Radiative transfer in cylindrical threads with incident radiation. VII. Multi-thread models

Aims. Our aim is to improve on previous radiative transfer calculations in illuminated cylindrical threads in order to better understand the physical conditions in cool solar chromospheric and coronal structures commonly observed in hydrogen and helium lines. Methods. We solve the radiative transfer and statistical equilibrium equations in a two-dimensional cross-section of a cylindrical structure oriented horizontally and lying above the solar surface. The cylinder is filled with a mixture of hydrogen and helium, and is illuminated at a given altitude from the solar disc. We construct simple models made from a single thread, or from an ensemble of several threads along the line of sight. This first use of 2D multi-thread fine structure modelling combining hydrogen and helium radiative transfer allows us to compute synthetic emergent spectra from cylindrical structures and to study the effect of line-of-sight integration of an ensemble of threads under a range of physical conditions. We analyse the effects of variations in temperature distribution and in gas pressure.We consider the effect of multi-thread structures within a given field of view and the effect of peculiar velocities between the structures in a multi-thread model. These new models are compared to the single thread model, and tested with varying parameters. Results. The presence of a temperature gradient, with temperature increasing towards the edge of the cylindrical thread, reduces the relative importance of the incident radiation coming from the solar disc on the emergent intensities of most hydrogen and helium lines. We also find that when assuming randomly displaced threads in a given field of view, the integrated intensities of optically thick and thin transitions behave considerably differently. In optically thin lines, the emergent intensity increases proportionally with the number of threads, and the spatial variation of the intensity becomes increasingly homogeneous. Optically thick lines however saturate after only a few threads. As a consequence, the spatial variation of the intensity retains much similarity with that of the first few threads. The multi-thread model produces complex line profiles with significant asymmetries if randomly generated line-of-sight velocities are added for each thread. Conclusions. These new computations show for the first time the effect of integrating the radiation emitted in H and He lines by several cylindrical threads static or moving along the line of sight. They can be used to interpret high-spatial and spectral resolutions of cylindrical structures found in the solar atmosphere, such as cool coronal loops or prominence threads

Solar prominence modelling and plasma diagnostics at ALMA wavelengths

Our aim is to test potential solar prominence plasma diagnostics as obtained with the new solar capability of the Atacama Large Millimeter / submillimeter Array (ALMA). We investigate the thermal and plasma diagnostic potential of ALMA for solar prominences through the computation of brightness temperatures at ALMA wavelengths. The brightness temperature, for a chosen line of sight, is calculated using densities of hydrogen and helium obtained from a radiative transfer code under non local thermodynamic equilibrium (NLTE) conditions, as well as the input internal parameters of the prominence model in consideration. Two distinct sets of prominence models were used: isothermal-isobaric fine-structure threads, and large-scale structures with radially increasing temperature distributions representing the prominence-to-corona transition region. We compute brightness temperatures over the range of wavelengths in which ALMA is capable of observing (0.32 - 9.6mm), however we particularly focus on the bands available to solar observers in ALMA cycles 4 and 5, namely 2.6 - 3.6mm (Band 3) and 1.1 - 1.4mm (Band 6). We show how the computed brightness temperatures and optical thicknesses in our models vary with the plasma parameters (temperature and pressure) and the wavelength of observation. We then study how ALMA observables such as the ratio of brightness temperatures at two frequencies can be used to estimate the optical thickness and the emission measure for isothermal and non-isothermal prominences. From this study we conclude that, for both sets of models, ALMA presents a strong thermal diagnostic capability, provided that the interpretation of observations is supported by the use of non-LTE simulation results.Comment: Submitted to Solar Physic

Earth's Inner Core dynamics induced by the Lorentz force

Seismic studies indicate that the Earth's inner core has a complex structure and exhibits a strong elastic anisotropy with a cylindrical symmetry. Among the various models which have been proposed to explain this anisotropy, one class of models considers the effect of the Lorentz force associated with the magnetic field diffused within the inner core. In this paper we extend previous studies and use analytical calculations and numerical simulations to predict the geometry and strength of the flow induced by the poloidal component of the Lorentz force in a neutrally or stably stratified growing inner core, exploring also the effect of different types of boundary conditions at the inner core boundary (ICB). Unlike previous studies, we show that the boundary condition that is most likely to produce a significant deformation and seismic anisotropy is impermeable, with negligible radial flow through the boundary. Exact analytical solutions are found in the case of a negligible effect of buoyancy forces in the inner core (neutral stratification), while numerical simulations are used to investigate the case of stable stratification. In this situation, the flow induced by the Lorentz force is found to be localized in a shear layer below the ICB, which thickness depends on the strength of the stratification, but not on the magnetic field strength. We obtain scaling laws for the thickness of this layer, as well as for the flow velocity and strain rate in this shear layer as a function of the control parameters, which include the magnitude of the magnetic field, the strength of the density stratification, the viscosity of the inner core, and the growth rate of the inner core. We find that the resulting strain rate is probably too small to produce significant texturing unless the inner core viscosity is smaller than about $10^{12}$ Pa.s.Comment: submitted to Geophysical Journal Internationa

