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Temperature determination from a cloud of alkali vapour in the upper atmosphere
TEMPERATURE DETERMINATION FROM A CLOUD ALKALI VAPOUR IN THE UPPER ATMOSPHERE
OF
G. T. Department
BEST and T. N. L. PATTERSOS* of Applied Mathematics, Queen’s University, (Rewired
Belfast
25 bf~/_y 1962)
new method is discussed for measuring the temperature in an artificial cloud of alkali vapour. This method overcomes the complications introduced by the process of selfabsorption. Estimates of the intensities of the relevant emission lines to be observed are made. It is concluded that observations made on lithium capour present the best means of measurcment.
Abstract-A
1. INTRODUCTION
The presence of the Earth’s natural sodium layer and the resonance scattering which it causes during the evening and morning twilight periods led Bates”) to suggest that useful scientific information might be obtained from observations of artificial clouds of sodium in the upper atmosphere. Experiments concerned with the measurement of high altitude winds have been carried out by tracking the motion of the cloud. The use of vaporizers which eject sodium continuously as the rocket ascends or descends leads to some uncertainty about the vertical motions in the regions which may be studied. In spite of this, winds have been measured in the altitude range 70-230 km at sites widely distributed over the Earth’s surface during the last seven years.(2p18) Values of the diffusion coefficient for sodium and other alkali atoms in the atmosphere have been deduced from the rate of growth of the diameter of the trail,‘“,11~13~1G~1R) Few spectrographic studies have been made on the trail, The first firing(*) was observed by a grating spectrograph. With a dispersion of 150 A/mm the only conclusion that could be drawn was that the visibility of the trail was due to resonance scattering of solar radiation. In this paper some of the difficulties of the method at present used for temperature determinations are discussed and a method which should be more accurate is suggested. 2. OBSERVATIONS
If the optical thickness could be reduced sufficiently the examination of the sodium D-doublet by a high resolution instrument would yield the Doppler width and hence the temperature. The method has been applied to the 01 green line of the nightglow by Armstrong(1”,20) and by Wark and Stone .(21) A suitable Fabry-Perot interferometer was built in this department with a view to investigating this possibility. The results obtained, which are similar to those of Blamont,(22) will be published separately.‘2:s) Blamont has used the technique developed by Bricard and Kastler(“Q to examine the sodium twilight lines. (25) He has also applied the technique to an examination of the lines emitted by a high altitude sodium cloud with some success.(26~2i) Approximations must inevitably be introduced in interpreting the data. The optical thickness must be small otherwise the line profiles become so broad because of multiple scattering and self-absorption that they have no simple relation to the ambient temperature. In the case of the method using the Fabry-Perot interferometer the D,/D,ratio may indicate * Now at the Graduate Research Ccntre of the Southwest, Dallas, 5, Texas. 521 I
G. T. BEST and T. N. L. PATTERSON
522
when the optical thickness has become small but the line profiles at the expected temperatures are then far from true Doppler profiles due to hyperfine structure(28). The use of an instrument capable of resolving the hyperfine structure would not be easy in the field and the reduction of the observed profile to the true profile would be laborious. The results obtained by Blamont using the absorption cell technique are very interesting; particularly the manner in which the shadow thrown by the natural sodium layer is seen to modify the D,/D, ratio in the trail in a predictable manner. The method becomes more accurate as the optical thickness decreases but, as in the case of the Fabry-Perot profile determinations, the difficulty of detection becomes acute. The presence of the Earth’s natural sodium layer can also distort the profiles of the direct and scattered radiation. It thus appears that true temperatures cannot readily be obtained from measurements on the sodium D-doublet. 3. AN IMPROVED
METHOD
OF TEMPERATURE
DETERMINATION
Advantage may be taken of the fact that a line is not modified by self-absorption if its upper level is not populated by direct transitions from the ground level. The 42P level of sodium is de-populated by direct transitions to the ground state giving the 3303 8, doublet and by indirect transitions through the 42S and 32P levels giving doublets at 2.2 /L and 1.14 p followed by the D-doublet. The 3303& 5893 A and the 2.2 p lines suffer self-absorption so that it is not easy to infer the temperature from measurements made on their profiles.Only the 1.14 ,u lines have a true unmodified Doppler profile. Similar arguments apply to the other members of the alkali series, the unmodified lines for Li, K, Rb, and Cs occurring at about 8126 A, 1.25 p, 1.34 1~and 1.4 1~ respectively. Bedinger et a/.(3,4) and Vassy and Vassy (2g,30)have detected the second resonance lines of sodium at 3303 A in the morning but not in the evening. The observed ratio, l?, of the photon intensity of the 5893 8, radiation to that of the 3303 A radiation appears to vary greatly. The theoretical considerations of Cooper et al. w show that l? lies between 140 and 200 for resonance scattering whereas the observations by Vassy and Vassy indicate I? ranges between about 2 and 10. The latter also report that the 3303 A radiation is observed to be emitted from a small portion of the trail. It is possible that the localized source of high relative intensity 3303 A radiation is due to chemical excitation or to severe self absorption of the D-doublet. In the calculations no allowance appears to have been made for ozone absorption which is variable. This will affect both the intensity of the exciting radiation and of the downward scattered radiation. As is demonstrated later the attenuation of the exciting radiation is not serious but the intensity of downward scattered radiation may be affected’“‘) when the optical path is great (as for observations very near the horizon). Observational difficulties may be foreseen in any attempt to measure the profiles of the lines at 1.14 1~. Thus there is some difficulty in recording a feature in this spectral region Again the $ band of water vapour may cause absorption under the required conditions. and may modify the profile. The absorption has a maximum at about 11407 8, and falls off rapidly so that the attenuation at 11405 A, the nearest line, may not be unacceptably great, It was decided to investigate the possibility of using although the profile may be distorted. As a preliminary the intensities of all the lines in other members of the alkali group. question were calculated. 4. THEORETICAL
INTENSITIES
is apparent from the relevant Einstein A-coefficients c3zJthat the only significant contributions are from the lower S and P states of the alkali atoms. There are four terms which It
TEMPERATURE
FROM A CLOUD OF ALKALI
VAPOUR
523
must be taken into account: the ground term r2S and the excited terms (Y -+ 1)2S, r2P, (r + I)2P. These lead to four possible spectral doublets. 6) (ii)
r2Sk -- y2Pf,$
(iii)
r2P8,$ - (r + 1j2S3, (u + 1J25, - (v i l)*P,,,.
