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The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Suns 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 Suns 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.
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Over the solar-activity cycle, there are extended periods where significant discrepancies occur between the spacecraft-observed total (unsigned) open magnetic flux and that determined from coronal models. In this article, the total open heliospheric magnetic flux is computed using two different methods and then compared with results obtained from in-situ interplanetary magnetic-field observations. The first method uses two different types of photospheric magnetic-field maps as input to the Wang Sheeley Arge (WSA) model: i) traditional Carrington or diachronic maps, and ii) Air Force Data Assimilative Photospheric Flux Transport model synchronic maps. The second method uses observationally derived helium and extreme-ultraviolet coronal-hole maps overlaid on the same magnetic-field maps in order to compute total open magnetic flux. The diachronic and synchronic maps are both constructed using magnetograms from the same source, namely the National Solar Observatory Kitt Peak Vacuum Telescope and Vector Spectromagnetograph. The results of this work show that the total open flux obtained from observationally derived coronal holes agrees remarkably well with that derived from WSA, especially near solar minimum. This suggests that, on average, coronal models capture well the observed large-scale coronal-hole structure over most of the solar cycle. Both methods show considerable deviations from total open flux deduced from spacecraft data, especially near solar maximum, pointing to something other than poorly determined coronal-hole area specification as the source of these discrepancies.
Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 9/19/2010, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH was about 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in-situ measurements (by 2.2-4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it.
Solar activity in all its varied manifestations is driven by the magnetic field. Particularly important for many purposes are two global quantities, the Suns total and open magnetic flux, which can be computed from sunspot number records using models. Such sunspot-driven models, however, do not take into account the presence of magnetic flux during grand minima, such as the Maunder minimum. Here we present a major update of a widely used simple model, which now takes into account the observation that the distribution of all magnetic features on the Sun follows a single power law. The exponent of the power law changes over the solar cycle. This allows for the emergence of small-scale magnetic flux even when no sunspots are present for multiple decades and leads to non-zero total and open magnetic flux also in the deepest grand minima, such as the Maunder minimum, thus overcoming a major shortcoming of the earlier models. The results of the updated model compare well with the available observations and reconstructions of the solar total and open magnetic flux. This opens up the possibility of improved reconstructions of sunspot number from time series of cosmogenic isotope production rate.
The strength of the radial component of the interplanetary magnetic field (IMF), which is a measure of the Suns total open flux, is observed to vary by roughly a factor of two over the 11 yr solar cycle. Several recent studies have proposed that the Suns open flux consists of a constant or floor component that dominates at sunspot minimum, and a time-varying component due to coronal mass ejections (CMEs). Here, we point out that CMEs cannot account for the large peaks in the IMF strength which occurred in 2003 and late 2014, and which coincided with peaks in the Suns equatorial dipole moment. We also show that near-Earth interplanetary CMEs, as identified in the catalog of Richardson and Cane, contribute at most $sim$30% of the average radial IMF strength even during sunspot maximum. We conclude that the long-term variation of the radial IMF strength is determined mainly by the Suns total dipole moment, with the quadrupole moment and CMEs providing an additional boost near sunspot maximum. Most of the open flux is rooted in coronal holes, whose solar cycle evolution in turn reflects that of the Suns lowest-order multipoles.
(Abridged) Aim: We attempt to determine robust estimates of the heliospheric magnetic flux ($Phi_H$) using Parker Solar Probe (PSP) data, analyze how susceptible this is to overestimation compared to the true open flux ($Phi_{open}$), assess its dependence on time and space, and compare it to simple estimates from Potential Field Source Surface (PFSS) models. Methods: We compare different methods of computation using data from PSP, STEREO A and Wind. The effects of fluctuations and large scale structure on the estimate are probed by using measured radial trends to produce synthetic data. Best estimates are computed as a function of time and space, and compared to estimates from PFSS models. Results: Radially-varying fluctuations of the HMF vector and variation of the Parker spiral angle cause the standard metrics of the mean and mode to evolve with radius independent of the central value about which the vector fluctuates. This is best mitigated by projecting the vector into the background Parker spiral direction. Nevertheless, we find a small enhancement in flux close to 1AU. The fraction of locally inverted field lines grows with radial distance from the Sun which remains a possible physical reason for this excess, but is negligible at PSP`s perihelia. Similarly, the impact of fluctuations in general is much reduced at PSP`s perihelia. The overall best estimate is ~2.5 nT AU2 . No strong dependence on latitude or longitude is apparent. The PFSS models predict lower values from 1.2 to 1.8 nT AU2. Conclusions: The heliospheric flux is robustly estimated relative to a mean Parker spiral direction at PSP`s perihelia where the decay of fluctuations and weakening importance of local flux
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