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Wiegelmann T.,Max Planck Institute for Solar System Research | Petrie G.J.D.,U.S. National Solar Observatory | Riley P.,Predictive Science
Space Science Reviews | Year: 2015

Coronal magnetic field models use photospheric field measurements as boundary condition to model the solar corona. We review in this paper the most common model assumptions, starting from MHD-models, magnetohydrostatics, force-free and finally potential field models. Each model in this list is somewhat less complex than the previous one and makes more restrictive assumptions by neglecting physical effects. The magnetohydrostatic approach neglects time-dependent phenomena and plasma flows, the force-free approach neglects additionally the gradient of the plasma pressure and the gravity force. This leads to the assumption of a vanishing Lorentz force and electric currents are parallel (or anti-parallel) to the magnetic field lines. Finally, the potential field approach neglects also these currents. We outline the main assumptions, benefits and limitations of these models both from a theoretical (how realistic are the models?) and a practical viewpoint (which computer resources to we need?). Finally we address the important problem of noisy and inconsistent photospheric boundary conditions and the possibility of using chromospheric and coronal observations to improve the models. © 2015 The Author(s) Source

Patoul J.D.,University of Exeter | Patoul J.D.,Aix - Marseille University | Foullon C.,University of Exeter | Riley P.,Predictive Science
Astrophysical Journal | Year: 2015

Knowledge of the electron density distribution in the solar corona put constraints on the magnetic field configurations for coronal modeling and on initial conditions for solar wind modeling. We work with polarized SOHO/LASCO-C2 images from the last two recent minima of solar activity (1996-1997 and 2008-2010), devoid of coronal mass ejections. The goals are to derive the 4D electron density distributions in the corona by applying a newly developed time-dependent tomographic reconstruction method and to compare the results between the two solar minima and with two magnetohydrodynamic models. First, we confirm that the values of the density distribution in thermodynamic models are more realistic than in polytropic ones. The tomography provides more accurate distributions in the polar regions, and we find that the density in tomographic and thermodynamic solutions varies with the solar cycle in both polar and equatorial regions. Second, we find that the highest-density structures do not always correspond to the predicted large-scale heliospheric current sheet or its helmet streamer but can follow the locations of pseudo-streamers. We deduce that tomography offers reliable density distributions in the corona, reproducing the slow time evolution of coronal structures, without prior knowledge of the coronal magnetic field over a full rotation. Finally, we suggest that the highest-density structures show a differential rotation well above the surface depending on how they are magnetically connected to the surface. Such valuable information on the rotation of large-scale structures could help to connect the sources of the solar wind to their in situ counterparts in future missions such as Solar Orbiter and Solar Probe Plus. © 2015. The American Astronomical Society. All rights reserved.. Source

Riley P.,Predictive Science
AIP Conference Proceedings | Year: 2010

In this review we summarize our current knowledge regarding the three-dimensional structure of the quasi-steady, large-scale inner heliosphere. This understanding is based on the interpretation of a wide array of remote and in situ measurements, in conjunction with sophisticated numerical models. Observations by the Ulysses spacecraft, in particular, have provided an unprecedented set of measurements for more than 18 years, and observations by the STEREO spacecraft promise no less. Global MHD models of the solar corona and heliosphere have matured to the point that a wide range of measurements can now be reproduced with reasonable fidelity. In the absence of transient effects, this structure is dominated by corotating interaction regions which can be understood - to a large extent - from the consequence of solar rotation on a spatially-variable velocity profile near the Sun, leading to parcels of plasma with different plasma and magnetic properties becoming radially aligned. This interaction is one of the principal dynamic processes that shape the structure of the interplanetary medium. To illustrate some of these phenomena, we discuss the structural features of the current solar minimum, which has, thus far, displayed a number of distinct characteristics in relation to recent previous minima of the space age. © 2010 American Institute of Physics. Source

Riley P.,Predictive Science
Space Weather | Year: 2012

By virtue of their rarity, extreme space weather events, such as the Carrington event of 1859, are difficult to study, their rates of occurrence are difficult to estimate, and prediction of a specific future event is virtually impossible. Additionally, events may be extreme relative to one parameter but normal relative to others. In this study, we analyze several measures of the severity of space weather events (flare intensity, coronal mass ejection speeds, Dst, and >30 MeV proton fluences as inferred from nitrate records) to estimate the probability of occurrence of extreme events. By showing that the frequency of occurrence scales as an inverse power of the severity of the event, and assuming that this relationship holds at higher magnitudes, we are able to estimate the probability that an event larger than some criteria will occur within a certain interval of time in the future. For example, the probability of another Carrington event (based on Dst < -850 nT) occurring within the next decade is ∼12%. We also identify and address several limitations with this approach. In particular, we assume time stationarity, and thus, the effects of long-term space climate change are not considered. While this technique cannot be used to predict specific events, it may ultimately be useful for probabilistic forecasting. Copyright 2012 by the American Geophysical Union. Source

Riley P.,Predictive Science | Mikic Z.,Predictive Science | Lionello R.,Predictive Science | Linker J.A.,Predictive Science | And 3 more authors.
Journal of Geophysical Research: Space Physics | Year: 2010

The stark differences between the current solar minimum and the previous one offer a unique opportunity to develop new constraints on mechanisms for heating and acceleration of the solar wind. We have used a combination of numerical simulations and analysis of remote solar and in situ observations to infer that the coronal heating rate, H, scales with the average magnetic field strength within a coronal hole, Bch. This was accomplished in three steps. First, we analyzed Ulysses measurements made during its first and third orbit southern and northern polar passes (i.e., during near-solar minimum conditions) to deduce a linear relationship between proton number density (np) and radial magnetic field strength (Br) in the high-speed quiescent solar wind, consistent with the results of McComas et al. (2008) and Ebert et al. (2009). Second, we used Wilcox Solar Observatory measurements of the photospheric magnetic field to show that the magnetic field strength within coronal holes (Bch) is approximately correlated with the strength of the interplanetary field at the location of Ulysses. Third, we used hydrodynamic simulations to show that np in the solar wind scales linearly withH. Taken together, these results imply the chain:H ∞ np ∞ Br ∞ Bch. We also explored ideas that the correlation between np and Br could have resulted from interplanetary processes, or from the superradial expansion of the coronal magnetic field close to the Sun, but find that neither possibility can produce the observed relationship. The derived heating relationship is consistent with (1) empirical heating laws derived for closed-field line regions and (2) theoretical models aimed at understanding both the heating and acceleration of the solar wind. Copyright © 2010 by the American Geophysical Union. Source

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