(iv)
the D-doublet,
r2Si - (r i- l>“Pj,!,
It is assumed that the alkali atoms are in radiative equilibrium, that is, the rate of population of a state by radiative processes equals the rate of de-population by radiative processes. In an optically thin layer the ratios of the number densities in the excited levels to the number density in the ground level are given by:
x [A(r + I S, rP,> _t A(r + 1 S, rP,)]-l
where A( Y,X) is the Einstein coefficient for spontaneous decay from state Y to state X, B(X, I’) is the Einstein coefficient forexcitation from state X to Y, ,Q(cJ~~.) is the energy density per unit ~vavenumber at wavenumber o,-,- and ~.~r is the wavenumber for the transition between X and Y. Taking account of the solid angle from the Sun to the Earth and using the relationship between the A and B coefficients it can be shown that: (4) in se+ where I&Asl-) is the solar energy flux at wavelength AAyyA, as given by Minnaert.(33) The numbers of photons emitted per particle per set are then given by:
where: the transitions sA - j>B correspond to (i) to (iv). The Einstein A coefficients adopted are those calculated by E3eavens’32)using the tables of Bates and Damgaard. (3~ Table 1 presents the results for ail the alkali atoms. The data cited by MinnaerW represents the continuum radiation from the Sun and so the intensity of the exciting radiation must be muItipIied by the ration of the intensity at the bottom of the Fraunhofer absorption line to the intensity in the continuum. The correction factor is not known reliably except for the broad sodium fines, the values for Na being O-052 for D, and O-058 for D,.(36,3’) Estimates can be made of the order of magnitudes of the Fraunhofer depths. Potassium
524
G. T. BEST and T. N. L. PATTERSON TABLE I. PHOTON INTENSITIE?
Wavelength ([.A.)
A(l0”)
Photons/p3rticlclsec.
Lithium
6707.9 12 6707.761 3232,660 3232.660 8126,231 8126.452 26879.74 26879.74
36.7 36.1 I.09 1.09 I I.1 22.2 3.7 3.7
6.25 12.5 9.9% -4)(-j-) l,99( -3)(.V) 3.38( 3) 6.75(+3) 3.38(, 3) 6,75( -3)
Sodium
5895.924 5889.951 3302,993 3302.380 11381.64 11403.97 22083.56 22056.13
58.9 59, I 2.85 2.85 8.26 16.4 6.44 6.41
0.384(::) 0,690( 5, 4,11(-3)(-i-) 8,18(&3)(t) 9.33( -3) 1.X5( -2) 9.2X( - 3) 1.86( ~2)
Rubidium
7947.600 7800.263 4215,524 4201.792 13233.28 13663.00 279 12.95 21321.75
35.6 37.5 2.43 2.80 6.62 12.9 4.28 4.48
IO.2 20.5 2.44( ~ 2)(Vi-) 5.88( -2)(1-;-) 4.65( -2) 9.06( -2) 4.29( ~2) 9.41(-2)
Potassium
7698,977 7664.905 4047.208 4044.137 1243 I .89 12521.77 27206. I3 21067.94
36.9 37.2 1.98 2.14 7.15 14.2 4.4 4.44
1,09( ) 7.17( /I .**) ;.39( ~2)(: 3.15(,12)(g 3.22(-2) 6.40(&2) 3.10( -2) 6,53( 2)
8943.499 8521.104 4593.112 4555.229 13588.29 14695.03 30949.97 29307.64
28.6 32.4 2.12 2.97 6.23 11.4 3.52 4.05
I I.5 22.7 3.28(&2) 9.97( --~2) 6.73(,- 2) I .23( ~ 1) 5.45( -2) 1.36( ~--I)
Caesium
*
) )
* (+) (T) (8) ((I)
The numbers in brackets denote the power of ten Fraunhofer depth not determined. Fraunhofcr depth 0.058 Fraunhofer depth 0.052 Fraunhofer depth approximately 0.1 I. (’ ) Near the strong Fe1 Fraunhofer line (probably small). (*“;) Atmospheric absorption by 0,; assumed to have same depth ponent. (+f) Probably atmospheric absorption.
ns the other com-
TEMPERATURE
FROM
A CLOUD
OF ALKALI
VAPOUR
525
76998,does show a normal Fraunhofer profile which Lytle and Hunten(“al find to have a reduction factor 0.02 to 0.1 1 using the atlas of Minnaert PI CZ/.(~~) The Fraunhofer reduction factor of the D-lines as measured in the Minnaert atlas must be multiplied by g to obtain the actual reduction factor. If the observed sodium and potassium lines have the same shape the i correction factor should still apply and so the higher value ofO.11 is adopted. Table 1 column 4 gives the photon intensities with comments on the assumed Fraunhofcl reduction factors. It should be noted that some of these alkali lines. for example i4202 of RbI and i,7665 of K I, sufl-er strong atmospheric absorption. 5. TRAILS
OF LITHIUM
VAPOUR
In
this section some of the advantages of using lithium as distinct from any other al!
