun-as-a star observations. Past studies indicate that when the activity is low, the determination of Sun's differential rotation from integrated-sunlight measurements becomes uncertain. However, our study shows that using the proper technique, SDR can be detected from these type of measurements even during periods of extended solar minima. This paper describes results from the analysis of the temporal variations of Ca II K line profiles observed by the Integrated Sunlight Spectrometer (ISS) during the declining phase of Cycle 23 and the rising phase of Cycle 24, and discusses the signature of SDR in the power spectra computed from time series of parameters derived from these profiles. The described methodology is quite general, and could be applied to photometric time series of other Main-Sequence stars for detecting differential rotation.Comment: Accepted for publication in The Astrophysical Journal. 38 pages, 10 figure

Search for a Signature of Twist-Removal in the Magnetic Field of Sunspots in Relation with Major Flares

We investigate the restructuring of the magnetic field in sunspots associated with two flares: the X6.5 flare on 6 December 2006 and the X2.2 flare on 15 February 2011. The observed changes were evaluated with respect to the so-called twist-removal model, in which helicity (twist) is removed from the corona as the result of an eruption. Since no vector magnetograms were available for the X6.5 flare, we applied the azimuthal symmetry approach to line-of-sight magnetograms to reconstruct the pseudo-vector magnetic field and investigate the changes in average twist and inclination of magnetic field in the sunspot around the time of the flare. For the X2.2 flare, results from the full vector magnetograms were compared with the pseudo-vector field data. For both flares, the data show changes consistent with the twist-removal scenario. We also evaluate the validity of the azimuthal symmetry approach on simple isolated round sunspots. In general, the derivations based on the azimuthal symmetry approach agree with true-vector field data though we find that even for symmetric sunspots the distribution of the magnetic field may deviate from an axially symmetric distribution.Comment: accepted for publication in the Ap

Camera Gap Removal in SOLIS/VSM Images

The Vector Spectromagnetograph (VSM) instrument on the Synoptic Optical Longterm Investigations of the Sun (SOLIS) telescope is capable of obtaining spectropolarimetry for the full Sun (or a select latitudinal range) with one arcsecond spatial resolution and 0.05 Angstrom spectral resolution. This is achieved by scanning the Sun in declination and building up spectral cubes for multiple polarization states, utilizing a beamsplitter and two separate 2k x 2k CCD cameras. As a result, the eastern and western hemispheres of the Sun are separated in preliminary VSM images by a vertical gap with soft edges and variable position and width. Prior to the comprehensive analysis presented in this document, a trial-and-error approach to removing the gap had yielded an algorithm that was inconsistent, undocumented, and responsible for incorrectly eliminating too many image columns. Here we describe, in detail, the basis for a new, streamlined, and properly calibrated prescription for locating and removing the gap that is correct to within approximately one arcsecond (one column)

Correlation Between Sunspot Number and ca II K Emission Index

Long-term synoptic observations in the resonance line of Ca II K constitute a fundamental database for a variety of retrospective analyses of the state of the solar magnetism. Synoptic Ca II K observations began in late 1904 at the Kodaikanal Observatory, in India. In early 1970s, the National Solar Observatory (NSO) at Sacramento Peak (USA) started a new program of daily Sun-as-a-star observations in the Ca II K line. Today the NSO is continuing these observations through its Synoptic Optical Long-term Investigations of the Sun (SOLIS) facility. These different data sets can be combined into a single disk-integrated Ca II K index time series that describes the average properties of the chromospheric emission over several solar cycles. We present such a Ca II K composite and discuss its correlation with the new entirely revised sunspot number data series. For this preliminary investigation, the scaling factor between pairs of time series was determined assuming a simple linear model for the relationship between the monthly mean values during the duration of overlapping observations.Comment: 16 pages, 8 figures, accepted for publication in Solar Physic

Evolution of Magnetic Helicity in Solar Cycle 24

We propose a novel approach to reconstruct the surface magnetic helicity density on the Sun or sun-like stars. The magnetic vector potential is determined via decomposition of vector magnetic field measurements into toroidal and poloidal components. The method is verified using data from a non-axisymmetric dynamo model. We apply the method to vector field synoptic maps from Helioseismic and Magnetic Imager (HMI) onboard of Solar Dynamics Observatory (SDO) to study evolution of the magnetic helicity density during solar cycle 24. It is found that the mean helicity density of the non-axisymmetric magnetic field of the Sun evolves in a way which is similar to that reported for the current helicity density of the solar active regions. It has predominantly the negative sign in the northern hemisphere, and it is positive in the southern hemisphere. Also, the hemispheric helicity rule for the non-axisymmetric magnetic field showed the sign inversion at the end of cycle 24. Evolution of magnetic helicity density of large-scale axisymmetric magnetic field is different from that expected in dynamo theory. On one hand, the mean large- and small-scale components of magnetic helicity density display the hemispheric helicity rule of opposite sign at the beginning of cycle 24. However, later in the cycle, the two helicities exhibit the same sign in contrast with the theoretical expectations.Comment: 8 pages 5 figure

First use of synoptic vector magnetograms for global nonlinear force free coronal magnetic field models

The magnetic field permeating the solar atmosphere is generally thought to provide the energy for much of the activity seen in the solar corona, such as flares, coronal mass ejections (CMEs), etc. To overcome the unavailability of coronal magnetic field measurements, photospheric magnetic field vector data can be used to reconstruct the coronal field. Currently there are several modelling techniques being used to calculate three-dimension of the field lines into the solar atmosphere. For the first time, synoptic maps of photospheric vector magnetic field synthesized from Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) are used to model the coronal magnetic field and estimate free magnetic energy in the global scale. The free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. We solve the nonlinear force-free field equations using optimization principle in spherical geometry. The resulting three-dimensional magnetic fields are used to estimate the magnetic free energy content E_{free}=E_{nlfff}-E_{pot}, i.e., the difference of the magnetic energies between the nonpotential field and the potential field in the global solar corona. For comparison, we overlay the extrapolated magnetic field lines with the extreme ultraviolet (EUV) observations by the Atmospheric Imaging Assembly on board SDO. For a single Carrington rotation 2121, we find that the global NLFFF magnetic energy density is 10.3% higher than the potential one. Most of this free energy is located in active regions.Comment: Submitted to Astronomy and Astrophysics Journa

Zeemanfit: Use and Development of the solis_vms_zeemanfit code

The purpose of the SOLIS Zeemanfit Code is to provide a straight-forward, easily checked measure of the total magnetic-field strength in the high-strength umbral regions of the solar disk. In the highest-strength regions, the Zeeman splitting of the 6302-angstrom Fe line becomes wide enough for the triplet nature of the line to be visible by eye in non-polarized light. Therefore, a three-line fit to the spectra should, in principle, provide a fairly robust measure of the total magnetic-field strength. The code uses the Level-1.5 spec-cube data of the SOLIS VSM 6302-vector observations (specifically the Stokes-I and Stokes-V components) to fit the line profiles at each appropriate pixel and calculate the magnetic-field-strength from the line-center separation of the two fit 6302.5 sigma-components. The 6301.5-angstrom Fe line is also present and fit in the VSM 6302-vector data, but it is an anomalous-Zeeman line with a weaker response to magnetic fields. Therefore, no magnetic- field measure is derived from this portion of the spectral fit.Comment: 39 pages containing 30 figures. Represents the primary documentation for the new SOLIS VSM Zeemanfit data product; corrected confusing variable units listed below Equation