Hydrogen Balmer lines

Astrophysicists have always been interested in the Fraunhofer lines in absorption (or, under exceptional conditions, emission) spectra, a unique source of information on chemical elements at the stellar surface. The predominance of the iron lines and the lines of Na, Mg, Ca, Ca", Ti, V, Cr, Mn, Co, Ni, Sr, and Sr" in the solar spectrum, when compared with the hydrogen Balmer lines in Sirius and other stars with T close to 11000 K or the helium, carbon, nitrogen, and oxygen lines in Orion-type stars with T between 20000 and 30000 K, originally suggested essential differences in chemical composition and hinted at a Crookes evolution [53]. The question (quite legitimate before the small, inaccessible nuclei were established in 1911) of whether T above 6000 K or... 

B 10 000 0 000 Bluish white More lines neutral He lines dominate hydrogen Balmer lines developing... 

A 7 500-10 000 White Very strong hydrogen Balmer lines, decreasing later Ca line appears... 

F 6 000-7 500 White Hydrogen Balmer lines and ionized metal lines declining neutral metal lines increasing... 

Zeeman poiarimetry Photoelectric method for measuring the displacement in the hydrogen Balmer lines by measuring modulation in the line wing between two opposite circularly polarized states. 

The frequencies of hydrogen emission lines in the infrared region of the spectrum other than the visible region would be predicted by replacing the constant 2 in the Balmer equation by the variable m, where m is an integer smaller than n m = 3,4,... 

Balmer lines spect Lines in the hydrogen spectrum, produced by transitions between = 2 and > 2 levels either in emission or in absorption here is the principal quantum number. bobmor, lTnz ... 

When it became possible to obtain the spectrum of one of these objects in 1937, it was obvious that they looked like nothing yet known. All supernovas discovered in subsequent years displayed a remarkable uniformity, both in intensity and in behaviour. This observation led Zwicky to suggest that they might be used as standard candles to calibrate distance across the cosmos. But then, in 1940, a supernova with a completely different spectrum was discovered. It soon became clear that there were at least two classes of supernova, distinguished by their spectral features. It was the presence or absence of the Balmer lines of hydrogen near the maximum of the light curve that provided this classification. 

Fig. 2-1.—The Balmer series of spectral lines of atomic hydrogen. The line at the right, with the longest wavelength, is Ha. It corresponds to the transition from the state with n = 3 to the state n 2. The other lines correspond to the transitions from the states with n — 4, 5, 6, to the state with n = 2.

The R CrB variables and related hydrogen-deficient carbon stars show strong carbon features (except CH) and very weak Balmer lines. The R CrB stars are surrounded by circumstellar dust shells, and continue to eject puffs of new circumstellar material on time scales of a month or two mass loss rates of order 10- Mo yr- are reported by Walker 1986. The compositions of the R CrB stars and hydrogen-deficient carbon stars are were compiled by Lambert (1986). Hydrogen is extremely deficient in both groups (H/He 10 J-10 °), and C/Fe is enriched by typically an order of magnitude over the solar ratio. C/0 is typically 2 (more than is measured in the AGB stars, and [N/Fe] 1. R CrB itself contains a strong lithium... 

The velocities of the absorption minima of the Balmer lines are basically set by the density at a given velocity. The absorption minima are essentially independent of the luminosity of the model for reasonable values of the luminosity. At higher luminosity and temperature more hydrogen is ionized at lower radii and hence velocities, but more of the remaining hydrogen is excited, and these two effects are found to offset one another. Several aspects of the spectra do change significantly with the luminosity. One is the... 

But experiments to resolve the fine structure of the Balmer lines were difficult as you all know, resolution was impeded by the Doppler broadening of components. So ionized helium comes into the picture, because, as Sommerfeld s formula predicted, fine structure intervals are a function of (aZ)2, so in helium they are of order four times as wide as in hydrogen and one has more chance of resolving the Doppler-broadened lines. So PASCHEN [40], in 1916. undertook an extensive study of the He+ lines and in particular, 4686 A (n = 4->3). Fine structure, indeed, was found and matched against Sommerfeld s formula. The measurements were used to determine a value of a. But the structure did not really match the theory in that the quantum numbers bore no imprint of electron spin, so even the orbital properties - which dominated the intensity rules based on a correspondence with classical radiation theory - were wrongly associated with components, and the value of a derived from this first study was later abandoned. 

Fig. 1 shows an early saturation spectrum of the hydrogen Balmer-a line, recorded in this way at Stanford [4], together with the seven theoretically predicted fine structure components and the Doppler-... 

Fig. 5.9. Spectrum of hydrogen Balmer series lines observed in a detached divertor plasma [20]. The spectrum was observed with the viewing chord shown in Fig. 5.8. The fitted spectrum is also shown as a broken curve...

Simultaneously the intensity of the atomic Balmer lines (in this case D7) increases by nearly a factor of two. Thus, in the presence of molecules it obviously turns out that corrections to the estimated hydrogen flux may be required in such a form that the atomic S/XB (which is about 15 for densities 1018-1019 m 3 and temperatures above 15 eV) is replaced by an effective one, which is determined by the molecular deuterium flux rd-> ... 

A further problem is that the intrinsic hydrogen line ratios may deviate from case B theory. This occurs for example in nebulae with high electron temperature ( 20000 K), where collisional contribution to the emissivity of the lowest order Balmer lines may become significant. In that case, a line ratio corrected assuming case B for the hydrogen... 

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