The Open Flux Problem (1708.02342v2)

Abstract: The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun's photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes observed in emission, and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both MHD and PFSS solutions using fourteen different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding July, 2010. We have found that for all of the model/map combinations, models that have coronal hole areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than coronal holes observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected coronal holes for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun's magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission.

Analysis of the Open Flux Problem in Solar and Heliospheric Physics

This paper addresses the "open flux problem," examining discrepancies between modeled and observed heliospheric magnetic flux. The paper investigates the mismatch between predicted open magnetic flux, derived from solar models, and the open magnetic flux inferred from in situ space measurements. Using varying magnetic maps created from different observatory magnetograms and modeling techniques, the paper scrutinizes this problem with a focus on observations surrounding July 2010.

Magnetic flux maps are derived using magnetograms from observatories such as NSO VSM, NSO GONG, SOHO MDI, and SDO HMI. These maps serve as boundary conditions for coronal models employing techniques like Magnetohydrodynamic (MHD) and Potential Field Source Surface (PFSS) modeling. The paper assesses both diachronic and synchronic maps, recognizing that different constructions of these maps can lead to disparate predictions in the computed magnetic flux.

Key Observations

The research elucidates two core constraints: the predicted open field regions should correlate with coronally observed holes (CHs), and the open magnetic flux derived from the models should correspond to spacecraft in situ measurements. Specifically, it finds that models aligning with CHs often underestimate interplanetary magnetic flux unless open field regions extend beyond those observed.

Crucially, the paper suggests two potential explanations for the discrepancies in open magnetic flux:

1. Undetected Magnetic Flux in Maps: It posits the possibility that typical observatory maps underrepresent the solar magnetic flux. Issues in adequate polar region coverage and measurement techniques can contribute to this underestimation.
2. Atypical Origin of Open Fields: The data imply that significant open flux may arise from regions not identified as dark in EUV and X-ray emissions, challenging the conventional understanding of coronal structure.

Results and Implications

The paper provides empirical evaluations of several map/model combinations, concluding that all either underestimate flux or predict significantly larger open regions than observed in coronal images. This confirms a systemic issue across modeling techniques. The analysis of CHs via automated detection further substantiates the presence of unresolved open flux.

Experimentation with open field areas in models shows that reducing the source surface in PFSS models results in predicted flux values closer to those observed, albeit with incongruous open field regions in comparison to CHs. The theoretical implication is a need for improved model parameterization or enhanced observational data incorporation, especially from polar regions, which remain challenging with current observational technology.

Future Directions

Immediate future work should explore augmented data assimilation within models, using higher-resolution and more frequent measurements from new instruments like those facilitated by missions such as Parker Solar Probe and Solar Orbiter, which promise unprecedented solar and heliospheric observations. Additionally, a deeper inquiry into time-dependent dynamics and field line tracing could help elucidate transient phenomena contributing to the open flux budget, possibly involving interchange reconnection scenarios.

The paper provides a thorough assessment and foundational knowledge for ongoing research in heliophysics. The findings implicate not only refinements in observational techniques but also call for advances in dynamic solar modeling, catalyzing the potential for improved predictive capabilities in space weather forecasting.