277 research outputs found
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
Photospheric Injection of Magnetic Helicity: Connectivity--based Flux Density Method
Magnetic helicity quantifies how globally sheared and/or twisted is the
magnetic field in a volume. This quantity is believed to play a key role in
solar activity due to its conservation property. Helicity is continuously
injected into the corona during the evolution of active regions (ARs). To
better understand and quantify the role of magnetic helicity in solar activity,
the distribution of magnetic helicity flux in ARs needs to be studied. The
helicity distribution can be computed from the temporal evolution of
photospheric magnetograms of ARs such as the ones provided by SDO/HMI and
Hinode/SOT. Most recent analyses of photospheric helicity flux derive an
helicity flux density proxy based on the relative rotation rate of photospheric
magnetic footpoints. Although this proxy allows a good estimate of the
photospheric helicity flux, it is still not a true helicity flux density
because it does not take into account the connectivity of the magnetic field
lines. For the first time, we implement a helicity density which takes into
account such connectivity. In order to use it for future observational studies,
we test the method and its precision on several types of models involving
different patterns of helicity injection. We also test it on more complex
configurations - from magnetohydrodynamics (MHD) simulations - containing
quasi-separatrix layers. We demonstrate that this connectivity-based helicity
flux density proxy is the best to map the true distribution of photospheric
helicity injection.Comment: Solar Physics, June 2013 (this is the version of the author, a
definitive version is now available in the online journal
Testing predictors of eruptivity using parametric flux emergence simulations
Solar flares and coronal mass ejections (CMEs) are among the most energetic
events in the solar system, impacting the near-Earth environment. Flare
productivity is empirically known to be correlated with the size and complexity
of active regions. Several indicators, based on magnetic-field data from active
regions, have been tested for flare forecasting in recent years. None of these
indicators, or combinations thereof, have yet demonstrated an unambiguous
eruption or flare criterion. Furthermore, numerical simulations have been only
barely used to test the predictability of these parameters. In this context, we
used the 3D parametric MHD numerical simulations of the self-consistent
formation of the flux emergence of a twisted flux tube, inducing the formation
of stable and unstable magnetic flux ropes of Leake (2013, 2014). We use these
numerical simulations to investigate the eruptive signatures observable in
various magnetic scalar parameters and provide highlights on data analysis
processing. Time series of 2D photospheric-like magnetograms are used from
parametric simulations of stable and unstable flux emergence, to compute a list
of about 100 different indicators. This list includes parameters previously
used for operational forecasting, physical parameters used for the first time,
as well as new quantities specifically developed for this purpose. Our results
indicate that only parameters measuring the total non-potentiality of active
regions associated with magnetic inversion line properties, such as the
Falconer parameters , , and , as well as the
new current integral and length parameters, present a
significant ability to distinguish the eruptive cases of the model from the
non-eruptive cases, possibly indicating that they are promising flare and
eruption predictors.Comment: 46 pages, 16 figures, accepted for publication in Space Weather and
Space Climate on June, 8t
The Relation between Solar Eruption Topologies and Observed Flare Features I: Flare Ribbons
In this paper we present a topological magnetic field investigation of seven
two-ribbon flares in sigmoidal active regions observed with Hinode, STEREO, and
SDO. We first derive the 3D coronal magnetic field structure of all regions
using marginally unstable 3D coronal magnetic field models created with the
flux rope insertion method. The unstable models have been shown to be a good
model of the flaring magnetic field configurations. Regions are selected based
on their pre-flare configurations along with the appearance and observational
coverage of flare ribbons, and the model is constrained using pre-flare
features observed in extreme ultraviolet and X-ray passbands. We perform a
topology analysis of the models by computing the squashing factor, Q, in order
to determine the locations of prominent quasi-separatrix layers (QSLs). QSLs
from these maps are compared to flare ribbons at their full extents. We show
that in all cases the straight segments of the two J-shaped ribbons are matched
very well by the flux-rope-related QSLs, and the matches to the hooked segments
are less consistent but still good for most cases. In addition, we show that
these QSLs overlay ridges in the electric current density maps. This study is
the largest sample of regions with QSLs derived from 3D coronal magnetic field
models, and it shows that the magnetofrictional modeling technique that we
employ gives a very good representation of flaring regions, with the power to
predict flare ribbon locations in the event of a flare following the time of
