Solar Rotational Tomography Research Articles

The Application of the Filtered Backprojection Algorithm to Solar Rotational Tomography

Abstract Solar rotational tomography (SRT) is an important method to reconstruct the physical parameters of the three-dimensional solar corona. Here we propose an approach to apply the filtered backprojection (FBP) algorithm to the SRT. The FBP algorithm is generally not suitable for SRT due to the several issues with solar extreme ultraviolet (EUV) observations—in particular, a problem caused by missing data because of the unobserved back side of corona hidden behind the Sun. We developed a method to generate a modified sinogram that resolves the blocking problem. The modified sinogram is generated by combining the EUV data at two opposite sites observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory (SDO). We generated the modified sinogram for about one month in 2019 February and reconstructed the three-dimensional corona under the static state assumption. In order to obtain the physical parameters of the corona, we employed a differential emission measure inversion method. We tested the performance of the FBP algorithm with the modified sinogram by comparing the reconstructed data with the observed EUV image, electron density models, previous studies of electron temperature, and an observed coronagraph image. The results illustrate that the FBP algorithm reasonably reconstructs the bright regions and the coronal holes and can reproduce their physical parameters. The main advantage of the FBP algorithm is that it is easy to understand and computationally efficient. Thus, it enables us to easily probe the inhomogeneous coronal electron density and temperature distribution of the solar corona.

Anomalous Surge of the White-Light Corona at the Onset of the Declining Phase of Solar Cycle 24

In late 2014, when the current Solar Cycle 24 entered its declining phase, the white-light corona as observed by the LASCO-C2 coronagraph underwent an unexpected surge that increased its global radiance by 60%, reaching a peak value comparable to the peak values of the more active Solar Cycle 23. A comparison of the temporal variation of the white-light corona with the variations of several indices and proxies of solar activity indicate that it best matches the variation of the total magnetic field. The daily variations point to a localized enhancement or bulge in the electron density that persisted for several months. Carrington maps of the radiance and of the HMI photospheric field allow connecting this bulge to the emergence of the large sunspot complex AR 12192 in October 2014, the largest since AR 6368 observed in November 1990. The resulting unusually high increase of the magnetic field and the distortion of the neutral sheet in a characteristic inverse S-shape caused the coronal plasma to be trapped along a similar pattern. A 3D reconstruction of the electron density based on time-dependent solar rotational tomography supplemented by 2D inversion of the coronal radiance confirms the morphology of the bulge and reveals that its level was well above the standard models of a corona of the maximum type, by typically a factor of 3. A rather satisfactory agreement is found with the results of the thermodynamic MHD model produced by Predictive Sciences, although discrepancies are noted. The specific configuration of the magnetic field that led to the coronal surge resulted from the interplay of various factors prevailing at the onset of the declining phase of the solar cycles, which was particularly efficient in the case of Solar Cycle 24.

Time-dependent tomographic reconstruction of the solar corona

Solar rotational tomography (SRT) applied to white-light coronal images observed at multiple aspect angles has been the preferred approach for determining the three-dimensional (3D) electron density structure of the solar corona. However, it is seriously hampered by the restrictive assumption that the corona is time-invariant which introduces significant errors in the reconstruction. We first explore several methods to mitigate the temporal variation of the corona by decoupling the "fast-varying" inner corona from the "slow-moving" outer corona using multiple masking (either by juxtaposition or recursive combination) and radial weighting. Weighting with a radial exponential profile provides some improvement over a classical reconstruction but only beyond 3 Rsun. We next consider a full time-dependent tomographic reconstruction involving spatio-temporal regularization and further introduce a co-rotating regularization aimed at preventing concentration of reconstructed density in the plane of the sky. Crucial to testing our procedure and properly tuning the regularization parameters is the introduction of a time-dependent MHD model of the corona based on observed magnetograms to build a time-series of synthetic images of the corona. Our procedure, which successfully reproduces the time-varying model corona, is finally applied to a set of of 53 LASCO-C2 pB images roughly evenly spaced in time from 15 to 29 March 2009. Our procedure paves the way to a time-dependent tomographic reconstruction of the coronal electron density to the whole set of LASCO-C2 images presently spanning 20 years.

