Reconstruction of RHESSI Solar Flare Images with a Forward Fitting Method

We describe a forward-fitting method that has been developed to reconstruct hard X-ray images of solar flares from the Ramaty High-Energy Solar Spectroscopic Imager (RHESSI), a Fourier imager with rotation-modulated collimators that was launched on 5 February 2002. The forward-fitting method is based on geometric models that represent a spatial map by a superposition of multiple source structures, which are quantified by circular gaussians (4 parameters per source), elliptical gaussians (6 parameters), or curved ellipticals (7 parameters), designed to characterize real solar flare hard X-ray maps with a minimum number of geometric elements. We describe and demonstrate the use of the forward-fitting algorithm. We perform some 500 simulations of rotation-modulated time profiles of the 9 RHESSI detectors, based on single and multiple source structures, and perform their image reconstruction. We quantify the fidelity of the image reconstruction, as function of photon statistics, and the accuracy of retrieved source positions, widths, and fluxes. We outline applications for which the forward-fitting code is most suitable, such as measurements of the energy-dependent altitude of energy loss near the limb, or footpoint separation during flares. Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1022469811115     

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. I. Theory

We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components B _x (x), B _y (x), B _z (x), the force-free parameter α(x), the electric current density j(x), and are accurate to second-order (of the nonlinear force-free α-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena.     

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. II. Numeric Code and Tests

Based on a second-order approximation of nonlinear force-free magnetic field solutions in terms of uniformly twisted field lines derived in Paper I, we develop here a numeric code that is capable to forward-fit such analytical solutions to arbitrary magnetogram (or vector magnetograph) data combined with (stereoscopically triangulated) coronal loop 3D coordinates. We test the code here by forward-fitting to six potential field and six nonpotential field cases simulated with our analytical model, as well as by forward-fitting to an exactly force-free solution of the Low and Lou (Astrophys. J. 352, 343, 1990) model. The forward-fitting tests demonstrate: i) a satisfactory convergence behavior (with typical misalignment angles of μ≈1^°?–?10^°), ii) relatively fast computation times (from seconds to a few minutes), and iii) the high fidelity of retrieved force-free α-parameters (α _fit/α _model≈0.9?–?1.0 for simulations and α _fit/α _model≈0.7±0.3 for the Low and Lou model). The salient feature of this numeric code is the relatively fast computation of a quasi-force-free magnetic field, which closely matches the geometry of coronal loops in active regions, and complements the existing nonlinear force-free field (NLFFF) codes based on photospheric magnetograms without coronal constraints.     

Magnetic field structures of hard X-ray flares observed by HINOTORI spacecraft

The magnetic field structure of five flares observed by HINOTORI spacecraft is studied. The double source structure of impulsive flares seems to indicate hard X-ray emission from the two footpoints of a flaring loop, but the potential field computation does not reproduce a loop connecting the two sources. Therefore the magnetic field could be in a sheared configuration and the force-free field modeling would be the next step to examine. On the other hand gradual flares are characterized by hard X-ray sources located in the corona, 2–4 x 10⁴ km above the photosphere. The potential field modeling is found to give a reasonable fitting in this type of flares, and the hard X-ray sources are located at the top of the magnetic loop or arcade. This configuration is consistent with the thick-target trap model of the hard X-ray bursts.     

Pole wandering of Mars: Evidence from paleomagnetic poles

We use the mapping-phase high-altitude magnetic measurements provided by Mars Global Surveyor (MGS) between March 1999 and April 2003 to model nine relatively isolated magnetic anomalies of Mars. Each anomaly is modeled with an elliptical prism. Each component of the observed magnetic field is modeled independently using an elliptical prism in order to assess the reliability of the results and suppress non-crustal and nearby crustal source contaminations. The paleomagnetic pole positions are obtained from the magnetization vectors of the model source bodies. We clean the data by removing the bad tracks and then divide the entire data into two sets that are measured at different times. Applying covariance analysis in the Fourier domain to two maps of the same magnetic component that are derived from the two sets provides a means to extract the most common features of the maps. The quality of a model is evaluated and only good models are used in the final geophysical interpretation. Most poles that come from good models cluster in the Tharsis region, suggesting that Mars experienced polar motion since the magnetic source bodies were magnetized.     

