The red line of atomic oxygen at twilight

Planet. Space Sci. 1973, Vol. 21, pp. 1937 to 1943. Pergamon Press. Printed in Northern Ireland

THE RED LINE OF ATOMIC

OXYGEN

G. LEJEUNE* and A. DALGARNO Harvard College Observatory and Smithsonian Astrophysical Cambridge, Massachusetts, U.S.A.

AT TWILIGHT Observatory,

(Receiued 16 May 1973) 1. INTRODUCTION

A detailed study of the emission of the red line of atomic oxygen at twilight has been carried out by Noxon and Johanson, (1972), who conclude from a comparison of the observations with the intensities predicted as a result of ionic recombination of 0,’ and photodissociation of O2 that a third source must exist, which they postulate as local photoelectron excitation of 0 atoms. Their suggestions can be tested quantitatively by explicit calculation of the absorption of photoelectrons in the atmosphere (Dalgarno and Lejeune, 1971) but the effects of escape are significant and must be incorporated into the theory. 2. THEORY

At twilight, the peak in the production rate of OID atoms is located at an altitude above 300 km where the mean free paths of the photoelectrons are greater than the scale height of the atmosphere. An upward moving photoelectron loses its energy in a region where the ratio of the electron density n, to the atomic oxygen density n, is larger than at the source altitude so that the fraction of the photoelectron energy that appears as a red line photon is less. The downward moving photoelectrons produce more OID excitation than would local deposition of energy but the quenching efficiency of OID atoms increases with decreasing altitude and the net excitation rate is not greatly modified. However the altitude profile may be much different from that corresponding to local absorption of energy. A detailed description of the calculation of the absorption of energetic electrons in a gas of atomic oxygen has been presented (Dalgarno and Lejeune, 1971). In it, a set of discrete energies Ei is chosen in order of increasing energy Ei+, > Ei. If vi is the electron velocity and oj(Ei) is the cross section for excitation or ionization of atomic oxygen by impact with an electron of energy Ei, the frequency Vj at which discrete energy loss AE, occurs through excitation or ionization is given by vi = noviaj(Ei) set-l.

(1)

If -dE/dt is the rate at which energy is lost continuously in collisions with the electron gas (Schunk and Hays, 1971), a mean collision frequency v6 for an electron of energy E, to slow down to Ei_, in collisions with the electron gas is given by 1

v, =

(2)

E, - 4-l We introduce an elastic cross section

(3) * Present address: Centre National Issy-les-Moulineaux, France. 8

d’8tudes

des Ttkommunications, 1937

2 av. de la Rkpublique,

92

1938

G. LEJEUNE and A. DALGARNO

Then the mean time between collisions, t,, is given by r,-’ = u,(&Q,(E,) + ne@i)). The probability Pi that any particular discrete process occurs is given by P* = ~*~~t~~j(E~},

(4) 0)

and the probability P, that elastic loss occurs is given by P, = n,vt,a,(Ex).

(6)

Necessarily, &Pj+P,=l;

(7) the summation includes an integration j’P, de, over the ionization continuum. During the time t,, the electron traverses an ahitude range AZ,. Thus an electron moving at an altitude z, with energy Ei has a probability Ps of undergoing an energy loss AEj and being transformed into an electron of energy Es - AEj at z, - AZ; there appear also at r7n - AZ, P, secondary electrons with energies e, = AE* - I, I being the ionization threshold. The calculation of energy deposition in the atmosphere proceeded by the selection of two neighbouring energies E, and En_1 and two neighbouring altitudes zt and zt_r that bracket the energy Ei - LIE, of the electron and the altitude z, - AZ where it is produced. Linear inte~olation was used to construct the resulting production of electrons at the plane. To four points (&, zt), (-%+ ~3, UG, .Q), (.%.+ z& on the altitud~nergy the production from the electron originally at (El, z,,J was added the direct contributions of ionization by solar ultraviolet radiation and the contributions from other primary electrons of higher energies, produced at other altitudes. The calculation is then repeated for other energies and altitudes. To complete the atmospheric calculation, an estimate of the altitude AZ traversed in the time t, is needed. We assumed that during the time t, the electron undergoes a random walk so that AZ = ut, sin I cos ~~~lf2 where I is the magnetic dip angle, CLis the pitch angle and N is the ratio of the mean free path 1 = vt, to the mean free path I, for purely elastic collisions with neutral particles. Upward moving photoelectrons and downward moving photoelectrons may then be treated separateIy. Given an initial photoeIectron energy spectrum, which may be computed foliowing standard procedures (cf. Dalgarno et al., 1969), the calculation of the energy degradation of the photoelectrons gives the energy lost at any altitude z in the various excitation, ionization and heating processes and also the number of electrons P(E, z) produced with a given energy Eat altitude z. The equilibrium photoelectron flux distribution F(E, z) may then be derived from the relationship F(E, z) = ut,P(E, z) cm-2 set-l eV-l. The calculations may be tested for consistency because the rate of excitation of any selected process at z is also given by the integral co na,(E)F(E, z) dE cmm3see-‘.

