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A Code for Automated Tracing of Coronal Loops Approaching Visual Perception
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Markus J. Aschwanden Submitted: 2009-10-21 15:45
Here we develop a new numeric code with automated pattern recognition,
customized for tracing of coronal loops, which for the first time breaks even
with the results of visual tracing. The used method is based on oriented-directivity tracing of curvi-linear features, but in contrast to other general pattern recognition algorithms, it is customized to solar EUV and SXR images by taking advantage of the specific property that coronal loops have large curvature radii compared with their widths. We evaluate the performance of this new code by comparing the cumulative distribution of loop lengths, the median and maximum loop lengths, the completeness of detection, and the congruency of the detected patterns with other numeric codes and visual tracings. We find that the new code closely approaches the results of visual perception and outperforms the other existing numeric codes. This algorithm is useful for the 3D reconstruction of the geometry, motion, and oscillations of coronal loops, with single or stereoscopic spacecraft, as well as for
modeling of the loop hydrodynamics and the coronal magnetic field.
Authors: Markus J. Aschwanden
Projects: TRACE
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Publication Status: Solar Physics, (subm. 2009 Oct 20)
Last Modified: 2009-10-22 02:04
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First Measurements of the Mass of Coronal Mass Ejections from the EUV Dimming Observed with STEREO EUVI A+B Spacecraft
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Markus J. Aschwanden Submitted: 2009-04-03 17:21
The masses of Coronal Mass Ejections (CMEs) have traditionally
been determined from white-light coronagraphs, based on the Thomson
scattering of electrons, which depends on the (generally unknown)
angle of the CME propagation direction. Here we develop a new method
of measuring CME masses from the EUV dimming seen with EUV imaging
telescopes in multiple temperature filters. As a test we investigate
8 CME events with previous mass determinations from STEREO/COR2,
of which 5 cases are fully detected with EUVI, 2 partially, and 1 not,
using an automated multi-wavelength detection code.
We find CME masses in the range of m_CME = (2-7) x 10^15 g.
The agreement between the two EUVI/A and B spacecraft is m_A/m_B
=1.3 +/- 0.6 and the consistency with white-light measurements by
COR2 is m_EUVI/m_COR2 = 1.1+/-0.3.
The consistency between EUVI and COR2 implies no significant
mass backflows (or inflows) at r < 4 R_sun and adequate
temperature coverage for the bulk of the CME mass in the range of
T = 0.5-3.0 MK. The temporal evolution of the EUV dimming
allows us also to model the evolution of the CME density n_e(t),
volume V(t), height-time h(t), and propagation speed
v(t) in terms of an adiabatically expanding self-similar
geometry. We determine e-folding EUV dimming times of
1.3+/-1.4 hr. We test the adiabatic expansion model in terms of
the predicted detection delay (0.7 hr) between EUVI
and COR2 for the fastest CME event (2008-Mar-25) and find good agreement with the observed delay ( 0.8 hr).
Authors: Aschwanden,M.J., Nitta,N.V., Wuelser,J.P., Lemen,J.R., Sandman,A., Vourlidas,A., Colaninno,R.C.
Projects: STEREO
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Publication Status: ApJ, subm. 2009 Apr 3
Last Modified: 2009-04-04 09:20
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The 3D Geometry, 3D Motion, and Hydrodynamics of Oscillating Coronal Loops
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Markus J. Aschwanden Submitted: 2009-01-31 12:19
We transition from two-dimensional (2D) imaging observations of kink-mode loop
oscillations in the solar corona to three-dimensional (3D) reconstructions by
exploring two new methods: (1) De-projection of 2D loop tracings using the
strategy of curvature maximization in 3D space, based on the assumption of
force-free magnetic fields; and (2) stereoscopic triangulation of epipolar
loop coordinates using coaligned images from the STEREO EUVI/A and B spacecraft.
Both methods reveal new features of oscillating loops: non-circularity,
non-planarity, and helical geometries. We extend the 3D reconstruction
techniques into the time domain and find indications of circularly
polarized (torsional) kink-mode oscillations, in contrast to linearly
polarized modes assumed previously. We discuss also hydrodynamic effects
of coronal loops in non-equilibrium state that are essential for
the detection and modeling of kink-mode oscillations.
