A Fast Model for the Reconstruction of Spectral Solar Irradiance in the Near- and Mid-Ultraviolet

We present a model for the reconstruction of spectral solar irradiance between 200 and 400?nm. This model is an extension of the total solar irradiance (TSI) model of Crouch et al. (Astrophys.?J. 677, 723, 2008) which is based on a data-driven Monte Carlo simulation of sunspot emergence, fragmentation, and erosion. The resulting time-evolving daily area distribution of magnetic structures of all sizes is used as input to a four-component irradiance model including contributions from the quiet Sun, sunspots, faculae, and network. In extending the model to spectral irradiance in the near- and mid-ultraviolet, the quiet Sun and sunspot emissivities are calculated from synthetic spectra at T _eff=5750?K and 5250?K, respectively. Facular emissivities are calculated using a simple synthesis procedure proposed by Solanki and Unruh (Astron. Astrophys. 329, 747, 1998). The resulting time series of ultraviolet flux is calibrated against the data from the SOLSTICE instrument on the Upper Atmospheric Research Satellite (UARS). Using a genetic algorithm, we invert quiet Sun corrections, profile of facular temperature variations with height, and network model parameters which yield the best fit to these data. The resulting best-fit time series reproduces quite well the solar-cycle timescale variations of UARS ultraviolet observations, as well as the short-timescale fluctuations about the 81 day running mean. We synthesize full spectra between 200 and 400?nm, and validate these against the spectra obtained by the ATLAS-1 and ATLAS-3 missions, finding good agreement, to better than 3?% at most wavelengths. We also compare the UV variability predicted by our reconstructions in the descending phase of sunspot cycle 23 to SORCE/SIM data as well as to other reconstructions. Finally, we use the model to reconstruct the time series of spectral irradiance starting in 1874, and investigate temporal correlations between pairs of wavelengths in the bands of interest for stratospheric chemistry and dynamics.     

Validation of the 3D AMR SIP–CESE Solar Wind Model for Four Carrington Rotations

We carry out the adaptive mesh refinement (AMR) implementation of our solar–interplanetary space-time conservation element and solution element (CESE) magnetohydrodynamic model (SIP–CESE MHD model) using a six-component grid system (Feng, Zhou, and Wu, Astrophys. J. 655, 1110, 2007; Feng et al., Astrophys. J. 723, 300, 2010). By transforming the governing MHD equations from the physical space (x,y,z) to the computational space (ξ,η,ζ) while retaining the form of conservation (Jiang et al., Solar Phys. 267, 463, 2010), the SIP–AMR–CESE MHD model is implemented in the reference coordinates with the aid of the parallel AMR package PARAMESH available at http://sourceforge.net/projects/paramesh/ . Meanwhile, the volumetric heating source terms derived from the topology of the magnetic-field expansion factor and the minimum angular separation (at the photosphere) between an open-field foot point and its nearest coronal-hole boundary are also included. We show the preliminary results of applying the SIP–AMR–CESE MHD model for simulating the solar-wind background of different solar-activity phases by comparison with SOHO observations and other spacecraft data from OMNI. Our numerical results show overall good agreements in the solar corona and in interplanetary space with these multiple-spacecraft observations.     

Increase of the mean Sun–Earth distance caused by a secular mass accumulation

Based on many planetary observations between the years 1971 and 2003, Krasinsky and Brumberg (Celest. Mech. Dyn. Astron. 90:267–288, 2004) have estimated a rate of increase in the mean Sun-Earth distance of (15±4) m per century. Together with other anomalous observations in the solar system, this increase appears to be unexplained (Lämmerzahl et al. in Astrophys. Space Sci. Lib., vol. 349, pp. 75–101, 2008). We explain these findings by invoking a recently proposed gravitational impact model (Wilhelm et al. in Astrophys. Space Sci. 343:135–144, 2013) that implies a secular mass increase of all massive bodies. This allows us to formulate a quantitative understanding of the effect within the parameter range of the model with a mass accumulation rate of the Sun of (6.4±1.7)×10¹⁰ kg?s^?1.     

