From coronal observations to MHD simulations, the building blocks for 3D models of solar flares

Solar flares are energetic events taking place in the Suns atmosphere, and their effects can greatly impact the environment of the surrounding planets. In particular, eruptive flares, as opposed to confined flares, launch coronal mass ejections into the interplanetary medium, and as such, are one of the main drivers of space weather. After briefly reviewing the main characteristics of solar flares, we summarize the processes that can account for the build up and release of energy during their evolution. In particular, we focus on the development of recent 3D numerical simulations that explain many of the observed flare features. These simulations can also provide predictions of the dynamical evolution of coronal and photospheric magnetic field. Here we present a few observational examples that, together with numerical modelling, point to the underlying physical mechanisms of the eruptions.

Evidence of Twisted flux-tube Emergence in Active Regions

Elongated magnetic polarities are observed during the emergence phase of bipolar active regions (ARs). These extended features, called magnetic tongues, are interpreted as a consequence of the azimuthal component of the magnetic flux in the toroidal flux-tubes that form ARs. We develop a new systematic and user-independent method to identify AR tongues. Our method is based on determining and analyzing the evolution of the AR main polarity inversion line (PIL). The effect of the tongues is quantified by measuring the acute angle [ tau] between the orientation of the PIL and the direction orthogonal to the AR main bipolar axis. We apply a simple model to simulate the emergence of a bipolar AR. This model lets us interpret the effect of magnetic tongues on parameters that characterize ARs ( e.g. the PIL inclination and the tilt angles, and their evolution). In this idealized kinematic emergence model, tau is a monotonically increasing function of the twist and has the same sign as the magnetic helicity. We systematically apply our procedure to a set of bipolar ARs that were observed emerging in line-of-sight magnetograms over eight years. For most of the cases studied, the tongues only have a small influence on the AR tilt angle since tongues have a much lower magnetic flux than the more concentrated main polarities. From the observed evolution of tau, corrected for the temporal evolution of the tilt angle and its final value when the AR is fully emerged, we estimate the average number of turns in the subphotospherically emerging flux-rope. These values for the 41 observed ARs are below unity, except for one. This indicates that subphotospheric flux-ropes typically have a low amount of twist, i.e. highly twisted flux-tubes are rare. Our results demonstrate that the evolution of the PIL is a robust indicator of the presence of tongues and constrains the amount of twist in emerging flux-tubes

Comparing generic models for interplanetary shocks and magnetic clouds axis configurations at 1 AU

Interplanetary Coronal Mass Ejections are the manifestation of solar transient eruptions, which can significantly modify the plasma and magnetic conditions in the heliosphere. They are often preceded by a shock, and a magnetic flux rope is detected in situ in a third to half of them. The main aim of this study is to obtain the best quantitative shape for the flux rope axis and for the shock surface from in situ data obtained during spacecraft crossings of these structures. We first compare the orientation of the flux ropes axes and shock normals obtained from independent data analyses of the same events, observed in situ at 1AU from the Sun. Then, we carry out an original statistical analysis of axes/shock normals by deriving the statistical distributions of their orientations. We fit the observed distributions using the distributions derived from several synthetic models describing these shapes. We show that the distributions of axis/shock orientations are very sensitive to their respective shape. One classical model, used to analyze interplanetary imager data, is incompatible with the in situ data. Two other models are introduced, for which the results for axis and shock normals lead to very similar shapes; the fact that the data for MCs and shocks are independent strengthen this result. The model which best fit all the data sets has an ellipsoidal shape with similar aspect ratio values for all the data sets. These derived shapes for the flux rope axis and shock surface have several potential applications. First, these shapes can be used to construct a consistent ICME model. Second, these generic shapes can be used to develop a quantitative model to analyze imager data, as well as constraining the output of numerical simulations of ICMEs. Finally, they will have implications for space weather forecasting, in particular for forecasting the time arrival of ICMEs at the Earth.

Are There Different Populations of Flux Ropes in the Solar Wind?