Authors: Markus J. Aschwanden
Projects: STEREO
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Publication Status: Space Science Reviews, Topical Issue on Coronal Seismology, (subm, Jan-31,2009)
Last Modified: 2009-02-01 10:17
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Hydrodynamic Modeling of Coronal Loops with Hinode and STEREO
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Markus J. Aschwanden Submitted: 2009-01-08 16:54
The hydrodynamic evolution of impulsively-heated coronal loops
and their subsequent cooling can now be modeled with multi-wavelength
imaging instruments in soft X-ray (SXR) and extreme ultraviolet (EUV)
wavelengths. Using analytical approximations to the hydrodynamic
evolution of the density n(s,t) and temperature T(s,t) of an
impulsively-heated loop (as a function of the loop length coordinate s
and time t) we show an example how lightcurves observed with
HINODE/XRT, EIS, GOES, and STEREO/EUVI can be modeled with
a forward-fitting method in order to infer the maximum heating rate,
the heating duration, and the cooling time of a heated loop during a small
B1-class flare on 2007-Feb-01, previously analyzed by
Warren et al. (2007).
Authors: Aschwanden M.J.
Projects: Hinode/EIS
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Publication Status: Astronomical Society of the Pacific Conference Series, Beyond Discovery - Toward Understanding, Second Hinode Science Meeting, 29 Sept - 3 Oct 2008, Boulder, Colorado, USA, (eds. M.Cheung, B.Lites, T.Magara, J.Mariska, and K.Reeves), Vol ..., (subm., 2009 Jan 8)
Last Modified: 2009-01-09 09:37
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First 3D Reconstructions of Coronal Loops with the STEREO A+B Spacecraft: III. Instant Stereoscopic Tomography of Active Regions
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Markus J. Aschwanden Submitted: 2008-12-17 15:15
Here we develop a novel 3D reconstruction method of the coronal plasma
of an active region by combining stereoscopic triangulation of loops
with density and temperature modeling of coronal loops with a filling
factor equivalent to tomographic volume rendering. Because this method
requires only a stereoscopic image pair in multiple temperature filters,
which are sampled within $approx 1$ minute with the recent STEREO/EUVI
instrument, this method is about 4 orders of magnitude faster than
conventional solar rotation-based tomography. We reconstruct the 3D
density and temperature distribution of active region NOAA 10955 by
stereoscopic triangulation of 70 loops, which are used as a skeleton for
a 3D field interpolation of some 7000 loop components, leading to a 3D model
that reproduces the observed fluxes in each stereosocpic image pair with an
accuracy of a few percent (of the average flux) in each pixel. With
the stereoscopic tomography we infer also a differential emission measure
(DEM) distribution over the entire temperature range of $Tapprox 10^4-10^7$,
with predictions for the transition region and hotter corona in soft X-rays.
The tomographic 3D model provides also large statistics of physical
parameters. We find that the EUV loops with apex temperatures of
$T_m lapprox 3.0$ MK tend to be super-hydrostatic, while hotter loops
with $T_m approx 4-7$ MK are near-hydrostatic. The new
3D reconstruction model is fully independent of any magnetic field data
and is promising for future tests of theoretical magnetic field models
and coronal heating models.
Authors: Markus J. Aschwanden, Jean-Pierre Wuelser, Nariaki V. Nitta,
Projects: STEREO
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Publication Status: ApJ 695 (2009 April 1 issue), on-line 12-29
Last Modified: 2009-03-30 12:37
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Solar Flare and CME Observations with STEREO/EUVI
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Markus J. Aschwanden Submitted: 2008-12-04 09:26
STEREO/EUVI observed 185 flare events (detected above the GOES-class
C1 level or at >25 keV with RHESSI) during the first two years
of the mission (Dec 2006 - Nov 2008), while coronal mass ejections
(CME) were reported in about a third of these events. We compile a
comprehensive catalog of these EUVI-observed events, containing the
peak fluxes in soft X-rays, hard X-rays, and EUV, as well as
a classification and statistics of prominent EUV features: 79 % show
impulsive EUV emission (coincident with hard X-rays), 73 % show
delayed EUV emission from postflare loops and arcades, 24 % represent
occulted flares, 17 % exhibit EUV dimming, 5 % show loop oscillations
or propagating waves, and at least 3 % show erupting filaments.
