Accuracy of magnetic energy computations

For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional models of the solar atmosphere, eg in coronal fields reconstructions or numerical simulations. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources

First observational application of a connectivity--based helicity flux density

Measuring the magnetic helicity distribution in the solar corona can help in understanding the trigger of solar eruptive events because magnetic helicity is believed to play a key role in solar activity due to its conservation property. A new method for computing the photospheric distribution of the helicity flux was recently developed. This method takes into account the magnetic field connectivity whereas previous methods were based on photospheric signatures only. This novel method maps the true injection of magnetic helicity in active regions. We applied this method for the first time to an observed active region, NOAA 11158, which was the source of intense flaring activity. We used high-resolution vector magnetograms from the SDO/HMI instrument to compute the photospheric flux transport velocities and to perform a nonlinear force-free magnetic field extrapolation. We determined and compared the magnetic helicity flux distribution using a purely photospheric as well as a connectivity-based method. While the new connectivity-based method confirms the mixed pattern of the helicity flux in NOAA 11158, it also reveals a different, and more correct, distribution of the helicity injection. This distribution can be important for explaining the likelihood of an eruption from the active region. The connectivity-based approach is a robust method for computing the magnetic helicity flux, which can be used to study the link between magnetic helicity and eruptivity of observed active regions.Comment: 4 pages, 3 figures; published online in A&A 555, L6 (2013

Flux rope, hyperbolic flux tube, and late EUV phases in a non-eruptive circular-ribbon flare

We present a detailed study of a confined circular flare dynamics associated with 3 UV late phases in order to understand more precisely which topological elements are present and how they constrain the dynamics of the flare. We perform a non-linear force free field extrapolation of the confined flare observed with the HMI and AIA instruments onboard SDO. From the 3D magnetic field we compute the squashing factor and we analyse its distribution. Conjointly, we analyse the AIA EUV light curves and images in order to identify the post-flare loops, their temporal and thermal evolution. By combining both analysis we are able to propose a detailed scenario that explains the dynamics of the flare. Our topological analysis shows that in addition to a null-point topology with the fan separatrix, the spine lines and its surrounding Quasi-Separatix Layers halo (typical for a circular flare), a flux rope and its hyperbolic flux tube (HFT) are enclosed below the null. By comparing the magnetic field topology and the EUV post-flare loops we obtain an almost perfect match 1) between the footpoints of the separatrices and the EUV 1600~\AA{} ribbons and 2) between the HFT's field line footpoints and bright spots observed inside the circular ribbons. We showed, for the first time in a confined flare, that magnetic reconnection occured initially at the HFT, below the flux rope. Reconnection at the null point between the flux rope and the overlying field is only initiated in a second phase. In addition, we showed that the EUV late phase observed after the main flare episode are caused by the cooling loops of different length which have all reconnected at the null point during the impulsive phase.Comment: Astronomy & Astrophysics, in pres

On-disc observations of flux rope formation prior to its eruption

Coronal mass ejections (CMEs) are one of the primary manifestations of solar activity and can drive severe space weather effects. Therefore, it is vital to work towards being able to predict their occurrence. However, many aspects of CME formation and eruption remain unclear, including whether magnetic flux ropes are present before the onset of eruption and the key mechanisms that cause CMEs to occur. In this work, the pre-eruptive coronal configuration of an active region that produced an interplanetary CME with a clear magnetic flux rope structure at 1 AU is studied. A forward-S sigmoid appears in extreme-ultraviolet (EUV) data two hours before the onset of the eruption (SOL2012-06-14), which is interpreted as a signature of a right-handed flux rope that formed prior to the eruption. Flare ribbons and EUV dimmings are used to infer the locations of the flux rope footpoints. These locations, together with observations of the global magnetic flux distribution, indicate that an interaction between newly emerged magnetic flux and pre-existing sunspot field in the days prior to the eruption may have enabled the coronal flux rope to form via tether-cutting-like reconnection. Composition analysis suggests that the flux rope had a coronal plasma composition, supporting our interpretation that the flux rope formed via magnetic reconnection in the corona. Once formed, the flux rope remained stable for two hours before erupting as a CME

Sensorimotor Research Utilising Immersive Virtual Reality: A Pilot Study with Children and Adults with Autism Spectrum Disorders