Speeds and Arrival Times of Solar Transients Approximated by Self-similar Expanding Circular Fronts

The NASA Solar TErrestrial RElations Observatory (STEREO) mission offered the possibility to forecast the arrival times, speeds, and directions of solar transients from outside the Sun–Earth line. In particular, we are interested in predicting potentially geoeffective interplanetary coronal mass ejections (ICMEs) from observations of density structures at large observation angles from the Sun (with the STEREO Heliospheric Imager instrument). We contribute to this endeavor by deriving analytical formulas concerning a geometric correction for the ICME speed and arrival time for the technique introduced by Davies et al. (Astrophys. J., 2012, in press), called self-similar expansion fitting (SSEF). This model assumes that a circle propagates outward, along a plane specified by a position angle (e.g., the ecliptic), with constant angular half-width (λ). This is an extension to earlier, more simple models: fixed-Φ fitting (λ=0°) and harmonic mean fitting (λ=90°). In contrast to previous models, this approach has the advantage of allowing one to assess clearly if a particular location in the heliosphere, such as a planet or spacecraft, might be expected to be hit by the ICME front. Our correction formulas are especially significant for glancing hits, where small differences in the direction greatly influence the expected speeds (up to 100?–?200 km?s^?1) and arrival times (up to two days later than the apex). For very wide ICMEs (2λ>120°), the geometric correction becomes very similar to the one derived by Möstl et al. (Astrophys. J. 741, 34, 2011) for the harmonic mean model. These analytic expressions can also be used for empirical or analytical models to predict the 1 AU arrival time of an ICME by correcting for effects of hits by the flank rather than the apex, if the width and direction of the ICME in a plane are known and a circular geometry of the ICME front is assumed.     

Long-Term Variations of Solar Differential Rotation and Sunspot Activity: Revisited

Long-term variations of solar differential rotation and sunspot activity are investigated through re-analyzing the data on parameters of the differential-rotation law obtained by Makarov, Tlatov, and Callebaut (Solar Phys. 170, 373, 1997), Javaraiah, Bertello, and Ulrich (Astrophys. J. 626, 579, 2005a; Solar Phys. 232, 25, 2005b), and Javaraiah et al. (Solar Phys. 257, 61, 2009). Our results indicate that the solar-surface-rotation rate at the Equator (indicated by the A-parameter of the standard solar-rotation law) shows a secular decrease since Cycle 12 onwards, given by about 1?–?1.5×10^?3 (deg?day^?1?year^?1). The B-parameter of the standard differential-rotation law seems to also show a secular decrease since Cycle 12 onwards, but of weak statistical significance. The rotation rate averaged over latitudes 0^°?–?40^° does not show a secular trend of statistical significance. Moreover, the average sunspot area shows a secular increase of statistical significance since Cycle 12 onwards, while a negative correlation is found between the level of sunspot activity (indicated by the average sunspot area) and the solar equatorial rotation on long-term scales.     

Implementation and Comparison of Acoustic Travel-Time Measurement Procedures for the Solar Dynamics Observatory/Helioseismic and Magnetic Imager Time?–?Distance Helioseismology Pipeline

The Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) satellite is designed to produce high-resolution Doppler-velocity maps of oscillations at the solar surface with high temporal cadence. To take advantage of these high-quality oscillation data, a?time?–?distance helioseismology pipeline (Zhao et al., Solar Phys. submitted, 2010) has been implemented at the Joint Science Operations Center (JSOC) at Stanford University. The aim of this pipeline is to generate maps of acoustic travel times from oscillations on the solar surface, and to infer subsurface 3D flow velocities and sound-speed perturbations. The wave travel times are measured from cross-covariances of the observed solar oscillation signals. For implementation into the pipeline we have investigated three different travel-time definitions developed in time?–?distance helioseismology: a Gabor-wavelet fitting (Kosovichev and Duvall, SCORE’96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997), a?minimization relative to a reference cross-covariance function (Gizon and Birch, Astrophys. J. 571, 966, 2002), and a linearized version of the minimization method (Gizon and Birch, Astrophys. J. 614, 472, 2004). Using Doppler-velocity data from the Michelson Doppler Imager (MDI) instrument onboard SOHO, we tested and compared these definitions for the mean and difference travel-time perturbations measured from reciprocal signals. Although all three procedures return similar travel times in a quiet-Sun region, the method of Gizon and Birch (Astrophys. J. 614, 472, 2004) gives travel times that are significantly different from the others in a magnetic (active) region. Thus, for the pipeline implementation we chose the procedures of Kosovichev and Duvall (SCORE’96: Solar Convection and Oscillations and Their Relationship, ASSL, Dordrecht, 241, 1997) and Gizon and Birch (Astrophys. J. 571, 966, 2002). We investigated the relationships among these three travel-time definitions, their sensitivities to fitting parameters, and estimated the random errors that they produce.     

Torsional Oscillations in a Global Solar Dynamo

We characterize and analyze rotational torsional oscillations developing in a large-eddy magnetohydrodynamical simulation of solar convection (Ghizaru, Charbonneau, and Smolarkiewicz, Astrophys. J. Lett. 715, L133, 2010; Racine et al., Astrophys. J. 735, 46, 2011) producing an axisymmetric, large-scale, magnetic field undergoing periodic polarity reversals. Motivated by the many solar-like features exhibited by these oscillations, we carry out an analysis of the large-scale zonal dynamics. We demonstrate that simulated torsional oscillations are not driven primarily by the periodically varying large-scale magnetic torque, as one might have expected, but rather via the magnetic modulation of angular-momentum transport by the large-scale meridional flow. This result is confirmed by a straightforward energy analysis. We also detect a fairly sharp transition in rotational dynamics taking place as one moves from the base of the convecting layers to the base of the thin tachocline-like shear layer formed in the stably stratified fluid layers immediately below. We conclude by discussing the implications of our analyses with regard to the mechanism of amplitude saturation in the global dynamo operating in the simulation, and speculate on the possible precursor value of torsional oscillations for the forecast of solar-cycle characteristics.     

Reconstructing CME Structures from IPS Observations Using a Phenomenological Model

We present an extension of the Tappin?–?Howard (TH) phenomenological model (Tappin and Howard, Space Sci. Rev. 147, 55, 2009) for coronal mass ejection reconstruction to use interplanetary scintillation g-map data. The necessary changes to the model are discussed. We then use the modified model to reconstruct two major interplanetary disturbances observed using the Cambridge 3.6 ha Array in September 1980. We find that despite the lower cadence of IPS observations compared with white-light imagers, a consistent reconstruction can be generated which is in agreement with in-situ measurements and solar observations.     

Global spectral energy distributions of the Large Magellanic Cloud with interstellar dust

The effects of dust on infrared emission vary among galaxies of different morphological types. We investigated integrated spectral energy distributions (SEDs) in infrared and submillimeter/millimeter emissions from the Large Magellanic Cloud (LMC) based on observations from the Herschel Space Observatory (HSO) and near- to mid-infrared observations from the Spitzer Space Telescope (SST). We also used IRAS and WMAP observations to constrain the SEDs and present the results of radiative transfer calculations using the spectrophotometric galaxy model. We explain the observations by using dust models with different grain size distributions in the interstellar medium of the LMC, noting that the LMC has undergone processes that differ from those in the Milky Way. We determined a spectral index and a normalization factor in the range of ?3.5 to ?3.45 with grain radii in the range of 1 nm–300 nm for the silicate grain and 2 nm–1 μm for the graphite grain. The best fit to the observed SED was obtained with a spectral index of ?3.47, similar to the value derived by Piovan et al. (Mon. Not. R. Astron. Soc. 366(3):923, 2006a). The grain size distribution is described using a power law but with a break that is introduced below a _b , where a larger exponent is used. Changing the graphite grain size distribution significantly changed the SED pattern within the observational uncertainties. Based on the SED fits to the observations from submillimeter wavelengths to infrared radiation from the LMC using GRASIL (Silva et al., Astrophys. J. 509(1):103, 1998), we obtained a reasonable set of parameter values in chemical and geometric space together with the grain size distributions (Weingartner and Draine, Astrophys. J. 548(1):296, 2001) and a modified MRN model with the LMC extinction curve (Piovan et al., Mon. Not. R. Astron. Soc. 366(3):923, 2006a). For a given set of parameters including the disc scale height, synthesis of the starlight spectrum, optical depth, escape time scale, dust model, and star formation efficiency, the adopted dust-to-gas ratio for modeling the observed SEDs, ～1/300 (from the literature) yields a reasonable fit to the observed SEDs and similar results with the metallicity of the LMC as those reported in Russell and Bessell (Astrophys. J. Suppl. Ser. 70:865, 1989). The dust-to-gas ratios that are given as the metallicity caused the variation in the model fits. The difference mainly appears at the wavelengths near 100 μm.     

