An approximate self-consistent theory of the magnetic field of fluted penumbrae

A self-consistent mathematical description of the magnetic field of fluted sunspot penumbrae is presented. This description is based on an expansion of the nonlinear force-free magnetohydrostatic equations written in cylindrical coordinates. The lowest order solutions are mathematically equivalent to laminated force-free equilibria in Cartesian geometry. The lowest order solutions have no toroidal component of the magnetic field and the magnetic pressure does not vary with azimuth but the solutions allow arbitrary variations of the magnetic field components with azimuth. Explicit solutions are presented which have a realistic radial profile of the magnetic field strength and reproduce the basic features of the observations.Comment: 8 pages, 4 figures, accepted for publication in Astronomy and Astrophysic

Kinematics of coronal rain in a transversely oscillating loop : ponderomotive force and rain-excited oscillations

E.V. acknowledges support from the Warwick STFC Consolidated Grant ST/L000733/I. P.A. acknowledges support from the EU Horizon 2020 Research and Innovation programme (grant agreement No. 647214). P.K. acknowledges support from a UK STFC PhD studentship. T.N. acknowledges support from the St Andrews STFC Consolidated Grant SN/N000609/1.Context. Coronal rain are cool dense blobs that form in solar coronal loops and are a manifestation of catastrophic cooling linked to thermal instability. Once formed, rain falls towards the solar surface at sub-ballistic speeds, which is not well-understood. Pressure forces seem to be the prime candidate to explain this. In many observations rain is accompanied by transverse oscillations and the interaction between the two needs to be explored. Aims. Therefore, an alternative kinematic model for coronal rain kinematics in transversely oscillating loops is developed to understand the physical nature of the observed sub-ballistic falling motion of rain. It explicitly explores the role of the ponderomotive force arising from the transverse oscillation on the rain motion as well as the capacity of rain to excite wave motion. Methods. An analytical model is presented that describes a rain blob guided by the coronal magnetic field supporting a one dimensional shear Alfvén wave as a point mass on an oscillating string. The model includes gravity and the ponderomotive force from the oscillation acting on the mass, as well as the inertia of the mass acting on the oscillation. Results. The kinematics of rain in the limit of negligible rain mass are explored and falling and trapped regimes are found, depending on wave amplitude. In the trapped regime for the fundamental mode, the rain blob bounces back and forth around the loop top at a long period inversely proportional to the oscillation amplitude. The model is compared with several observational rain studies, including one in-depth comparison with an observation that shows rain with up-and down bobbing motion. The role of rain inertia in exciting transverse oscillations is explored in inclined loops. Conclusions. It is found that the model requires displacement amplitudes of the transverse oscillation that are typically an order of magnitude larger than observed to explain the measured sub-ballistic motion of the rain. Therefore, it is concluded that the ponderomotive force is not the primary reason for understanding sub-ballistic motion, but it plays a role in cases of large loop oscillations.The appearance of rain causes the excitation of small-amplitude transverse oscillations that may explain observed events and provide a seismological tool to measure rain mass.Publisher PDFPeer reviewe

Optimization approach for the computation of magnetohydrostatic coronal equilibria in spherical geometry

Context: This paper presents a method which can be used to calculate models of the global solar corona from observational data. Aims: We present an optimization method for computing nonlinear magnetohydrostatic equilibria in spherical geometry with the aim to obtain self-consistent solutions for the coronal magnetic field, the coronal plasma density and plasma pressure using observational data as input. Methods: Our code for the self-consistent computation of the coronal magnetic fields and the coronal plasma solves the non-force-free magnetohydrostatic equilibria using an optimization method. Previous versions of the code have been used to compute non-linear force-free coronal magnetic fields from photospheric measurements in Cartesian and spherical geometry, and magnetostatic-equilibria in Cartesian geometry. We test our code with the help of a known analytic 3D equilibrium solution of the magnetohydrostatic equations. The detailed comparison between the numerical calculations and the exact equilibrium solutions is made by using magnetic field line plots, plots of density and pressure and some of the usual quantitative numerical comparison measures. Results: We find that the method reconstructs the equilibrium accurately, with residual forces of the order of the discretisation error of the analytic solution. The correlation with the reference solution is better than 99.9% and the magnetic energy is computed accurately with an error of <0.1%. Conclusions: We applied the method so far to an analytic test case. We are planning to use this method with real observational data as input as soon as possible.Comment: 6 pages, 4 figure

Beiträge zur Physiologie des isolierten Säugetierherzens

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Getting DNA twist rigidity from single molecule experiments

We use an elastic rod model with contact to study the extension versus rotation diagrams of single supercoiled DNA molecules. We reproduce quantitatively the supercoiling response of overtwisted DNA and, using experimental data, we get an estimation of the effective supercoiling radius and of the twist rigidity of B-DNA. We find that unlike the bending rigidity, the twist rigidity of DNA seems to vary widely with the nature and concentration of the salt buffer in which it is immerged

Fine Selmer Groups and Isogeny Invariance

We investigate fine Selmer groups for elliptic curves and for Galois representations over a number field. More specifically, we discuss Conjecture A, which states that the fine Selmer group of an elliptic curve over the cyclotomic extension is a finitely generated $\mathbb{Z}_p$-module. The relationship between this conjecture and Iwasawa's classical $\mu=0$ conjecture is clarified. We also present some partial results towards the question whether Conjecture A is invariant under isogenies.Comment: 20 page

Representations of integers by certain positive definite binary quadratic forms

We prove part of a conjecture of Borwein and Choi concerning an estimate on the square of the number of solutions to n=x^2+Ny^2 for a squarefree integer N.Comment: 8 pages, submitte

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