Tzitzeica solitons versus relativistic Calogero–Moser three-body clusters

We establish a connection between the hyperbolic relativistic Calogero–Moser systems and a class of soliton solutions to the Tzitzeica equation (also called the Dodd–Bullough–Zhiber–Shabat–Mikhailov equation). In the 6N-dimensional phase space Omega of the relativistic systems with 2N particles and N antiparticles, there exists a 2N-dimensional Poincaré-invariant submanifold OmegaP corresponding to N free particles and N bound particle-antiparticle pairs in their ground state. The Tzitzeica N-soliton tau functions under consideration are real valued and obtained via the dual Lax matrix evaluated in points of OmegaP. This correspondence leads to a picture of the soliton as a cluster of two particles and one antiparticle in their lowest internal energy state

Solar filament eruptions and their physical role in triggering Coronal Mass Ejections

Solar filament eruptions play a crucial role in triggering coronal mass ejections (CMEs). More than 80 % of eruptions lead to a CME. This correlation has been studied extensively during the past solar cycles and the last long solar minimum. The statistics made on events occurring during the rising phase of the new solar cycle 24 is in agreement with this finding. Both filaments and CMEs have been related to twisted magnetic fields. Therefore, nearly all the MHD CME models include a twisted flux tube, called a flux rope. Either the flux rope is present long before the eruption, or it is built up by reconnection of a sheared arcade from the beginning of the eruption. In order to initiate eruptions, different mechanisms have been proposed: new emergence of flux, and/or dispersion of the external magnetic field, and/or reconnection of field lines below or above the flux rope. These mechanisms reduce the downward magnetic tension and favor the rise of the flux rope. Another mechanism is the kink instability when the configuration is twisted too much. In this paper we open a forum of discussions revisiting observational and theoretical papers to understand which mechanisms trigger the eruption. We conclude that all the above quoted mechanisms could bring the flux rope to an unstable state. However, the most efficient mechanism for CMEs is the loss-of-equilibrium or torus instability, when the flux rope has reached an unstable threshold determined by a decay index of the external magnetic field.Comment: 23 pages, 13 figures, revie

Accuracy of magnetic energy computations

For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional models of the solar atmosphere, eg in coronal fields reconstructions or numerical simulations. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources

Investigation of Dynamics of Self-Similarly Evolving Magnetic Clouds

Magnetic clouds (MCs) are "magnetized plasma clouds" moving in the solar wind. MCs transport magnetic flux and helicity away from the Sun. These structures are not stationary but feature temporal evolution. Commonly, simplified MC models are considered. The goal of the present study is to investigate the dynamics of more general, radially expanding MCs. They are considered as cylindrically symmetric magnetic structures with low plasma {\beta}. In order to study MC`evolution the self-similar approach method and a numerical approach are used. It is shown that the forces are balanced in the considered self-similarly evolving, cylindrically symmetric magnetic structures. Explicit analytical expressions for magnetic field, plasma velocity, density and pressure within MCs are derived. These solutions are characterized by conserved values of magnetic flux and helicity. We also investigate the dynamics of self-similarly evolving MCs by means of the numerical code "Graale". In addition, their expansion in a medium with higher density and higher plasma {\beta} is studied. It is shown that the physical parameters of the MCs maintain their self-similar character throughout their evolution. Conclusions. A comparison of the different self-similar and numerical solutions allows us to conclude that the evolving MCs are quite adequately described by our self-similar solutions - they retain their self-similar, coherent nature for quite a long time and over large distances from the Sun

Constraints on filament models deduced from dynamical analysis

The conclusions deduced from simultaneous observations with the Ultra-Violet Spectrometer and Polarimeter (UVSP) on the Solar Maximum Mission satellite, and the Multichannel Subtractive Double Pass (MSPD) spectrographs at Meudon and Pic du Midi observatories are presented. The observations were obtained in 1980 and 1984. All instruments have almost the same field of view and provide intensity and velocity maps at two temperatures. The resolution is approx. 0.5 to 1.5" for H alpha line and 3" for C IV. The high resolution and simultaneity of the two types of observations allows a more accurate description of the flows in prominences as functions of temperature and position. The results put some contraints on the models and show that dynamical aspects must be taken into account

Observation of the Halo of NGC 3077 Near the "Garland" Region Using the Hubble Space Telescope

We report the detection of upper main sequence stars and red giant branch stars in the halo of an amorphous galaxy, NGC3077. The observations were made using Wide Field Planetary Camera~2 on board the Hubble Space Telescope. The red giant branch luminosity function in I-band shows a sudden discontinuity at I = 24.0 +- 0.1 mag. Identifying this with the tip of the red giant branch (TRGB), and adopting the calibration provided by Lee, Freedman, & Madore (1993) and the foreground extinction of A_B = 0.21 mag, we obtain a distance modulus of (m-M)_0 = 27.93 +- 0.14(random) +- 0.16(sys). This value agrees well with the distance estimates of four other galaxies in the M81 Group. In addition to the RGB stars, we observe a concentration of upper main sequence stars in the halo of NGC3077, which coincides partially with a feature known as the ``Garland''. Using Padua isochrones, these stars are estimated to be <150 Myrs old. Assuming that the nearest encounter between NGC3077 and M81 occurred 280 Myrs ago as predicted by the numerical simulations (Yun 1997), the observed upper main sequence stars are likely the results of the star formation triggered by the M81-NGC3077 tidal interaction.Comment: 15 pages, 8 figures. Accepted for publication in Astrophysical Journa