cossq~) ,
u,,
cos-l( -&) -
0,)
2
f=
(6)
0, being the depression of the Sun when observations commence and R being the radius of the Earth. If L is taken to be 200 km and S to be 40 kmJ‘is about 0.8. It can be seen therefore that a suitable choice of the observation time can eliminate some of the trouble from absorption of the excitin g radiation. Equation (6) indicates that L must be at least 95 km. To estimate the factor/C by which the intensity of the 3232A exciting radiation is reduced by Rayleigh scattering it is sufficient to assume an isothermal atmosphere. If/l,< is the number density of molecules at altitude S, (TV, is the scattering cross-section at \+avelength 3, and H is the scale height then
Ke
exp [-II,(T~.\ 2-rr(S it- R)Hj
(7)
Taking N and S to be respectively 7 km and 40 km it is found that A’ is 0.96 so that the reduction is quite small. It is difficult to estimate the effect of absorption of water vapour because of its variability but it can scarcely be serious since the nearest absorption peaks (cf. Goldberg(J1)) in the vicinity of 8126 A are at 8059 8, (weak) and at 8226 A (medium). It is of importance to consider the background radiation which is due mainly to the Meinel system of hydroxyl. The strong OH (9.4) band is just below the region of 8126 A but tracings of the nightglow spectrum shows that an intensity minimum occurs near 8126 A. The emission is certainly less than 5 Rayleighs,‘A.
526
G. T. BEST and T. N. L. PATTERSON
For comparison with background radiation it is of interest to estimate the theoretical emission rate for lithium using Table I. Taking the trail of vapour to be about 40 km long and 1 km in diameter, a release of 2 kg of Li leads to about 6 x lo9 atoms cme3, which corresponds to 6 x 1014 atoms per cm2 column along the line of sight. The quantity, q, defined by:
is a measure of the optical thickness of thelayer (cf. Batesand Dalgarno@2)); hl is the molecular weight of the species, T the temperature in “K, 1 the wavelength in A, f the oscillator
p: 71.4 ii', 2'Pt-3'S1 i B
L,=_22P;-325, 2 14~3 -6*2(-4) ‘/~3.7&4)
3m-4) zs-4) 76.5) .2.3(-4)
5)
jl 5)
--+A%
s $ _ m
FIG. 1. RELATIVEINTENSITIESAND WAVELENGTHSOFTHE Lie AND Li’ LINESAT 8126A. THENUMBERSABOVE THE LINES INDICATE THE RELATWEINTENSITIES. THE HYPERFINE SPLITTINGS ARE NOT TO SCALE. LINES A AND B ARE THE LINES TO BE OBSERVED. THE WAVELENGTHS OF THE CENTRES OF GRAVITY OF THE MULTIPLETS ARE GIVEN.
strength associated with the initial transition and N the total number of atoms per cm” column along line of sight. The layer is optically thin or thick according as q is much less than or much greater than unity. For the 3233 A line of lithium 4 is about 14, when the temperature is 200°K. It is therefore necessary to consider the optically thick case. The emission is limited by the number of solar 3233 A photons within the absorption equivalent width of the line, AR,, and can be written as: \ Pma E=-.---- W% IO-” Rayleighs (9) 47r CPm3 -I- Pnlza1 where Al,
is the Doppler
half width the photon Earth and $‘sr26 and p3233, is found that F is about IO5 Rayleighs radiation. A slight complication arises since the former about 12 times as abundant it is estimated that the isotope shift of for the 5 --A 2 transition.
of the 3233 8, line, P is the solar flux at 3233 A at the emission rates per particle, are as given in Table 1. It which is considerably greater than the background Li exists in two dominant isotopic forms Li7 and LP, as the latter. Using the data of Jackson and Kuhn’43) 8 126 A is 0.188 8, for the f --j $ transition and 0.196 8,
TEMPERATURE
FROM
A CLOUD
OF
ALKALI
VAPOUR
527
As regards the distortion of the profiles due to the hyperfine structure which markedly influences the resonance lines, (cf. Chamberlain et al. czs)),it can be seen that little disturbance is to be expected here since the first excited state, with much smaller splittings, is the final state in the 8 I26 A transition. When calculating the hyperfine structure of the lithium lines it \vas assumed that the 3S, state has zero splittings. By comparison with Na, estimates were made of the 2P, splitting. Fig. I Sives the positions of the important lines together with the distributions of the intensities. The hyperfine splittings may be completely neglected in their effect on the Doppler profile of the lines. The Li”(2P, - 3s;) and Li7(2PJ - 3P,) at Bon Fig. 1 are very close together being separated by about 0.03 A. However, the former corresponds to the weak component of Li” and the latter to the strong component of Li;. Taking account of the relative abundances the ratio of the intensity of the two lines is about 1 were calculated and led to the conclusion that the “4’ Some profiles of this combination error in