The Comparison of Total Electron Content Between Radio and Thompson Scattering

The total electron content (TEC) of the solar corona in June 2002 is calculated by three observational techniques and the results are compared. The first technique is solar rotational tomography (SRT) applied to a 14-day time series of LASCO-C2 polarized brightness images, and the other two techniques use the Cassini spacecraft radio beacon for Doppler tracking (phase delay) and ranging (group delay). While the Doppler-tracking technique has an arbitrary zero-point, it is otherwise found that the three methods produce consistent estimates of the TEC to within established uncertainties, providing an independent check on the calibrations. The verification of the accuracy of the Doppler-tracking technique enables a significant improvement to the use of spacecraft data sets in studying the heliosphere: the density component to Faraday rotation can be separated from the magnetic-field component as variable structures cross, such as coronal mass ejections and magnetohydrodynamic waves. Furthermore, we show that the unique frequency-time variable characteristics of the hydrodynamic components of waves can be studied. Based on this work, future Faraday rotation studies of variable solar phenomena will isolate the electron density changes from the magnetic-field contribution. This capability will enable advanced research into variable heliospheric magnetic fields.

A GLOBAL TWO-TEMPERATURE CORONA AND INNER HELIOSPHERE MODEL: A COMPREHENSIVE VALIDATION STUDY

The recent solar minimum with very low activity provides us a unique opportunity for validating solar wind models. During CR2077 (2008 November 20 through December 17), the number of sunspots was near the absolute minimum of solar cycle 23. For this solar rotation, we perform a multi-spacecraft validation study for the recently developed three-dimensional, two-temperature, Alfven-wave-driven global solar wind model (a component within the Space Weather Modeling Framework). By using in situ observations from the Solar Terrestrial Relations Observatory (STEREO) A and B, Advanced Composition Explorer (ACE), and Venus Express, we compare the observed proton state (density, temperature, and velocity) and magnetic field of the heliosphere with that predicted by the model. Near the Sun, we validate the numerical model with the electron density obtained from the solar rotational tomography of Solar and Heliospheric Observatory/Large Angle and Spectrometric Coronagraph C2 data in the range of 2.4 to 6 solar radii. Electron temperature and density are determined from differential emission measure tomography (DEMT) of STEREO A and B Extreme Ultraviolet Imager data in the range of 1.035 to 1.225 solar radii. The electron density and temperature derived from the Hinode/Extreme Ultraviolet Imaging Spectrometer data are also used to compare with the DEMT as well as the model output. Moreover, for the first time, we compare ionic charge states of carbon, oxygen, silicon, and iron observed in situ with the ACE/Solar Wind Ion Composition Spectrometer with those predicted by our model. The validation results suggest that most of the model outputs for CR2077 can fit the observations very well. Based on this encouraging result, we therefore expect great improvement for the future modeling of coronal mass ejections (CMEs) and CME-driven shocks.

THE ROTATION OF THE WHITE LIGHT SOLAR CORONA AT HEIGHT 4R☉FROM 1996 TO 2010: A TOMOGRAPHICAL STUDY OF LARGE ANGLE AND SPECTROMETRIC CORONAGRAPH C2 OBSERVATIONS

Solar rotational tomography is applied to Large Angle and Spectrometric Coronagraph (LASCO) C2/Solar and Heliospheric Observatory (SOHO) observations covering the period 1996-2010, resulting in a set of electron density maps at a height of 4 R ? from which rotation rates can be calculated. Large variation of rotation rates is measured. Rates are dominated by the Carrington rotation rate (14.18?deg?d?1 sidereal), but at times over the solar cycle, rates are measured between ?3 and 3?deg?d?1 relative to the Carrington rotation rate. Rotation rates can vary considerably between latitudes, even between neighboring latitudes. They can remain relatively stable or change smoothly over long periods of times, or can change rather abruptly. There are periods for certain latitudes (for example, the equator at solar maximum) when the movement is dominated by rapid structural reconfiguration, not a coherent rotation. These results raise new questions regarding the link between the Sun and the corona, and provide fresh challenges to interpretations of the coronal structural evolution and the development of large-scale coronal models. In particular, can interchange reconnection provide an explanation of the considerable latitudinal differences in rotation rates, and what mechanism can explain abrupt changes in rotation rates?

LONGITUDINAL DRIFTS OF STREAMERS ACROSS THE HELIOSPHERIC CURRENT SHEET

Potential field source surface (PFSS) extrapolations of the photospheric magnetic field provide a qualitatively correct model of the coronal magnetic structure. We show that the magnetic structure provided by PFSS describes a framework within which high-density coronal streamers are distributed. However, the density structures have considerable freedom to drift longitudinally along the magnetic structure. Some caution must therefore be taken when using PFSS models as proxies for the coronal density structure. In particular, while measurements of coronal rotation using PFSS models provide an estimate of the large-scale magnetic structure rotation, they are not valid measurements of the density rotation. Furthermore, attempts to assign a consistent rate of rotation to the electron corona over long time periods are not always valid since the movement is dominated by structural reconfiguration. These conclusions are reached by the application of solar rotational tomography to LASCO C2/Solar and Heliospheric Observatory observations during solar minimum (1996-1997), revealing the changing density structure of the equatorial streamer belt at a height of 4 R ?.

