Transcript Slide 1

Free Magnetic Energy in Solar Active Regions
above the Minimum-Energy Relaxed State
(Regnier, S., Priest, E.R. 2007 ApJ)
Use magnetic field extrapolations to calculate the amount of
free magnetic energy available for processes such as solar
flares.
In the solar corona above an active region, we can neglect the
effects of gravity and pressure with respect to those from the
magnetic field.
Then we have
For currents along the field lines, this becomes
There are three types of fields that satisfy the above equations:
1.A potential field, j=0 everywhere
2.A linear force-free field, where α is constant everywhere
3.A non-linear force-free field, where α= α(x, y ,z)
The Woljter-Taylor theory states that in a weak but finite resistive
regime, the free magnetic energy available from a relaxation
process is the energy above the linear force-free field that satisfies
the boundary conditions and has the same helicity as the observed
field. Heyvaerts & Priest (1984) extended the theory to coronal
fields.
The authors calculate the magnetic energy in each configuration
with
They then calculate the free energy using
Regions studied
AR 8151, a decaying region
AR 8210, a newly emerged region
Actual photospheric
field data obtained
from the MSO/IVM
(Mees Solar
Observatory /
Imaging Vector
Magnetograph)
AR 9077, Bastille Day flare
AR 10486, Halloween events of ‘03
Conclusions
• Free magnetic energy can vary by at least 2 orders of magnitude.
This is because it depends greatly on the total magnetic flux and on
the arrangement of the polarities.
• By noting the calculated free magnetic energy to the activity level
associated with the various regions, they found that the value
computed with the linear force-free configuration as the reference field
gives a better estimate of the energy available for flaring and
associated processes.
Nonlinear force-free models for the solar corona
1. Two active regions with very different structure
(Regnier, S., Priest, E.R. 2006 A&A)
Use the same extrapolation methods described in the previous
paper to investigate how the various current density
distributions change the geometry of the field lines, where and
how much magnetic energy is stored, and the amount of
magnetic helicity.
The vertical current density, Jz, is used to obtain a suitable α (α =Jz/Bz)
Again, AR 8151 was a decaying active region at the time of observation.
Other studies of the region found twisted flux tubes with various numbers
of turns and handedness.
AR 8210 was a newly emerged active region with a complex topology. It
consisted of a strongly negative sunspot surrounded by several positive
polarities. However, studies of this region have not found any twisted flux
tubes.
First let’s see the effects of current density on the shape of the field lines.
In AR 8151, high
current densities
strongly influence the
geometry of the field
lines.
The angle of the
polarity inversion line
with respect to the top
of the loops changes.
The locations of the
footpoints are quite
different.
The chosen field lines
seem to indicate that
the nlff field lines top
out lower than the
potential ones.
However, statistical analysis revealed that the nlff
field lines are generally taller, longer, and
stronger.
In AR 8210, the weak
current densities modify
the geometry only
slightly. Even the
heights seem the same.
This field reconstruction
does not produce any
twisted flux bundles,
which agrees with
observations.
The authors claim that
the low influence of
increased current along
the lines means that
these field lines can
store magnetic energy, since an input of current density would modify
the field strength, but not the configuration.
AR 8151
Free magnetic energy is
mostly in he mid-corona,
at heights where the
twisted flux tubes are
found.
Calculated energy
budget of 2.6 x 1031 erg
(40% of the total energy
in nlff) is enough to
trigger a small flare.
AR 8210
Free magnetic energy is
mostly in the low
corona, near the
photosphere.
Calculated energy
budget of 2.4 x 1031 erg
(only 2.5% of the total
energy in nlff) is still
enough to trigger a
small flare. Several Cclass flares occurred
around the time of
observation.
(Note the logarithmic nature of the plot. )
References
Regnier, S., Priest, E.R. 2007, Free Magnetic Energy in Solar Active Regions
above the Minimum-Energy Relaxed State, preprint, accepted into ApJ
Regnier, S., Priest, E.R. 2006 A&A 468,701