temperature deduced by treating the observed profile as that due to a single line is about 4 per cent in the worst case. Measurement made on the 2P, -- 3S, line of Li’ introduce no such errors although the intensity is reduced by a factor bf 2. _ Finally, it may be noted that the 8126 A line is easily observed both photographically and photoelectrically, a fact which, together with the previous discussion, makes lithium more promising than the other alkali atoms whose unmodified lines lie much further into the infra-red. At present preparations are being made to measure the profile of this line and results should be published later. Ack/ralv/~~~eme/rrs-The authors thank Professor D. R. Bates. F.R.S., for his interest in this work. The research reported has been supported in part by the CambridgeResearchLaboratories,OAR, through the European Office, Aerospace Research, United States Air Force, under Grant No. AF-EOARDC 61-16, and in part by the Department of Scientific and Industrial Research. REFERENCES 1. D. R. BATES, J. Geophys. Res., 55, 347, 1950. am/Airrorae (cd. E. B. ARMSTRONG 2. H. D. EDWARDS, J. F. BEDINGER and E. R. MANRING; The Air;plol~~ and A. DALGARNO), Pergamon Press, London, 122, 1956. 3. J. F. BELXNGER, E. R. MANRING and S. N. GHOSH. J. Gcophys. Res.. 63, 19, 1958. 4. C. D. COOPER, E. R. MANRING and J. F. BEDINGER, J. Geophys. Res., 63, 369, 1958. 5. E. R. MANRING, J. F. BEINNGER and H. B. PETTIT, J. Geophys. Rex., 64, 587, 1959. Co., Amsterdam, 6. G. V. GROVES, Spcrce Research-I (rd. H. KALLMANN BIJL), North Holland Publishing 1960, p. 144. 7. E. R. MANRING and J. F. BEDINGER, Spuce Research-Z (ed. H. KALL~IANN BIJL), North Holland Publishing Co., Amsterdam, 1960, p. 154. Pub8. W. G. ELFORD and E. L. MURRAY, Space Rrsearch-I (ed. H. KALLMANN BIJL). North Holland lishing Co.. Amsterdam, 1960, p. 158. Co., Amsterdam, 1960, 9. A. VASSY. Spce Re.warc/r-I (cd. H. KALLMANN BIJL), North Holland Publishing p. 203. 10. J. A. REES, Space Rmxrch-l(ed. H. KALLMANN BIJL), North Holland Publishing Co., Amsterdam, 1960, p. 207. II. E. MANRING. J. BEDINGER and H. KNAFLICH, Space Rc~scarch-II (ed. H. C. VAN DE HUL~T, C. DE JAGER and A. F. MOORE), North Holland Publishing Co., Amsterdam, 1961, p. 1107. 12. L. BROGLIO, Space Rescrrrch-If (cd. H. C. VAN DE HuLs-~, C. UE JAGER and A. F. MOORE), North Holland Publishing Co., Amsterdam, 1961, p. 1125. 13. E. R. MANRING and J. F. BEDINGER, J. Geopl~~.r.Rrs.. 62, 170. 1957. 14. F. F. MARMO. J. PREssnrsN, E. R. MANRING and L. ASCHENBR~~D, PImet. Space SC;., 2, 174, 1960. 15. J. E. BLAMONT, C. R. Am;/. Sri. Paris, 249, 1248, 1959. 16. J. E. BLAMONT, Space Rrsetrrch-I (,ed. H. KALLMANN BIJL), North Holland Publishing Co., Amsterdam, 1960, p. 199. 17. G. V. GROVES. N&LIIY, Loncl. 187, 1001, 1960. 18. J. A. REES, Plmct Space Sri., 8, 35. 1961.
528 19. 20. 21. ‘72. 23. 24. 25. 26. 27. 2X. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 30. 41. 42. 43.
G. T. BEST and T. N. L. PATTERSON E. B. ARMSTRONG, J. Phys. Rd., 19, 358, 1958. E. B. ARMSTRONG, J. Atrrros. Terr. Phys., 13, 205. 1959. D. Q. WARK and J. M. STONE, Nrrtuw, Lad. 175, 254, 1955. J. E. BLAMONI‘, Am. GPO&W., 16, 435, 1960. E. B. ARMSTROUG, G. T. BEST and J. MAZUR (to be published). J. BRICARD and A. KASTLER, Am. Gcophys., 1, 53, 1944. J. E. BLAMOUT, The Airglow and Aurorae (ed. E. B. ARMSTRONG and A. DALC;*\RNO), Pergamon Press, London, p. 99, 1956. T. M. DONAHUE, J. E. BLAMON~ and M. L. LORY, P/u/let. Spurt. Sci.. 5, 185, 1961. J. E. BLAMONT, T. M. DONAHUE and M. L. LORY, Phys. Rev. LrttPr.r, 6, 403, 1961. J. W. CHAMBERLAIN, D. M. HLJNTEN and J. E. MACK, J. Atmos. Tcw. Pi7y.s.. 12, 153, 1958. A. V.&SSY and E. VASSY, C’. R. Acud. Sri. foris, 248, 2235, 1959. A. VASSY and E. VASSY, Plrrwt. Spuw. Sri., 1, 71, 1959. F. S. JOHNSON.J. D. PURCELL.,R. TOUSEY nnd K. WAIANABE. J. Geophys. Rev.. 57, 157, 1952. 0. S. HEAVENS, J. Opt. Sot. Anw., 51, 1058, 1961. M. MINNAEKT, The Sun (ed. G. P. KUIPER), University of Chicago Press, Chicngo, 1953. D. R. BA’TES and A. DAMGAARD, Phil. TIYU~S.,242, 101, 1949. M. MINNAERT, G. F. W. MUL.DEKS and J. HOU I‘GAST,Phototwtric At/w of the So/or S/wctrron, 1.3-7/6-7.8771. Schnabel, Knmpert and Helm, Amsterdam, 1940. C. D. SHANE, Lick. Ohs. 81111.507, 1941. J. H~UXAST, Review of dissertation (1942) by L. SMZER. A.strop/l_y.s.J., 99, 107, 1944. E. A. LYTI.E and D. M. HUNTEN, J. Atmo.y. Twr. P/I,vs., 16, 236. 1959. V. G. FESENKOV, Ap. J. Akud. Sci. SSSR., 36, 207, 1959. R. PENNDORF, J. Opt. Sot. Auwr., 47, 176, 1957. L. GOLIIBERG, The Earth us u Pkuwt (ed. G. P. K~JII%K), University of Chicqo Press, Chicago. 1953. p. 457. D. R. BATES and A. DALC;ARNO, J. Atttlos. Tw. Phv.~.. 5, 329, 1954. D. A. JACKSONand H. KLJHN, Proc. Roy. Sot., 173; 778, 1939.