OBSERVATIONAL ASPECTS OF THE THREE-DIMENSIONAL CORONAL STRUCTURE OVER A SOLAR ACTIVITY CYCLE

Solar rotational tomography is applied to almost eleven years of Large Angle Spectrometric Coronagraph C2/Solar and Heliospheric Observatory data, revealing for the first time the behavior of the large-scale coronal density structures, also known as streamers, over almost a full solar activity cycle. This study gives an overview of the main results of this project. (1) Streamers are most often shaped as extended, narrow plasma sheets. The sheets can be extremely narrow at times (⩽0.14 × 106 km at 4 R☉). This is over twice their heliocentric angular thickness at 1 AU. (2) At most times outside the height of solar maximum, there are two separate stable large helmet streamer belts extending from mid-latitudes (in both north and south). At solar minimum, the streamers converge and join near the equator, giving the impression of a single large helmet streamer. Outside of solar minimum, the two streamers do not join, forming separate high-density sheets in the extended corona (one in the north, another in the south). At solar maximum, streamers rise radially from their source regions, while during the ascending and descending activity phases, streamers are skewed toward the equator. (3) For most of the activity cycle, streamers share the same latitudinal extent as filaments on the disk, showing that large-scale stable streamers are closely linked to the same large-scale photospheric magnetic configuration, which give rise to large filaments. (4) The poleward footpoints of the streamers are often above crown polar filaments and the equatorial footpoints are above filaments or active regions (or above the photospheric neutral lines which underlie these structures). The high-density structures arising from the equatorial active regions either rise and form the equatorial footpoints of mid-latitude quiescent streamers, or form unstable streamers at the equator, not connected to the quiescent streamer structure at higher latitude (so there are often three streamer sheets sharing the same extended longitudinal region). (5) Comparison between the tomography results and a potential field source surface model shows that streamers are not necessarily associated with a magnetic polarity reversal, but rather are regions containing field lines arising from widely separated sources at the Sun. We call these convergence sheets. (6) There is considerable differential rotation of streamers at high latitudes, which makes comparison between disk and coronal structure complicated. The presence of differential rotation has implications for many areas of coronal and heliospheric research.

MAPPING THE STRUCTURE OF THE CORONA USING FOURIER BACKPROJECTION TOMOGRAPHY

Estimating the structure, or density distribution, of the solar corona from a set of two-dimensional white-light images made by coronagraphs is a critical challenge in coronal physics. This work describes new data-analysis procedures which are used to create global maps of the coronal structure at heights where the corona becomes approximately radial (≥ 3 R ☉). The technique, which is named Qualitative Solar Rotational Tomography (QSRT), uses total brightness white light observations, processed with a suitable background subtraction and a Normalizing Radial Graded Filter (NRGF). These observations are made with high frequency by the Large Angle and Spectrometric Coronagraph Experiment (LASCO) C2 coronagraph, which allows a standard Fourier-transform-based tomographical reconstruction. In this paper, we first test the technique using a model corona. QSRT is then applied to a set of observations made during Carrington Rotation (CR) 2000-2001 (2003 March 16 to 2003 March 31). Since the maps are constructed from data which are normalized using the NRGF process, QSRT cannot give electron density directly. Nevertheless, the tests using the model corona demonstrate the technique's ability to give a good qualitative reconstruction of the coronal structure at high latitude, with decreasing but acceptable accuracy at the equator. These tests also demonstrate QSRT's insensitivity to noise. For the LASCO C2 observations, good agreement is found between synthetic images calculated from the reconstructed corona and the original observations, and good agreement is found between the distribution of density in a QSRT reconstruction and that found using a global MHD model. Despite their lack of quantitative information on absolute electron density, the resulting maps (which are constructed directly from high-resolution coronal data observed at the appropriate height), contain useful information on the distribution of density in the corona.

Validation of Two MHD Models of the Solar Corona with Rotational Tomography

We demonstrate a validation of two 3D MHD models of the corona by comparing density values from solar rotational tomography (SRT) to densities and morphological properties of the two MHD solutions for CR 2029 (2005 April 21-May 18). The two MHD models are given by the Stanford and Michigan models, and both use the same synoptic magnetogram from MDI as a lower boundary condition. The SRT reconstructions are based on polarized white-light images MLSO Mk IV data for the region between 1.1 and 1.5 R☉ (solar radii) and LASCO C2 for the region between 2.3 and 6.0 R☉. While the Stanford MHD model reasonably reproduces the tomographic density over the south pole, it fares less well over the north pole, and the Michigan MHD model underestimates the density over both poles. At lower latitudes, we find that while the MHD models have better agreement with the tomographic densities in the region below 3.5 R☉, at larger heights the agreement is more problematic. Our interpretation is that the base densities and temperatures of the models need to be improved, as well as their radial density gradients.