Subsurface Vorticity of Flaring <Emphasis Type="Italic">versus</Emphasis> Flare-Quiet Active Regions

We apply discriminant analysis to 1023 active regions and their subsurface-flow parameters, such as vorticity and kinetic helicity density, with the goal of distinguishing between flaring and non-flaring active regions. We derive synoptic subsurface flows by analyzing GONG high-resolution Doppler data with ring-diagram analysis. We include magnetic-flux values in the discriminant analysis derived from NSO Kitt Peak and SOLIS synoptic maps binned to the same spatial scale as the helioseismic analysis. For each active region, we determine the flare information from GOES and include all flares within 60° central meridian distance to match the coverage of the ring-diagram analysis. The subsurface-flow characteristics improve the ability to distinguish between flaring and non-flaring active regions. For the C- and M-class flare category, the most important subsurface parameter is the so-called structure vorticity, which estimates the horizontal gradient of the horizontal-vorticity components. The no-event skill score, which measures the improvement over predicting that no events occur, reaches 0.48 for C-class flares and 0.32 for M-class flares, when the structure vorticity at three depths combined with total magnetic flux are used. The contributions come mainly from shallow layers within about 2 Mm of the surface and layers deeper than about 7 Mm.     

The Lyman α forest in a truncated hierarchical structure formation

The Lyman α forest provides important constraints on the smoothness of the Universe on large scales. We calculate the flux distribution along the line of sight to quasars in a universe made of randomly distributed clumps, each of them with a Rayleigh–L'evy fractal structure with dimension D <2. We consider the probability distribution function of the normalized flux in the line of sight to quasars. We illustrate that the truncated clustering hierarchy model with D <2 shows far too many voids along the line of sight to quasars compared with the observed flux distribution and the distribution in a cold dark matter model. This supports the common view that on large scales the Universe is homogeneous, rather than fractal-like.     

Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms

This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar magnetic fields. In the model, the basic evolution of the magnetic elements is governed by a supergranular flow profile. In addition, magnetic elements may evolve through the processes of emergence, cancellation, coalescence and fragmentation. Model parameters for the emergence of bipoles are based upon the results of observational studies. Using this model, several simulations are considered, where the range of flux with which bipoles may emerge is varied. In all cases the model quickly reaches a steady state where the rates of emergence and cancellation balance. Analysis of the resulting magnetic field shows that we reproduce observed quantities such as the flux distribution, mean field, cancellation rates, photospheric recycle time and a magnetic network. As expected, the simulation matches observations more closely when a larger, and consequently more realistic, range of emerging flux values is allowed (4×10¹⁶ – 10¹⁹ Mx). The model best reproduces the current observed properties of the magnetic carpet when we take the minimum absolute flux for emerging bipoles to be 4×10¹⁶ Mx. In future, this 2D model will be used as an evolving photospheric boundary condition for 3D non-potential modeling.     

Modeling the formation of bright slope deposits associated with gullies in Hale Crater, Mars: Implications for recent liquid water

Our study investigates possible formation mechanisms of the very recent bright gully deposits (BGDs) observed on Mars in order to assess if liquid water was required. We use two models in our assessment: a one-dimensional (1D) kinematic model to model dry granular flows and a two-dimensional (2D) fluid-dynamic model, FLO-2D (O’Brien et al., 1993, FLO Engineering), to model water-rich and wet sediment-rich flows. Our modeling utilizes a high-resolution topographic model generated from a pair of images acquired by the High Resolution Imaging Science Experiment (HiRISE) aboard the Mars Reconnaissance Orbiter. For the 1D kinematic modeling of dry granular flows, we examine a range of particle sizes, flow thicknesses, initial velocities, flow densities, and upslope initiation points to examine how these parameters affect the flow run-out distances of the center of mass of a flow. Our 1D modeling results show that multiple combinations of realistic parameters could produce dry granular flows that travel to within the observed deposits’ boundaries. We run the 2D fluid-dynamic model, FLO-2D, to model both water-rich and wet sediment-rich flows. We vary the inflow volume, inflow location, discharge rate, water-loss rate (water-rich models only), and simulation time and examine the resulting maximum flow depths and velocities. Our 2D modeling results suggest that both wet sediment-rich and water-rich flows could produce the observed bright deposits. Our modeling shows that the BGDs are not definitive evidence of recent liquid water on the surface of Mars.     

New method of analysis for TeV gamma-ray data collected by the TACTIC telescope

We describe a new fractal and wavelet based framework for analysing atmospheric Cerenkov images of extensive air showers. The methodology developed using simulated data has been tested with the data collected from Mrk421 and Crab nebula directions during 10 October 2009–16 May 2010 by the TACTIC telescope. The telescope detected flaring activity in TeV gamma-rays from Mrk421 during 15th-17th February 2010. Hillas parameter analysis of Cerenkov images showed presence of TeV γ-ray signal with statistical significance of 12.5 σ beyond 1TeV energy for the 265 hours data set. Based on a Monte-Carlo simulated database of Cerenkov images recorded by the TACTIC telescope, the wavelet dimension B₆ can be exploited as a useful parameter to segregate gamma-ray initiated events from hadron initiated events with better efficiency. We derive a preliminary value of the relevant significance for gamma initiated events using wavelet parameter B₆ for the 265 hours long observation spell of Mrk421 including the flaring episode during 15th–17th February 2010 and 66 hours data of observations on Crab nebula. Wavelet analysis approach has also been tested on Crab OFF- source data of 27 hours. Application of wavelet parameter B₆ on the recorded Cerenkov images of the TACTIC telescope reveals better results in terms of segregation efficiency and enhancement of the determined value of statistical significance as compared to the Hillas parameters approach.     

