Rotational temperatures of auroral nitrogen bands

.lourr~~al of Atmosplmic nnd TerrestrinlPhysics, 1953,Yet. 4, pp. 5 to 9.

~tational

Pergamon 17ressLtd., London

temperatures of aurora1 nitr~e~ bands IV. PETME

Radio Physics Laboratory,

Defonce Research Board, Ottawa

(Receivecz 20 October 19.52) ABSTRACT Aurora1 spectrograms of dispersion 42-28 A/mm have been analyzed with a recording microphotometer Rotational temperatures were determined from the profiles of Regard-Kaplan and Negative Group nitrogen bands, and found to be in t,he range 450-750°K. It now appears that spectroscopic, r,ocket, and radio results, are in reasonable agreement.

Although the various determinations of the temperature oE the atmosphere up to the aurora1 layer are in fair agreement, this is not the case in the layer itself. The particle densities (HAVENS, 1952) in the height range 100-160 km as determined from rocket flights, indicat,e temperatures of 2dO”K and 570°K at these levels, Radio measurements (APPLETOS. 1937) point t’o still higher temperatures in the E’, and B, layers. In contrast, there are the extensive measurements of rotational temperatures by VEGARD and colleagues which have been summarized in !&RAWS’S recent book (1%51). The mean rotat,ional temperature of t,hc N.G. X2’ bands appears to be of t’he order of 230°K. A slightly lower value has been found by VEGARD and KVIFTE ( I95 1) from the analysis of a recent’ly secured higher dispersion spectxogram. Spectra of sunlit aurora and of the summits of aurora1 rap appear t,o yield tempera.tures of the same order (HARAYG, 195 1). The discrepancy between these la&r results and t.he rocket and radio ~~easuren~ents is a serious one, and must be removed or explained in a satisfactory manner. This paper discusses some recent determinat,ions of rot’ational temperatures from Jtloderate-dispersion aurora1 spectrogra*ms.

The spectrograms on which this discussion is based and the in&umen.t used to secure them, have been described elsewhere (PIWRIE and SXALL, 1952). The plates selected for a study of rotatio~lai structure were obtained from the seeond and third orders of the grat,ing, the dispersions in these orders being 42 and 28 X/mm respectively. From these spectrograms t,hc rotational temperatures of the Negative (kronp. Regard-Kaplan, and First’ Positive Group Nitrogen bands mny be estimnt.ed.

This band system a,rises from the transitions 3Xr,+ 1X;,-- and being forbidden. shoultl give a reliable value for the temperature of the region from which the emission arises, Regardless of how the molecules ent,er the excited electronic state, the lifetime of this stat,e is sufficient,ly long to ensure that, rotational equilittrium is cstablishetl. 5

w.

PETRIE

One method of estimating the temperature rotational line may be written as, I = cv4Se

is as follows.

1%! -B'K'(g'+l)hc/kT = cv4&-T

The intensity

of a

r(r+l)

The frequency factor v4 varies little within a band and may be neglected. S is the “line strength” factor, B’ the rotational constant of the upper state, K’ the rotational quantum number of the upper state, and T the temperature. In the case of the Vegard-Kaplan bands the P and ‘Q branches overlap, and the S values of the two branches add together. According to SCHLAPP (1937) the value of S is (K” + 3/2), K” referring to the lower 1x state. Then, -l?!.! B’R’(R’+1) + %)e T

I = c(K”

(2)

Since K” = (K’ + 1) for the P and ‘Q branches, I =

At the maximum

c(K’

+ 8)e

of the band &,

-‘$

B'R'(K+l)

= 0.

