Shock location and CME 3D reconstruction of a solar type II radio burst with LOFAR

Context. Type II radio bursts are evidence of shocks in the solar atmosphere and inner heliosphere that emit radio waves ranging from sub-meter to kilometer lengths. These shocks may be associated with coronal mass ejections (CMEs) and reach speeds higher than the local magnetosonic speed. Radio imaging of decameter wavelengths (20–90 MHz) is now possible with the Low Frequency Array (LOFAR), opening a new radio window in which to study coronal shocks that leave the inner solar corona and enter the interplanetary medium and to understand their association with CMEs. Aims. To this end, we study a coronal shock associated with a CME and type II radio burst to determine the locations at which the radio emission is generated, and we investigate the origin of the band-splitting phenomenon. Methods. Thetype II shock source-positions and spectra were obtained using 91 simultaneous tied-array beams of LOFAR, and the CME was observed by the Large Angle and Spectrometric Coronagraph (LASCO) on board the Solar and Heliospheric Observatory (SOHO) and by the COR2A coronagraph of the SECCHI instruments on board the Solar Terrestrial Relation Observatory(STEREO). The 3D structure was inferred using triangulation of the coronographic observations. Coronal magnetic fields were obtained from a 3D magnetohydrodynamics (MHD) polytropic model using the photospheric fields measured by the Heliospheric Imager (HMI) on board the Solar Dynamic Observatory (SDO) as lower boundary. Results. The type II radio source of the coronal shock observed between 50 and 70 MHz was found to be located at the expanding flank of the CME, where the shock geometry is quasi-perpendicular with θBn ~ 70°. The type II radio burst showed first and second harmonic emission; the second harmonic source was cospatial with the first harmonic source to within the observational uncertainty. This suggests that radio wave propagation does not alter the apparent location of the harmonic source. The sources of the two split bands were also found to be cospatial within the observational uncertainty, in agreement with the interpretation that split bands are simultaneous radio emission from upstream and downstream of the shock front. The fast magnetosonic Mach number derived from this interpretation was found to lie in the range 1.3–1.5. The fast magnetosonic Mach numbers derived from modelling the CME and the coronal magnetic field around the type II source were found to lie in the range 1.4–1.6

Studies of a nickel-based single molecule magnet: resonant quantum tunnelling in an S = 12 molecule

A cyclic dodecanuclear nickel complex is the first single molecule magnet based on nickel(II) centres; the material is also the highest spin molecule to show resonant quantum tunnelling of magnetisation

LOFAR tied-array imaging of Type III solar radio bursts

Context:\ud The Sun is an active source of radio emission which is often associated with energetic phenomena such as solar flares and coronal mass ejections (CMEs). At low radio frequencies (<100 MHz), the Sun has not been imaged extensively because of the instrumental limitations of previous radio telescopes. \ud \ud Aims:\ud Here, the combined high spatial, spectral, and temporal resolution of the LOw Frequency ARray (LOFAR) was used to study solar Type III radio bursts at 30–90 MHz and their association with CMEs.\ud \ud Methods:\ud The Sun was imaged with 126 simultaneous tied-array beams within ≤5 R⊙ of the solar centre. This method offers benefits over standard interferometric imaging since each beam produces high temporal (~83 ms) and spectral resolution (12.5 kHz) dynamic spectra at an array of spatial locations centred on the Sun. LOFAR’s standard interferometric output is currently limited to one image per second. \ud \ud Results:\ud Over a period of 30 min, multiple Type III radio bursts were observed, a number of which were found to be located at high altitudes (~4 R⊙ from the solar center at 30 MHz) and to have non-radial trajectories. These bursts occurred at altitudes in excess of values predicted by 1D radial electron density models. The non-radial high altitude Type III bursts were found to be associated with the expanding flank of a CME. \ud \ud Conclusions:\ud The CME may have compressed neighbouring streamer plasma producing larger electron densities at high altitudes, while the non-radial burst trajectories can be explained by the deflection of radial magnetic fields as the CME expanded in the low corona

Copula Theory: An Introduction

Abstract In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have been applie

Copula theory: an introduction

In this survey we review the most important properties of copulas, several families of copulas that have appeared in the literature, and which have been applied in various fields, and several methods of constructing multivariate copulas