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MEASURING THE AMOUNT OF OXYGEN ON THE SUN
Previous estimates of the amount of oxygen on the Sun, based on measurements of the intensity of two absorption multiplets located in the infrared region of the solar spectrum (near 7773 and 8446 Å), had a substantial defect. The extremely high excitation potentials of both permitted infrared multiplets—9.11 and 9.48 volts, respectively—lead to the fact that the Boltzmann factors determining the ratio of the number of molecules in the ground state to the number of molecules in the lower state of one or another of the observed multiplets turn out to be very large—of the order of \(10^9\). In addition, the effective excitation temperature, knowledge of which is necessary for finding the Boltzmann factors corresponding to states with high excitation potentials, may differ considerably from the temperature obtained from the relative intensity of lines belonging to metals and having small excitation potentials; moreover, this difference remains unknown.
Such uncertainty in the excitation temperature, together with the large values of the Boltzmann factors, creates a substantial uncertainty also in determining the number of oxygen atoms in the reversing layer.
A way out of this difficulty was found by Bowen *). The method he used, which made it possible to determine with sufficient reliability the excitation temperature and the number of oxygen atoms in the reversing layer of the Sun, will evidently also find application in a number of other questions of astrophysics. From this point of view it is of undoubted interest.
The only lines of atomic oxygen corresponding to low excitation potentials and located in a region of the spectrum accessible to astrophysical observations are the forbidden lines with wavelengths 5577, 6300, and 6363 Å (see table).
The wavelength of the absorption line of the solar spectrum \(\lambda = 5577.344\) Å is in good agreement with the measurements of the wavelength of the well-known green line of the aurorae (5577.350 Å) and with laboratory measurements
*) I. S. Bowen, Rev. Mod. Phys. 20, No. 1, 109 (1948).
FROM CURRENT LITERATURE
(5577.348 and 5577.341 Å). For the other two lines, reliable wavelength measurements were lacking because under terrestrial conditions their intensities are comparatively small. Their wavelengths, however, could be determined with high accuracy from the spectra of the star HD 45677, where they appear as sharp emission lines (see the table). The corresponding corrections for the radial velocity of the star were found from the Fe II lines. The term values \(2p^4\,{}^3P_2\) and \(2p^4\,{}^3P_1\) obtained from these measurements agree well with the values obtained on the basis of allowed transitions in the far ultraviolet region.
All three forbidden oxygen lines were obtained and measured by the author on a series of spectrograms (with dispersions of 0.34 and 0.7 Å/mm) of the solar surface both at the center of the disk and at the eastern and western edges of the limb (see the table). Comparison of the spectrograms showed that these lines are of solar, and not telluric, origin. On the basis of microphotograms the equivalent width \(W\) of each of the lines was determined as the mean of 6–11 independent measurements. Near the limb it proved to be approximately \(1/4\) larger than at the center. For the infrared lines the equivalent width \(W\) was determined by measuring the curves from the “Utrecht Photometric Atlas of the Solar Spectrum.” The values of \(W\) thus found are given in the table.
Some difficulty arose with the 6300 Å line, since the superposition of a weak Ni I line with \(\lambda = 6300.363\) Å could not be ruled out. Comparison of the shape and half-width of various oxygen and nickel lines led the author to the conclusion that superposition probably does occur, but that the nickel line accounts for no more than 10–30% of the total equivalent width. In view of the absence of sufficiently reliable data, the author disregarded this effect.
The number of atoms in the reversing layer that are in the lower state corresponding to the given transition was determined from the equivalent width \(W\) by the formula:
\[ N=\frac{Wmc^2}{f\pi e^2\lambda^2} = \frac{(2J''+1)8\pi cW}{(2J'+1)A\lambda^4}, \]
where \(J''\) and \(J'\) are the values of \(J\) in the lower and upper states, respectively, and \(A\) is the transition probability. Since the intensity of the absorption lines is small, Stäy’s formula is fully applicable.
The transition probabilities for the forbidden lines were taken from Pasternack’s work. For the permitted lines, for which such data are lacking, an estimate of the factor \(f\) was made by means of the Thomas–Kuhn rule. The corresponding data are given in the table.
