Magnetic cloud models with bent and oblate crosssection boundary 

Pascal Demoulin Submitted: 20090909 07:06
Magnetic clouds (MCs) are formed by magnetic flux ropes that are ejected
from the Sun as coronal mass ejections.
These structures generally have low plasma beta and travel through
the interplanetary medium interacting with the surrounding solar wind (SW).
Thus, the dynamical evolution of the internal magnetic structure of a MC
is a consequence of both the conditions of its environment
and of its own dynamical laws, which are mainly dominated by magnetic forces.
With insitu observations the magnetic field is only measured along the trajectory of the spacecraft across the MC. Therefore, a magnetic model is needed to reconstruct the magnetic configuration of the encountered MC.
The main aim of the present work is to extend the widely used cylindrical model
to arbitrary crosssection shapes.
The flux rope boundary is parametrized to account for a broad range of shapes.
Then, the internal structure of the flux rope is computed by expressing the magnetic field
as a series of modes of a linear forcefree field.
We analyze the magnetic field profile along straight cuts through the flux rope, in order to simulate the spacecraft crossing through a MC. We find that the magnetic field orientation is only weakly affected by the shape of the MC boundary. Therefore, the MC axis can approximately be found by the typical methods previously used (e.g., minimum variance).
The boundary shape affects mostly the magnetic field strength. The measure of how much the field strength peaks along the crossing provides an estimation for the aspect ratio
of the fluxrope crosssection. The asymmetry of the field strength between the front and
the back of the MC, after correcting the time evolution (i.e., its aging during the observation of the MC), provides an estimation of the crosssection global bending.
A flat or/and bent crosssection requires a large anisotropy of the total pressure imposed at the MC boundary by the surrounding medium.
The new theoretical model developed here relaxes the cylindrical symmetry hypothesis.
It is designed to estimate the crosssection shape of the flux rope using the insitu data of one spacecraft. This allows a more accurate determination of the global quantities, such as magnetic fluxes and helicity. These quantities are especially important for both linking an observed MC to its solar source and for understanding the corresponding evolution.
Authors: Demoulin P., Dasso S.
Projects: None

Publication Status: in press, A&A
Last Modified: 20090909 09:37



Causes and consequences of magnetic cloud expansion 

Pascal Demoulin Submitted: 20090305 07:40
A magnetic cloud (MC) is a magnetic flux rope in the solar wind (SW), which, at 1 AU, is observed ~ 25 days after its expulsion from the Sun. The associated solar eruption is observed as a coronal mass ejection (CME).
Both the in situ observations of plasma velocity distribution and the increase in their size with solar distance demonstrate that MCs are strongly expanding structures.
The aim of this work is to find the main causes of this expansion and to derive a model to explain the plasma velocity profiles typically observed inside MCs.
We model the flux rope evolution as a series of forcefree field states with two extreme limits: (a) ideal magnetohydrodynamics (MHD) and (b) minimization of the magnetic energy with conserved magnetic helicity. We consider cylindrical flux ropes to reduce the problem to the integration of ordinary differential equations. This allows us to explore a wide variety of magnetic fields at a broad range of distances to the Sun.
We demonstrate that the rapid decrease in the total SW pressure with solar distance is the main driver of the fluxrope radial expansion. Other effects, such as the internal overpressure, the radial distribution, and the amount of twist within the flux rope have a much weaker influence on the expansion. We demonstrate that any forcefree flux rope will have a selfsimilar expansion if its total boundary pressure evolves as the inverse of its length to the fourth power. With the total pressure gradient observed in the SW, the radial expansion of flux ropes is close to selfsimilar with a nearly linear radial velocity profile across the flux rope, as observed. Moreover, we show that the expansion rate is proportional to the radius and to the global velocity away from the Sun.
The simple and universal law found for the radial expansion of flux ropes in the SW predicts the typical size, magnetic structure, and radial velocity of MCs at various solar distances.
Authors: Demoulin P. & Dasso S.
Projects: None

