Richard A. Frazin

A DATA-DRIVEN, TWO-TEMPERATURE SOLAR WIND MODEL WITH ALFVEN WAVES

We have developed a new three-dimensional magnetohydrodynamic (MHD) solar wind model coupled to the Space Weather Modeling Framework (SWMF) that solves for the different electron and proton temperatures. The collisions between the electrons and protons are taken into account as well as the anisotropic thermal heat conduction of the electrons. The solar wind is assumed to be accelerated by the Alfven waves. In this paper, we do not consider the heating of closed magnetic loops and helmet streamers but do address the heating of the protons by the Kolmogorov dissipation of the Alfven waves in open field-line regions. The inner boundary conditions for this solar wind model are obtained from observations and an empirical model. The Wang-Sheeley-Arge model is used to determine the Alfven wave energy density at the inner boundary. The electron density and temperature at the inner boundary are obtained from the differential emission measure tomography applied to the extreme-ultraviolet images of the STEREO A and B spacecraft. This new solar wind model is validated for solar minimum Carrington rotation 2077 (2008 November 20 through December 17). Due to the very low activity during this rotation, this time period is suitable for comparing the simulated corotating interaction regions (CIRs) with in situ ACE/WIND data. Although we do not capture all MHD variables perfectly, we do find that the time of occurrence and the density of CIRs are better predicted than by our previous semi-empirical wind model in the SWMF that was based on a spatially reduced adiabatic index to account for the plasma heating.

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.

Quantitative, three-dimensional analysis of the global corona with multi-spacecraft differential emission measure tomography

A previous paper (Frazin et al. 2005b) introduced the concept of differential emission measure tomography (DEMT), which is a three-dimensional (3D) extension of the classical differential emission measure technique for determining the distribution of temperatures in a volume of plasma. The information for the reconstruction in the three spatial dimensions is provided by solar rotation and/or multi-spacecraft views. This paper describes, quantitatively, the procedure for implementing DEMT with data from NASAs STEREO/EUVI instrument, including the radiometry, line-of-sight geometry, and image preparation steps. An example of a quantitative, multiband, 3D reconstruction and local differential emission measure curves are given, and it is demonstrated that, when applicable, DEMT is a simple 3D analysis tool that obviates the need for structure-specific modeling.

THE SOLAR MINIMUM CORONA FROM DIFFERENTIAL EMISSION MEASURE TOMOGRAPHY

We present results derived from a dual-spacecraft tomographic reconstruction of the solar coronas three-dimensional (3D) extreme ultraviolet (EUV) emissivity. We use simultaneously taken STEREO A and B spacecraft EUVI images from Carrington rotation 2077 (UT 2008 November 20 06:56 through UT December 17 14:34). During this period, the spacecraft view angles were separated by an average 854 which allowed for the reconstruction to be performed with data gathered in about 3/4 of a full solar rotational time. The EUV reconstructions provide the 3D emissivity in each of the three EUVI Fe bands, in the range of heights 1.00-1.25 R s. We use this information to perform local differential emission measure (LDEM) analysis. Taking moments of the so-derived LDEM distributions gives the 3D values of the electron density, temperature, and temperature spread. We determine relationships between the moments of the LDEM and the coronal magnetic field by making longitudinal averages of the moments, and relating them to the global-scale structures of a potential field source surface magnetic field model. In this way, we determine how the electron density, mean temperature, and temperature spread vary for different coronal structures. We draw conclusions about the relationship between the LDEM moments and the sources of the fast and slow solar winds, and the transition between the two regimes.

CORONAL HEATING BY SURFACE ALFVÉN WAVE DAMPING: IMPLEMENTATION IN A GLOBAL MAGNETOHYDRODYNAMICS MODEL OF THE SOLAR WIND

The heating and acceleration of the solar wind is an active area of research. Alfv´ en waves, because of their ability to accelerate and heat the plasma, are a likely candidate in both processes. Many models have explored wave dissipation mechanisms which act either in closed or open magnetic field regions. In this work, we emphasize the boundary between these regions, drawing on observations which indicate unique heating is present there. We utilize a new solar corona component of the Space Weather Modeling Framework, in which Alfvwave energy transport is self-consistently coupled to the magnetohydrodynamic equations. In this solar wind model, the wave pressure gradient accelerates and wave dissipation heats the plasma. Kolmogorov-like wave dissipation as expressed by Hollweg along open magnetic field lines was presented in van der Holst et al. Here, we introduce an additional dissipation mechanism: surface Alfv´ en wave (SAW) damping, which occurs in regions with transverse (with respect to the magnetic field) gradients in the local Alfvspeed. For solar minimum conditions, we find that SAW dissipation is weak in the polar regions (where Hollweg dissipation is strong), and strong in subpolar latitudes and the boundaries of open and closed magnetic fields (where Hollweg dissipation is weak). We show that SAW damping reproduces regions of enhanced temperature at the boundaries of open and closed magnetic fields seen in tomographic reconstructions in the low corona. Also, we argue that Ulysses data in the heliosphere show enhanced temperatures at the boundaries of fast and slow solar wind, which is reproduced by SAW dissipation. Therefore, the models temperature distribution shows best agreement with these observations when both dissipation mechanisms are considered. Lastly, we use observational constraints of shock formation in the low corona to assess the Alfv´ speed profile in the model. We find that, compared to a polytropic solar wind model, the wave-driven model with physical dissipation mechanisms presented in this work is more aligned with an empirical Alfv´ en speed profile. Therefore, a wave-driven model which includes the effects of SAW damping is a better background to simulate coronal-mass-ejection-driven shocks.

