392 



NA TURE 



[September 15, 1923 



A Possible Origin of the Nebular Lines. 



The hypothesis that the lines of unknown origin 

 in the spectra of nebulae are due to the atom of some 

 hitherto undiscovered element (" nebulium ") is not 

 the only one that may be advanced. The recently 

 developed cjuantum theory of band spectra makes it 

 at least possible that these lines could have their 

 origin in a molecule with small moment of inertia 

 composed of atoms of those elements which are 

 known to exist in nebulae. It is proposed in this 

 letter to show that the existing astronomical evidence 

 is not in contradiction to this alternative hypothesis, 

 and also to indulge in some speculation as to the 

 nature of such a molecule. 



The Nebular Spectrum. — The absence of band heads 

 in the nebular spectrum does not necessarily preclude 

 the possibility of a molecular origin. In a band 

 spectrum the individual lines of a single band may be 

 arranged in a Deslandres formula, 



i'=A±2Bm +Cw', 



where m takes the successive values i, 2, 3, etc., and 

 the line corresponding to w = o is missing. The lines, 

 therefore, arrange themselves in a positive (R) and 

 negative (S) branch on either side of the missing line 

 m — o ; the band head is due to the overlaying of one 

 or other branch on itself, depending upon the sign 

 of C, and occurs in general only for large values of m. 

 To a first approximation, however, the lines in either 

 branch are equally spaced with a separation equal to 



i90ooNiNf 21000 



V 15000 17^000 



27000 29O0O 



6500 6000 5500 



5000 



4500 4000 



Fio. I. 



2B, where on the quantum theory of band spectra 

 (Sommerfeld, " Atombau," chap. 7) B is inversely 

 proportional to the moment of inertia of the molecule. 

 The smaller this moment of inertia the more widely 

 spaced will be the lines, and from the Boltzmann 

 probability factor the fewer there will be of them. 

 Accordingly, if the hypothetical molecular carrier of 

 the nebular spectrum has a small moment of inertia, 

 the resultant spectrum will consist of isolated lines 

 with no band heads — in general agreement with that 

 observed. 



Slightly more positive evidence can be gained 

 from a closer consideration of the nebular spectrum. 

 The important work of Wright (Lick Observatory' 

 Publications, vol. 13) has shown that the nebulas 

 may be arranged in a series from low excitation 

 (strong H, no He lines) through medium to high 

 excitation (H and strong He"*^ lines). At the top 

 of the accompanying diagram (Fig. i) are shown the 

 positions (on a wave number scale) and intensities, 

 as given by Wright, of the nebular lines of unknown 

 origin for B.D. +30° 3639 (low excitation) and N.G.C. 

 7027 (high excitation). For convenience of reference 

 the high excitation spectrum is also repeated at the 

 bottom of the diagram ; the dotted lines shown in 

 this spectrum are suspected nebular lines which 



NO. 281 I, VOL. I 12] 



occur in nebulae of medium excitation, but i ^t m 

 N.G.C. 7027. 



The change in intensity and in tl r of the 



nebular lines with increase in c.\ is very 



striking, and this fact may be used in an attempt to 

 select band lines in the spiectrum. For the intensity 

 of a line depends primarily on the number of n 

 which are in the particular quantum state 

 according to the Maxwellian distribution of r- 

 velocities, with increase in excitation the ri 

 of rotational speeds will shift to the higher quuaum 

 numbers. Thus, for low excitation, lines correspond- 

 ing to w -= ± I will be strong, but with increase in 

 excitation the lines w = 1 2, ±3 will gain at the 

 expense of m =-- r i . Using this as a guide, a number 

 of possible band groupings have been suspected in 

 the nebular spectrum, and these are shown as Nos. i, 

 2, 3, 4, in Fig. 1. A few words of comment may Ix; 

 made on these. 



Nos. I, 2. — These two groupings comprise the six 

 strongest lines in the spectrum, including N„ N,, 

 3967, 3868. It will be noted how the maximum of 

 intensity shifts from the red lines to the violet with 

 increase in excitation. It has been assumed that 

 each grouping is a positive (R) branch of a single 

 band, and the constants of the Deslandres formula 

 have been computed. 



(No. i) »'==io9i5-9 +39i6-3m +352-9W*, 

 (No. 2) »» = 1 1098-4 +3903-6m +265-4W*. 



The close similarity of the constants B for each 

 group suggests that i and 2 are two 

 positive branches of a single band 

 with zero line far out in the infra 

 red. Curtis has found in the He, 

 spectrum (Proc. Roy. Soc. A, loi, 

 38, 1922), a band (X5730) ^^^th two 

 positive branches with slightly 

 different (12 wave numbers) values 

 for the zero lines. 



No. J. — This suspected band con- 

 tains four lines with a dubious fifth, 

 and consists of a positive (R) and 

 negative (S) branch with the line 

 m=o as usual missing. Using the 



lines with wave numbers S (i) 



J500 A 17679, R (i) 21219-2 and R (2) 



22912-50 to compute constants, the 

 following formula is reached : 



V = 19474-7 ± i77o-im - 25-6m*. 



The computed wave number of S (2) is 15832, and 

 there is an observed line at 15836 (±3), which may- 

 be considered satisfactory agreement. The computed 

 wave length of R (3) is 24555, and there is a strong 

 line at 24571-5 (±0-1). The agreement is not satis- 

 factory, the intensity relations are not satisfactory, 

 and it is accordingly very doubtful whether this line 

 belongs to the group. The remaining four, however, 

 make a satisfactory group, and it will be noted that 

 while the lines R(i), S(i) make their appearance in 

 nebulae of medium excitation, the intensity- is trans- 

 ferred to R(2), S(2) in the nebula of high excitation. 



No. 4. — This suspected band contains eight lines, 

 which may be divided into a negative (S), a positive 

 (R), and a zero (Q) branch. The designations, wave 

 lengths, and w^ave numbers are given in the accom- 

 panying table. The lines marked with asterisks 

 were used in computing the constants for the R and 

 S branches, namely, 



v =27586-1 1 i56o-6m -f 7-4m* ; 



from this was computed in the usual way the formula 

 for the Q branch, namel)', 



1' = 26805-8 +7-4m*. 



