An Interpretation of the Heights of Lines in the Solar Chromosphere.
Abstract
General theory-The heights of different emission lines in the chromosphere, estimated from slitless flash spectrograms taken on a stationaryplate, depend on the total number of emitting atoms contained in a column along the line of sight, on the threshold sensitivity of the photographic emulsion, and on the transparency of the earth's atmosphere and of the optical system. Theoretical intensitis of a group of related lines originating from the same element are plotted against the estimated heights, H, and this plot is represented by a continuous function, E(H). The transformation of E(H) into the spatial density of the emitting atoms would be a straight problem of geometry if it were not for the interference of two physical effects introduced by the process of observation. First, the extra-terrestrial surface brightness of the chromosphere is distorted by atmospheric scintilla- tion,which produces a tremor disk around every surface element of the chromosophere as it appears in pro- jection. Second, since during the photographic exposure the moon covers, or uncovers, part of the lower chromosphere, the light emitted at different levels is recorded with different exposure times; and, for lack of optical resolving-power, the chromospheric crescents portrayed on a flash spectrogram are an aggregate of superimposed images taken with varying exposure times. The correction of the observed function E(H), obtained with a finite exposure time, to an infinitesimally short exposure, as it were, requires the solution of a certain integral equation, which can be effected simply by refrated differentia- tion. The resulting function,f(H), can then be freed from the distortion by scintillation, which proves to be numerically insignificant. This procedure has been applied to the comprehensive list of heights of flash lines estimated by S. A. MitcJiell. Density gradients-The radial decay of the density of hydrogen in the chromosphere is strictly expo- nential up to heights of the order of 15,000 km, numerically proportional to exp (-0.92 X 10-8 cm' H); the density gradients derived from the Balmer and the Paschen series are in good agreement. The same density gradient of hydrogen results from a comparison of the electron density at the base of the çhromo- sphere with that at the elevation of 15,000 km, deduced by Baumbach from the absolute intensity of the continuous spectrum of the solar corona, because the free electrons are nearly all produced by the ionization of hydrogen, by far the most abundant element in the solar atmosphere. The density laws of the metals can be represented as a sum of two or three exponentials. At heights less than 2000 km, their gradients are much steeper than that of hydrogen: but between 3000 and 6000 km they seem to approach the hydrogen gradient. The density gradients of Fe i and Fe ii are compatible with the existence of ionization equilibrium with constant temperature throughout the chromosphere. Excitation temperatures for Fe i and Ti ii are of the order of 30000_40000 K and increase with increasing excitation potentials. The density gradient of He i between 2000 and 6000 km is about one-quarter of that of hydrogen; the observations do not yield any confirmation of the density maximum of He i below the 2000 km claimed by other investigators. A bsolute densities.-On the Teller-Inglis theory, the quantum number (n = 40) of the last resolved member of the Paschen series implies an electron pressure of 0.11 dynes/cm-2 at the level H = 500 km. From this figure the partial pressure of hydrogen can be found if the abundance ratio, A, of hydrogen to all the electron-producing metals is known. Relative abundances of Na, Mg, Al, Ca, Fe, Cu, and Sr in the chromosphere are derived from the estimated heights and from absolute transition probabilities; these ratios agree quite well with those found by Russell from the Fraunhofer spectrum. While the chromosphere appears to be well mixed as regards the metals, the abundance ratio, A, of hydrogen to the sum of the metals increases greatly with height. This variation of A is evaluated by a comparison of lines of Fe i and the Balmer series; and the extrapolated value of A at the base of the chromosphere agrees as to order of magnitude with that re- sulting from B. Stromgren's model of the solar photosphere. The numbers of atoms per cubic centimeter at the level H = 500 km are: log CH = + 15.63 for neutral hydrogen, and log CFe = +9.53 for neutral iron
- Publication:
-
The Astrophysical Journal
- Pub Date:
- January 1947
- DOI:
- 10.1086/144883
- Bibcode:
- 1947ApJ...105...36W