Plasma diagnostic of a solar prominence from hydrogen and helium resonance lines

We present the first comparison of profiles of H et He resonance lines observed by SUMER with theoretical profiles computed with our non-LTE radiative transfer code. We use the H I Lyman-beta, H I Lyman-epsilon, and He I 584 A lines. Our code allows us to obtain the plasma parameters in prominences in conjunction with a multi-line, multi-element set of observations. The plasma temperature in the prominence core is ~ 8600 K and the pressure is 0.03 dyn/cm^2. The Ly-beta line is formed in a higher temperature region (more than 11000 K).Comment: 2 pages, 2 color figures. Proceedings of SF2A, Semaine de l'Astrophysique Francaise, Journees de la SF2A 2006, Pari

Effect of motions in prominences on the helium resonance lines in the extreme ultraviolet

<b>Context</b>: Extreme ultraviolet resonance lines of neutral and ionised helium observed in prominences are difficult to interpret as the prominence plasma is optically thick at these wavelengths. If mass motions are taking place, as is the case in active and eruptive prominences, the diagnostic is even more complex. <b>Aims</b>: We aim at studying the effect of radial motions on the spectrum emitted by moving prominences in the helium resonance lines and at facilitating the interpretation of observations, in order to improve our understanding of these dynamic structures. <b>Methods</b>: We develop our non-local thermodynamic equilibrium radiative transfer code formerly used for the study of quiescent prominences. The new numerical code is now able to solve the statistical equilibrium and radiative transfer equations in the non-static case by using velocity-dependent boundary conditions for the solution of the radiative transfer problem. This first study investigates the effects of different physical conditions (temperature, pressure, geometrical thickness) on the emergent helium radiation. <b>Results</b>: The motion of the prominence plasma induces a Doppler dimming effect on the resonance lines of HE i and HE ii. The velocity effects are particularly important for the HE ii λ 304 Å line as it is mostly formed by resonant diffusion of incident radiation under prominence conditions. The HE i resonance lines at 584 and 537 Å also show some sensitivity to the motion of the plasma, all the more when thermal emission is not too important in these lines. We also show that it is necessary to consider partial redistribution in frequency for the scattering of the incident radiation. Conclusions.This set of helium lines offers strong diagnostic possibilities that can be exploited with the SOHO spectrometers and with the EIS spectrometer on board the Hinode satellite. The addition of other helium lines and of lines from other elements (in particular hydrogen) in the diagnostics will further enhance the strength of the method

Exceptional collections, and the Néron–Severi lattice for surfaces

We work out properties of smooth projective varieties X over a (not necessarily algebraically closed) field $\textit{k}$ that admit collections of objects in the bounded derived category of coherent sheaves D$^{b}$(X) that are either full exceptional, or numerically exceptional of maximal length. Our main result gives a necessary and sufficient condition on the Néron–Severi lattice for a smooth projective surface S with χ(O$_{S}$)=1 to admit a numerically exceptional collection of maximal length, consisting of line-bundles. As a consequence we determine exactly which complex surfaces with p$_{g}$=q=0 admit a numerically exceptional collection of maximal length. Another consequence is that a minimal geometrically rational surface with a numerically exceptional collection of maximal length is rational.The author was supported by the Fund for Mathematics at the Institute for Advanced Study and by EPSRC Early Career Fellowship EP/K005545/1

On the motive of some hyperKähler varieties

We show that the motive of the Hilbert scheme of length-$n$ subschemes on a K3 surface or on an abelian surface admits a decomposition similar to the decomposition of the motive of an abelian variety obtained by Shermenev, Beauville, and Deninger and Murre.The author is supported by EPSRC Early Career Fellowship number EP/K005545/1.This is the final version of the article. It first appeared from De Gruyter at http://dx.doi.org/10.1515/crelle-2015-000

Partial redistribution effects in the formation of hydrogen lines in quiescent prominences

Departures from complete frequency redistribution (CRD) in hydrogen lines are investigated for solar prominences. Partial redistribution effects (PRD) are found both in the wings (their already known lowering) and in the central part of the L alpha line; a new feature is evidenced here: the partially coherent scattering in the near wings of the line leads to a double-peaked profile mirroring the incident solar radiation. With a low density model, we obtain a good agreement with OSO 8 observed profiles. On the contrary, the PRD computed L beta profile (lower density, no reversal) departs from the observed one, a result which calls for more progress in terms of non-LTE transfer and modelling