Flux ropes are twisted magnetic structures, which can be detected by in situ measurements in the solar wind. However, different properties of detected flux ropes suggest different types of flux-rope population. As such, are there different populations of flux ropes? The answer is positive, and is the result of the analysis of four lists of flux ropes, including magnetic clouds (MCs), observed at 1 AU. The in situ data for the four lists have been fitted with the same cylindrical force-free field model, which provides an estimation of the local flux-rope parameters such as its radius and orientation. Since the flux-rope distributions have a large dynamic range, we go beyond a simple histogram analysis by developing a partition technique that uniformly distributes the statistical fluctuations over the radius range. By doing so, we find that small flux ropes with radius R<0.1 AU have a steep power-law distribution in contrast to the larger flux ropes (identified as MCs), which have a Gaussian-like distribution. Next, from four CME catalogs, we estimate the expected flux-rope frequency per year at 1 AU. We find that the predicted numbers are similar to the frequencies of MCs observed in situ. However, we also find that small flux ropes are at least ten times too abundant to correspond to CMEs, even to narrow ones. Investigating the different possible scenarios for the origin of those small flux ropes, we conclude that these twisted structures can be formed by blowout jets in the low corona or in coronal streamers.

Expansion of magnetic clouds in the outer heliosphere

A large amount of magnetized plasma is frequently ejected from the Sun as coronal mass ejections (CMEs). Some of these ejections are detected in the solar wind as magnetic clouds (MCs) that have flux rope signatures. Magnetic clouds are structures that typically expand in the inner heliosphere. We derive the expansion properties of MCs in the outer heliosphere from one to five astronomical units to compare them with those in the inner heliosphere. We analyze MCs observed by the Ulysses spacecraft using insitu magnetic field and plasma measurements. The MC boundaries are defined in the MC frame after defining the MC axis with a minimum variance method applied only to the flux rope structure. As in the inner heliosphere, a large fraction of the velocity profile within MCs is close to a linear function of time. This is indicative of} a self-similar expansion and a MC size that locally follows a power-law of the solar distance with an exponent called zeta. We derive the value of zeta from the insitu velocity data. We analyze separately the non-perturbed MCs (cases showing a linear velocity profile almost for the full event), and perturbed MCs (cases showing a strongly distorted velocity profile). We find that non-perturbed MCs expand with a similar non-dimensional expansion rate (zeta=1.05+-0.34), i.e. slightly faster than at the solar distance and in the inner heliosphere (zeta=0.91+-0.23). The subset of perturbed MCs expands, as in the inner heliosphere, at a significantly lower rate and with a larger dispersion (zeta=0.28+-0.52) as expected from the temporal evolution found in numerical simulations. This local measure of the expansion also agrees with the distribution with distance of MC size,mean magnetic field, and plasma parameters. The MCs interacting with a strong field region, e.g. another MC, have the most variable expansion rate (ranging from compression to over-expansion).

Global and local expansion of magnetic clouds in the inner heliosphere

Observations of magnetic clouds (MCs) are consistent with the presence of flux ropes detected in the solar wind (SW) a few days after their expulsion from the Sun as coronal mass ejections (CMEs). Both the textit{in situ} observations of plasma velocity profiles and the increase of their size with solar distance show that MCs are typically expanding structures. The aim of this work is to derive the expansion properties of MCs in the inner heliosphere from 0.3 to 1 AU.We analyze MCs observed by the two Helios spacecraft using textit{in situ} magnetic field and velocity measurements. We split the sample in two subsets: those MCs with a velocity profile that is significantly perturbed from the expected linear profile and those that are not. From the slope of the textit{in situ} measured bulk velocity along the Sun-Earth direction, we compute an expansion speed with respect to the cloud center for each of the analyzed MCs. We analyze how the expansion speed depends on the MC size, the translation velocity, and the heliocentric distance, finding that all MCs in the subset of non-perturbed MCs expand with almost the same non-dimensional expansion rate ($zeta$). We find departures from this general rule for $zeta$ only for perturbed MCs, and we interpret the departures as the consequence of a local and strong SW perturbation by SW fast streams, affecting the MC even inside its interior, in addition to the direct interaction region between the SW and the MC. We also compute the dependence of the mean total SW pressure on the solar distance and we confirm that the decrease of the total SW pressure with distance is the main origin of the observed MC expansion rate. We found that $zeta$ was $0.91pm 0.23$ for non-perturbed MCs while $zeta$ was $0.48pm 0.79$ for perturbed MCs, the larger spread in the last ones being due to the influence of the environment conditions on the expansion.