Solar stereoscopy - where are we and what developments do we require to progress?

Observations from the two STEREO-spacecraft give us for the first time the possibility to use stereoscopic methods to reconstruct the 3D solar corona. Classical stereoscopy works best for solid objects with clear edges. Consequently an application of classical stereoscopic methods to the faint structures visible in the optically thin coronal plasma is by no means straight forward and several problems have to be treated adequately: 1.)First there is the problem of identifying one dimensional structures -e.g. active region coronal loops or polar plumes- from the two individual EUV-images observed with STEREO/EUVI. 2.) As a next step one has the association problem to find corresponding structures in both images. 3.) Within the reconstruction problem stereoscopic methods are used to compute the 3D-geometry of the identified structures. Without any prior assumptions, e.g., regarding the footpoints of coronal loops, the reconstruction problem has not one unique solution. 4.) One has to estimate the reconstruction error or accuracy of the reconstructed 3D-structure, which depends on the accuracy of the identified structures in 2D, the separation angle between the spacecraft, but also on the location, e.g., for east-west directed coronal loops the reconstruction error is highest close to the loop top. 5.) Eventually we are not only interested in the 3D-geometry of loops or plumes, but also in physical parameters like density, temperature, plasma flow, magnetic field strength etc. Helpful for treating some of these problems are coronal magnetic field models extrapolated from photospheric measurements, because observed EUV-loops outline the magnetic field. This feature has been used for a new method dubbed 'magnetic stereoscopy'. As examples we show recent application to active region loops.Comment: 12 Pages, 9 Figures, a Review articl

Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation

Exact numerical results for the full counting statistics (FCS) of a one-dimensional tight-binding model of noninteracting electrons are presented at finite temperatures using an identity recently presented by Abanov and Ivanov. A similar idea is used to derive a new expression for the cumulant generating function for a system consisting of two quasi-one-dimensional leads connected by a quantum dot in the long time limit. This provides a generalization of the Levitov-Lesovik formula for such systems.Comment: 17 pages, 6 figures, extended introduction, additional comment

Low polarized emission from the core of coronal mass ejections

In white-light coronagraph images, cool prominence material is sometimes observed as bright patches in the core of coronal mass ejections (CMEs). If, as generally assumed, this emission is caused by Thomson-scattered light from the solar surface, it should be strongly polarised tangentially to the solar limb. However, the observations of a CME made with the SECCHI/STEREO coronagraphs on 31 August 2007 show that the emission from these bright core patches is exceptionally low polarised. We used the polarisation ratio method of Moran and Davila (2004) to localise the barycentre of the CME cloud. By analysing the data from both STEREO spacecraft we could resolve the plane-of-the-sky ambiguity this method usually suffers from. Stereoscopic triangulation was used to independently localise the low-polarisation patch relative to the cloud. We demonstrated for the first time that the bright core material is located close to the centre of the CME cloud. We show that the major part of the CME core emission, more than 85% in our case, is H$\alpha$ radiation and only a small fraction is Thomson-scattered light. Recent calculations also imply that the plasma density in the patch is 8 10$^8$ cm$^{-3}$ or more compared to 2.6 10$^6$ cm$^{-3}$ for the Thomson-scattering CME environment surrounding the core material.Comment: 5 pages, 3 figure

Morphological evolution of a 3D CME cloud reconstructed from three viewpoints

The propagation properties of coronal mass ejections (CMEs) are crucial to predict its geomagnetic effect. A newly developed three dimensional (3D) mask fitting reconstruction method using coronagraph images from three viewpoints has been described and applied to the CME ejected on August 7, 2010. The CME's 3D localisation, real shape and morphological evolution are presented. Due to its interaction with the ambient solar wind, the morphology of this CME changed significantly in the early phase of evolution. Two hours after its initiation, it was expanding almost self-similarly. CME's 3D localisation is quite helpful to link remote sensing observations to in situ measurements. The investigated CME was propagating to Venus with its flank just touching STEREO B. Its corresponding ICME in the interplanetary space shows a possible signature of a magnetic cloud with a preceding shock in VEX observations, while from STEREO B only a shock is observed. We have calculated three principle axes for the reconstructed 3D CME cloud. The orientation of the major axis is in general consistent with the orientation of a filament (polarity inversion line) observed by SDO/AIA and SDO/HMI. The flux rope axis derived by the MVA analysis from VEX indicates a radial-directed axis orientation. It might be that locally only the leg of the flux rope passed through VEX. The height and speed profiles from the Sun to Venus are obtained. We find that the CME speed possibly had been adjusted to the speed of the ambient solar wind flow after leaving COR2 field of view and before arriving Venus. A southward deflection of the CME from the source region is found from the trajectory of the CME geometric center. We attribute it to the influence of the coronal hole where the fast solar wind emanated from.Comment: ApJ, accepte