the model
Electric current in flares ribbons: observations and 3D standard model
We present for the first time the evolution of the photospheric electric
currents during an eruptive X-class flare, accurately predicted by the standard
3D flare model. We analyze this evolution for the February 15, 2011 flare using
HMI/SDO magnetic observations and find that localized currents in \J-shaped
ribbons increase to double their pre-flare intensity. Our 3D flare model,
developed with the OHM code, suggests that these current ribbons, which develop
at the location of EUV brightenings seen with AIA imagery, are driven by the
collapse of the flare's coronal current layer. These findings of increased
currents restricted in localized ribbons are consistent with the overall free
energy decrease during a flare, and the shape of these ribbons also give an
indication on how much twisted the erupting flux rope is. Finally, this study
further enhances the close correspondence obtained between the theoretical
predictions of the standard 3D model and flare observations indicating that the
main key physical elements are incorporated in the model.Comment: 12 pages, 7 figure
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
The origin of net electric currents in solar active regions
There is a recurring question in solar physics about whether or not electric
currents are neutralized in active regions (ARs). This question was recently
revisited using three-dimensional (3D) magnetohydrodynamic (MHD) numerical
simulations of magnetic flux emergence into the solar atmosphere. Such
simulations showed that flux emergence can generate a substantial net current
in ARs. Another source of AR currents are photospheric horizontal flows. Our
aim is to determine the conditions for the occurrence of net vs. neutralized
currents with this second mechanism. Using 3D MHD simulations, we
systematically impose line-tied, quasi-static, photospheric twisting and
shearing motions to a bipolar potential magnetic field. We find that such
flows: (1) produce both {\it direct} and {\it return} currents, (2) induce very
weak compression currents - not observed in 2.5D - in the ambient field present
in the close vicinity of the current-carrying field, and (3) can generate
force-free magnetic fields with a net current. We demonstrate that neutralized
currents are in general produced only in the absence of magnetic shear at the
photospheric polarity inversion line - a special condition rarely observed. We
conclude that, as magnetic flux emergence, photospheric flows can build up net
currents in the solar atmosphere, in agreement with recent observations. These
results thus provide support for eruption models based on pre-eruption magnetic
fields possessing a net coronal current.Comment: 14 pages and 11 figures (Accepted in The Astrophysical Journal
Photospheric flux density of magnetic helicity
Copyright © 2005 EDP Sciences. This article appeared in Astronomy & Astrophysics 439 (2005) and may be found at http://www.aanda.org/index.php?option=article&access=doi&doi=10.1051/0004-6361:20052663Several recent studies have developed the measurement of magnetic helicity flux from the time evolution of photospheric magnetograms. The total flux is computed by summing the flux density over the analyzed region. All previous analyses used the density GA (=−2(A•u)Bn) which involves the vector potential A of the magnetic field. In all the studied active regions, the density GA has strong polarities of both signs with comparable magnitude. Unfortunately, the density GA can exhibit spurious signals which do not provide a true helicity flux density. The main objective of this study is to resolve the above problem by defining the flux of magnetic helicity per unit surface. In a first step, we define a new density, Gθ, which reduces the fake polarities by more than an order of magnitude in most cases (using the same photospheric data as GA). In a second step, we show that the coronal linkage needs to be provided in order to define the true helicity flux density. It represents how all the elementary flux tubes move relatively to a given elementary flux tube, and the helicity flux density is defined per elementary flux tube. From this we define a helicity flux per unit surface, GΦ. We show that it is a field-weighted average of Gθ at both photospheric feet of coronal connections. We compare these three densities (GA, Gθ, GΦ) using theoretical examples representing the main cases found in magnetograms (moving magnetic polarities, separating polarities, one polarity rotating around another one and emergence of a twisted flux tube). We conclude that Gθ is a much better proxy of the magnetic helicity flux
density than GA because most fake polarities are removed. Indeed Gθ gives results close to GΦ and should be used to monitor the photospheric injection of helicity (when coronal linkages are not well known). These results are applicable to the results of any method determining the photospheric velocities. They can provide separately the flux density coming from shearing and advection motions if plasma motions are known
A model for straight and helical solar jets: II. Parametric study of the plasma beta
Jets are dynamic, impulsive, well-collimated plasma events that develop at
many different scales and in different layers of the solar atmosphere.