When learning and interacting with the world, people with Autism Spectrum Disorders (ASD) show compromised use of vision and enhanced reliance on body-based information. As this atypical profile is associated with motor and social difficulties, interventions could aim to reduce the potentially isolating reliance on the body and foster the use of visual information. To this end, head-mounted displays (HMDs) have unique features that enable the design of Immersive Virtual Realities (IVR) for manipulating and training sensorimotor processing. The present study assesses feasibility and offers some early insights from a new paradigm for exploring how children and adults with ASD interact with Reality and IVR when vision and proprioception are manipulated. Seven participants (five adults, two children) performed a self-turn task in two environments (Reality and IVR) for each of three sensory conditions (Only Proprioception, Only Vision, Vision + Proprioception) in a purpose-designed testing room and an HMD-simulated environment. The pilot indicates good feasibility of the paradigm. Preliminary data visualisation suggests the importance of considering inter-individual variability. The participants in this study who performed worse with Only Vision and better with Only Proprioception seemed to benefit from the use of IVR. Those who performed better with Only Vision and worse with Only Proprioception seemed to benefit from Reality. Therefore, we invite researchers and clinicians to consider that IVR may facilitate or impair individuals depending on their profiles

Magnetic Helicity Estimations in Models and Observations of the Solar Magnetic Field. Part III: Twist Number Method

We study the writhe, twist and magnetic helicity of different magnetic flux ropes, based on models of the solar coronal magnetic field structure. These include an analytical force-free Titov--D\'emoulin equilibrium solution, non force-free magnetohydrodynamic simulations, and nonlinear force-free magnetic field models. The geometrical boundary of the magnetic flux rope is determined by the quasi-separatrix layer and the bottom surface, and the axis curve of the flux rope is determined by its overall orientation. The twist is computed by the Berger--Prior formula that is suitable for arbitrary geometry and both force-free and non-force-free models. The magnetic helicity is estimated by the twist multiplied by the square of the axial magnetic flux. We compare the obtained values with those derived by a finite volume helicity estimation method. We find that the magnetic helicity obtained with the twist method agrees with the helicity carried by the purely current-carrying part of the field within uncertainties for most test cases. It is also found that the current-carrying part of the model field is relatively significant at the very location of the magnetic flux rope. This qualitatively explains the agreement between the magnetic helicity computed by the twist method and the helicity contributed purely by the current-carrying magnetic field.Comment: To be published in Ap

Additivity of relative magnetic helicity in finite volumes

CONTEXT: Relative magnetic helicity is conserved by magneto-hydrodynamic evolution even in the presence of moderate resistivity. For that reason, it is often invoked as the most relevant constraint on the dynamical evolution of plasmas in complex systems, such as solar and stellar dynamos, photospheric flux emergence, solar eruptions, and relaxation processes in laboratory plasmas. However, such studies often indirectly imply that relative magnetic helicity in a given spatial domain can be algebraically split into the helicity contributions of the composing subvolumes, in other words that it is an additive quantity. A limited number of very specific applications have shown that this is not the case. AIMS: Progress in understanding the nonadditivity of relative magnetic helicity requires removal of restrictive assumptions in favor of a general formalism that can be used in both theoretical investigations and numerical applications. METHODS: We derive the analytical gauge-invariant expression for the partition of relative magnetic helicity between contiguous finite volumes, without any assumptions on either the shape of the volumes and interface, or the employed gauge. RESULTS: We prove the nonadditivity of relative magnetic helicity in finite volumes in the most general, gauge-invariant formalism, and verify this numerically. We adopt more restrictive assumptions to derive known specific approximations, which yields a unified view of the additivity issue. As an example, the case of a flux rope embedded in a potential field shows that the nonadditivity term in the partition equation is, in general, non-negligible. CONCLUSIONS: The nonadditivity of relative magnetic helicity can potentially be a serious impediment to the application of relative helicity conservation as a constraint on the complex dynamics of magnetized plasmas. The relative helicity partition formula can be applied to numerical simulations to precisely quantify the effect of nonadditivity on global helicity budgets of complex physical processes

Evaluation of the natural risk perception, awareness, and preparedness at school by means of ad hoc questionnaires