Geophysically consistent values of the perovskite to post-perovskite transition Clapeyron slope

International audienceThe doublecrossing hypothesis posits that post-perovskite bearing rock in Earth's D 00 layer exists as a layer above the core-mantle boundary bounded above and below by intersections between a curved thermal boundary layer geotherm and a relatively steep phase boundary. Increasing seismic evidence for the existence of pairs of discontinuities predicted to occur at the top and bottom of this layer motivates an examination of the consistency of this model with mineral physics constraints for the Clapeyron slope of this phase transition. Using independent constraints for a lower bound on temperature in Earth's deep mantle and the temperature of Earth's inner core boundary, we show that a post-perovskite doublecrossing is inconsistent with plausible core temperatures for a Clapeyron slope less than about 7 MPa/K, with the higher range of experimental values yielding better agreement with recent estimates of the melting temperature of Earth's core

Upper bound of heat flux in an anelastic model for Rayleigh-B\'enard convection

Bounds on heat transfer have been the subject of previous studies concerning convection in the Boussinesq approximation: in the Rayleigh-B\'enard configuration, the first result obtained by \cite{howard63} states that $Nu < (3/64 \ Ra)^{1/2}$ for large values of the Rayleigh number $Ra$, independently of the Prandtl number $Pr$. This is still the best known upper bound, only with the prefactor improved to $Nu < 1/6 \ Ra^{1/2}$ by \cite{DoeringConstantin96}. In the present paper, this result is extended to compressible convection. An upper bound is obtained for the anelastic liquid approximation, which is similar to the anelastic model used in astrophysics based on a turbulent diffusivity for entropy. The anelastic bound is still scaling as $Ra^{1/2}$, independently of $Pr$, but depends on the dissipation number $\mathcal{D}$ and on the equation of state. For monatomic gases and large Rayleigh numbers, the bound is $Nu < 146\, Ra^{\frac{1}{2}} / (2-\mathcal{D} )^{\frac{5}{2}}$.Comment: 12 pages, 1 figur

Solar prominence diagnostic with hinode/EIS

No abstract available

Modeling of the hydrogen Lyman lines in solar flares

The hydrogen Lyman lines (91.2 nm &lt; λ &lt; 121.6 nm) are significant contributors to the radiative losses of the solar chromosphere, and they are enhanced during flares. We have shown previously that the Lyman lines observed by the Extreme Ultraviolet Variability instrument onboard the Solar Dynamics Observatory exhibit Doppler motions equivalent to speeds on the order of 30 km s−1. However, contrary to expectations, both redshifts and blueshifts were present and no dominant flow direction was observed. To understand the formation of the Lyman lines, particularly their Doppler motions, we have used the radiative hydrodynamic code, RADYN, along with the radiative transfer code, RH, to simulate the evolution of the flaring chromosphere and the response of the Lyman lines during solar flares. We find that upflows in the simulated atmospheres lead to blueshifts in the line cores, which exhibit central reversals. We then model the effects of the instrument on the profiles, using the Extreme Ultraviolet Variability Experiment (EVE) instrument's properties. What may be interpreted as downflows (redshifted emission) in the lines, after they have been convolved with the instrumental line profile, may not necessarily correspond to actual downflows. Dynamic features in the atmosphere can introduce complex features in the line profiles that will not be detected by instruments with the spectral resolution of EVE, but which leave more of a signature at the resolution of the Spectral Investigation of the Coronal Environment instrument onboard the Solar Orbiter

Visibility of prominences using the He i D3 line filter on PROBA-3/ASPIICS coronagraph

We determine the optimal width and shape of the narrow-band filter centered on the He i D3 line for prominence and coronal mass ejection (CME) observations with the ASPIICS (Association of Spacecraft for Polarimetric and Imaging Investigation of the Corona of the Sun) coronagraph onboard the PROBA-3 (Project for On-board Autonomy) satellite, to be launched in 2020. We analyze He i D3 line intensities for three representative non-local thermal equilibrium prominence models at temperatures 8, 30, and 100 kK computed with a radiative transfer code and the prominence visible-light (VL) emission due to Thomson scattering on the prominence electrons. We compute various useful relations at prominence line-of-sight velocities of 0, 100, and 300 km s−1 for 20 Å wide flat filter and three Gaussian filters with a full-width at half-maximum (FWHM) equal to 5, 10, and 20 Å to show the relative brightness contribution of the He i D3 line and the prominence VL to the visibility in a given narrow-band filter. We also discuss possible signal contamination by Na i D1 and D2 lines, which otherwise may be useful to detect comets. Our results mainly show that i) an optimal narrow-band filter should be flat or somewhere between flat and Gaussian with an FWHM of 20 Å in order to detect fast-moving prominence structures, ii) the maximum emission in the He i D3 line is at 30 kK and the minimal at 100 kK, and iii) the ratio of emission in the He i D3 line to the VL emission can provide a useful diagnostic for the temperature of prominence structures. This ratio is up to 10 for hot prominence structures, up to 100 for cool structures, and up to 1000 for warm structures