Publication Status: A&A in press
Last Modified: 20090305 07:43



Modeling and Observations of Photospheric Magnetic Helicity 

Pascal Demoulin Submitted: 20080903 08:00
Mounting observational evidence of the emergence of twisted magnetic flux tubes through the photosphere have now been published. Such flux tubes, formed by the solar dynamo and transported through the convection zone, eventually reach the solar atmosphere. Their accumulation in the solar corona leads to flares and coronal mass ejections. Since reconnections occur during the evolution of the flux tubes, the concepts of twist and magnetic stress become inappropriate. Magnetic helicity, as a well preserved quantity, even during reconnection, is a more suitable physical quantity to use.
Only recently, it has been realized that the flux of magnetic helicity can be derived from magnetogram time series. This paper reviews the advances made in measuring the helicity injection rate at the photospheric level, mostly in active regions. It relates the observations to our present theoretical understanding of the emergence process. Most of the helicity injection is found during magnetic flux emergence, whereas the effect of differential rotation is small, and the longterm evolution of active regions is still puzzling. The photospheric maps for the injection of magnetic helicity provide a new spatial information about the basic properties of the link between the solar activity and its subphotospheric roots. Finally, the newest technique to measure photospheric flows are reviewed.
Authors: Demoulin, P. & Pariat, E.
Projects: None

Publication Status: Advances in Space Research, submitted
Last Modified: 20080903 13:35



Subject will be restored when possible 

Pascal Demoulin Submitted: 20080602 11:08
In situ data provide only a one dimensional sample of the plasma velocity
along the spacecraft trajectory crossing an interplanetary coronal mass ejection
(ICME). Then, to understand the dynamics of ICMEs it is necessary to consider some
model to describe it. We derive a series of equations in a hierarchical order, from more general to more specific cases, to provide a general theoretical basis for the interpretation of in situ observations, extending and generalizing previous studies.
The main hypothesis is a selfsimilar expansion, but with the freedom of possible
different expansion rates in three orthogonal directions.
The most detailed application of the equations is though for a subset of ICMEs,
magnetic clouds (MCs), where a magnetic flux rope can be identified.
The main conclusions are the following ones. First, we
obtain theoretical expressions showing that the observed velocity
gradient within an ICME is not a direct characteristic of its
expansion, but that it depends also on other physical quantities
such as its global velocity and acceleration. The derived equations
quantify these dependencies for the three components of the
velocity.
Second, using three different types of data we show that the global
acceleration of ICMEs has, at most, a small contribution to the in situ measurements
of the velocity. This eliminates practically one contribution to the
observed velocity gradient within ICMEs.
Third, we provide a method to quantify the expansion rate from velocity data.
We apply it to a set of 26~MCs observed by Wind or ACE spacecrafts.
They are typical MCs, and their main physical parameters cover the
typical range observed in MCs in previous statistical studies.
Though the velocity difference between their front and back includes
a broad range of values, we find a narrow range for the determined
dimensionless expansion rate. This implies that MCs are expanding at a comparable
rate, independently of their size or field strength, despite very
different magnitudes in their velocity profiles.
Furthermore, the equations derived provide a base to further analyze the
dynamics of MCs/ICMEs.
Authors: Demoulin, P., Nakwacki, M.S., Dasso, S., Mandrini, C.H.
Projects: None

Publication Status: in press, Solar Physics
Last Modified: 20080603 09:13



Expected in Situ Velocities from a Heirarchical Model for Exapnding Interplanetary Coronal Mass Ejections 