Diagnostics of active and eruptive prominences through hydrogen and helium lines modelling

In this study we show how hydrogen and helium lines modelling can be used to make a diagnostic of active and eruptive prominences. One motivation for this work is to identify the physical conditions during prominence activation and eruption. Hydrogen and helium lines are key in probing different parts of the prominence structure and inferring the plasma parameters. However, the interpretation of observations, being either spectroscopic or obtained with imaging, is not straightforward. Their resonance lines are optically thick, and the prominence plasma is out of local thermodynamic equilibrium due to the strong incident radiation coming from the solar disk. In view of the shift of the incident radiation occurring when the prominence plasma flows radially, it is essential to take into account velocity fields in the prominence diagnostic. Therefore we need to investigate the effects of the radial motion of the prominence plasma on hydrogen and helium lines. The method that we use is the resolution of the radiative transfer problem in the hydrogen and helium lines out of local thermodynamic equilibrium. We study the variation of the computed integrated intensities in H and He lines with the radial velocity of the prominence plasma. We can confirm that there exist suitable lines which can be used to make a diagnostic of the plasma in active and eruptive prominences in the presence of velocity fields.Comment: 5 pages, 4 colour figure

IRIS Observations of Spicules and Structures Near the Solar Limb

We have analyzed IRIS spectral and slit-jaw observations of a quiet region near the South Pole. In this article we present an overview of the observations, the corrections, and the absolute calibration of the intensity. We focus on the average profiles of strong (Mg ii h and k, C ii and Si iv), as well as of weak spectral lines in the near ultraviolet (NUV) and the far ultraviolet (FUV), including the Mg ii triplet, thus probing the solar atmosphere from the low chromosphere to the transition region. We give the radial variation of bulk spectral parameters as well as line ratios and turbulent velocities. We present measurements of the formation height in lines and in the NUV continuum, from which we find a linear relationship between the position of the limb and the intensity scale height. We also find that low forming lines, such as the Mg ii triplet, show no temporal variations above the limb associated with spicules, suggesting that such lines are formed in a homogeneous atmospheric layer and, possibly, that spicules are formed above the height of 2 arc sec. We discuss the spatio-temporal structure near the limb from images of intensity as a function of position and time. In these images, we identify p-mode oscillations in the cores of lines formed at low heights above the photosphere, slow moving bright features in O i and fast moving bright features in C ii. Finally, we compare the Mg ii k and h line profiles, together with intensity values of the Balmer lines from the literature, with computations from the PROM57Mg non-LTE model developed at the Institut d'Astrophysique Spatiale and estimated values of the physical parameters. We obtain electron temperatures in the range of $\sim8000$ K at small heights to $\sim20000$ K at large heights, electron densities from $1.1 \times 10^{11}$ to $4 \times 10^{10}$ cm$^{-3}$ and a turbulent velocity of $\sim24$km/s.Comment: Accepted for publication in Solar Physic

The fourier transform for certain HyperKähler fourfolds

Using a codimension-$1$ algebraic cycle obtained from the Poincar\'e line bundle, Beauville defined the Fourier transform on the Chow groups of an abelian variety $A$ and showed that the Fourier transform induces a decomposition of the Chow ring $CH^*(A)$. By using a codimension-$2$ algebraic cycle representing the Beauville--Bogomolov class, we give evidence for the existence of a similar decomposition for the Chow ring of hyperK\"ahler varieties deformation equivalent to the Hilbert scheme of length-$2$ subschemes on a K3 surface. We indeed establish the existence of such a decomposition for the Hilbert scheme of length-$2$ subschemes on a K3 surface and for the variety of lines on a very general cubic fourfold.The first author is supported by the Simons Foundation as a Simons Postdoctoral Fellow. The second author is supported by EPSRC Early Career Fellowship number EP/K005545/1.This is the author accepted manuscript. The final version is available from the American Mathematical Sociery via http://dx.doi.org/10.1090/memo/113

Solving the p -Median Problem with a Semi-Lagrangian Relaxation

Lagrangian relaxation is commonly used in combinatorial optimization to generate lower bounds for a minimization problem. We study a modified Lagrangian relaxation which generates an optimal integer solution. We call it semi-Lagrangian relaxation and illustrate its practical value by solving large-scale instances of the p-median proble