Jets are believed to be induced by magnetic reconnection, a process central
to many astrophysical phenomena. Within the solar atmosphere, jet-like events
develop in many different environments, e.g., in the vicinity of active regions
as well as in coronal holes, and at various scales, from small photospheric
spicules to large coronal jets. In all these events, signatures of helical
structure and/or twisting/rotating motions are regularly observed. The present
study aims to establish that a single model can generally reproduce the
observed properties of these jet-like events.
In this study, using our state-of-the-art numerical solver ARMS, we present a
parametric study of a numerical tridimensional magnetohydrodynamic (MHD) model
of solar jet-like events. Within the MHD paradigm, we study the impact of
varying the atmospheric plasma on the generation and properties of
solar-like jets.
The parametric study validates our model of jets for plasma ranging
from to , typical of the different layers and magnetic
environments of the solar atmosphere. Our model of jets can robustly explain
the generation of helical solar jet-like events at various . This
study introduces the new result that the plasma modifies the morphology
of the helical jet, explaining the different observed shapes of jets at
different scales and in different layers of the solar atmosphere.
Our results allow us to understand the energisation, triggering, and driving
processes of jet-like events. Our model allows us to make predictions of the
impulsiveness and energetics of jets as determined by the surrounding
environment, as well as the morphological properties of the resulting jets.Comment: Accepted in Astronomy and Astrophysic
Comparison of magnetic energy and helicity in coronal jet simulations
Context. While non-potential (free) magnetic energy is a necessary element of any active phenomenon in the solar corona, its role as a marker of the trigger of the eruptive process remains elusive. Meanwhile, recent analyses of numerical simulations of solar active events have shown that quantities based on relative magnetic helicity could highlight the eruptive nature of solar magnetic systems. Aims. Based on the unique decomposition of the magnetic field into potential and non-potential components, magnetic energy and helicity can also both be uniquely decomposed into two quantities. Using two 3D magnetohydrodynamics parametric simulations of a configuration that can produce coronal jets, we compare the dynamics of the magnetic energies and of the relative magnetic helicities. Methods. Both simulations share the same initial setup and line-tied bottom-boundary driving profile. However, they differ by the duration of the forcing. In one simulation, the system is driven sufficiently so that a point of no return is passed and the system induces the generation of a helical jet. The generation of the jet is, however, markedly delayed after the end of the driving phase; a relatively long phase of lower-intensity reconnection takes place before the jet is eventually induced. In the other reference simulation, the system is driven during a shorter time, and no jet is produced. Results. As expected, we observe that the jet-producing simulation contains a higher value of non-potential energy and non-potential helicity compared to the non-eruptive system. Focussing on the phase between the end of the driving-phase and the jet generation, we note that magnetic energies remain relatively constant, while magnetic helicities have a noticeable evolution. During this post-driving phase, the ratio of the non-potential to total magnetic energy very slightly decreases while the helicity eruptivity index, which is the ratio of the non-potential helicity to the total relative magnetic helicity, significantly increases. The jet is generated when the system is at the highest value of this helicity eruptivity index. This proxy critically decreases during the jet-generation phase. The free energy also decreases but does not present any peak when the jet is being generated. Conclusions. Our study further strengthens the importance of helicities, and in particular of the helicity eruptivity index, to understand the trigger mechanism of solar eruptive events
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