We analyze an example of each EUV feature by stereoscopic modeling
of their 3D geometry. We find that impulsive EUV emission indicates
compression of cold coronal plasma during the flare energy release,
in contrast to the delayed postflare EUV emission that results from cooling
of the soft X-ray emitting flare loops. Occulted flares allow us to
determine CME-related coronal dimming uncontaminated from flare-related
EUV emission. From modeling the time evolution of EUV dimming we can
accurately quantify the initial expansion of CMEs and determine
their masses. Further we find evidence that coronal loop oscillations
are excited by the rapid initial expansion of CMEs. These examples
demonstrate that stereoscopic EUV data provide powerful new methods
to model the 3D aspects in the hydrodynamics of flares and kinematics
of CMEs.
Authors: Aschwanden,M.J., Wuelser,J.P., Nitta,N.V., and Lemen,J.R.
Projects:
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Publication Status: Solar Physics, Topical Issue on STEREO Results during the Solar Minimum, (subm. 2008 Dec 4; accepted 2009 Mar 27)
Last Modified: 2009-04-11 08:24
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Markus J. Aschwanden Submitted: 2008-09-02 14:16
Coronal loops that exhibit kink-mode oscillations have generally been assumed
to have a constant density and temperature during the observed time interval.
Analyzing their intensities in an EUV waveband, however, clearly shows
that their brightness varies in a way that is consistent with a
temperature cooling through the EUV passband, which limits their
detection time, observed damping time, and number of observable periods.
We study kink-mode oscillations of eight loops observed during the so-called
``harmonica event'' on 2001-Apr-15, 21:58-22:27 UT in 171 ang . We find
loop densities of $n_e=1.4pm0.6 imes 10^9$ cm$^{-3}$, loop widths of
$w=2.0pm2.6$ Mm, and e-folding cooling times of $ au_{cool}=17pm7$ min,
when they cool through the peak temperature $T=0.95$ MK of the 171 ang band.
We conclude that oscillations of a single loop can not be detected
longer than 10-20 min in one single filter and appropriate light curve modeling
is necessary to disentangle the subsequent oscillation phases of multiple
near-cospatial loops.
Authors: Markus J. Aschwanden and Jaume Terradas
Projects: TRACE
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Publication Status: ApJ Lett. (accepted, Sept 1, 2008; in press)
Last Modified: 2008-09-03 07:49
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The Effect of Radiative Cooling on Coronal Loop Oscillations
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Markus J. Aschwanden Submitted: 2008-09-02 14:16
Coronal loops that exhibit kink-mode oscillations have generally been assumed
to have a constant density and temperature during the observed time interval.
Analyzing their intensities in an EUV waveband, however, clearly shows
that their brightness varies in a way that is consistent with a
temperature cooling through the EUV passband, which limits their
detection time, observed damping time, and number of observable periods.
We study kink-mode oscillations of eight loops observed during the so-called
``harmonica event'' on 2001-Apr-15, 21:58-22:27 UT in 171 ang . We find
loop densities of n_e=(1.4+/-0.6) x 10^9 cm^-3, loop widths of
w=2.0 +/- 2.6 Mm, and e-folding cooling times of t_cool=17 +/- 7 min,
when they cool through the peak temperature T=0.95 MK of the 171 A band.
We conclude that oscillations of a single loop can not be detected
longer than 10-20 min in one single filter and appropriate light curve modeling
is necessary to disentangle the subsequent oscillation phases of multiple
near-cospatial loops.
Authors: Markus J. Aschwanden and Jaume Terradas
Projects: TRACE
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Publication Status: ApJ 686, L127-L130
Last Modified: 2008-12-02 09:30
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-12-24 13:07
The physical state of coronal loops is often studied with scaling
laws that are derived from an equilibrium solution, where the heating
rate balances the loss rates by radiation and thermal conduction.
Recent analysis of EUV data at
temperatures of $T_1 approx 1.0$ MK, however, exhibit huge
overpressures (or overdensities) $q_1$ up to a few orders of magnitude
for long loops, compared with stationary equilibrium models.
This overpressure can naturally be explained by the non-stationary
cooling process alone, in the absence of any heating, which follows
approximately the {sl Jakimiec scaling} of $T(t) propto n(t)^2$.
In this Letter we show that the observed overpressure $q_1=n_1/n_0$
(with respect to the RTV density $n_0 propto T_1^2/L$) can be used
as a new diagnostic
to determine the peak density, $n_p approx n_0 q_1^{4/3}$, and peak
temperature, $T_p approx T_1 q_1^{2/3}$, to which the loop was heated
before onset of the cooling phase. This new non-equlibirum scaling law
provides soft X-ray predictions based on EUV observations.