OF
G. T. Department
BEST and T. N. L. PATTERSOS* of Applied Mathematics, Queen’s University, (Rewired
Belfast
25 bf~/_y 1962)
new method is discussed for measuring the temperature in an artificial cloud of alkali vapour. This method overcomes the complications introduced by the process of selfabsorption. Estimates of the intensities of the relevant emission lines to be observed are made. It is concluded that observations made on lithium capour present the best means of measurcment.
Abstract-A
1. INTRODUCTION
The presence of the Earth’s natural sodium layer and the resonance scattering which it causes during the evening and morning twilight periods led Bates”) to suggest that useful scientific information might be obtained from observations of artificial clouds of sodium in the upper atmosphere. Experiments concerned with the measurement of high altitude winds have been carried out by tracking the motion of the cloud. The use of vaporizers which eject sodium continuously as the rocket ascends or descends leads to some uncertainty about the vertical motions in the regions which may be studied. In spite of this, winds have been measured in the altitude range 70-230 km at sites widely distributed over the Earth’s surface during the last seven years.(2p18) Values of the diffusion coefficient for sodium and other alkali atoms in the atmosphere have been deduced from the rate of growth of the diameter of the trail,‘“,11~13~1G~1R) Few spectrographic studies have been made on the trail, The first firing(*) was observed by a grating spectrograph. With a dispersion of 150 A/mm the only conclusion that could be drawn was that the visibility of the trail was due to resonance scattering of solar radiation. In this paper some of the difficulties of the method at present used for temperature determinations are discussed and a method which should be more accurate is suggested. 2. OBSERVATIONS
If the optical thickness could be reduced sufficiently the examination of the sodium D-doublet by a high resolution instrument would yield the Doppler width and hence the temperature. The method has been applied to the 01 green line of the nightglow by Armstrong(1”,20) and by Wark and Stone .(21) A suitable Fabry-Perot interferometer was built in this department with a view to investigating this possibility. The results obtained, which are similar to those of Blamont,(22) will be published separately.‘2:s) Blamont has used the technique developed by Bricard and Kastler(“Q to examine the sodium twilight lines. (25) He has also applied the technique to an examination of the lines emitted by a high altitude sodium cloud with some success.(26~2i) Approximations must inevitably be introduced in interpreting the data. The optical thickness must be small otherwise the line profiles become so broad because of multiple scattering and self-absorption that they have no simple relation to the ambient temperature. In the case of the method using the Fabry-Perot interferometer the D,/D,ratio may indicate * Now at the Graduate Research Ccntre of the Southwest, Dallas, 5, Texas. 521 I
G. T. BEST and T. N. L. PATTERSON
522
when the optical thickness has become small but the line profiles at the expected temperatures are then far from true Doppler profiles due to hyperfine structure(28). The use of an instrument capable of resolving the hyperfine structure would not be easy in the field and the reduction of the observed profile to the true profile would be laborious. The results obtained by Blamont using the absorption cell technique are very interesting; particularly the manner in which the shadow thrown by the natural sodium layer is seen to modify the D,/D, ratio in the trail in a predictable manner. The method becomes more accurate as the optical thickness decreases but, as in the case of the Fabry-Perot profile determinations, the difficulty of detection becomes acute. The presence of the Earth’s natural sodium layer can also distort the profiles of the direct and scattered radiation. It thus appears that true temperatures cannot readily be obtained from measurements on the sodium D-doublet. 3. AN IMPROVED
METHOD
OF TEMPERATURE
DETERMINATION
Advantage may be taken of the fact that a line is not modified by self-absorption if its upper level is not populated by direct transitions from the ground level. The 42P level of sodium is de-populated by direct transitions to the ground state giving the 3303 8, doublet and by indirect transitions through the 42S and 32P levels giving doublets at 2.2 /L and 1.14 p followed by the D-doublet. The 3303& 5893 A and the 2.2 p lines suffer self-absorption so that it is not easy to infer the temperature from measurements made on their profiles.Only the 1.14 ,u lines have a true unmodified Doppler profile. Similar arguments apply to the other members of the alkali series, the unmodified lines for Li, K, Rb, and Cs occurring at about 8126 A, 1.25 p, 1.34 1~and 1.4 1~ respectively. Bedinger et a/.(3,4) and Vassy and Vassy (2g,30)have detected the second resonance lines of sodium at 3303 A in the morning but not in the evening. The observed ratio, l?, of the photon intensity of the 5893 8, radiation to that of the 3303 A radiation appears to vary greatly. The theoretical considerations of Cooper et al. w show that l? lies between 140 and 200 for resonance scattering whereas the observations by Vassy and Vassy indicate I? ranges between about 2 and 10. The latter also report that the 3303 A radiation is observed to be emitted from a small portion of the trail. It is possible that the localized source of high relative intensity 3303 A radiation is due to chemical excitation or to severe self absorption of the D-doublet. In the calculations no allowance appears to have been made for ozone absorption which is variable. This will affect both the intensity of the exciting radiation and of the downward scattered radiation. As is demonstrated later the attenuation of the exciting radiation is not serious but the intensity of downward scattered radiation may be affected’“‘) when the optical path is great (as for observations very near the horizon). Observational difficulties may be foreseen in any attempt to measure the profiles of the lines at 1.14 1~. Thus there is some difficulty in recording a feature in this spectral region Again the $ band of water vapour may cause absorption under the required conditions. and may modify the profile. The absorption has a maximum at about 11407 8, and falls off rapidly so that the attenuation at 11405 A, the nearest line, may not be unacceptably great, It was decided to investigate the possibility of using although the profile may be distorted. As a preliminary the intensities of all the lines in other members of the alkali group. question were calculated. 4. THEORETICAL
INTENSITIES
is apparent from the relevant Einstein A-coefficients c3zJthat the only significant contributions are from the lower S and P states of the alkali atoms. There are four terms which It
TEMPERATURE
FROM A CLOUD OF ALKALI
VAPOUR
523
must be taken into account: the ground term r2S and the excited terms (Y -+ 1)2S, r2P, (r + I)2P. These lead to four possible spectral doublets. 6) (ii)
r2Sk -- y2Pf,$
(iii)
r2P8,$ - (r + 1j2S3, (u + 1J25, - (v i l)*P,,,.
