Theory Of Line Formation Research Articles

Molecular spectroscopy of planetary atmospheres

Clearly spectroscopy has already provided considerable insight into the nature of the planetary atmospheres. Several molecular constituents have been positively identified and upper limits have been placed on the abundances of others which are of particular significance in devising planetary models. But, equally clearly, the inadequacy of the spectral data, due to low spectral and/or spatial resolution, renders deductions of abundances, temperatures and pressures very uncertain. With the sole exception of the Martian CO2 abundance, knowledge of the concentrations of planetary atmospheric constituents is unsatisfactory, and all numbers given must be regarded as only crude estimates. This latter comment applies equally well to the derived temperatures and pressures. What is urgently needed is the development of a reasonably complete theory of line formation in planetary atmospheres. This, coupled with more detailed spectroscopic work, should produce numerical values of atmospheric parameters which can be used with assurance.

The Solar Lyman-Alpha Emission Line.

The Jefferies and Thomas theory of line formation by non-coherent scattering in a non-equilibrium chromosphere is applied to the solar Lyman- alpha profiles recently photographed by a rocket spectrograph. A Planck function decreasing exponentially with increasing optical depth is assumed for the electron-temperature distribution. The theory successfully accounts for the cores of the observed profiles with their two peaks separated by shallow reversals, but the predicted wings always fall off too sharply. The depths of the reversals show that the line originates in the regions of steepest temperature gradient. The separations of the peaks suggest electron temperatures of 70,000 deg K for the plages and 90,000 deg K for the surrounding darker areas. The absolute intensities require electron densities ranging from 3 x 10/sup 10/ to 2 x 10/sup 9/ cm-/sup 3/ for these respective regions. (auth)

Spectral and Angular Distribution of Cyclotron Radiation Emitted by Colliding Particles

An attempt is made to describe the cyclotron radiation of colliding particles in close analogy to optical theory of line formation. If the velocities are small compared with the velocity of light and the collision frequency is not too high, simple expressions are derived for the frequency and angular distribution of the radiation in terms of the basic physical properties of the plasma, such as temperature, density, and collision parameters.

The Atmospheres of the B Stars. III. The Composition of Tau Scorpii.

New measurements of line intensities in the spectrum of r Scorp , based on coude' plates secured at the Mount Wilson and McDonald Ohservatories, are discussed with the aid of a model atmosphere and Pecker's theory for medium-strong lines. The computational procedures are described in detail, with a view to their application to other stellar atmospheres. he abundances derived differ from those and by Traving for three reasons: (1) the newer equivalent widths differ systematically from those found with the older McDonald spectrographs; (2) a slightly different model atmosphere is employed; and (3) a precise theory of line formation is utilized. Different ions of the same element yield different curves of growth, whereas lines formed in the same layers tend to have similar curves of growth. The agreement between theory and observation is improved with the aid of a differential correction to the model atmosphere, but all ions of all elements cannot be equally well represented by the same model atmosphere. The largest uncertainties appear to come from poor f-values. Helium, carbon, nitrogen, oxygen, and silicon are observed in two stages of ionization; other elements are observed in only one stage of ionization.

The composition of τ Scorpii.

view Abstract Citations (5) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The composition of τ Scorpii. Aller, L. H. ; Elste, G. ; Jugaku, J. Abstract Measurements of line intensities in the spectrum of r Scorpii are discussed with th~ aid of a model atmosphere and Pecker's theory for lines of medium strength. The abundances derived differ from those found by Unsold and by Traving for three reasons: (i) the newer equivalent widths are systematically smaller, (2) a slightly different model atmosphere is employed, and (3) a precise theory of line formation is utilized. As has been noted previously for silicon, different ions of the same element have different curves of growth. This effect is strikingly exhibited in ~ Pegasi where silicon is observed in three stages of ionization. Differential corrections may be applied when the model does not quite represent the observations. The largest uncertainties arise from poor J-values. The abundance of helium is particularly difficult to establish because of uncertainties in the line-broadening theory and in the damping constants. The abundances of the heavier elements, expressed as log NeIern~t~Nhydr0g~, are as follows: Carbon' -4.3 Neon -3.14 Nitrogen -3.74 Magnesium - 3.7 Oxygen -3.37 Aluminum -5.6 Silicon -4.37 Helium, carbon, nitrogen, oxygen, and silicon are observed in two stages of ionization; other elements are observed in only one stage of ionization. The Observatory, University of i~Iichigan, Ann Arbor, AIThh. Publication: The Astronomical Journal Pub Date: 1957 DOI: 10.1086/107603 Bibcode: 1957AJ.....62R...2A full text sources ADS | data products SIMBAD (4)

THEORETICAL LINE INTENSITIES AND THE SPECTRUM OF TAU SCORPII

The labor involved in the determination of the physical state and chemical composition of a stellar atmosphere from a precise theoretical interpretation of its observed spectrum is considerable. Frequently, approximate procedures, such as the curve of growth, have been used in place of more exact methods. Some writers, particularly Unsold, have argued that the curve of growth procedure is sufficiently accurate. The analysis of Unsold's data for t Scorpii by Traving1 shows that the technique of a model atmosphere used with an approximate formula for the shape of a spectral line gives results that agree with those from the curve of growth. The question as to what happens if one uses a precise theory of line formation remains to be studied. In our analysis of the spectrum of t Scorpii we have adopted the same temperature distribution as that given by Traving, but have assumed log # = 4. 30, whereas Traving chose log ?7 = 4 . 80, a value which is much higher than those deduced from the data of eclipsing binaries. The pressure distribution therefore differs from that in Traving's model. We did not check the new model for constancy of flux. The error made by neglecting the Lyman lines is greater than any error introduced by a slight change in the surface gravity.2 Figure 1 compares the observed and computed profile of the hydrogen line Hy. The observational data come from coude plates obtained at the Mount Wilson and McDonald observatories. The mean profiles obtained from the two spectrographs are in excellent agreement. The theoretical profiles are those of Traving, who used the Holtsmark theory and log g = 4 . 8, the profile by the Holtsmark theory for log g = 4 . 30, and finally the Kolb theory profile for logg = 4.30. The Kolb theory3 takes into account the contributions of the electrons and the influence of the ionic motions, but it -neglects nonadiabatic effects. Kolb estimates that the correct theoretical line profile may be even

Coherent and Non-coherent Scattering in the Theory of Line Formation

When the scattering of light is coherent, the exact solution of the problem of line formation in the Milne–Eddington model, with a linear Planck function |${B}_{\nu}\,=\,{{b}_{\nu}}^{(0)}\,+\,{{b}_{\nu}}^{(1)}\,{\tau}_{\nu}$| , has been given by Chandrasekhar. In Section 2 this solution is found by a new method, and in Sections 3–5 the method is used to solve the parallel problem when the scattering of light is completely non-coherent. This solution is exact when |${{b}_{\nu}}^{(0)}$| and |${k}_{\nu}\,{{b}_{v}}^{(1)}$| are independent of the frequency ν and the depth z , K v being the continuous absorption coefficient. The solution agrees with that found by Sobolev for the case |${k}_{\nu}={k},\,{{b}_{\nu}}^{(0)}=B,\,{{b}_{\nu}}^{(1)}=0$| . In Sections 6–8 the magnitudes of the terms appearing in the solution are discussed. Sobolev's assertion that the resulting central intensities of absorption lines are much lighter than those found on the hypothesis of coherent scattering is shown to be true for lines at the limb. No definite conclusions can be drawn for other lines until the H -functions involved have been computed, but the same result is likely to hold.