Authors: Markus J. Aschwanden
Projects: TRACE
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Publication Status: ApJ Letter (revised, Version 2008 jan 9)
Last Modified: 2008-01-09 12:10
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-12-24 13:06
The physical state of coronal loops is often studied with scaling
laws that are derived from an equilibrium solution of the energy
balance equation, which equates heating to the losses by radiation
and thermal conduction, such as the RTV law ($n_e propto T_{max}^2/L$),
or the generalization by Serio. Recent analysis of EUV data in the
temperature range of $Tapprox 1-2$ MK, however, exhibit an
unexplained overpressure up to a few orders of magnitude compared
with these stationary equilibrium models. In this Letter we show that
this overpressure can naturally be explained by the non-stationary cooling
process alone, in the absence of any heating, which has a scaling
of $(n/n_p) approx (T/T_p)^{1/2}$ and even allows to determine the peak
density $n_p$ and temperature $T_p lapprox T_{max}$ to which the loop
was heated before onset of the cooling phase.
Authors: Markus J. Aschwanden, Nariaki Nitta, Jean-Pierre Wuelser, and James Lemen
Projects: None
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Publication Status: ApJ Letter (subm., Dec 24, 2007)
Last Modified: 2007-12-24 13:06
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Markus J. Aschwanden Submitted: 2007-12-19 15:59
Using the stereoscopically derived 3D geometry of 30 loops observed with
STEREO/EUVI (described in Paper I), we determine here the electron density
profiles $n_e(s)$ and electron temperature profiles $T_e(s)$ from a
triple-filter analysis of the stereoscopic images taken in the wavelengths
of $lambda=$ 171, 195, and 284 ang .
The statistical results of our analysis of 7 complete loops are:
observed loop widths $w_{obs}=2.6pm 0.1$ Mm, corresponding to effective
loop widths of $w=1.1pm0.3$ Mm if corrected for the instrumental
point-spread function, loop flux ratios $f_{loop}/f_{total} = 0.11 pm 0.04$,
mean loop (DEM peak) temperatures $T_p=1.1 pm 0.2$ MK,
DEM temperature gaussian widths $sigma_{DEM}=0.35pm 0.04$ MK,
temperature variations along loops $sigma_T/T_p=0.24 pm 0.05$,
(resolution-corrected) loop base densities
$n_e=(2.2 pm 0.5) imes 10^{9}$ cm$^{-3}$, loop lengths of
$L=130 pm 67$ Mm, and all quantities are found to agree between
STEREO/A and B within a few percent.
The temperature profiles $T(s)$ along loops are found to be nearly constant,
within the uncertainties of the background subtraction.
The density profiles $n_e(s)$ are consistent
with hydrostatic loops, $n_e(h)=n_{base} exp(-h/lambda_T)$, predicted by
the temperature scale heights $lambda_T$, using the stereoscopically
measured height profiles $h(s)$. The stereoscopic 3D reconstruction allows us
for the first time to accurately measure the loop length $L$ and to test
loop scaling laws. We find that the observations are not consistent with the
RTV scaling law (based on a uniform heating function), but are more
consistent with Serio's scaling (adapted for footpoint heating) with heating
scale heights in the range of $s_H approx 5-10$ Mm, which corroborates
earlier EIT and TRACE results.
Authors: Markus J. Aschwanden, Nariaki Nitta, Jean-Pierre Wuelser, and James Lemen
Projects: STEREO
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Publication Status: ApJ (in press, accepted March 4, 2008)
Last Modified: 2008-03-04 14:49
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-12-19 15:59
Using the stereoscopically derived 3D geometry of 30 loops observed with
STEREO/EUVI (described in Paper I), we determine here the electron density
profiles $n_e(s)$ and electron temperature profiles $T_e(s)$ from a
triple-filter analysis of the stereoscopic images taken in the wavelengths
of $lambda=$ 171, 195, and 284 ang .
The statistical results of our analysis of 7 complete loops are:
observed loop widths $w_{obs}=2.6pm 0.1$ Mm, corresponding to effective
loop widths of $w=1.1pm0.3$ Mm if corrected for the instrumental
point-spread function, loop flux ratios $f_{loop}/f_{total} = 0.11 pm 0.04$,
mean loop (DEM peak) temperatures $T_p=1.1 pm 0.2$ MK,
DEM temperature gaussian widths $sigma_{DEM}=0.35pm 0.04$ MK,
temperature variations along loops $sigma_T/T_p=0.24 pm 0.05$,
(resolution-corrected) loop base densities
$n_e=(2.2 pm 0.5) imes 10^{9}$ cm$^{-3}$, loop lengths of
$L=130 pm 67$ Mm, and all quantities are found to agree between
STEREO/A and B within a few percent.