The excitation temperature was selected with the consideration of obtaining the greatest agreement in the data on the amount of oxygen obtained on the basis of lines with small and large excitation potentials. The author points out that such a selection is quite unambiguous, for a change of the temperature by \(100^\circ\) changes the ratio of the amounts of oxygen obtained on the basis of the indicated two groups of lines by a factor of one and a half. Moreover, the permitted lines with high excitation potentials are in fact used only to determine the excitation temperature, while the amount of oxygen is determined almost exclusively from the forbidden lines with small excitation potentials.
As a result, a value of \(5200^\circ\) was obtained for the excitation temperature. The mean value of the number of atoms per \(1\ \mathrm{cm}^2\) of the reversing layer proved to be \(7\cdot 10^{20}\), which corresponds to \(18\ \mathrm{mg}/\mathrm{cm}^2\). This value is almost twice as large as the results of previous measurements.
Discussing the possibility of using an analogous method to determine the amounts of carbon, nitrogen, silicon, and sulfur, the author comes to the conclusion that for most lines of these elements the equivalent
Table
| \(\lambda\) according to tables and measurements of HD 45677, Å | \(\lambda\) from measurements in the solar spectrum, Å | Transition | Transition probability \(A^{-1}\), sec. | \(f\) | Excitation potential, volts | Observed equivalent width \(W\), Å | Number of atoms in the lower state | Total number of atoms per \(1\ \mathrm{cm}^2\) of the surface of the reversing layer |
|---|---|---|---|---|---|---|---|---|
| 5577,350 | ,341 | \(2p^{4}\,{}^{1}D — 2p^{4}\,{}^{1}S\) | 2,2 | — | 1,96 | 0,036 | \(6\cdot10^{18}\) | \(9\cdot10^{20}\) |
| 6300,32 | ,331 | \(2p^{4}\,{}^{3}P_{2} — 2p^{4}\,{}^{1}D\) | 0,0078 | — | 0,00 | 0,047 | \(3\cdot10^{20}\) | \(5\cdot10^{20}\) |
| 6363,75 | ,83 | \(2p^{4}\,{}^{3}P_{1} — 2p^{4}\,{}^{1}D\) | 0,0226 | — | 0,02 | 0,0018 | \(2\cdot10^{20}\) | \(6\cdot10^{20}\) |
| 7771,96 | ,954 | \(3s^{5}S — 3p^{5}P_{3}\) | — | 0,35 | 9,11 | 0,071 | \(4\cdot10^{11}\) | \(5\cdot10^{20}\) |
| 7774,18 | ,177 | \(3s^{5}S — 3p^{5}P_{2}\) | — | 0,25 | 9,11 | 0,065 | \(5\cdot10^{11}\) | \(6\cdot10^{20}\) |
| 7775,40 | ,395 | \(3s^{5}S — 3p^{5}P_{1}\) | — | 0,15 | 9,11 | 0,049 | \(6\cdot10^{11}\) | \(7\cdot10^{20}\) |
| 8446,35 | ,359 | \(3s^{3}S — 3p^{3}P_{0}\) | — | 1,0 | 9,48 | 0,124 | \(2\cdot10^{11}\) | \(9\cdot10^{20}\) |
| 8446,76 | ,741 | \(3s^{3}S — 3p^{3}P_{1}\) | — | 1,0 | 9,48 | 0,124 | \(2\cdot10^{11}\) | \(9\cdot10^{20}\) |
| Average | \(7\cdot10^{20}\) |
width is less than \(1\cdot 10^{-3}\) Å, i.e., it lies beyond the limits of present-day measurement technique. Of the remaining lines of these elements, the lines of carbon (8727.4 Å) and sulfur (7724.7 Å) cannot as yet be confidently identified in the solar spectrum because of insufficiently accurate data on their wavelengths, while the silicon line (10991.52 Å) is situated too close to the atmospheric line 10991.40 Å for measurements of the equivalent width to be at all reliable. Thus, the author sees no possibility for a reliable determination of the quantities of the indicated elements on the Sun, which, however, in no way diminishes the interest of the method proposed by him and does not preclude its application to other elements.
G. Rozenberg.