Asteroseismic modelling of the solar-like star β Hydri

We present the results of modelling the subgiant star β Hydri using seismic observational constraints. We have computed several grids of stellar evolutionary tracks using the Aarhus STellar Evolution Code (ASTEC, Christensen-Dalsgaard in Astrophys. Space Sci. 316:13, 2008a), with and without helium diffusion and settling. For those models on each track that are located at the observationally determined position of β Hydri in the Hertzsprung-Russell (HR) diagram, we have calculated the oscillation frequencies using the Aarhus adiabatic pulsation package (ADIPLS, Christensen-Dalsgaard in Astrophys. Space Sci. 316:113, 2008b). Applying the near-surface corrections to the calculated frequencies using the empirical law presented by Kjeldsen et al. (Astrophys. J. 683:L175, 2008), we have compared the corrected model frequencies with the observed frequencies of the star. We show that after correcting the frequencies for the near-surface effects, we have a fairly good fit for both l=0 and l=2 frequencies. We also have good agreement between the observed and calculated l=1 mode frequencies, although there is room for improvement in order to fit all the observed mixed modes simultaneously.     

Three-Dimensional Properties of Coronal Mass Ejections from STEREO/SECCHI Observations

We identify 565 coronal mass ejections (CMEs) between January 2007 and December 2010 in observations from the twin STEREO/SECCHI/COR2 coronagraphs aboard the STEREO mission. Our list is in full agreement with the corresponding SOHO/LASCO CME Catalog ( http://cdaw.gsfc.nasa.gov/CME_list/ ) for events with angular widths of 45^° and up. The monthly event rates behave similarly to sunspot rates showing a three- to fourfold rise between September 2009 and March 2010. We select 51 events with well-defined white-light structure and model them as three-dimensional (3D) flux ropes using a forward-modeling technique developed by Thernisien, Howard and Vourlidas (Astrophys. J. 652, 763??C?773, 2006). We derive their 3D properties and identify their source regions. We find that the majority of the CME flux ropes (82?%) lie within 30^° of the solar equator. Also, 82?% of the events are displaced from their source region, to a lower latitude, by 25^° or less. These findings provide strong support for the deflection of CMEs towards the solar equator reported in earlier observations, e.g. by Cremades and Bothmer (Astron. Astrophys. 422, 307??C?322, 2004).     

On the Origin of Pulsations of Sub-THz Emission from Solar Flares

We propose a model to explain fast pulsations in sub-THz emission from solar flares. The model is based on the approach of a flaring loop as an equivalent electric circuit and explains the pulse-repetition rate, the high-quality factor, Q≥10³, low modulation depth, pulse synchronism at different frequencies, and the dependence of the pulse-repetition rate on the emission flux, observed by Kaufmann et al. (Astrophys. J. 697, 420, 2009). We solved the nonlinear equation for electric current oscillations using a Van der Pol method and found the steady-state value for the amplitude of the current oscillations. Using the pulse rate variation during the flare on 4 November 2003, we found a decrease of the electric current from 1.7×10¹² A in the flare maximum to 4×10¹⁰ A just after the burst. Our model is consistent with the plasma mechanism of sub-THz emission suggested recently by Zaitsev, Stepanov, and Melnikov (Astron. Lett. 39, 650, 2013).     