(iv)
the D-doublet,
r2Si - (r i- l>“Pj,!,
It is assumed that the alkali atoms are in radiative equilibrium, that is, the rate of population of a state by radiative processes equals the rate of de-population by radiative processes. In an optically thin layer the ratios of the number densities in the excited levels to the number density in the ground level are given by:
x [A(r + I S, rP,> _t A(r + 1 S, rP,)]-l
where A( Y,X) is the Einstein coefficient for spontaneous decay from state Y to state X, B(X, I’) is the Einstein coefficient forexcitation from state X to Y, ,Q(cJ~~.) is the energy density per unit ~vavenumber at wavenumber o,-,- and ~.~r is the wavenumber for the transition between X and Y. Taking account of the solid angle from the Sun to the Earth and using the relationship between the A and B coefficients it can be shown that: (4) in se+ where I&Asl-) is the solar energy flux at wavelength AAyyA, as given by Minnaert.(33) The numbers of photons emitted per particle per set are then given by:
where: the transitions sA - j>B correspond to (i) to (iv). The Einstein A coefficients adopted are those calculated by E3eavens’32)using the tables of Bates and Damgaard. (3~ Table 1 presents the results for ail the alkali atoms. The data cited by MinnaerW represents the continuum radiation from the Sun and so the intensity of the exciting radiation must be muItipIied by the ration of the intensity at the bottom of the Fraunhofer absorption line to the intensity in the continuum. The correction factor is not known reliably except for the broad sodium fines, the values for Na being O-052 for D, and O-058 for D,.(36,3’) Estimates can be made of the order of magnitudes of the Fraunhofer depths. Potassium
524
G. T. BEST and T. N. L. PATTERSON TABLE I. PHOTON INTENSITIE?
Wavelength ([.A.)
A(l0”)
Photons/p3rticlclsec.
Lithium
6707.9 12 6707.761 3232,660 3232.660 8126,231 8126.452 26879.74 26879.74
36.7 36.1 I.09 1.09 I I.1 22.2 3.7 3.7
6.25 12.5 9.9% -4)(-j-) l,99( -3)(.V) 3.38( 3) 6.75(+3) 3.38(, 3) 6,75( -3)
Sodium
5895.924 5889.951 3302,993 3302.380 11381.64 11403.97 22083.56 22056.13
58.9 59, I 2.85 2.85 8.26 16.4 6.44 6.41
0.384(::) 0,690( 5, 4,11(-3)(-i-) 8,18(&3)(t) 9.33( -3) 1.X5( -2) 9.2X( - 3) 1.86( ~2)
Rubidium
7947.600 7800.263 4215,524 4201.792 13233.28 13663.00 279 12.95 21321.75
35.6 37.5 2.43 2.80 6.62 12.9 4.28 4.48
IO.2 20.5 2.44( ~ 2)(Vi-) 5.88( -2)(1-;-) 4.65( -2) 9.06( -2) 4.29( ~2) 9.41(-2)
Potassium
7698,977 7664.905 4047.208 4044.137 1243 I .89 12521.77 27206. I3 21067.94
36.9 37.2 1.98 2.14 7.15 14.2 4.4 4.44
1,09( ) 7.17( /I .**) ;.39( ~2)(: 3.15(,12)(g 3.22(-2) 6.40(&2) 3.10( -2) 6,53( 2)
8943.499 8521.104 4593.112 4555.229 13588.29 14695.03 30949.97 29307.64
28.6 32.4 2.12 2.97 6.23 11.4 3.52 4.05
I I.5 22.7 3.28(&2) 9.97( --~2) 6.73(,- 2) I .23( ~ 1) 5.45( -2) 1.36( ~--I)
Caesium
*
) )
* (+) (T) (8) ((I)
The numbers in brackets denote the power of ten Fraunhofer depth not determined. Fraunhofcr depth 0.058 Fraunhofer depth 0.052 Fraunhofer depth approximately 0.1 I. (’ ) Near the strong Fe1 Fraunhofer line (probably small). (*“;) Atmospheric absorption by 0,; assumed to have same depth ponent. (+f) Probably atmospheric absorption.
ns the other com-
TEMPERATURE
FROM
A CLOUD
OF ALKALI
VAPOUR
525
76998,does show a normal Fraunhofer profile which Lytle and Hunten(“al find to have a reduction factor 0.02 to 0.1 1 using the atlas of Minnaert PI CZ/.(~~) The Fraunhofer reduction factor of the D-lines as measured in the Minnaert atlas must be multiplied by g to obtain the actual reduction factor. If the observed sodium and potassium lines have the same shape the i correction factor should still apply and so the higher value ofO.11 is adopted. Table 1 column 4 gives the photon intensities with comments on the assumed Fraunhofcl reduction factors. It should be noted that some of these alkali lines. for example i4202 of RbI and i,7665 of K I, sufl-er strong atmospheric absorption. 5. TRAILS
OF LITHIUM
VAPOUR
In
this section some of the advantages of using lithium as distinct from any other al!