The temperature profiles $T(s)$ along loops are found to be nearly constant,
within the uncertainties of the background subtraction.
The density profiles $n_e(s)$ are consistent with the gravitational stratification
of hydrostatic loops, $n_e(h)=n_{base} exp(-h/lambda_T)$, defined by
the temperature scale heights $lambda_T$ and stereoscopically measured
from the height profiles $h(s)$. The stereoscopic 3D reconstruction allows us
for the first time to accurately measure the loop length $L$ and to test
loop scaling laws. We find that the observations are not consistent with
equilibrium solutions, but rather display the typical overpressures of
loops that have been previously heated to higher temperatures and cool down
in a non-equilibrium state, similarly to earlier EIT and TRACE measurements.
Authors: Markus J. Aschwanden, Nariaki Nitta, Jean-Pierre Wuelser, and James Lemen
Projects: STEREO
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Publication Status: ApJ (in press, accepted March 4, 2008)
Last Modified: 2008-03-04 14:52
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-12-19 15:59
Using the stereoscopically derived 3D geometry of 30 loops observed with
STEREO/EUVI (described in Paper I), we determine here the electron density
profiles $n_e(s)$ and electron temperature profiles $T_e(s)$ from a
triple-filter analysis of the stereoscopic images taken in the wavelengths
of $lambda=$ 171, 195, and 284 ang .
The inference of the density and temperature at a given loop
position $s$ is defined by the background-subtracted loop cross-section profiles
$f_{lambda,loop}(x) = f_{lambda,total}(x) - f_{lambda,back}(x)$
in perpendicular direction $x$ to the loop,
which crucially depend on the definition of the background profiles
$f_{lambda,back}(x)$, often amounting to $gapprox 90\%$ of the total
flux. Since this crucial aspect is the main limitation in the accuracy
of inferring temperature and density parameters and has been treated
inappropriately in many previous studies, we investigate up to
10 different background-subtraction methods here and test their
self-consistency from the dual stereoscopic line-of-sights.
The statistical results of our analysis of 7 complete loops are:
observed loop widths $w_{obs}=2.6pm 0.1$ Mm, corresponding to effective
loop widths of $w=1.1pm0.3$ Mm if corrected for the instrumental
point-spread function, loop flux ratios $f_{loop}/f_{total} = 0.11 pm 0.04$,
mean loop (DEM peak) temperatures $T_p=1.1 pm 0.2$ MK,
DEM temperature gaussian widths $sigma_{DEM}=0.35pm 0.04$ MK,
temperature variations along loops $sigma_T/T_p=0.24 pm 0.05$,
(resolution-corrected) loop base densities
$n_e=(2.2 pm 0.5) imes 10^{9}$ cm$^{-3}$, loop lengths of
$L=130 pm 67$ Mm, and all quantities are found to agree between
STEREO/A and B within a few percent.
The temperature profiles $T(s)$ along loops are found to be nearly constant,
within the uncertainties of the background subtraction.
The density profiles $n_e(s)$ are consistent
with hydrostatic loops, $n_e(h)=n_{base} exp(-h/lambda_T)$, predicted by
the temperature scale heights $lambda_T$, using the stereoscopically
measured height profiles $h(s)$. The stereoscopic 3D reconstruction allows us
for the first time to accurately measure the loop length $L$ and to test
loop scaling laws. We find that the observations are not consistent with the
RTV scaling law (based on a uniform heating function), but are more
consistent with Serio's scaling (adapted for footpoint heating) with heating
scale heights in the range of $s_H approx 5-10$ Mm, which corroborates
earlier EIT and TRACE results.
Authors: Markus J. Aschwanden, Nariaki Nitta, Jean-Pierre Wuelser, and James Lemen
Projects: STEREO
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Publication Status: ApJ (in press, accepted March 4, 2008)
Last Modified: 2008-03-04 14:48
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-11-01 09:16
We present the first triangulation and 3D reconstruction of coronal loops,
using the EUVI telescopes of the two STEREO A and B spacecraft.
This first triangulation of coronal loops is performed in an active region,
observed with STEREO A and B on 2007 May 9 with a spacecraft separation
angle of alpha_sep=7.3 deg, at a wavelength of 171 A .