Forming

(3)

this derivative

from

(3) and

solving for T we find, T =

1*44B’(2K’

+ 1) (K’ + 5/2)

The lines of the P branch may be represented (v Substituting

vO) =

the constants

-(B’

(v -

by the formula

+ B”)K” + (B’ -

of the (1,ll)

(4)

Vegard-Kaplan

v,,) = 3.23K”

-

B”)K”2 band,

0.37K”z

(5)

The distance from the zero gap v,, to the maximum of the P branch of the (1,ll) band appears to be of the order of 14A or 103 cm-l. From (5) the corresponding K” value is 13; hence K’ = 12. Then from (4) T N 750°K. The mean temperature derived from five Vegard-Kaplan bands in the wavelength range 3400-3800A is 850°K. These results have already been reported (PETRIE, 1952), and refer to the spectrum of an intense aurora1 display which occurred on February 23, 1952. The figures quoted here are preliminary and it is very desirable that denser, higher dispersion spectra of the Vegard-Kaplan bands be secured. Nevertheless, the plates examined show the rotational structure clearly, and the profiles of the bands cannot be reconciled with temperatures of the order of 230°K. It is worth noting that the spectrograph was pointed near the summit of the visible aurora during the exposure, and was likely receiving radiation from heights considerably above 100 km. Furthermore, the greater than normal intensity of the VegardKaplan bands in this spectrogram suggests that the radiation originated ab higher levels. Fig. 1 shows the (1,ll) and (2,12) bands. (b) First Negative Bands This system arises from the transitions

2CU+ 6

2I;8+. With moderate

dispersion

Fig. 1. (1,ll)

and (2,12)

Vegard-Kaplan

bands.

Fig.

2. (0,O) Negative

Group

band.

Rotational temperatures of aurorttl nitrogen bands

each band shows a single P and R branch; overlapping & branches of low intensity The R branch extends to shorter wavelengths and the rotamay be neglected. tional structure may be seen. The spectrograms discussed here have sufficiently high resolution to show the alternate weak lines of the R branch. According to MULLIKEN (1931) the S factor of the R branch lines is J13 ) s =; (J” + and since J’ = (J” + 1) for the R branch, S = -__-. J’ (J" + 1) Each line is an unresolved doublet with J’ values J’ = (K’ + +) and

-

1p- f

J’ = (K’ -

4). Hence S, = zic$F,

S, = giF-EF

and (S, + S,) =

2

For our purpose a satisfactory

the derivative

g,,

is t,o write S = ZK”.

rrn.

Then,

-

K’ 4

1-44B’R’(K’+l)

I = dZK’e_7 Forming

2

approximation

2K’3

and equating to zero we find,

T = liT’(2iY’ -j- 1) 1*44B’

(7)

The formula for the R branch is, (Y -

Y()) == 2B’

+

(3B’

-.

B”)K”

+

Substituting the values of the rotat.ional constants for the {O,O) and (0:l) bands. (O>O)

(Y --Ye) = 4.2 + 4.3X”

(0.1)

(Y -

PO)-

4.2 +

+

4~41K-” +

(B’

-

B”)K”2

gives the following

(8)

expressions

0~15K”~ O*laP

(9) (10)

A few of the sharpest plates were select,ed and analyzed with a Jarrell-Ash recording microphotometer. A picture and a trace of the (0,O) band at 39148 are shown in Figs. 2 and 3. The resolution is such that the intensities of a number of the individual lines may be determined, and it appears that the position of the intensity maximum is ~59 cm-l from the zero gap. From equations (9) and (7), h’” = 10, K’ = 11, and T N 750°K. Even if the maximum is displaced two lines towards the zero gap, the wave-number difference between this line and the zero gap is 47 cx11-1, and T N 500°K. The temperature range determined from the (0,l) band at 4278A was 50~~00’~. From (6) it can be seen that,

1%; = Hence,

by plotting

the factors

log $

log c -

7

and K’fK’

B’KS’(fi’ + 1) + I), the temperature

(11) may be

determined from the slope. The I factors were obtained by converting the profiles of the lines on the microphotometer tracings from a logarithmic to a direct intensity scale, and them measuring the areas with a planimeter. On the other hand, since the individual rotational lines are very narrow it is satisfactory to use the central 7

W. PETRIE

intensity of each line as a measure of its total intensity. The spectra were secured with an instrument which used a step-slit, and each spectral feature acts as a source from which the “characteristic curve” of the emulsion may be determined. Plots were made using both central intensities and total intensities for the I values, and the derived temperatures were in the range 450”-700°K.

60

t-------+q

i

j

--00---

Fig. 3.

Fig. 5.

