206 research outputs found
Validation and Benchmarking of a Practical Free Magnetic Energy and Relative Magnetic Helicity Budget Calculation in Solar Magnetic Structures
In earlier works we introduced and tested a nonlinear force-free (NLFF)
method designed to self-consistently calculate the free magnetic energy and the
relative magnetic helicity budgets of the corona of observed solar magnetic
structures. The method requires, in principle, only a single, photospheric or
low-chromospheric, vector magnetogram of a quiet-Sun patch or an active region
and performs calculations in the absence of three-dimensional magnetic and
velocity-field information. In this work we strictly validate this method using
three-dimensional coronal magnetic fields. Benchmarking employs both synthetic,
three-dimensional magnetohydrodynamic simulations and nonlinear force-free
field extrapolations of the active-region solar corona. We find that our
time-efficient NLFF method provides budgets that differ from those of more
demanding semi-analytical methods by a factor of ~3, at most. This difference
is expected from the physical concept and the construction of the method.
Temporal correlations show more discrepancies that, however, are soundly
improved for more complex, massive active regions, reaching correlation
coefficients of the order of, or exceeding, 0.9. In conclusion, we argue that
our NLFF method can be reliably used for a routine and fast calculation of free
magnetic energy and relative magnetic helicity budgets in targeted parts of the
solar magnetized corona. As explained here and in previous works, this is an
asset that can lead to valuable insight into the physics and the triggering of
solar eruptions.Comment: 32 pages, 14 figures, accepted by Solar Physic
Validation of the magnetic energy vs. helicity scaling in solar magnetic structures
We assess the validity of the free magnetic energy - relative magnetic
helicity diagram for solar magnetic structures. We used two different methods
of calculating the free magnetic energy and the relative magnetic helicity
budgets: a classical, volume-calculation nonlinear force-free (NLFF) method
applied to finite coronal magnetic structures and a surface-calculation NLFF
derivation that relies on a single photospheric or chromospheric vector
magnetogram. Both methods were applied to two different data sets, namely
synthetic active-region cases obtained by three-dimensional
magneto-hydrodynamic (MHD) simulations and observed active-region cases, which
include both eruptive and noneruptive magnetic structures. The derived
energy--helicity diagram shows a consistent monotonic scaling between relative
helicity and free energy with a scaling index 0.840.05 for both data sets
and calculation methods. It also confirms the segregation between noneruptive
and eruptive active regions and the existence of thresholds in both free energy
and relative helicity for active regions to enter eruptive territory. We
consider the previously reported energy-helicity diagram of solar magnetic
structures as adequately validated and envision a significant role of the
uncovered scaling in future studies of solar magnetism
An observationally-driven kinetic approach to coronal heating
Coronal heating through the explosive release of magnetic energy remains an
open problem in solar physics. Recent hydrodynamical models attempt an
investigation by placing swarms of 'nanoflares' at random sites and times in
modeled one-dimensional coronal loops. We investigate the problem in three
dimensions, using extrapolated coronal magnetic fields of observed solar active
regions. We apply a nonlinear force-free field extrapolation above an observed
photospheric magnetogram of NOAA active region (AR) 11158. We then determine
the locations, energy contents, and volumes of 'unstable' areas, namely areas
prone to releasing magnetic energy due to locally accumulated electric current
density. Statistical distributions of these volumes and their fractal dimension
are inferred, investigating also their dependence on spatial resolution.
Further adopting a simple resistivity model, we infer the properties of the
fractally distributed electric fields in these volumes. Next, we monitor the
evolution of 10^5 particles (electrons and ions) obeying an initial Maxwellian
distribution with a temperature of 10 eV, by following their trajectories and
energization when subjected to the resulting electric fields. For computational
convenience, the length element of the magnetic-field extrapolation is 1
arcsec, much coarser than the particles collisional mean free path in the low
corona. The presence of collisions traps the bulk of the plasma around the
unstable volumes, or current sheets (UCS), with only a tail of the distribution
gaining substantial energy. Assuming that the distance between UCS is similar
to the collisional mean free path we find that the low active-region corona is
heated to 100-200 eV, corresponding to temperatures exceeding 2 MK, within tens
of seconds for electrons and thousands of seconds for ions. Fractally
distributed, nanoflare-triggening fragmented UCS ...Comment: accepted by A&
Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical Strings
We propose an electric-magnetic duality and conjecture an exact conformal
window for a class of non-supersymmetric U(N_c) gauge theories with fermions in
the (anti)symmetric representation of the gauge group and N_f additional scalar
and fermion flavors. The duality exchanges N_c with N_f -N_c \mp 4 leaving N_f
invariant, and has common features with Seiberg duality in N=1 SQCD with SU or
SO/Sp gauge group. At large N the duality holds due to planar equivalence with
N=1 SQCD. At finite N we embed these gauge theories in a setup with D-branes
and orientifolds in a non-supersymmetric, but tachyon-free, non-critical type
0B string theory and argue in favor of the duality in terms of boundary and
crosscap state monodromies as in analogous supersymmetric situations. One can
verify explicitly that the resulting duals have matching global anomalies.
Finally, we comment on the moduli space of these gauge theories and discuss
other potential non-supersymmetric examples that could exhibit similar
dualities.Comment: 45 pages, 1 figur
Relative field line helicity of a large eruptive solar active region
Context. Magnetic helicity is a physical quantity of great importance in the
study of astrophysical and natural plasmas. Although a density for helicity
cannot be defined, a good proxy for it is field line helicity. The appropriate
quantity for use in solar conditions is relative field line helicity (RFLH).
Aims. This work aims to study in detail the behaviour of RFLH, for the first
time, in a solar active region (AR). Methods. The target active region is the
large, eruptive AR 11158. In order to compute RFLH and all other quantities of
interest we use a non-linear force-free reconstruction of the AR coronal
magnetic field of excelent quality. Results. We find that the photospheric
morphology of RFLH is quite different than that of the magnetic field or of the
electrical current, and this is not sensitive to the chosen gauge in the
computation of RFLH. The value of helicity experiences a large decrease, 25% of
its pre-flare value, during an X-class flare of the AR, a change that is also
depicted in the photospheric morphology of RFLH. Moreover, the area of this
change coincides with the area that encompasses the flux rope, the magnetic
structure that later erupted. Conclusions. The use of RFLH can provide
important information about the value and location of the magnetic helicity
expelled from the solar atmosphere during eruptive events.Comment: accepted by Astronomy & Astrophysic
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
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
On the rapid TeV flaring activity of Markarian 501
Aims: We investigate the one-zone SSC model of TeV blazars in the presence of
electron acceleration. In this picture electrons reach a maximum energy where
acceleration saturates from a combination of synchrotron and inverse Compton
scattering losses. Methods: We solve the spatially averaged kinetic equations
which describe the simultaneous evolution of particles and photons, obtaining
the multi-wavelength spectrum as a function of time. Results: We apply the
model to the rapid flare of Mrk 501 of July 9, 2005 as this was observed by the
MAGIC telescope and obtain the relevant parameters for the pre-flare quasi
steady state and the ones during the flare. We show that a hard lag flare can
be obtained with parameters which lie well within the range already accepted
for this source. Especially the choice of a high value of the Doppler factor
seems to be necessary.Comment: 4 pages, 4 figures, to appear in A&A (Letters
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