The Sun as an X-ray Star: Spectral Models of Solar Coronal Regions and Their Application to Stellar Coronae

Abstract

Understanding stellar coronae requires connecting the integrated X-ray emis- sion I observe from unresolved stars to the physical magnetic structures pro- ducing that emission. The Sun uniquely enables this connection: I can ob- serve both its spatially resolved coronal structures and its integrated X-ray spec- trum as it would appear from a stellar distance. This dissertation develops a new implementation of the "Sun as an X-ray Star" (SaXS) methodology that di- rectly retrieves the surface coverage (filling factors) of different coronal region types—background corona, active regions, cores, and flares—from X-ray spec- tral fitting. I construct spectral models for XSPEC from emission measure distributions derived from Yohkoh observations of solar coronal regions. Each region type becomes a multi-temperature model with fixed temperature structure and free normalization corresponding to its projected surface area. This direct fitting ap- proach eliminates the computational overhead of synthetic spectral grids while providing transparent physical interpretation: fitted normalizations immedi- ately yield filling factors without intermediate parameter-space matching. I validate the method on the Sun itself using full-disk soft X-ray spectra from the DAXSS (Dual Aperture X-ray Solar Spectrometer) CubeSat instrument at two activity levels. Comparing spectral-fit-derived filling factors with the actual spatial distribution visible in contemporaneous Hinode/XRT images demon- strates that the method successfully recovers known coronal structure. The qui- escent Sun shows ∼21% active region coverage (with refined fits using variable abundances), while flaring periods show ∼15% active region coverage, ∼3% core coverage, and ∼0.07% flare coverage (with refined fits using variable abundances and non-equilibrium ionization for flares). Spectral filling factors systematically exceed image-based measurements because spectra naturally in- clude limb emission extending to coronal scale heights, providing a more com- plete picture of total coronal output as seen from stellar distances. Application to AD Leo, a nearby active M3.5V dwarf, reveals both capa- bilities and limitations of solar-derived templates. During quiescent periods, the corona appears dominated by hot cores with significant background but minimal active region contribution, suggesting either fundamentally different magnetic structures or templates that incompletely capture stellar active re- gions. The star exhibits continuous low-level flaring even in nominally qui- escent phases. The spectacular November 2021 "November 2021 Great Flare" (GOES X1445 equivalent) produces systematic high-energy residuals: even our hottest solar flare template (X9.0, ∼30 MK) cannot reproduce emission above 2–3 keV. Adding thermal components reaching several tens of MK eliminates residuals, demonstrating that AD Leo’s superflares produce plasma significantly hotter than any solar analog. This analysis reveals a fundamental degeneracy in X-ray spectral analysis: for fixed emission measure, electron density and filling factor trade off (EM ∝ n2 e f ). Initial density estimates from literature extrapolation yielded unphysi- cally small filling factors, requiring iterative density refinement constrained by the requirement that regions occupy at least one coronal loop’s projected area. Breaking this degeneracy definitively requires independent density measure- ments from high-resolution spectroscopy, underscoring the importance of com- plementary observations for future applications. The dissertation establishes that solar-derived spectral models can charac- terize stellar coronae in terms of physical magnetic structures, validates the filling factor retrieval methodology through direct comparison with spatially resolved solar observations, and identifies critical limitations—particularly the need for expanded emission measure libraries extending to super-solar temper- atures and independent density constraints—that must be addressed for robust application to active stellar populations.