Pascal Demoulin Submitted: 20080602 11:08
In situ data provide only a one dimensional sample of the plasma velocity
along the spacecraft trajectory crossing an interplanetary coronal mass ejection
(ICME). Then, to understand the dynamics of ICMEs it is necessary to consider some
model to describe it. We derive a series of equations in a hierarchical order, from more general to more specific cases, to provide a general theoretical basis for the interpretation of in situ observations, extending and generalizing previous studies.
The main hypothesis is a selfsimilar expansion, but with the freedom of possible
different expansion rates in three orthogonal directions.
The most detailed application of the equations is though for a subset of ICMEs,
magnetic clouds (MCs), where a magnetic flux rope can be identified.
The main conclusions are the following ones. First, we
obtain theoretical expressions showing that the observed velocity
gradient within an ICME is not a direct characteristic of its
expansion, but that it depends also on other physical quantities
such as its global velocity and acceleration. The derived equations
quantify these dependencies for the three components of the
velocity.
Second, using three different types of data we show that the global
acceleration of ICMEs has, at most, a small contribution to the in situ measurements
of the velocity. This eliminates practically one contribution to the
observed velocity gradient within ICMEs.
Third, we provide a method to quantify the expansion rate from velocity data.
We apply it to a set of 26~MCs observed by Wind or ACE spacecrafts.
They are typical MCs, and their main physical parameters cover the
typical range observed in MCs in previous statistical studies.
Though the velocity difference between their front and back includes
a broad range of values, we find a narrow range for the determined
dimensionless expansion rate. This implies that MCs are expanding at a comparable
rate, independently of their size or field strength, despite very
different magnitudes in their velocity profiles.
Furthermore, the equations derived provide a base to further analyze the
dynamics of MCs/ICMEs.
Authors: Demoulin, P., Nakwacki, M.S., Dasso, S., Mandrini, C.H.
Projects:

Publication Status: Solar Physics, 2008, 250, 347
Last Modified: 20080903 08:04



Where will efficient energy release occur in 3D magnetic configurations? 

Pascal Demoulin Submitted: 20070217 07:13
The energy needed to power flares is thought to be stored in the
coronal magnetic field. However, the energy release
is efficient only at very small scales.
Magnetic configurations with a complex topology, i.e. with
separatrices, are the most obvious configurations where current
sheets can form, and then, reconnection can efficiently occur.
This has been confirmed for several flares computing the coronal field and
comparing the locations of the flare loops and ribbons to the deduced
3D magnetic topology. However, this view is too restrictive taking
into account the variety of observed solar flaring configurations.
Indeed, ``QuasiSeparatrix Layers'' (QSLs), which are regions where there
is a drastic change in fieldline linkage, generalize the definition
of separatrices. They let us understand where reconnection
occurs in a broader variety of flares than separatrices do. The
strongest electric field and current are generated at, or close to
where the QSLs are thinnest. This defines the region where
particle acceleration can efficiently occur. A new feature of 3D
reconnection is the natural presence of fast field line slippage along the
QSLs, a process called ``sliprunning reconnection''.
This is a plausible origin for the motions of the Xray sources
along flare ribbons.
Authors: Demoulin, P.
Projects: None

Publication Status: Advances in Space Research, in press
Last Modified: 20070217 10:09



A Multiple flare scenario where the classic long duration flare was not the source of a CME 

Pascal Demoulin Submitted: 20061122 04:18
A series of flares (GOES class M, M and C) and a CME were observed in
close succession on 20th January 2004 in NOAA 10540. Radio
observations, which took the form of types II, III and N bursts, were
associated with these events. We use the combined observations from
TRACE, EIT, Hα images from Kawsan, MDI magnetograms, and GOES
to understand the complex development of this event.
Contrary to a standard interpretation, we conclude that the first two
impulsive flares are part of the CME launch process while the
following LDE flare represents simply the recovery phase.
Observations show that the flare ribbons not only separate but also
shift along the magnetic inversion line so that magnetic reconnection
progresses stepwise to neighbouring flux tubes. We conclude that
''tether cutting'' reconnection in the sheared arcade progressively
transforms it to a twisted flux tube which becomes unstable, leading
to a CME. We interpret the third flare, a longduration event, as
a combination of the classical tworibbon flare with the
relaxation process following forced reconnection between
the expanding CME structure and neighbouring magnetic fields.
Authors: Goff, C.P., van DrielGesztelyi, L., Démoulin, P., Culhane, J.L., Matthews, S.A., Harra, L.K., Mandrini, C.H., Klein, K.L., Kurokawa, H.
Projects: SoHOEIT,SoHOMDI