Segmentation of Loops from Coronal EUV Images

We present a procedure which extracts bright loop features from solar EUV images. In terms of image intensities, these features are elongated ridge-like intensity maxima. To discriminate the maxima, we need information about the spatial derivatives of the image intensity. Commonly, the derivative estimates are strongly affected by image noise. We therefore use a regularized estimation of the derivative which is then used to interpolate a discrete vector field of ridge points ``ridgels'' which are positioned on the ridge center and have the intrinsic orientation of the local ridge direction. A scheme is proposed to connect ridgels to smooth, spline-represented curves which fit the observed loops. Finally, a half-automated user interface allows one to merge or split, eliminate or select loop fits obtained form the above procedure. In this paper we apply our tool to one of the first EUV images observed by the SECCHI instrument onboard the recently launched STEREO spacecraft. We compare the extracted loops with projected field lines computed from almost-simultaneously-taken magnetograms measured by the SOHO/MDI Doppler imager. The field lines were calculated using a linear force-free field model. This comparison allows one to verify faint and spurious loop connections produced by our segmentation tool and it also helps to prove the quality of the magnetic-field model where well-identified loop structures comply with field-line projections. We also discuss further potential applications of our tool such as loop oscillations and stereoscopy.Comment: 13 pages, 9 figures, Solar Physics, online firs

First Stereoscopic Coronal Loop Reconstructions from Stereo Secchi Images

We present the first reconstruction of the three-dimensional shape of magnetic loops in an active region from two different vantage points based on simultaneously recorded images. The images were taken by the two EUVI telescopes of the SECCHI instrument onboard the recently launched STEREO spacecraft when the heliocentric separation of the two space probes was 12 degrees. We demostrate that these data allow to obtain a reliable three-dimensional reconstruction of sufficiently bright loops. The result is compared with field lines derived from a coronal magnetic field model extrapolated from a photospheric magnetogram recorded nearly simultaneously by SOHO/MDI. We attribute discrepancies between reconstructed loops and extrapolated field lines to the inadequacy of the linear force-free field model used for the extrapolation.Comment: 6 pages, 5 figure

Full counting statistics for noninteracting fermions: Joint probability distributions

The joint probability distribution in the full counting statistics (FCS) for noninteracting electrons is discussed for an arbitrary number of initially separate subsystems which are connected at t=0 and separated at a later time. A simple method to obtain the leading order long time contribution to the logarithm of the characteristic function is presented which simplifies earlier approaches. New explicit results for the determinant involving the scattering matrices are found. The joint probability distribution for two leads is discussed for Y-junctions and dots connected to four leads.Comment: 17 pages, 3 figure

Break up of returning plasma after the 7 June 2011 filament eruption by Rayleigh-Taylor instabilities

A prominence eruption on 7 June 2011 produced spectacular curtains of plasma falling through the lower corona. At the solar surface they created an incredible display of extreme ultraviolet brightenings. The aim is to identify and analyze some of the local instabilities which produce structure in the falling plasma. The structures were investigated using SDO/AIA 171A and 193A images in which the falling plasma appeared dark against the bright coronal emission. Several instances of the Rayleigh-Taylor instability were investigated. In two cases the Alfven velocity associated with the dense plasma could be estimated from the separation of the Rayleigh-Taylor fingers. A second type of feature, which has the appearance of self-similar branching horns, is also discussed.Comment: 6 pages, 7 figures, submitted A&A. Movies are at http://www.mps.mpg.de/data/outgoing/innes/arcs_movie.avi and http://www.mps.mpg.de/data/outgoing/innes/horns_movie.av

Stereoscopic Polar Plume Reconstructions from Stereo/Secchi Images

We present stereoscopic reconstructions of the location and inclination of polar plumes of two data sets based on the two simultaneously recorded images taken by the EUVI telescopes in the SECCHI instrument package onboard the \emph{STEREO (Solar TErrestrial RElations Observatory)} spacecraft. The ten plumes investigated show a superradial expansion in the coronal hole in 3D which is consistent with the 2D results. Their deviations from the local meridian planes are rather small with an average of $6.47^{\circ}$. By comparing the reconstructed plumes with a dipole field with its axis along the solar rotation axis, it is found that plumes are inclined more horizontally than the dipole field. The lower the latitude is, the larger is the deviation from the dipole field. The relationship between plumes and bright points has been investigated and they are not always associated. For the first data set, based on the 3D height of plumes and the electron density derived from SUMER/\emph{SOHO} Si {\sc viii} line pair, we found that electron densities along the plumes decrease with height above the solar surface. The temperature obtained from the density scale height is 1.6 to 1.8 times larger than the temperature obtained from Mg {\sc ix} line ratios. We attribute this discrepancy to a deviation of the electron and the ion temperatures. Finally, we have found that the outflow speeds studied in the O {\sc vi} line in the plumes corrected by the angle between the line of sight and the plume orientation are quite small with a maximum of 10 $\mathrm{km s^{-1}}$. It is unlikely that plumes are a dominant contributor to the fast solar wind.Comment: 25 pages, 13 figure

Observations of a rotating macrospicule associated with an X-ray jet

We attempt to understand the driving mechanism of a macrospicule and its relationship with a coronal jet. We study the dynamics of a macrospicule and an associated coronal jet captured by multi-spacecraft observations. Doppler velocities both in the macrospicule and the coronal jet are determined by EIS and SUMER spectra. Their temporal evolution is studied using X-ray and He II 304 images. A blueshift of -120+/-15 km/s is detected on one side of the macrospicule, while a redshift of 50+/-6 km/s is found at the base of the other side. The inclination angle of the macrospicule inferred from a stereoscopic analysis with STEREO suggests that the measured Doppler velocities can be attributed to a rotating motion of the macrospicule rather than a radial flow or an expansion. The macrospicule is driven by the unfolding motion of a twisted magnetic flux rope, while the associated X-ray jet is a radial outflow.Comment: 4 pages, 3 figures, accepted for publication in A&