Untangling the Coronal Magnetic Field

Society is increasingly dependent on technologies that are vulnerable to the variable output of radiation, energetic particles and magnetized plasma from the Sun. These outputs can drive radical disturbances in the Earth’s environment known as “space weather”. Space weather has become a national priority, driving a requirement for advanced observation-based modeling throughout the Sun-Earth system.

FORWARD-generatedSyntheticData image
Figure 1: FORWARD-generated synthetic data including a) visible and b) extreme ultraviolet intensity, and c) infrared and d) radio circular polarization, generated for simulated prominence-cavity system based on a model of a confined magnetic flux rope (from Gibson et al., 2016).
FORWARD-modeled Flux Rope Vs Ground-truth Synthetic Data image
Figure 2: Establishing efficient methods for a full grid search of parameter space represents a challenge to data science. Shown here are maps of goodness of fit, or likelihood (log) in parameter space (tilt angle vs. latitude), determined from comparison of forward-modeled flux rope vs “ground-truth” synthetic data. Top plot shows full map evaluated at regular grid. Bottom plot is approximation using radial basis functions to form an interpolated log-likelihood surface, reducing the need for model evaluations by a factor of 100. Ground truth is represented by white +. From Dalmasse et al. (2016).

The Data-Optimized Coronal Field Model (DOCFM) project is a collaboration between NCAR (HAO and CISL) and the Harvard/Smithsonian Center for Astrophysics (CfA), with funding from the Air Force Office of Scientific Research (AFOSR). Its goal is to develop a new methodology for assimilating solar coronal observations into boundary-driven magnetic models in order to establish not only the magnetic structure of the source region of solar eruptions, but also the global field into which they erupt. Such comprehensively data-constrained models of pre-eruption solar magnetic configurations can then be used as initial conditions for ensemble modeling of space weather events.

In essence, the goal of DOCFM is to solve an inverse problem. Given magnetically-sensitive coronal observations, the challenge is to determine the magnetic field distribution that generates them. Solving such an inverse problem requires three things: a means of specifying the physical state (e.g., the distribution of density, temperature, velocity, and magnetic field), a well-defined forward calculation (i.e., the physical process relating the physical state and the observations), and the observations themselves. We have brought all three of these requirements together via the FORWARD software package, a community resource that may be used both to synthesize a broad range of coronal observables, and to compare synthetic observables to existing data. It enables forward fitting of specific observations, and helps to build intuition into how the physical properties of coronal magnetic structures translate to observable properties. We have also used FORWARD to generate synthetic test beds from MHD simulations (Fig. 1) in order to develop efficient optimization methods (e.g., Fig. 2).

Physical Processes Solar Corona Table image
Table 1. Physical processes operating in the solar corona, highlighting dependency on attributes of the physical state, which observations are sensitive to them, and diagnostic sensitivity to the 3D coronal magnetic field. From Gibson et al. (2016).

As described in Table 1, many currently-available coronal observations have sensitivities to coronal magnetic field, including white light coronagraph data obtained by NCAR’s COSMO K-Coronagraph (K-Cor) and extreme ultraviolet data obtained by NASA’s Solar Dynamics Observatory Atmospheric Imaging Assembly (SDO/AIA). However, these measurements only indirectly depend upon magnetism. Observations in the infrared (IR) from NCAR’s Coronal Multichannel Polarimeter (CoMP; Tomczyk et al (2008)) have allowed us for the first time to obtain daily observations that directly measure the effects of magnetism on the solar atmosphere through spectropolarimetry. These observations together measure of plane-of-sky magnetic field strength and direction (see Table 1) and have proven to be good diagnostics of coronal magnetic topology (Tomczyk et al 2007; Dove et al. 2009; Bak-Steslicka et al. 2013; Rachmeler et al. 2014). The U-CoMP telescope currently under development will increase the range of wavelengths available for spectroscopic and spectropolarimetric analysis, and also increase the field of view. The proposed much larger COSMO Large Coronagraph telescope (COSMO-LC) would also obtain circular polarization (Stokes V; Fig. 1) providing a measurement directly proportional to the line-of-sight component of the magnetic field strength so that all three components of the vector magnetic field are constrained. The overarching goal of DOCFM is to exploit these complementary sets of observations in inverting the coronal magnetic field.