cossq~) ,
u,,
cos-l( -&) -
0,)
2
f=
(6)
0, being the depression of the Sun when observations commence and R being the radius of the Earth. If L is taken to be 200 km and S to be 40 kmJ‘is about 0.8. It can be seen therefore that a suitable choice of the observation time can eliminate some of the trouble from absorption of the excitin g radiation. Equation (6) indicates that L must be at least 95 km. To estimate the factor/C by which the intensity of the 3232A exciting radiation is reduced by Rayleigh scattering it is sufficient to assume an isothermal atmosphere. If/l,< is the number density of molecules at altitude S, (TV, is the scattering cross-section at \+avelength 3, and H is the scale height then
Ke
exp [-II,(T~.\ 2-rr(S it- R)Hj
(7)
Taking N and S to be respectively 7 km and 40 km it is found that A’ is 0.96 so that the reduction is quite small. It is difficult to estimate the effect of absorption of water vapour because of its variability but it can scarcely be serious since the nearest absorption peaks (cf. Goldberg(J1)) in the vicinity of 8126 A are at 8059 8, (weak) and at 8226 A (medium). It is of importance to consider the background radiation which is due mainly to the Meinel system of hydroxyl. The strong OH (9.4) band is just below the region of 8126 A but tracings of the nightglow spectrum shows that an intensity minimum occurs near 8126 A. The emission is certainly less than 5 Rayleighs,‘A.
526
G. T. BEST and T. N. L. PATTERSON
For comparison with background radiation it is of interest to estimate the theoretical emission rate for lithium using Table I. Taking the trail of vapour to be about 40 km long and 1 km in diameter, a release of 2 kg of Li leads to about 6 x lo9 atoms cme3, which corresponds to 6 x 1014 atoms per cm2 column along the line of sight. The quantity, q, defined by:
is a measure of the optical thickness of thelayer (cf. Batesand Dalgarno@2)); hl is the molecular weight of the species, T the temperature in “K, 1 the wavelength in A, f the oscillator
p: 71.4 ii', 2'Pt-3'S1 i B
L,=_22P;-325, 2 14~3 -6*2(-4) ‘/~3.7&4)
3m-4) zs-4) 76.5) .2.3(-4)
5)
jl 5)
--+A%
s $ _ m
FIG. 1. RELATIVEINTENSITIESAND WAVELENGTHSOFTHE Lie AND Li’ LINESAT 8126A. THENUMBERSABOVE THE LINES INDICATE THE RELATWEINTENSITIES. THE HYPERFINE SPLITTINGS ARE NOT TO SCALE. LINES A AND B ARE THE LINES TO BE OBSERVED. THE WAVELENGTHS OF THE CENTRES OF GRAVITY OF THE MULTIPLETS ARE GIVEN.
strength associated with the initial transition and N the total number of atoms per cm” column along line of sight. The layer is optically thin or thick according as q is much less than or much greater than unity. For the 3233 A line of lithium 4 is about 14, when the temperature is 200°K. It is therefore necessary to consider the optically thick case. The emission is limited by the number of solar 3233 A photons within the absorption equivalent width of the line, AR,, and can be written as: \ Pma E=-.---- W% IO-” Rayleighs (9) 47r CPm3 -I- Pnlza1 where Al,
is the Doppler
half width the photon Earth and $‘sr26 and p3233, is found that F is about IO5 Rayleighs radiation. A slight complication arises since the former about 12 times as abundant it is estimated that the isotope shift of for the 5 --A 2 transition.
of the 3233 8, line, P is the solar flux at 3233 A at the emission rates per particle, are as given in Table 1. It which is considerably greater than the background Li exists in two dominant isotopic forms Li7 and LP, as the latter. Using the data of Jackson and Kuhn’43) 8 126 A is 0.188 8, for the f --j $ transition and 0.196 8,
TEMPERATURE
FROM
A CLOUD
OF
ALKALI
VAPOUR
527
As regards the distortion of the profiles due to the hyperfine structure which markedly influences the resonance lines, (cf. Chamberlain et al. czs)),it can be seen that little disturbance is to be expected here since the first excited state, with much smaller splittings, is the final state in the 8 I26 A transition. When calculating the hyperfine structure of the lithium lines it \vas assumed that the 3S, state has zero splittings. By comparison with Na, estimates were made of the 2P, splitting. Fig. I Sives the positions of the important lines together with the distributions of the intensities. The hyperfine splittings may be completely neglected in their effect on the Doppler profile of the lines. The Li”(2P, - 3s;) and Li7(2PJ - 3P,) at Bon Fig. 1 are very close together being separated by about 0.03 A. However, the former corresponds to the weak component of Li” and the latter to the strong component of Li;. Taking account of the relative abundances the ratio of the intensity of the two lines is about 1 were calculated and led to the conclusion that the “4’ Some profiles of this combination error in