We identify 30 loop structures (7 complete loops and 23 partial segments)
and compute their 3D coordinates [x, y, z], [the full 3D coordinates
are available as an electronic file]. We quantify the height range,
the stereoscopic height measurement errors, the loop plane inclination angles,
and the coplanarity and circularity of the analyzed loops.
The background of the active region shows also ``moss''
features, for which we determine a mean height of h_{moss} ~ 4 Mm.
The knowledge of the exact 3D geometry of a loop with respect to the observers
line-of-sight has important consequences for determining the correct vertical
density scale height (used in hydrostatic models), the aspect angle of
loop cross-sections (used in inferring electron densities from optically thin
emission measures), the absolute flow speeds (used in siphon flow models),
the correct loop length (used in loop scaling laws), as well as the 3D vectors
of the coronal magnetic field (used in testing theoretical magnetic field
extrapolation models). The hydrodynamic and magnetic modeling of the
analyzed loops will be described in subsequent papers.
Authors: Markus J. Aschwanden, Jean-Pierre Wuelser, Nariaki Nitta, Jim Lemen
Projects: STEREO
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Publication Status: ApJ (to be submitted), Version 2007 Nov 1
Last Modified: 2007-11-08 14:09
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-11-01 09:16
We present the first triangulation and 3D reconstruction of coronal loops,
using the EUVI telescopes of the two STEREO A and B spacecraft.
This first triangulation of coronal loops is performed in an active region,
observed with STEREO A and B on 2007 May 9 with a spacecraft separation
angle of alpha_sep=7.3 deg, at a wavelength of 171 A .
We identify 30 loop structures (7 complete loops and 23 partial segments)
and compute their 3D coordinates [x, y, z], [the full 3D coordinates
are available as an electronic file]. We quantify the height range,
the stereoscopic height measurement errors, the loop plane inclination angles,
and the coplanarity and circularity of the analyzed loops.
The background of the active region shows also ``moss''
features, for which we determine a mean height of h_{moss} ~ 4 Mm.
The knowledge of the exact 3D geometry of a loop with respect to the observers
line-of-sight has important consequences for determining the correct vertical
density scale height (used in hydrostatic models), the aspect angle of
loop cross-sections (used in inferring electron densities from optically thin
emission measures), the absolute flow speeds (used in siphon flow models),
the correct loop length (used in loop scaling laws), as well as the 3D vectors
of the coronal magnetic field (used in testing theoretical magnetic field
extrapolation models). The hydrodynamic and magnetic mo
Authors: Markus J. Aschwanden, Jean-Pierre Wuelser, Nariaki Nitta, Jim Lemen
Projects: STEREO
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Publication Status: ApJ (to be submitted), Version 2007 Nov 1
Last Modified: 2007-11-01 19:49
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Subject will be restored when possible
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Markus J. Aschwanden Submitted: 2007-11-01 09:15
We present the first triangulation and 3D reconstruction of coronal loops,
using the EUVI telescopes of the two STEREO A and B spacecraft.
This first triangulation of coronal loops is performed in an active region,
observed with STEREO A and B on 2007 May 9 with a spacecraft separation
angle of alpha_sep=7.3 deg, at a wavelength of 171 A .
We identify 30 loop structures (7 complete loops and 23 partial segments)
and compute their 3D coordinates [x, y, z], [the full 3D coordinates
are available as an electronic file]. We quantify the height range,
the stereoscopic height measurement errors, the loop plane inclination angles,
and the coplanarity and circularity of the analyzed loops.
The background of the active region shows also ``moss''
features, for which we determine a mean height of h_{moss} ~ 4 Mm.
The knowledge of the exact 3D geometry of a loop with respect to the observers
line-of-sight has important consequences for determining the correct vertical
density scale height (used in hydrostatic models), the aspect angle of
loop cross-sections (used in inferring electron densities from optically thin
emission measures), the absolute flow speeds (used in siphon flow models),
the correct loop length (used in loop scaling laws), as well as the 3D vectors
of the coronal magnetic field (used in testing theoretical magnetic field
extrapolation models). The hydrodynamic and magnetic mo
Authors: Markus J. Aschwanden, Jean-Pierre Wuelser, Nariaki Nitta, Jim Lemen
Projects: STEREO
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Publication Status: ApJ (in preparation)
Last Modified: 2007-11-01 09:15
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