s0 If AZ is taken to be zero, the results reduce to the local computations Lejeune (1971).

of Dalgarno and

THE

RED

LINE

OF ATOMIC

3. RESULTS

OXYGEN

AT TWILIGHT

1939

AND DISCUSSION

The atmospheric calculations were carried out for a mean pitch angle of 60”, a value suggested by the angular scattering calculations of Banks and Nagy (1970), and a magnetic dip angle of 72”, which is appropriate to the measurements of red line intensities by Noxon and Johanson (1972). We adopted the three different ambient electron profiles listed in Table 1. The first profile is representative of sunrise conditions and the third of sunset conditions. They were provided by Dr. J. Evans who constructed them from backscatter data taken during the period of the red line measurements. The second profile is an arbitrary low density profile whose adoption should provide an upper limit to the possible 63008L emission intensity. TABLE 1. ELECTRONDENWYPROFILES Altitude (km)

600 550 500 450 400 350 300 250 200

n,( 1OScm-*) (3)?

(I)*

(2)

1.0 1.5 2-o 2.6 3.0 3.2 3.3 3.2 2.0

0.55 0.75 1.03 1.41 1.95 2.34 2.18 0.76 0.20

1.3 2.0 3.0 3.7 4.7 6.0 7.0 7.4 6.0

* Sunrise; t sunset.

Figure 1 is a comparison of the predicted rates of emission of 6300 A radiation for a model atmosphere (Dalgarno et al., 1969) with an exospheric temperature of 900°K and a solar zenith angle of 90”, calculated with the sunrise electron profile on the assumption that excitation is local (curve b) and on the assumption that the electrons move down (curve a) or move up (curve c). Quenching of the O(lO) level in collisions with iV, was

,0°2

I;:

.

300 -

6300A

IO EMISSION RATE

IO (cm-3sec+l

FIG. 1. THE PREDICTED EMISSION RATES OF 63OOA LUMINOSITY AT S~NRISEASSUMINGLOCAL EXCITAT~ON(CURVE~),DOWNWARDMOVINGPHOTOELECTRONS (CURVE a) ANDUPWARDMOVING PHOTOELECTRONS (CIJRVEC).

1940

G. LEJEUNE and A. DALGARNO

10-Z

IO-’

JO

I

6300

i EMISSION

RATE

40

(cm+sec?)

FIG. 2. THE PREDICTION 63OOa

EMISSION PROFILES FOR VARIOUSSOLARDEPRESSIONANGLESIN THELOCALAPPROxIMATIONSFORSUNRISEELECTRONDENSITIES.

included with a rate coefficient of 7 x lo-l1 cm3 set-l. The integrated emission rate arising from the downward moving photoeiectrons is somewhat smaher than that given by the local approximation because the increased quenching efficiency outweighs the increased production of O(lD) atoms. The integrated emission rate arising from upward moving photoelectrons is half that given by the local approximation, a greater fraction of the photoelectron energy appearing as ambient electron heating. The profiles differ considerably. The profile obtained by assuming that half the photoelectrons are moving upwards and half downwards is much wider than the local profile, because electrons produced at the altitude of peak production can travel large distances before falling below the O(lD) excitation threshold. The effect is less for more energetic transitions. Figures 2 and 3 illustrate the dependence of the emission profiles on the solar zenith

600

r

/

I

1

i

500 "

i

1

IO

40

98" Id2

1 I6 6300

I I i

EMISSION

FIG. 3. THE SAMEASFIG.