Preprocessing the Photospheric Vector Magnetograms for an NLFFF Extrapolation Using a Potential-Field Model and an Optimization Method

Numerical reconstruction/extrapolation of the coronal nonlinear force-free magnetic field (NLFFF) usually takes the photospheric vector magnetogram as input at the bottom boundary. The magnetic field observed at the photosphere, however, contains a force that is in conflict with the fundamental assumption of the force-free model. It also contains measurement noise, which hinders the practical computation. Wiegelmann, Inhester, and Sakurai (Solar Phys. 233, 215, 2006) have proposed to preprocess the raw magnetogram to remove the force and noise to provide better input for NLFFF modeling. In this paper we develop a new code of magnetogram preprocessing that is consistent with our extrapolation method CESE–MHD–NLFFF (Jiang, Feng, and Xiang in Astrophys. J. 755, 62, 2012; Jiang and Feng in Astrophys. J. 749, 135, 2012a). Based on the magnetic-splitting rule that a magnetic field can be split into a potential-field part and a non-potential part, we split the magnetogram and dealt with the two parts separately. The preprocessing of the magnetogram’s potential part is based on a numerical potential-field model, and the non-potential part is preprocessed using the similar optimization method of Wiegelmann, Inhester, and Sakurai (2006). The code was applied to the SDO/HMI data, and results show that the method can remove the force and noise efficiently and improve the extrapolation quality.     

Very Fast and Accurate Azimuth Disambiguation of Vector Magnetograms

We present a method for fast and accurate azimuth disambiguation of vector magnetogram data regardless of the location of the analyzed region on the solar disk. The direction of the transverse field is determined with the principle of minimum deviation of the field from the reference (potential) field. The new disambiguation (NDA) code is examined on the well-known models of Metcalf et al. (Solar Phys. 237, 267, 2006) and Leka et al. (Solar Phys. 260, 83, 2009), and on an artificial model based on the observed magnetic field of AR 10930 (Rudenko, Myshyakov, and Anfinogentov, Astron. Rep. 57, 622, 2013). We compare Hinode/SOT-SP vector magnetograms of AR 10930 disambiguated with three codes: the NDA code, the nonpotential magnetic-field calculation (NPFC: Georgoulis, Astrophys. J. Lett. 629, L69, 2005), and the spherical minimum-energy method (Rudenko, Myshyakov, and Anfinogentov, Astron. Rep. 57, 622, 2013). We then illustrate the performance of NDA on SDO/HMI full-disk magnetic-field observations. We show that our new algorithm is more than four times faster than the fastest algorithm that provides the disambiguation with a satisfactory accuracy (NPFC). At the same time, its accuracy is similar to that of the minimum-energy method (a very slow algorithm). In contrast to other codes, the NDA code maintains high accuracy when the region to be analyzed is very close to the limb.     

New face in the spectral behavior of Capella in the UV

We present low and high resolution ultraviolet spectra of the Capella spectroscopic binary system from the observations taken by the International Ultraviolet Explorer (IUE) during the period between 1978–1990 and 1978–1995. Thirteen profile of Capella showing variations of line fluxes at different orbital phases are presented. This paper focuses on the C IV emission line at 1550 Å produced in the transition region of the secondary star and Mg II emission lines at 2800 Å produced in the stellar chromosphere of the secondary star by calculating spectral line fluxes. Our results show that there are significant variations of line fluxes with time. These spectral variations are similar to that found in the EUV by Dupree and Brickhouse (in Int. Astron. Union Symp. 176P:184D, 1995) in the UV for H 1 Ly?α by Ayres et al. (in Astrophys. J. 402:710A, 1993), and in the near IR by Katsova (in Astrophys. Space Sci. 252:427K, 1997). We attribute these variations in line fluxes to the variations of both density and temperature in the line emitting regions as a result of the intermediate-scale magnetic fields responsible for stellar activity leading to these spectral variations.     

