Tables of the Line Broadening Function H(a,  )

Finn, G. D.; Mugglestone, D.

doi:10.1093/mnras/129.2.221

Cited by 64 publications

(8 citation statements)

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“…The additional calculation cost of terms is linear beyond the second term. Values from the process are compared against tables in Finn & Mugglestone (1965) and are seen to agree to the five significant figures used in saving values from our Fortran process: for a values 0 to 1 steps of 0.1 and for x values from 0 to 6 in steps of 0.5 and to a slightly lower, but tolerable accuracy for x from 6.5 to 15.…”

Section: 2: Particle Conservationmentioning

confidence: 75%

HYDRO2GEN: Non-thermal hydrogen Balmer and Paschen emission in solar flares generated by electron beams

Druett

Zharkova

2018

A&A

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Aims. Sharp rises of hard X-ray (HXR) emission accompanied by H↵ line profiles with strong red-shifts up to 4 Å from the central wavelength, often observed at the onset of flares with the Specola Solare Ticinese Telescope (STT) and the Swedish Solar Telescope (SST), are not fully explained by existing radiative models. Moreover, observations of white light (WL) and Balmer continuum emission with the Interface Region Imaging Spectrograph (IRIS) reveal strong co-temporal enhancements and are often nearly cospatial with HXR emission. These effects indicate a fast effective source of excitation and ionisation of hydrogen atoms in flaring atmospheres associated with HXR emission. In this paper we investigate electron beams as the agents accounting for the observed hydrogen line and continuum emission. Methods. Flaring atmospheres are considered to be produced by a 1D hydrodynamic response to the injection of an electron beam defining their kinetic temperatures, densities, and macro velocities. We simulated a radiative response in these atmospheres using a fully non-local thermodynamic equilibrium (NLTE) approach for a 5-level plus continuum hydrogen atom model, considering its excitation and ionisation by spontaneous, external, and internal diffusive radiation and by inelastic collisions with thermal and beam electrons. Simultaneous steady-state and integral radiative transfer equations in all optically thick transitions (Lyman and Balmer series) were solved iteratively for all the transitions to define their source functions with the relative accuracy of 10 5 . The solutions of the radiative transfer equations were found using the L2 approximation. Resulting intensities of hydrogen line and continuum emission were also calculated for Balmer and Paschen series. Results. We find that inelastic collisions with beam electrons strongly increase excitation and ionisation of hydrogen atoms from the chromosphere to photosphere. This leads to an increase in Lyman continuum radiation, which has high optical thickness, and after the beam is off it governs hydrogen ionisation and leads to the long lasting order of magnitude enhancement of emission in Balmer and Paschen continua. The ratio of Balmer-to-other-continuum head intensities are found to be correlated with the initial flux of the beam. The height distribution of contribution functions for Paschen continuum emission indicate a close correlation with the observations of heights of WL and HXR emission reported for limb flares. This process also leads to a strong increase of wing emission (Stark's wings) in Balmer and Paschen lines, which is superimposed on large red-shifted enhancements of H↵-H line emission resulting from a downward motion by hydrodynamic shocks. The simulated line profiles are shown to fit the observations for various flaring events closely.

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Section: 2: Particle Conservationmentioning

confidence: 75%

HYDRO2GEN: Non-thermal hydrogen Balmer and Paschen emission in solar flares generated by electron beams

Druett

Zharkova

2018

A&A

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“…6,19].) Numerical quadrature of the convolution integral can also be used [1,[20][21][22][23][24][25][26][27][28][29], but algorithms based on Gauss-Hermite quadrature [1,21,28,29] are confined to large arguments only and are therefore not considered as closed-form.…”

Section: Introductionmentioning

confidence: 99%

An assessment of some closed-form expressions for the Voigt function II: Utilizing rational approximations for the Gauss function

Schreier

2017

Journal of Quantitative Spectroscopy and Radiative Transfer

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Rational approximations for the Gauss function can be used to construct closedform expressions of the Voigt function K(x, y) in terms of rational functions, logarithms and inverse trigonometric functions. The comparison with accurate reference values indicates a relative accuracy in the percent range for y 1, but serious problems for smaller y. Furthermore, these expressions are not competitive with other algorithms with respect to computational speed. Both accuracy and speed tests indicate that supposedly "good" approximations of the integrand do not necessarily provide good approximations of the integral, i.e. Voigt function.

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“…The Voigt function has been described by Hjerting (1938) and tabulated by Harris (1948), Faddeyeva and Terentev (1961), Fried and Conte (1961), Finn and Mugglestone (1965), and Hummer (1965). Computer programs to calculate the Voigt function have been described by Young (1965) and Armstrong (1967), who also reviewed its mathematical properties.…”

Section: Doppler Broadeningmentioning

confidence: 99%