One of the Sendai Framework 2015-2030 targets is to reduce the disruption of basic services, like educational facilities. Disaster education is actually considered to be an important factor to promote disaster risk reduction. The school resilience is not related to a specific hazard and vulnerability, but it takes into account many factors, including the people’s natural risk perception and awareness, along with their knowledge and capability of how to behave in an emergency. The scientific literature provides various notions of risk, risk perception, risk awareness, and risk preparedness. The literature on children’s natural risk perception is scarce and very recent compared with that about adults. Indeed, children’s perceptions about nature and environment are truly different from those of adults. The available research mainly concerns the implementation of earthquake emergency measures, while not much is available on flood-risk perception and even less on landslides. The relationship between risk perception, awareness, and preparedness is widely studied, but once again, there is no unambiguous or unique result that depends on the approach and the context. We decided to refine the questionnaire that contributes to assess the school-resilience employed in the Geo-hazard Safety Classification method (GSC). We designed 7 different questionnaires, one for the adult personnel and six for the students, taking into account the peculiarity of each age. These questionnaires were thought through and designed to investigate three main awareness fundamentals: i) knowledge of the correct behaviours and procedure during a natural emergency that occurs at school; ii) perception of the natural risk of the area where the school is located; and iii) general knowledge of the correct behaviours during a natural emergency at school. Three different analyses were carried out on the 5899 filled in questionnaires (820 by personnel and 5079 by students of each school stage) distributed in 27 schools of Tuscany Region (Central Italy): a) school by school; b) questionnaire typology (i.e., different school age); and c) topics (awareness fundamentals i, ii, and iii) and questionnaire typology (i.e., different school age). The results are coherent and show that a) young children’s knowledge is perfectly adequate to their age, b) as the age and responsibilities increase, the awareness and preparation do not increase proportionally, and c) the competences of the school personnel are not sufficient, probably caused by critical issues emerged (i.e., it is not clear where family reunification must take place) and because the wrong hazard perception leads to underestimating the importance of prevention actions and disaster education and. This last outcome turns out to be unexpected. These questionnaires are a suitable, quick, easy and low-cost tool, even if considered separately from the GSC method. The school head-masters or the local and national educational offices actually could use them a) to evaluate the geo-hydrological and seismic risk knowledge and awareness of students, professors and school personnel; b) to project and design actions needed to improve the school-resilience; c) to verify the goodness of the activities developed at point b); and d) as an educational tool to improve the disaster education

Disambiguation of Vector Magnetograms by Stereoscopic Observations from the Solar Orbiter/Polarimetric and Helioseismic Imager (PHI) and the Solar Dynamic Observatory (SDO)/Helioseismic and Magnetic Imager (HMI)

Spectropolarimetric reconstructions of the photospheric vector magnetic field are intrinsically limited by the 180∘ ambiguity in the orientation of the transverse component. The successful launch and operation of Solar Orbiter have made the removal of the 180∘ ambiguity possible using solely observations obtained from two different vantage points. While the exploitation of such a possibility is straightforward in principle, it is less so in practice, and it is therefore important to assess the accuracy and limitations as a function of both the spacecrafts’ orbits and measurement principles. In this work, we present a stereoscopic disambiguation method (SDM) and discuss thorough testing of its accuracy in applications to modeled active regions and quiet-Sun observations. In the first series of tests, we employ magnetograms extracted from three different numerical simulations as test fields and model observations of the magnetograms from different angles and distances. In these more idealized tests, SDM is proven to reach a 100% disambiguation accuracy when applied to moderately-to-well resolved fields. In such favorable conditions, the accuracy is almost independent of the relative position of the spacecraft with the obvious exceptions of configurations where the spacecraft are within a few degrees of co-alignment or quadrature. Even in the case of disambiguation of quiet-Sun magnetograms with significant under-resolved spatial scales, SDM provides an accuracy between 82% and 98%, depending on the field strength. The accuracy of SDM is found to be mostly sensitive to the variable spatial resolution of Solar Orbiter in its highly elliptic orbit, as well as to the intrinsic spatial scale of the observed field. Additionally, we provide an example of the expected accuracy as a function of time that can be used to optimally place remote-sensing observing windows during Solar Orbiter observation planning. Finally, as a more realistic test, we consider magnetograms that are obtained using a radiative-transfer inversion code and the SO/PHI Software siMulator (SOPHISM) applied to a 3D-simulation of a pore, and we present a preliminary discussion of the effect of the viewing angle on the observed field. In this more realistic test of the application of SDM, the method is able to successfully remove the ambiguity in strong-field areas

Magnetic Helicity Evolution and Eruptive Activity in NOAA Active Region 11158

Coronal mass ejections are among the Sun’s most energetic activity events yet the physical mechanisms that lead to their occurrence are not yet fully understood. They can drive major space weather impacts at Earth, so knowing why and when these ejections will occur is required for accurate space weather forecasts. In this study we use a 4 day time series of a quantity known as the helicity ratio, ∣H J ∣/∣H V ∣ (helicity of the current-carrying part of the active region field to the total relative magnetic helicity within the volume), which has been computed from nonlinear force-free field extrapolations of NOAA active region 11158. We compare the evolution of ∣H J ∣/∣H V ∣ with the activity produced in the corona of the active region and show this ratio can be used to indicate when the active region is prone to eruption. This occurs when ∣H J ∣/∣H V ∣ exceeds a value of 0.1, as suggested by previous studies. We find the helicity ratio variations to be more pronounced during times of strong flux emergence, collision and reconnection between fields of different bipoles, shearing motions, and reconfiguration of the corona through failed and successful eruptions. When flux emergence, collision, and shearing motions have lessened, the changes in helicity ratio are somewhat subtle despite the occurrence of significant eruptive activity during this time