Magnetic configurations of the fast CP rotators HD3360, HD4778, HD5737, HD112413, and HD215441

The method of “magnetic charges” is used to model magnetic fields of five rapidly rotating stars (P < 25^d) and to find the basic parameters of their magnetic fields. A table containing all the modeling results obtained using the adopted method as well as the parameters obtained for the same stars by other authors is presented. Significant discrepances are found in a number of cases, which can apparently be explained by insufficient accuracy of the estimated inclinations of the stars to the line of sight.     

Bayesian modelling of the cool core galaxy group NGC 4325

We present an X-ray analysis of the radio-quiet cool-core galaxy group NGC 4325  ( z = 0.026)  based on Chandra and ROSAT observations. The Chandra data were analysed using xspec deprojection, 2D spectral mapping and forward-fitting with parametric models. Additionally, a Markov Chain Monte Carlo method was used to perform a joint Bayesian analysis of the Chandra and ROSAT data. The results of the various analysis methods are compared, particularly those obtained by forward-fitting and deprojection. The spectral mapping reveals the presence of cool gas displaced up to 10 kpc from the group centre. The Chandra X-ray surface brightness shows the group core to be highly disturbed, and indicates the presence of two small X-ray cavities within 15 kpc of the group core. The xspec deprojection analysis shows that the group has a particularly steep entropy profile, suggesting that an active galactic nucleus (AGN) outburst may be about to occur. With the evidence of prior AGN activity, but with no radio emission currently observed, we suggest that the group in a pre-outburst state, with the cavities and displaced gas providing evidence of a previous, weak AGN outburst.     

Gyrosynchrotron Emission from Anisotropic Pitch-Angle Distribution of Electrons in 3-D Solar Flare Sources

We present calculations, made for the first time, of the gyrosynchrotron emission by mildly relativistic electrons with anisotropic pitch-angle distribution using a realistic magnetic loop model in three dimensions. We investigated the intensity, spectral index of the optically thin region of the spectrum, the spatial morphology and the dependency on the source position on the solar disk. The method to describe a three-dimensional source and the procedure to perform the calculations are presented. We have modified the Ramaty’s gyrosynchrotron code to allow the evaluation of anisotropic pitch-angle electron distributions, as described in the complete formalism. We found that anisotropic electron distributions affect the intensity of the radiation, spatial morphology and spectrum of spatially resolved sources. However, the spatially integrated spectrum of the emission seems to be insensitive to the electron pitch-angle distribution, as the magnetic field inhomogeneity smooths out the effects of the anisotropic distribution in the produced radiation, in contrast to homogeneous sources.     

A Burst with Double Radio Spectrum Observed up to 212 GHz

We study a solar flare that occurred on 10 September 2002, in active region NOAA 10105, starting around 14:52 UT and lasting approximately 5 minutes in the radio range. The event was classified as M2.9 in X-rays and 1N in Hα. Solar Submillimeter Telescope observations, in addition to microwave data, give a good spectral coverage between 1.415 and 212 GHz. We combine these data with ultraviolet images, hard and soft X-ray observations, and full-disk magnetograms. Images obtained from Ramaty High Energy Solar Spectroscopic Imager data are used to identify the locations of X-ray sources at different energies, and to determine the X-ray spectrum, while ultraviolet images allow us to characterize the coronal flaring region. The magnetic field evolution of the active region is analyzed using Michelson Doppler Imager magnetograms. The burst is detected at all available radio frequencies. X-ray images (between 12 keV and 300 keV) reveal two compact sources. In the 212 GHz data, which are used to estimate the radio-source position, a single compact source is seen, displaced by 25″ from one of the hard X-ray footpoints. We model the radio spectra using two homogeneous sources, and we combine this analysis with that of hard X-rays to understand the dynamics of the accelerated particles. Relativistic particles, observed at radio wavelengths above 50 GHz, have an electron index evolving with the typical soft–hard–soft behavior.     