Toward Reconstruction of Coronal Mass Ejection Density from Only Three Points of View

Understanding the structure of coronal mass ejections (CMEs) is one of the primary challenges in solar astrophysics. White-light coronagraphs make images of line-of-sight projections of the CME electron density (Ne). The combination of the coronagraphs on the STEREO and SOHO spacecraft provides three simultaneous viewpoints that vary in angle with time, according to the spacecraft orbits. Three viewpoints are not enough to permit tomographic reconstruction via classical methods, but we argue here that recent advances in image processing methods that take into account prior information about the CME geometry may allow one to determine the CME density structure with only three viewpoints. The prior information considered here is that the CME is separated from a known (or simple) background by a closed surface, which may be described by a level set. We propose an alternating iterative procedure in which the surface is evolved via geometric partial differential equations in one step and the interior (and exterior) Ne values are determined in the next step.

A Steady-state Picture of Solar Wind Acceleration and Charge State Composition Derived from a Global Wave-driven MHD Model

The higher charge states found in slow (<400 km s−1) solar wind streams compared to fast streams have supported the hypothesis that the slow wind originates in closed coronal loops and is released intermittently through reconnection. Here we examine whether a highly ionized slow wind can also form along steady and open magnetic field lines. We model the steady-state solar atmosphere using the Alfven Wave Solar Model (AWSoM), a global MHD model driven by Alfven waves, and apply an ionization code to calculate the charge state evolution along modeled open field lines. This constitutes the first charge state calculation covering all latitudes in a realistic magnetic field. The ratios and are compared to in situ Ulysses observations and are found to be higher in the slow wind, as observed; however, they are underpredicted in both wind types. The modeled ion fractions of S, Si, and Fe are used to calculate line-of-sight intensities, which are compared to Extreme-ultraviolet Imaging Spectrometer (EIS) observations above a coronal hole. The agreement is partial and suggests that all ionization rates are underpredicted. Assuming the presence of suprathermal electrons improved the agreement with both EIS and Ulysses observations; importantly, the trend of higher ionization in the slow wind was maintained. The results suggest that there can be a sub-class of slow wind that is steady and highly ionized. Further analysis shows that it originates from coronal hole boundaries (CHBs), where the modeled electron density and temperature are higher than inside the hole, leading to faster ionization. This property of CHBs is global and observationally supported by EUV tomography.

Tomographic Imaging of Dynamic Objects With the Ensemble Kalman Filter

We address the image formation of a dynamic object from projections by formulating it as a state estimation problem. The problem is solved with the ensemble Kalman filter (EnKF), a Monte Carlo algorithm that is computationally tractable when the state dimension is large. In this paper, we first rigorously address the convergence of the EnKF. Then, the effectiveness of the EnKF is demonstrated in a numerical experiment where a highly variable object is reconstructed from its projections, an imaging modality not yet explored with the EnKF. The results show that the EnKF can yield estimates of almost equal quality as the optimal Kalman filter but at a fraction of the computational effort. Further experiments explore the rate of convergence of the EnKF, its performance relative to an idealized particle filter, and implications of modeling the system dynamics as a random walk.

THREE-DIMENSIONAL TOMOGRAPHIC ANALYSIS OF A HIGH-CADENCE LASCO-C2 POLARIZED BRIGHTNESS SEQUENCE

We present the first 3D tomographic reconstructions of the coronal electron density from an extended, high-cadence sequence of images of the coronas polarized brightness (pB). While the standard LASCO synoptic sequence is only 1 pB image per day, during the 14 day period covering 2006 June 9-22, the C2 coronagraph took about 6.5 pB images per day. We show that the high cadence dramatically improves the quality of the tomographic reconstructions when compared to a reconstruction that only uses one image per day. In particular, the reconstruction that uses only one image per day misses important features and has lower spatial resolution. We find that the spatial resolution of the tomographic inversion is ultimately limited by smearing due to coronal dynamics that take place during the 14 days required for data acquisition. We show that when only C2 images are available, about 4 pB images per day are enough for nearly optimal tomographic reconstruction, but more will be required when STEREO observations are included in the tomographic analysis.

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.