Three‐dimensional estimates of the coronal electron density at times of extreme solar activity

This paper presents quantitative three‐dimensional (3‐D) reconstructions of the electron density (Ne) in the solar corona between 1.14 and 2.7 solar radii (R⊙) formed from polarized brightness (pB) measurements made by the Mauna Loa Solar Observatory Mark‐IV (Mk4) K‐coronameter at the time of the extreme solar events of October and November 2003. The 3‐D reconstructions are made by a process called solar rotational tomography that exploits the view angles provided by solar rotation during a 2‐week period. Although this method is incapable of resolving dynamic evolution on timescales of less than about 2 weeks, a qualitative comparison of the reconstructions to instantaneous Extreme ultraviolet Imaging Telescope images (EIT) shows good agreement between coronal holes, active regions, and “quiet Sun” structures on the disk and their counterparts in the corona at 1.2 R⊙.

On the Combination of Differential Emission Measure Analysis and Rotational Tomography for Three‐dimensional Solar EUV Imaging

Conventional differential emission measure (DEM) analysis allows one to determine the amount of plasma as a function of temperature along a given line of sight. A completely different technique called solar rotational tomography (SRT) exploits the view angles provided by solar rotation to determine the spatial distribution of emissivity in three dimensions. These two techniques can be combined in a procedure called differential emission measure tomography (DEMT) to determine the DEM at each point in the corona with the same spatial resolution as can normally be achieved by SRT. In this paper the theory of DEMT is presented, and numerical examples based on the Atmospheric Imaging Assembly (AIA) are given. The results demonstrate promising potential for the methods to be adapted for use with other EUV and X-ray imaging and/or spectroscopy instruments.

On the Use of Total Brightness Measurements for Tomography of the Solar Corona

A time series of polarized white light coronagraph images may be used to make a tomographic estimate of the electron density (Ne) in three dimensions, as has been demonstrated by several authors. This technique has come to be known as solar rotational tomography (SRT). SRT relies on the fact that the polarized brightness (pB) is dominated by the electron-scattered K corona. In contrast, the total brightness contains a large contribution from the dust-scattered F-corona with some signal from the K corona. The K-corona contribution to the total brightness (B) is of interest because the Thomson scattering has different angular dependences for the polarized and unpolarized components. This difference in angular dependence in principle allows one to exploit total brightness measurements as a source of independent information for SRT. In this paper the problem of making optimal tomographic estimates of Ne using both total and polarized brightness data is considered under the assumption that the F-corona contribution can be determined with a known level of precision. Formulae for the reconstructions and the likely errors are given in terms of the singular value decomposition of the weighted measurement operators. It is shown that in order for the total brightness measurements to be useful for SRT, the process of removing the F-corona contribution must be almost perfect in the sense that it contributes uncertainty that is not much greater than the measurement noise in the polarized images. This result holds at heights below roughly 15 solar radii, where the F corona is almost completely unpolarized.

Rotational Tomography For 3d Reconstruction Of The White-Light And Euv Corona In The Post-Soho Era

Improving our understanding of the mechanisms that energize the solar wind and heat structures in the solar corona requires the development of empirical methods that can determine the three-dimensional (3D) temperature and density distributions with as much spatial and temporal resolution as possible. This paper reviews the solar rotational tomography (SRT) methods that will be used for 3D reconstruction of the solar corona from data obtained by the next generation of space-based missions such as the Solar and Terrestrial Relations Observatory (STEREO), Solar-B and the Solar Dynamics Observatory (SDO). In the next decade, SRT will undergo rapid advancement on several frontiers of 3D image reconstruction: Although the principles described apply to many different wavelength regimes, this paper concentrates on white-light and EUV data. Previous work on all of these subjects is reviewed, and major technical issues and future directions are discussed.

Tomography of the Solar Corona. II. Robust, Regularized, Positive Estimation of the Three‐dimensional Electron Density Distribution from LASCO‐C2 Polarized White‐Light Images

Solar rotational tomography is used to determine the three-dimensional electron density distribution of the solar corona from 2.4 to 6.0 R☉. The robust, regularized, positive estimation method, described in a previous paper, is demonstrated on test cases and on LASCO-C2 data. Because the solar rotational pole is inclined to the plane of the ecliptic by about 7°, the tomographic inversion requires a full three-dimensional treatment instead of a series of two-dimensional inversions. The LASCO data are taken from the first Whole Sun Month, which was a period of low solar activity.