Force-free twisted magnetospheres of neutron stars

Context. The X-ray spectra observed in the persistent emission of magnetars are evidence for the existence of a magnetosphere. The high-energy part of the spectra is explained by resonant cyclotron upscattering of soft thermal photons in a twisted magnetosphere, which has motivated an increasing number of efforts to improve and generalize existing magnetosphere models. Aims. We want to build more general configurations of twisted, force-free magnetospheres as a first step to understanding the role played by the magnetic field geometry in the observed spectra. Methods. First we reviewed and extended previous analytical works to assess the viability and limitations of semi-analytical approaches. Second, we built a numerical code able to relax an initial configuration of a nonrotating magnetosphere to a force-free geometry, provided any arbitrary form of the magnetic field at the star surface. The numerical code is based on a finite-difference time-domain, divergence-free, and conservative scheme, based of the magneto-frictional method used in other scenarios. Results. We obtain new numerical configurations of twisted magnetospheres, with distributions of twist and currents that differ from previous analytical solutions. The range of global twist of the new family of solutions is similar to the existing semi-analytical models (up to some radians), but the achieved geometry may be quite different. Conclusions. The geometry of twisted, force-free magnetospheres shows a wider variety of possibilities than previously considered. This has implications for the observed spectra and opens the possibility of implementing alternative models in simulations of radiative transfer aiming at providing spectra to be compared with observations.

NHC-Ligand Effectiveness in the Fluorine-Free Hiyama Reaction of Aryl Halides

1-Benzyl-3-(2-hydroxy-2-phenylethyl)imidazolium chloride (5), which is a precursor of an N-heterocyclic carbene ligand, in combination with palladium acetate, has been employed as an effective catalyst for the fluorine-free Hiyama reaction. A systematic study of the catalytic mixture, by a 32 factorial design, has revealed that both the amount of palladium and the Pd/NHC precursor ratio are important factors for obtaining good yields of the coupling products, indicating an interaction between them. The best catalytic system involves mixing 0.1 mol-% palladium acetate in a 1:5 ratio (Pd/salt 5), which allows the effective coupling of a range of aryl bromides and chlorides with trimethoxy(phenyl)silane. The Hiyama reactions are carried out in NaOH solution (50 % H2O w/w), at 120 °C under microwave irradiation during 60 min.

1,2-Functionalized Imidazoles as Palladium Ligands: An Efficient and Robust Catalytic System for the Fluorine-Free Hiyama Reaction

A variety of hydroxy- and amino-functionalized imidazoles were prepared from 1-methyl- and 1-(diethoxymethyl)imidazole by means of isoprene-mediated lithiation followed by reaction with an electrophile. These compounds in combination with palladium acetate were screened as catalyst systems for the Hiyama reaction under fluorine-free conditions using microwave irradiation. The systematic study of the catalytic system showed 1-methyl-2-aminoalkylimidazole derivative L1 to be the best ligand, which was employed under solvent-free conditions with a 1:2 Pd/ligand ratio and TBAB (20 mol-%) as additive. The study has revealed an interaction between the Pd/ligand ratio and the amount of TBAB. The established catalytic system presented a certain degree of robustness, and it has been successfully employed in the coupling of a range of aryl bromides and chlorides with different aryl siloxanes. Furthermore, both reagents were employed in an equimolecular amount, without an excess of organosilane.