Vectorial Ribaucour Transformations for the Lame Equations

The vectorial extension of the Ribaucour transformation for the Lame equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an example we apply the vectorial Ribaucour transformation to the Cartesian background.Comment: 12 pages. LaTeX2e with AMSLaTeX package

Coronal magnetic reconnection driven by CME expansion -- the 2011 June 7 event

Coronal mass ejections (CMEs) erupt and expand in a magnetically structured solar corona. Various indirect observational pieces of evidence have shown that the magnetic field of CMEs reconnects with surrounding magnetic fields, forming, e.g., dimming regions distant from the CME source regions. Analyzing Solar Dynamics Observatory (SDO) observations of the eruption from AR 11226 on 2011 June 7, we present the first direct evidence of coronal magnetic reconnection between the fields of two adjacent ARs during a CME. The observations are presented jointly with a data-constrained numerical simulation, demonstrating the formation/intensification of current sheets along a hyperbolic flux tube (HFT) at the interface between the CME and the neighbouring AR 11227. Reconnection resulted in the formation of new magnetic connections between the erupting magnetic structure from AR 11226 and the neighboring active region AR 11227 about 200 Mm from the eruption site. The onset of reconnection first becomes apparent in the SDO/AIA images when filament plasma, originally contained within the erupting flux rope, is re-directed towards remote areas in AR 11227, tracing the change of large-scale magnetic connectivity. The location of the coronal reconnection region becomes bright and directly observable at SDO/AIA wavelengths, owing to the presence of down-flowing cool, dense (10^{10} cm^{-3}) filament plasma in its vicinity. The high-density plasma around the reconnection region is heated to coronal temperatures, presumably by slow-mode shocks and Coulomb collisions. These results provide the first direct observational evidence that CMEs reconnect with surrounding magnetic structures, leading to a large-scale re-configuration of the coronal magnetic field.Comment: 12 pages, 12 figure

Testing magnetofrictional extrapolation with the Titov-D\'emoulin model of solar active regions

We examine the nonlinear magnetofrictional extrapolation scheme using the solar active region model by Titov and D\'emoulin as test field. This model consists of an arched, line-tied current channel held in force-free equilibrium by the potential field of a bipolar flux distribution in the bottom boundary. A modified version, having a parabolic current density profile, is employed here. We find that the equilibrium is reconstructed with very high accuracy in a representative range of parameter space, using only the vector field in the bottom boundary as input. Structural features formed in the interface between the flux rope and the surrounding arcade-"hyperbolic flux tube" and "bald patch separatrix surface"-are reliably reproduced, as are the flux rope twist and the energy and helicity of the configuration. This demonstrates that force-free fields containing these basic structural elements of solar active regions can be obtained by extrapolation. The influence of the chosen initial condition on the accuracy of reconstruction is also addressed, confirming that the initial field that best matches the external potential field of the model quite naturally leads to the best reconstruction. Extrapolating the magnetogram of a Titov-D\'emoulin equilibrium in the unstable range of parameter space yields a sequence of two opposing evolutionary phases which clearly indicate the unstable nature of the configuration: a partial buildup of the flux rope with rising free energy is followed by destruction of the rope, losing most of the free energy.Comment: 14 pages, 10 figure

Measuring supermassive black holes with gas kinematics - II. The LINERs IC 989, NGC 5077, and NGC 6500

We present results from a kinematical study of the gas in the nucleus of a sample of three LINER galaxies, obtained from archival HST/STIS long-slit spectra. We found that, while for the elliptical galaxy NGC 5077, the observed velocity curves are consistent with gas in regular rotation around the galaxy's center, this is not the case for the two remaining objects. By modeling the surface brightness distribution and rotation curve from the emission lines in NGC 5077, we found that the observed kinematics of the circumnuclear gas can be accurately reproduced by adding to the stellar mass component a black hole mass of M_bh = 6.8 (-2.8,+4.3) 10**8 M_sun (uncertainties at a 1 sigma level); the radius of its sphere of influence (R_sph ~ 0".34) is well-resolved at the HST resolution. The BH mass estimate in NGC 5077 is in fairly good agreement with both the M_bh-M_bul (with an upward scatter of ~ 0.4 dex) and M_bh-sigma correlations (with an upward scatter of 0.5 dex in the Tremaine et al. form and essentially no scatter using the Ferrarese et al. form) and provides further support for the presence of a connection between the ``residuals'' from the M_bh-sigma correlation and the bulge effective radius. This indicates the presence of a black hole's ``fundamental plane'' in the sense that a combination of at least sigma and R_e drives the correlations between M_bh and host bulge properties.Comment: Accepted for publication in A&