Publication Status: submitted, Solar Physics
Last Modified: 20061122 09:53



Decametric N burst: a consequence of the interaction of two coronal mass ejections 

Pascal Demoulin Submitted: 20061108 04:15
Radio emissions of electron beams in the solar corona and
interplanetary space are tracers of the underlying magnetic
configuration and of its evolution. We analyse radio observations
from the Culgoora and Wind/WAVES spectrographs, in combination with
SOHO/LASCO and SOHO/MDI data, to understand the origin of a type
N burst originating from NOAA AR 10540 on January 20, 2004,
and its relationship with type II and type III emissions.
All bursts are related to the flares and the CME analysed in a
previous paper (Goff et al., 2006).
A very unusual feature of this event was a decametric type N burst,
where a type IIIlike burst, drifting toward low frequencies (negative
drift), changes drift first to positive, then again to negative. At
metre wavelengths, i.e. heliocentric distances
< 1.5 Rs, these bursts are ascribed to electron beams
bouncing in a closed loop. Neither U nor N bursts are
expected at decametric wavelengths because closed quasistatic loops
are not thought to extend to distances >> 1.5 Rs.
We take the opportunity of the good multiinstrument coverage of this
event to analyse the origin of type N bursts in the high corona.
Reconnection of the expanding ejecta with the magnetic structure of a
previous CME, launched about 8 hours earlier, injects electrons in the
same manner as with type III bursts but into open field lines having a
local dip and apex. The latter shape was created by magnetic
reconnection between the expanding CME and neighbouring (open)
streamer field lines. This particular flux tube shape in the
high corona, between 510 Rs, explains the observed
type N burst. Since the required magnetic configuration is only a
transient phenomenon formed by reconnection, severe timing and
topological constraints are present to form the observed decametric
Nburst. They are therefore expected to be rare features.
Authors: Demoulin, P., Klein, K.L., Goff, C.P., van DrielGesztelyi, L., Culhane, J.L., Mandrini, C.H., Matthews, S.A., Harra, L.K.
Projects:

Publication Status: In press, Solar Physics
Last Modified: 20061123 08:56



Magnetic topologies: where will reconnection occur ? 

Pascal Demoulin Submitted: 20051012 06:05
The energy needed to power flares is thought to come from the coronal
magnetic field. However, such energy release is efficient only at
very small scales. Magnetic configurations with a complex topology,
i.e. with separatrices, are the most obvious configurations where
current layers can spontaneously form. 3D magnetic configurations
have a variety of magnetic topologies not suspected before. If the
photospheric field is described by an ensemble of magnetic charges,
separated by fluxfree regions, a complete topological description of
the associated potential field is provided by the skeleton formed by
the null points, spines, fans and separators. In order to better
match the observed photospheric magnetograms, the magnetic charges can
be set below the photosphere; then an extra topological element can
appear, socalled bald patches with associated separatrices. In
several flaring configurations the computed separatrices allows to
understand the localization of the flare ribbons in the framework of
magnetic reconnection. However, this view is too restrictive taking
into account the variety of observed solar flaring configurations.
Indeed ``quasiseparatrix layers'' (QSLs), which are regions where
there is a drastic change in fieldline linkage, generalize the
definition of separatrices for magnetic fields extending in the full
volume (photosphere and corona). The concept of ``hyperbolic flux
tube'' (HFT) also generalizes the concept of separator. These studies
indeed teach us that coronal magnetic reconnection occurs in a broader
variety of magnetic configurations than traditionally thought, and
this variety is reviewed.
Authors: Demoulin, P.
Projects: None