RATE

2 BUTINTHE

bn-3sec-i) NON-LOCAL APPROXIMATION.

THE RED LINE OF ATOMIC

90

92

94

96

SOLAR ZENITH

FIG. 4. THE INTEGRATED

OXYGEN

96

100

AT TWILIGHT

102

1941

104

ANGLE 2 (degrees)

NON-LOCAL 63OOA EMISSION RATES FOR THE ELECTRON DENSTY PROFILES (l), (2) AND (3) OF TABLE 1.

angle in respectively the local and non-local approximations. The calculations employed the sunrise electron densities of Table 1. In the local approximation, the shape of the profile varies rapidly with solar zenith angle 2 whereas in the non-local approximation the profile is insensitive to 2, the altitude of peak emission remaining near 300 km as 2 increases from 90 to 104”. In both the local and non-local descriptions, the magnitudes of the emission rates decrease rapidly with increasing 2. The influence of the ionospheric ambient electron densities is shown in Fig. 4, which contains the integrated non-local column emission rates for solar zenith angles between 90 and 104” appropriate to the electron densities listed in Table 1. The integrated rates decrease by a factor of two as the peak electron density increases by 2.5. Noxon and Johanson (1972) have measured the 6300 A intensity at solar zenith angles between 90 and 105”. They conclude that for Z > 95”, the measured intensities can be interpreted as a result of the production of O(lD) atoms by ionic recombination and by photodissociation in the Schumann-Runge continuum of molecular oxygen, but that for Z < 95” another source is necessary. The magnitude of the additional source is reproduced in Fig. 5 together with the results of the non-local photoelectron calculations for an atmosphere with an exospheric temperature of 1000°K and the sunrise electron density profile; such an atmosphere reproduces the data for Z > 95” (Noxon and Johanson, 1972). Although the theoretical and observational curves are similar in shape, there is a discrepancy of almost an order of magnitude. There are a number of ways by which the discrepancy could be resolved. A reduction in the resonance line excitation cross section below that claimed by Stone and Zipf (1971) is not improbable and an enhancement in the predicted intensity by a factor of two may be appropriate. Further factors of two could be gained by ignoring the non-local nature of the excitation (Figs. 2 and 3) or by adopting a minimum electron density ionosphere

1942

G. LEJEUNE

SOLAR FIG. WITH (1972)

5.

A COMPARISON

THE

ZENITH

OF THE PREDICTED

OBSERVATIONS,

AFTER THE COMPUTED

INDICATED

and A. DALGARNO

ANGLE

(degrees)

PHOTOOELECTON BY

CONTRIBUTIONS HAVE

CROSSES

EXCITATION

AND

CIRCLES,

OF PHOTODISSOCIATION

RATE OF OF

6300 A RADIATION

NOXON

AND

IONIC

AND

JOHANSON

RECOMBINATION

BEEN SUBTRACTED.

(Fig. 1) but neither assumption is realistic. The O(lO) quenching coefficient that we adopted may be too large even at 300°K and the quenching efficiency could conceivably decrease rapidly with temperature so that at 1000°K it is much less than the value measured at room temperature. Neither theory nor observation supports the latter possibility (Sipler and Biondi, 1972). The omission of any deactivation of the O(lO) level would lead to an enhancement in the predicted intensities of a factor of about three. There is also some uncertainty over the absolute accuracy of the solar flux values and various arguments have been advanced that suggest that the intensities of Hall and Hinteregger (1970) are too low (Swartz, 1972; Roble and Dickinson, 1973; Lejeune, 1973) by a factor of between two and three. Accordingly our production rates which were based upon the greater intensities obtained by Hinteregger, Hall and Schmidtke (1963) should be increased by a factor of between 15 and 2.3. However support for the values we adopted is provided by recent measurements at 2 = 86” of the 1356 A line (Rottman, Feldman and Moos, 1972) and of the 63OOA and 5577A lines (Schaeffer, Feldman and Zipf, 1972) of atomic oxygen at altitudes below 250 km. From an analysis of the various contributions to the excitation of O(lO), Schaeffer et al. (1972) derived a value of 600 Rayleighs for the electron impact excitation source whereas we predict 400 Rayleighs. The measured and predicted profiles are in harmony between 220 and 250 km, where the data terminate, but the theoretical profile decreases less rapidly below 220 km. The partitioning of the measured O(lO) excitation into photodissociation, recombination and electron impact is not unique and the discrepancy below 220 km may not be significant. Schaeffer et al. (1972) derived similarly a value of 30 Rayleighs for the electron impact excitation source of the green line below 240 km. We predict 130 Rayleighs but again the discrepancy is not necessarily significant. In their analysis, Schaeffer et al. use a value of 40 for the relative contributions of electron impact excitation to the O(?!?) and O(lO) levels, a value derived from an earlier flight (Doering et al., 1970; Feldman et al., 1970; Schaeffer et al., 1971) at a solar zenith angle of 60”. We predict for 86” a ratio of about five. A small discrepancy exists between