temperature deduced by treating the observed profile as that due to a single line is about 4 per cent in the worst case. Measurement made on the 2P, -- 3S, line of Li’ introduce no such errors although the intensity is reduced by a factor bf 2. _ Finally, it may be noted that the 8126 A line is easily observed both photographically and photoelectrically, a fact which, together with the previous discussion, makes lithium more promising than the other alkali atoms whose unmodified lines lie much further into the infra-red. At present preparations are being made to measure the profile of this line and results should be published later. Ack/ralv/~~~eme/rrs-The authors thank Professor D. R. Bates. F.R.S., for his interest in this work. The research reported has been supported in part by the CambridgeResearchLaboratories,OAR, through the European Office, Aerospace Research, United States Air Force, under Grant No. AF-EOARDC 61-16, and in part by the Department of Scientific and Industrial Research. REFERENCES 1. D. R. BATES, J. Geophys. Res., 55, 347, 1950. am/Airrorae (cd. E. B. ARMSTRONG 2. H. D. EDWARDS, J. F. BEDINGER and E. R. MANRING; The Air;plol~~ and A. DALGARNO), Pergamon Press, London, 122, 1956. 3. J. F. BELXNGER, E. R. MANRING and S. N. GHOSH. J. Gcophys. Res.. 63, 19, 1958. 4. C. D. COOPER, E. R. MANRING and J. F. BEDINGER, J. Geophys. Res., 63, 369, 1958. 5. E. R. MANRING, J. F. BEINNGER and H. B. PETTIT, J. Geophys. Rex., 64, 587, 1959. Co., Amsterdam, 6. G. V. GROVES, Spcrce Research-I (rd. H. KALLMANN BIJL), North Holland Publishing 1960, p. 144. 7. E. R. MANRING and J. F. BEDINGER, Spuce Research-Z (ed. H. KALL~IANN BIJL), North Holland Publishing Co., Amsterdam, 1960, p. 154. Pub8. W. G. ELFORD and E. L. MURRAY, Space Rrsearch-I (ed. H. KALLMANN BIJL). North Holland lishing Co.. Amsterdam, 1960, p. 158. Co., Amsterdam, 1960, 9. A. VASSY. Spce Re.warc/r-I (cd. H. KALLMANN BIJL), North Holland Publishing p. 203. 10. J. A. REES, Space Rmxrch-l(ed. H. KALLMANN BIJL), North Holland Publishing Co., Amsterdam, 1960, p. 207. II. E. MANRING. J. BEDINGER and H. KNAFLICH, Space Rc~scarch-II (ed. H. C. VAN DE HUL~T, C. DE JAGER and A. F. MOORE), North Holland Publishing Co., Amsterdam, 1961, p. 1107. 12. L. BROGLIO, Space Rescrrrch-If (cd. H. C. VAN DE HuLs-~, C. UE JAGER and A. F. MOORE), North Holland Publishing Co., Amsterdam, 1961, p. 1125. 13. E. R. MANRING and J. F. BEDINGER, J. Geopl~~.r.Rrs.. 62, 170. 1957. 14. F. F. MARMO. J. PREssnrsN, E. R. MANRING and L. ASCHENBR~~D, PImet. Space SC;., 2, 174, 1960. 15. J. E. BLAMONT, C. R. Am;/. Sri. Paris, 249, 1248, 1959. 16. J. E. BLAMONT, Space Rrsetrrch-I (,ed. H. KALLMANN BIJL), North Holland Publishing Co., Amsterdam, 1960, p. 199. 17. G. V. GROVES. N&LIIY, Loncl. 187, 1001, 1960. 18. J. A. REES, Plmct Space Sri., 8, 35. 1961.
528 19. 20. 21. ‘72. 23. 24. 25. 26. 27. 2X. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 30. 41. 42. 43.
G. T. BEST and T. N. L. PATTERSON E. B. ARMSTRONG, J. Phys. Rd., 19, 358, 1958. E. B. ARMSTRONG, J. Atrrros. Terr. Phys., 13, 205. 1959. D. Q. WARK and J. M. STONE, Nrrtuw, Lad. 175, 254, 1955. J. E. BLAMONI‘, Am. GPO&W., 16, 435, 1960. E. B. ARMSTROUG, G. T. BEST and J. MAZUR (to be published). J. BRICARD and A. KASTLER, Am. Gcophys., 1, 53, 1944. J. E. BLAMOUT, The Airglow and Aurorae (ed. E. B. ARMSTRONG and A. DALC;*\RNO), Pergamon Press, London, p. 99, 1956. T. M. DONAHUE, J. E. BLAMON~ and M. L. LORY, P/u/let. Spurt. Sci.. 5, 185, 1961. J. E. BLAMONT, T. M. DONAHUE and M. L. LORY, Phys. Rev. LrttPr.r, 6, 403, 1961. J. W. CHAMBERLAIN, D. M. HLJNTEN and J. E. MACK, J. Atmos. Tcw. Pi7y.s.. 12, 153, 1958. A. V.&SSY and E. VASSY, C’. R. Acud. Sri. foris, 248, 2235, 1959. A. VASSY and E. VASSY, Plrrwt. Spuw. Sri., 1, 71, 1959. F. S. JOHNSON.J. D. PURCELL.,R. TOUSEY nnd K. WAIANABE. J. Geophys. Rev.. 57, 157, 1952. 0. S. HEAVENS, J. Opt. Sot. Anw., 51, 1058, 1961. M. MINNAEKT, The Sun (ed. G. P. KUIPER), University of Chicago Press, Chicngo, 1953. D. R. BA’TES and A. DAMGAARD, Phil. TIYU~S.,242, 101, 1949. M. MINNAERT, G. F. W. MUL.DEKS and J. HOU I‘GAST,Phototwtric At/w of the So/or S/wctrron, 1.3-7/6-7.8771. Schnabel, Knmpert and Helm, Amsterdam, 1940. C. D. SHANE, Lick. Ohs. 81111.507, 1941. J. H~UXAST, Review of dissertation (1942) by L. SMZER. A.strop/l_y.s.J., 99, 107, 1944. E. A. LYTI.E and D. M. HUNTEN, J. Atmo.y. Twr. P/I,vs., 16, 236. 1959. V. G. FESENKOV, Ap. J. Akud. Sci. SSSR., 36, 207, 1959. R. PENNDORF, J. Opt. Sot. Auwr., 47, 176, 1957. L. GOLIIBERG, The Earth us u Pkuwt (ed. G. P. K~JII%K), University of Chicqo Press, Chicago. 1953. p. 457. D. R. BATES and A. DALC;ARNO, J. Atttlos. Tw. Phv.~.. 5, 329, 1954. D. A. JACKSONand H. KLJHN, Proc. Roy. Sot., 173; 778, 1939.