(0,O) Negative Group band

(5,2) First Positive Group band

The question now arises, why is there a serious discrepancy between these results and those of VEGAED and his collaborators? The method used is quite straightforward, and the error involved in the temperature determination is much smaller than the differences between the two sets of results. As far as the writer can judge from VEBARD’S r.ecent paper (1951), the latter has picked out the portion of the band corresponding to the smallest microphotometer deflection, and has called the line at this point the one with maximum intensity. But underlying the lines in this portion of the band there is a continuous spectrum due to convergence of the rotational lines and possibly due to the presence of the (3,6) Second Positive Band (PETRIE and SMALL, 1952). If the background is caused by a foreign band, then it is the Mackening of the line relative to the background, rather than the total If the background is caused by the blackening which determines the line intensity. overlapping of rotational lines, the relationship between true and measured intensity is complex, and the interpretation of the profile of this region of the band must be treated with caution.* Hence the relative intensities of the lines well away from the head should give the best indication of the temperature. The spectra analyzed by the writer are of relat’ively high resolution, the dispersion being in the range * The writer w.ishesto thank Dr. A. H. DOUGLASof the National Research Council of Co.nada for discussions on this point.

8

Fig. 4.

First Positive

Gronp bands

4%/&&/mm: and it was possible t’o measure t,he intensities of individual lines. This has not been done in t,he Fast. It, is wort’hwhile noting that the profile of t’he (0.1) band at 42588 appears similar to the illustrated profile (HERZBERG, 19.50) at, a t,emperat,ure of 673°K. (c)

I;‘ilst Positive Bands

bands, from the transitions 37r,,-- 3CU-+are very complex, and are poorly resolved in the spectra discussed here. As can be seen from Figs. 4 and 5 each band consi& of three sharp regions and three diffuse regions. Each of these region>; Since t’he line structure of these bands cannot be includes several branches. resolved, only a rough est’imate may be made of the rotational t’emperature. factors depend upon whet8her the coupling approaches The “line strength” Hr-:,-n’s cases (a) or (b). NAUDI? (193’) has shown that the coupling is according t#o case (a) for small rotational quantum numbers, and approaches case (b) for “Line strength” factors have been given by NOLA& larger quantum numbers. and JEXKIXS (1936) for both cases (a) and (b). The simplest part of one of these bands is the diffuse region to the long wavelength side of the first strong head and this region consists of the branches “P,,. OQ13.OP,,: and *‘P,,, the latt’er bran& bring weak compared with the other three. If we substit,ut#e the “line st,rength” ‘t’hwe

factor in bhe intensity

equation

and form the deriva,tive $$,

= 0. then it appear:;

that for each of the first three branches given above an approximate expressiorl is 1 = J’(2J’ + 1) 1.44B’. From the apparent position of the maximum of thr region referred to, the writer judges that the temperature is 350°K. The accurncJ of this figure is not comparable t’o the temperature values derivecl from the other band systems. CONCLUDIXG REMARKS In view of the fact that the results quoted here contradict earlier spectroscopic investigations, it is important that additional observations be made with higher Several spectrographs now under construction will be resolution equipment. adequate for a careful study of the rotational structure of aurora1 bands, and a definite decision regarding spectroscopic temperatures should soon be reached. REFERENCES 1937

APPLETON,E.V. HARANG,L. HAVENS, R. J., KOLL, R. T.

1951 1952 1950

and La Cow, H. E.

HERZBERG, G. MGLLIKEN, R. S. NaIJDl& S. M. NoLAN,P.~~~ JENKINS,F.

A.

PETRIE,~. PETRIE, W.and SMALL,K. SCHLAPP,R. VEGARD, L. and KVIFTE, G..

1931 1932 1936 1952 1952 1937 1951

Proc. Royal Sot. London A. 162, 451 The Aurorae, Wiley and Sons Jour. Geophy, Res. 57 59 Spectra of Diatomic Molecules, 2nd Edition. D. VAN NOSTRAND, page 50. Rev. Mod. Physics, 3 87 Proc. Roy. Sot. London 136, 114 Phys. Rev. 50, 943 Phys. Rev. 86, 790 Astrophys. J; 116, 433

Phys. Rev. 51, 342 Geofys. Publikasjoner, 18 (No. 3) 9