THE RED LINE OF ATOMIC OXYGEN

AT TWILIGHT

1943

our calculations of the 1356 A line (Dalgarno and Lejeune, 1971) and the measurements (Rottman et al., 1972) but it is of little significance because of the uncertainty in the excitation cross sections. We note finally that the relatively small magnitude of the contribution from photoelectron impact at twilight is at least consistent with the observations by Noxon and Johanson (1972) that there is little difference between the morning and evening and twilight intensities. The theory predicts a 25 per cent enhancement in the photoelectron contribution at morning twilight. Despite the approximate nature of our description of non-local excitation, there appears to be a real quantitative discrepancy between theory and the observational analysis of Noxon and Johanson (1972). None of the analyses has allowed for the presence of additional sources of O(lO) atoms such as N(20) + O(3P) -+ N(4S) + O(lO). This source may be more important at twilight. At smaller zenith angles, the main production of N(20) atoms occurs at lower altitudes where N(20) atoms are destroyed in collisions with molecular oxygen. A measurement of the twilight profile of the red line emission at altitudes above 300 km would be instructive. Acknowledgements-We are grateful to Dr. J. Evans for providing us with twilight electron density profiles derived from his backscatter data and we are indebted to Dr. J. F. Noxon for several informative discussions. This work was supported by the Atmospheric Sciences Section, National Science Foundation, NSF Grant GA-21492. REFERENCES BANKS,P. M. and NAQY, A. F. (1970). J. geophys. Res. 75,1902. DALGARNO,A., MCELROY,M. B. and STEWART,A. J. (1969). J. atmos. Sci. 26,753. DAU;ARNO,A. and LEJEUNE,G. (1971). Planet. Space Sci. 19,1653. DOERING,J. P., FA~TIE,W. G. and FELDMAN,P. D. (1970). J.geophys. Res. 75,4787. FELDMAN,P. D. DOERING,J. P. and ZIPF, E. C. (1971). J.geophys. Res. 76,3087. HALL, L. A. and HINTEREGOER, H. E. (1970). J. geophys. Res. 75,6959. HINTEREGGER, H. E., HALL, L. A. and SCHMIDTKE, G. (1963). Space Research, Vol. V, pp. 1175-1190. North Holland, Amsterdam. LEIEUNE,G. (1973) Photo&ctrons et bilans tnerg&iques des 6lectrons dans l’ionosph&re diurne. Th&se de doctorat d’Etat de l’universite de Paris. NOXON,J. F. and JOHANSON, A. E. (1972). Planet. Space Sci. 20,2125. ROTTMAN,G. J., FELDMAN,P. D. and Moos, H. W. (1973). J.geophys. Res. 78,258. ROSLE,R. G. and DICKINSON,R. E. (1973). J. geophys. Res. 78,249. SCHAEFFER, R. C., FELDMAN,P. D. and FA~TIE,W. G. (1971). J.geophys. Res. 76,3168. SCHAEFFER, R. C., FELDMAN,P. D. and ZIPF, E. C. (1972). J.geophys. Res. 77,6828. SCHUNK,R. W. and HAYS, P. B. (1971). Planet. Space Sci. 19,113. SIPLER,D. P. and BIONDI,M. A. (1972). J. geophys. Res. 77.6202.