Apparent Solar Tornado-Like Prominences

Recent high-resolution observations from the Solar Dynamics Observatory (SDO) have reawakened interest in the old and fascinating phenomenon of solar tornado-like prominences. This class of prominences was first introduced by Pettit (Astrophys. J. 76, 9, 1932), who studied them over many years. Observations of tornado prominences similar to the ones seen by SDO had already been documented by Secchi (Le Soleil, 1877). High-resolution and high-cadence multiwavelength data obtained by SDO reveal that the tornado-like appearance of these prominences is mainly an illusion due to projection effects. We discuss two different cases where prominences on the limb might appear to have a tornado-like behavior. One case of apparent vortical motions in prominence spines and barbs arises from the (mostly) 2D counterstreaming plasma motion along the prominence spine and barbs together with oscillations along individual threads. The other case of apparent rotational motion is observed in a prominence cavity and results from the 3D plasma motion along the writhed magnetic fields inside and along the prominence cavity as seen projected on the limb. Thus, the “tornado” impression results either from counterstreaming and oscillations or from the projection on the plane of the sky of plasma motion along magnetic-field lines, rather than from a true vortical motion around an (apparent) vertical or horizontal axis. We discuss the link between tornado-like prominences, filament barbs, and photospheric vortices at their base.     

Spectral behavior of AM Her and QQ Vul in high and intermediate states in the UV

We present low resolution UV spectra of two polar systems, AM Her and QQ Vul from the observations taken by the IUE (International Ultraviolet Explorer) of the period between 1978–1996 and 1983–1996 for both systems respectively, to accomplish a large scale study of what happens to the ultraviolet flux of C IV 1550 Å spectral line during different orbital phases. Two spectra for both systems showing the variations in line fluxes and line widths at different orbital phases in high and intermediate states are presented. We concentrated on calculating the line fluxes and line widths of C IV 1550 Å emission line originating in the accretion stream. Our results show that there is spectral variability for the aformentioned physical parameters at different times, similar to that known for the light curve (Heise and Verbunt, Astron. Astrophys. 189:112, 1988; Gansicke et al., Astron. Astrophys. 303:127, 1995; Kafka and Honeycutt, Astron. J. 125:2188K, 2003). We attribute it to the variations of both density and temperature as a result of changing the mass transfer rate (Hutchings et al., Astron. J. 123:2841H, 2002; King and Lasota, Astron. Astrophys. 140L:16K, 1984) which is responsible for this spectral variability. Also we found that the line fluxes of AM Her are greater than the line fluxes of QQ Vul, while the line widths of both systems are approximately the same.     

Inclusion of sdBs in evolutionary population synthesis for binary stellar populations and the application: the determination of photo-z and galaxy morphology

Subdwarf B stars (sdBs) can significantly change the ultraviolet spectra of populations at age t～1 Gyr, and have been even included in the evolutionary population synthesis (EPS) models by Han et al. (Mon. Not. R. Astron. Soc. 380:1098, 2007). In this study we present the spectral energy distributions (SEDs) of binary stellar populations (BSPs) by combining the EPS models of Han et al. (Mon. Not. R. Astron. Soc. 380:1098, 2007) and those of the Yunnan group (Zhang et al. in Astron. Astrophys. 415:117, 2004; Mon. Not. R. Astron. Soc. 357:1088, 2005), which have included various binary interactions (except sdBs) in EPS models. This set of SEDs is available upon request from the authors. Using this set of SEDs of BSPs we build the spectra of Burst, E, S0–Sd and Irr types of galaxies by using the package of Bruzual and Charlot (Mon. Not. R. Astron. Soc. 344:1000, 2003). Combined with the photometric data (filters and magnitudes), we obtain the photometric redshifts and morphologies of 1502 galaxies by using the Hyperz code of Bolzonella et al. (Astron. Astrophys. 363:476, 2000). This sample of galaxies is obtained by removing those objects, mismatched with the SDSS/DR7 and GALEX/DR4, from the catalogue of Fukugita et al. (Astron. J. 134:579, 2007). By comparison the results with the SDSS spectroscopic redshifts and the morphological index of Fukugita et al. (Astron. J. 134:579, 2007), we find that the photo-z fluctuate with the SDSS spectroscopic redshifts, while the Sa–Sc galaxies in the catalogue of Fukugita et al. (Astron. J. 134:579, 2007) are classified earlier as Burst-E galaxies.     