The MHD stability of a twisted flux tube prominence model

The ideal MHD stability of the 2D twisted magnetic flux tube prominence model of Cartledge and Hood (1993) is investigated. The model includes a temperature profile that varies from realistic prominence values up to typical coronal values. The prominence is considered to be of finite-width and finite height. The stability properties of the prominence models are studied by using a method that generates a separate necessary condition and a sufficient condition. These conditions give bounds on the parameters that define marginal stability. In many cases these bounds are quite close so that further, more detailed, stability calculations are not necessary. A number of parameter regimes are examined, corresponding to different profiles of the prominence temperatures, densities, and magnetic field shear. It is found that the model admits realistic stable and unstable loop lengths for observed prominence parameters when the axial magnetic field component does not vanish.     

Evaluating Uncertainties in Coronal Electron Temperature and Radial Speed Measurements Using a Simulation of the Bastille Day Eruption

Obtaining reliable measurements of plasma parameters in the Sun’s corona remains an important challenge for solar physics. We previously presented a method for producing maps of electron temperature and speed of the solar corona using K-corona brightness measurements made through four color filters in visible light, which were tested for their accuracies using models of a structured, yet steady corona. In this article we test the same technique using a coronal model of the Bastille Day (14 July 2000) coronal mass ejection, which also contains quiet areas and streamers. We use the coronal electron density, temperature, and flow speed contained in the model to determine two K-coronal brightness ratios at (410.3, 390.0 nm) and (423.3, 398.7 nm) along more than 4000 lines of sight. Now assuming that for real observations, the only information we have for each line of sight are these two K-coronal brightness ratios, we use a spherically symmetric model of the corona that contains no structures to interpret these two ratios for electron temperature and speed. We then compare the interpreted (or measured) values for each line of sight with the true values from the model at the plane of the sky for that same line of sight to determine the magnitude of the errors. We show that the measured values closely match the true values in quiet areas. However, in locations of coronal structures, the measured values are predictably underestimated or overestimated compared to the true values, but can nevertheless be used to determine the positions of the structures with respect to the plane of the sky, in front or behind. Based on our results, we propose that future white-light coronagraphs be equipped to image the corona using four color filters in order to routinely create coronal maps of electron density, temperature, and flow speed.     

Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent Than Others?

Multiple recent investigations of solar magnetic-field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17?733 magnetograms in total) observed by SOHO’s Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i)?a?widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii)?a?lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately, for major solar-flare prediction.     

From Small-Scale Dynamo to Isotropic MHD Turbulence

We consider the problem of incompressible, forced, nonhelical, homogeneous, isotropic MHD turbulence with no mean magnetic field. This problem is essentially different from the case with externally imposed uniform mean field. There is no scale-by-scale equipartition between magnetic and kinetic energies as would be the case for the Alfvén-wave turbulence. The isotropic MHD turbulence is the end state of the turbulent dynamo which generates folded fields with small-scale direction reversals. We propose that the statistics seen in numerical simulations of isotropic MHD turbulence could be explained as a superposition of these folded fields and Alfvén-like waves that propagate along the folds.     

Uncertainties in Solar Synoptic Magnetic Flux Maps

Magnetic flux synoptic charts are critical for a reliable modeling of the corona and heliosphere. Until now, however, these charts were provided without uncertainty estimates. The uncertainties are due to instrumental noise in the measurements and to the spatial variance of the magnetic flux distribution that contributes to each bin in the synoptic chart. We describe here a simple method to compute synoptic magnetic flux maps and their corresponding magnetic flux spatial variance charts that can be used to estimate the uncertainty in the results of coronal models. We have tested this approach by computing a potential-field source-surface model of the coronal field for a Monte Carlo simulation of Carrington synoptic magnetic flux maps generated from the variance map. We show that these uncertainties affect both the locations of source-surface neutral lines and the distributions of coronal holes in the models.     

VLA polarimetry observations of PKS 2322−123: estimating magnetic fields in the Abell 2597 cluster

We present 5-, 8-, and 15-GHz total intensity and polarimetric observations of the radio source PKS 2322−123 taken with the Very Large Array (VLA). This small (11 kpc) source is located at the centre of the cooling-core cluster Abell 2597. The inner X-ray structure, the radio morphology and the steep spectral index  (α=−1.8)  in the lobes all suggest that the radio emission is confined by the ambient X-ray gas. We detect a small region of polarized flux in the southern lobe and are able to calculate a Faraday rotation measure (RM) of 3620 rad m⁻² over this region. Based on these observations and Chandra X-ray data, we suggest that the southern lobe has been deflected from its original south-western orientation to the south and into our line of sight. Using the observed rotation measures (RMs) and our calculated electron density profiles, and assuming both a uniform and tangled magnetic field topology, we estimate a lower limit of the line-of-sight cluster magnetic field,   B _∥= 2.1  μG  .