293 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
Energy and helicity budgets of solar quiet regions
We investigate the free magnetic energy and relative magnetic helicity
budgets of solar quiet regions. Using a novel non-linear force-free method
requiring single solar vector magnetograms we calculate the instantaneous free
magnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vector
magnetograms. As in a previous work on active regions, we construct here for
the first time the (free) energy-(relative) helicity diagram of quiet-Sun
regions. We find that quiet-Sun regions have no dominant sense of helicity and
show monotonic correlations a) between free magnetic energy/relative helicity
and magnetic network area and, consequently, b) between free magnetic energy
and helicity. Free magnetic energy budgets of quiet-Sun regions represent a
rather continuous extension of respective active-region budgets towards lower
values, but the corresponding helicity transition is discontinuous due to the
incoherence of the helicity sense contrary to active regions. We further
estimate the instantaneous free magnetic-energy and relative magnetic-helicity
budgets of the entire quiet Sun, as well as the respective budgets over an
entire solar cycle. Derived instantaneous free magnetic energy budgets and, to
a lesser extent, relative magnetic helicity budgets over the entire quiet Sun
are comparable to the respective budgets of a sizeable active region, while
total budgets within a solar cycle are found higher than previously reported.
Free-energy budgets are comparable to the energy needed to power fine-scale
structures residing at the network, such as mottles and spicules
Simulating Flaring Events in Complex Active Regions Driven by Observed Magnetograms
We interpret solar flares as events originating from active regions that have
reached the Self Organized Critical state, by using a refined Cellular
Automaton model with initial conditions derived from observations. Aims: We
investigate whether the system, with its imposed physical elements,reaches a
Self Organized Critical state and whether well-known statistical properties of
flares, such as scaling laws observed in the distribution functions of
characteristic parameters, are reproduced after this state has been reached.
Results: Our results show that Self Organized Criticality is indeed reached
when applying specific loading and relaxation rules. Power law indices obtained
from the distribution functions of the modeled flaring events are in good
agreement with observations. Single power laws (peak and total flare energy) as
well as power laws with exponential cutoff and double power laws (flare
duration) are obtained. The results are also compared with observational X-ray
data from GOES satellite for our active-region sample. Conclusions: We conclude
that well-known statistical properties of flares are reproduced after the
system has reached Self Organized Criticality. A significant enhancement of our
refined Cellular Automaton model is that it commences the simulation from
observed vector magnetograms, thus facilitating energy calculation in physical
units. The model described in this study remains consistent with fundamental
physical requirements, and imposes physically meaningful driving and
redistribution rules.Comment: 14 pages; 12 figures; 6 tables - A&A, in pres
Combining particle acceleration and coronal heating via data-constrained calculations of nanoflares in coronal loops
We model nanoflare heating of extrapolated active-region coronal loops via
the acceleration of electrons and protons in Harris-type current sheets. The
kinetic energy of the accelerated particles is estimated using semi-analytical
and test-particle-tracing approaches. Vector magnetograms and photospheric
Doppler velocity maps of NOAA active region 09114, recorded by the Imaging
Vector Magnetograph (IVM), were used for this analysis. A current-free field
extrapolation of the active-region corona was first constructed. The
corresponding Poynting fluxes at the footpoints of 5000 extrapolated coronal
loops were then calculated. Assuming that reconnecting current sheets develop
along these loops, we utilized previous results to estimate the kinetic-energy
gain of the accelerated particles and we related this energy to nanoflare
heating and macroscopic loop characteristics. Kinetic energies of 0.1 to 8 keV
(for electrons) and 0.3 to 470 keV (for protons) were found to cause heating
rates ranging from to 1 . Hydrodynamic
simulations show that such heating rates can sustain plasma in coronal
conditions inside the loops and generate plasma thermal distributions which are
consistent with active region observations. We concluded the analysis by
computing the form of X-ray spectra generated by the accelerated electrons
using the thick target approach that were found to be in agreement with
observed X-ray spectra, thus supporting the plausibility of our
nanoflare-heating scenario.Comment: 11 figure
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&
Magnetic Helicity and Free Magnetic Energy as Tools to Probe Eruptions in two Differently Evolving Solar Active Regions
Using vector magnetograms from the HMI/SDO and a magnetic connectivity-based
method, we calculate the instantaneous relative magnetic helicity and free
magnetic energy budgets for several days in two solar active regions (ARs),
AR11890 and AR11618, both with complex photospheric magnetic field
configurations. The ARs produced several major eruptive flares while their
photospheric magnetic field exhibited primarily flux decay in AR11890 and
primarily flux emergence in AR11618. Throughout much of their evolution both
ARs featured substantial budgets of free magnetic energy and of both positive
and negative helicity. In fact, the imbalance between the signed components of
their helicity was as low as in the quiet Sun and their net helicity eventually
changed sign 14-19 hours after their last major flare. Despite such
incoherence, the eruptions occurred at times of net helicity peaks that were
co-temporal with peaks in the free magnetic energy. The losses associated with
the eruptive flares in the normalized free magnetic energy were in the range
10-60%. For the helicity, changes ranged from 25% to the removal of the entire
excess helicity of the prevailing sign, leading a roughly zero net helicity,
but with significant equal and opposite budgets of both helicity senses. The
removal of the slowly varying background component of the free energy and
helicity timeseries revealed that all eruption-related peaks of both quantities
exceeded the 2 levels of their detrended timeseries. There was no
eruption when only one or none of these quantities exceeded its 2
level. Our results indicate that differently evolving ARs may produce major
eruptive flares even when, in addition to the accumulation of significant free
magnetic energy budgets, they accumulate large amounts of both negative and
positive helicity without a strong dominance of one handedness over the other.Comment: 17 pages, 11 figures, accepted for publication in Astronomy &
Astrophysics (abbreviated abstract
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