Investigation of the Coronal Magnetic Field Using a Type II Solar Radio Burst

The type II solar radio burst recorded on 13 June 2010 by the Hiraiso Solar Observatory Radio Spectrograph was employed to estimate the magnetic-field strength in the solar corona. The burst was characterized by a well-pronounced band splitting, which we used to estimate the density jump at the shock and Alfvén Mach number using the Rankine–Hugoniot relation. We convert the plasma frequency of the type II burst into height [R] in solar radii using an appropriate density model, and then we estimated the shock speed [V _s], coronal Alfvén velocity [V _A], and the magnetic-field strength at different heights. The relative bandwidth of the band splitting was found to be in the range 0.2?–?0.25, corresponding to a density jump of X=1.44?–?1.56, and an Alfvén Mach number of M _A=1.35?–?1.45. The inferred mean shock speed was on the order of V≈667 km?s^?1. From the dependencies V(R) and M _A(R) we found that the Alfvén speed slightly decreases at R≈1.3?–?1.5 R_⊙. The magnetic-field strength decreases from a value between 2.7 and 1.7 G at R≈1.3?–?1.5 R_⊙, depending on the coronal-density model employed. Our results are in good agreement with the empirical scaling by Dulk and McLean (Solar Phys. 57, 279, 1978) and Gopalswamy et al. (Astrophys. J. 744, 72, 2012). Our results show that the type II band-splitting method is an important tool for inferring the coronal magnetic field, especially when independent measurements are made from white-light observations.     

The Free Energy of NOAA Solar Active Region AR 11029

The NOAA active region (AR) 11029 was a small but highly active sunspot region which produced 73 GOES soft X-ray flares during its transit of the disk in late October 2009. The flares appear to show a departure from the well-known power law frequency-size distribution. Specifically, too few GOES C-class and no M-class flares were observed by comparison with a power law distribution (Wheatland, Astrophys. J. 710, 1324, 2010). This was conjectured to be due to the region having insufficient magnetic energy to power the missing large events. We construct nonlinear force-free extrapolations of the coronal magnetic field of AR 11029 using data taken on 24 October by the SOLIS Vector SpectroMagnetograph (SOLIS/VSM) and data taken on 27 October by the Hinode Solar Optical Telescope SpectroPolarimeter (Hinode/SP). Force-free modeling with photospheric magnetogram data encounters problems, because the magnetogram data are inconsistent with a force-free model. We employ a recently developed “self-consistency” procedure which addresses this problem and accommodates uncertainties in the boundary data (Wheatland and Régnier, Astrophys. J. 700, L88, 2009). We calculate the total energy and free energy of the self-consistent solution, which provides a model for the coronal magnetic field of the active region. The free energy of the region was found to be ≈?4×10²⁹?erg on 24 October and ≈?7×10³¹?erg on 27 October. An order of magnitude scaling between RHESSI non-thermal energy and GOES peak X-ray flux is established from a sample of flares from the literature and is used to estimate flare energies from the observed GOES peak X-ray flux. Based on the scaling, we conclude that the estimated free energy of AR 11029 on 27 October when the flaring rate peaked was sufficient to power M-class or X-class flares; hence, the modeling does not appear to support the hypothesis that the absence of large flares is due to the region having limited energy.