Publication Status: ESA publication, in press
Last Modified: 20051012 06:05



Radio and Xray signatures of magnetic reconnection behind an ejected flux rope 

Pascal Demoulin Submitted: 20050210 07:09
We present a detailed study of a complex solar event observed on June 02 2002. Joint imaging EUV, Xray and multiwavelength radio observations allow us to trace the development of the magnetic structure involved in this solar event up to a radial distance of the order of two solar radii . The event involves type II, III and IV bursts. The type~IV burst is formed by two sources: a fast moving one (M) and a ``quasistationary'' one (S). The time coincidence in the flux peaks of these radio sources and the underlying hard Xray sources implies a causal link.
In a first part we provide a summary of the observations without reference to any CME model. The experimental results impose strong constraints on the physical processes. In a second part, we find that a model with an erupting twisted flux rope, with the formation of a current sheet behind, best relates the different observations in a coherent physical evolution (even if there is no direct evidence of the twisted flux rope).
Our results show that multiwavelength radio imaging represent a
powerful tool to trace the dynamical evolution of the reconnecting current sheet behind ejected fluxropes (in between sources M and S) and over an altitude range not accessible by Xray observations.
Authors: Pick, M., DÃ©moulin, P., Krucker, S., Malandraki, O., Maia, D.
Projects: RHESSI,SohoEIT

Publication Status: ApJ, in press (625, June 2 issue)
Last Modified: 20050210 07:09



Amplitude and orientation of prominence magnetic fields from constant α magnetohydrostatic models 

Pascal Demoulin Submitted: 20030425 08:30
We analyze outputs from threedimensional models for three
observed filaments, which belong to the quiescent, intermediate
and plage class respectively. Each model was calculated from a
constant α magnetohydrostatic extrapolation,
assuming that the prominence material is located in magnetic
dips, so that the field is nearly horizontal throughout
the prominence body and feet.
We calculate the spatial distribution of the magnetic field
amplitude B and orientation theta with respect to the filament
axis, neither of which were imposed a priori in the models.
In accordance with past magnetic field measurements within prominence
bodies, we also obtain nearly homogeneous magnetic fields, respectively
of about B ~ 3, 14 and 40 G for the quiescent, intermediate and
plage prominence, with a systematic weak vertical field gradient of
dB / dz ~ 0.11.5 X 10^{4} G.km^{1}.
We also find that the inverse polarity configuration is dominant
with theta ~ 20 to 0 degrees, which is slightly
smaller than in some observations.
We also report some other properties, which have either
rarely or never been observed. We find at prominence tops
some localized normal polarity regions with theta < +10 degrees.
At prominence bottoms below 20 Mm in altitude, we find
stronger field gradients dB / dz ~ 110 X 10^{4} G.km^{1}
and a wider range of field directions theta ~ 90 to 0 degrees.
These properties can be interpreted by the perturbation of the prominence flux tube by strong photospheric polarities located in the neighborhood of the prominence. We also report some full portions of prominences that have the normal polarity. The latter are simply due to
the local curvature of the filaments with respect to their
average axis, which was used to define theta.
These results could either be used as predictions for further
testing of this class of models with new observations, or as
quantitative tools for the interpretation of observations which
show complex patterns.
Authors: Aulanier, G., Demoulin, P.
Projects: None

Publication Status: 2003, A&A, 402, 769
Last Modified: 20030425 08:30



The scalings of the coronal plasma parameters with the mean
photospheric magnetic field: The longterm evolution of AR 7978 

Pascal Demoulin Submitted: 20021205 08:20
We analyze the evolution of the fluxes observed in Xrays and
correlate them with the magnetic flux density in active region
NOAA 7978 from its birth throughout its decay, for five solar
rotations. We use SoHO/MDI data to derive magnetic observables,
together with Yohkoh/SXT and Yohkoh/BCS data to determine the
global evolution of the temperature and the emission measure of
the coronal plasma at times when no significant brightenings were
observed. We show that the mean Xray flux and derived
parameters, temperature and emission measure (together with other
quantities deduced from them, such as the density and the
pressure), of the plasma in the AR follow powerlaw relationships
with the mean magnetic flux density (ar{B}). The exponents
(b) of these powerlaw functions (a ar{B}^{b}) are derived
using two different statistical methods, a classical leastsquares
method in loglog plots and a nonparametric method, which takes
into account the fact that errors in the data may not be normally
distributed. Both methods give similar exponents, within error
bars, for the mean temperature and for both instruments (SXT and
BCS); in particular, b stays in the range [0.27,0.31] and
[0.24,0.55] for full resolution SXT images and BCS
data, respectively. For the emission measure the exponent b
lies in the range [0.85,1.35] and [0.45,1.96] for SXT and BCS,
respectively. The determination of such powerlaw relations, when
combined with the results from coronal heating models, can provide
us with powerful tools for determining the mechanism responsible for
the existence of the high temperature corona.
Authors: van DrielGesztelyi L., Demoulin, P., Mandrini C.H., Harra, L., Klimchuk, J.A.
Projects:

Publication Status: ApJ, preprint, in press
Last Modified: 20021205 08:20



Testing coronal heating models: The longterm evolution of AR 7978 

Pascal Demoulin Submitted: 20021205 08:15
We derive the dependence of the mean coronal heating rate on the
magnetic flux density. Our results are based on a previous study of
the plasma parameters and the magnetic flux density (ar{B}) in the
active region NOAA 7978 from its birth to its decay, throughout five
solar rotations using SoHO/MDI, Yohkoh/SXT and Yohkoh/BCS. We use the
scaling laws of coronal loops in thermal equilibrium to derive four
observational estimates of the scaling of the coronal heating with
ar{B} (two from SXT and two from BCS observations). These results
are used to test the validity of coronal heating models. We find that
models based on the dissipation of stressed, currentcarrying magnetic
fields are in better agreement with the observations than models that
attribute coronal heating to the dissipation of MHD waves injected at
the base of the corona. This confirms, with smaller error bars,
previous results obtained for individual coronal loops, as well as for
the global coronal emission of the Sun and cool stars. Taking into
account that the photospheric field is concentrated in thin magnetic
flux tubes, both SXT and BCS data are in best agreement with models
invoking a stochastic buildup of energy, current layers and MHD
turbulence.
Authors: D'emoulin, P., van DrielGesztelyi, L., Mandrini C.H., Klimchuk, J.A., Harra, L.
Projects:

Publication Status: ApJ, preprint, in press
Last Modified: 20021205 08:15



What is the source of the magnetic helicity shed by CMEs. The longterm helicity budget of AR 7978 

Pascal Demoulin Submitted: 20011219 08:57
An isolated active region (AR) was observed on the Sun during seven
rotations, starting from its birth in July 1996 to its full dispersion
in December 1996. We analyse the longterm budget of the AR relative
magnetic helicity. Firstly, we calculate the helicity injected by
differential rotation at the photospheric level using MDI/SoHO
magnetograms. Secondly, we compute the coronal magnetic field and its
helicity selecting the model which best fits the soft Xray loops
observed with SXT/Yohkoh. Finally, we identify all the coronal mass
ejections (CMEs) that originated from the AR during its lifetime using
LASCO and EIT/SoHO. Assuming a one to one correspondence between CMEs
and magnetic clouds, we estimate the magnetic helicity which could be
shed via CMEs.
We find that differential rotation can neither provide the required
magnetic helicity to the coronal field (at least a factor 2.5 to 4
larger), nor to the field ejected to the interplanetary space (a factor
4 to 20 larger), even in the case of this AR for which the total
helicity injected by differential rotation is close to the maximum
possible value. However, the total helicity ejected is equivalent to
that of a twisted flux tube having the same magnetic flux as the
studied AR and a number of turns in the interval [0.5,2.0]. We
suggest that the main source of helicity is the inherent twist of the
magnetic flux tube forming the active region. This magnetic helicity
is transferred to the corona either by the continuous
emergence of the flux tube for several solar rotations (i.e. on a
time scale much longer than the classical emergence phase), or by
torsional Alfvén waves.
Authors: DÃ©moulin P., van DrielGesztelyi L., Mandrini C.H., Thompson B., Plunkett S., Kovari Zs., Aulanier, G. & Young A.
Projects:

Publication Status: A&A (in press)
Last Modified: 20011219 09:01



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