Planet. Space Sci. Pergamon Press 1961. Vol. 5, pp, l-32. Printed in Great Britain.

STRUCTURE OF THE

MARCEL NICOL~ Research Laboratory, Pennsylvania State University, University Park, Pennsylvania

(Received 3 July 1960)

Abstract-The vertical distribution of the density in the thermosphere, deduced from satellite observations, must be explained by an increase of the scale height with altitude. A varying gradient of the scale heighht cannot be interpreted by assuming an increase of the temperature gradient with altitude. An examination of the interrelationships between the absolute values of density in a dark atmosphere and diurnal conditions of heat conduction reveals that the varying gradient of the scale height above 200 km is essentially due to the decrease of the molecular weight, mg, of the atmos- pheric constituents subject to diffusion. In the night atmosphere the isothermy above a certain altitude (~200 km) is the critical factor characterizing the vertical distribution of density. The temperature of the isothermal region, resulting from conduction, is related to the ultra-violet heating which was available during the day. The effect of diffusion has been clearly shown by establishing a thermo-isobaric relation connecting the temperature of the isothermal region with an isobaric level where atomic oxygen has a specific concentration. From observational data on the variation of the night-time density at high levels, it is possible to deduce the variation of the temperature of the isothermal region. The gradient of temperature in a sunlit atmosphere is related to the fraction of the ultra-violet Solar energy absorbed, which determines the magnitude of the variation of the scale height with altitude. Since heat transport is a function of the atomic or molecular concentrations and the square of the distance, it is shown that anomalies in the temperature gradient cannot be permanent.

1. INTRODUCI’ION above satellites. See for example, Jacchia@“, The effect of air resistance on the motion of Jacchia and Briggs (u) Harris and JastroW(*Q an artificial earth satellite makes it possible to Siry”“, Steme”8*‘9), &hilling et al.crr), Schillini derive the atmospheric density in the region of and Whitney@* ‘3), Sedo~(‘~), King-Hele@‘~, (3rOVeS(19,20.21) the perigee of its orbit. Formulae relating , Mikhnevich et a1.‘62) and satellite drag to orbital elements have been Paetz,old(6s) derived by various authors; see for example It is evident that the absolute values of the Groves(ZOJ, King-Hele(3B) and Sterne@Q. Deter- density which have been deduced from these minations of density have been made by various observations may vary according to the methods authors following the initial calculations of the and satellite parameters used by the various acceleration of the first two satellites 1957 a and authors. Thus, the drag parameter qs is P (Sputniks 1 and 2), whose perigees were at dependent on the mass of the satellite ms. on about 220 km; see for example Mullard Radio the effective cross-section of the satellite ss. and Astronomy Observatory@Q, Royal Aircraft on the satellite’s drag coefficient Cs; qs=s.Cs/ms Establishment’7”), Sterne et a1.@*), Sterne and can differ according to the values used by the Schilling’*‘), Harris and Jastrow(22), Jacchia(26*2e), authors. Consequently, the absolute values of Groves(“) Sterne(‘** 7s), E1’Yasberg”6), the density deduced can be different even if the Lido@‘), ’ Mikhnevich’JZ1, Priester et al.(ss), formulae relating density to acceleration are the Warwick’*‘) and Paetzold’63) same. In addition, the values of the density do From the spring of 1958,‘the satellites Van- not necessarily relate to the same period in the guard I (1958 /3 2), Explorer I (1958 a), Explorer life of a satellite and can correspond. therefore, IV (1958 E), and Sputnik III (1958 6). made to difTerent physical states of the high atmos- possible an analysis of the densities at altitudes phere. In this case, the scale height associated of approximately 650 km, 350 km, 260 km and with the density may not be appropriate. 220 km corresponding to the perigees of the Finally, because the altitudes of certain satellites 1 2 MARCEL NICOLET are not given with adequate precision the densi- although certain differences can be expected ties obtained do not correspond with the since measurements made with rockets involve approximate altitude indicated. the collection of samples which can relate to From the beginning of these observations, sporadic conditions that are not necessarily Groves(l’) stressed the importance of the equa- representative. As a result, values of density torial bulge which changes the altitudes by between 200 and 250 km as given by 12~5km between the equator and latitude 50”. Mikhnevich(sl’ are perhaps too small when After JacchiacZ7) had indicated the existence of compared with satellite data. irregularities in the acceleration of satellite If we consider the results of LaGow et aZ.‘46) 1957 /3 many variations were detected and and Horowitz et aZ.@Q,the densities, p, at 200 ascribed to many different causes but it was km, at Churchill, i.e. immediately obvious that the atmosphere was 1956, Nov. 17, day; p=3.6 (?:.,) x 10-ls gcmm3 responsible for these irregularities. Neverthe- less, the special effects were attributed to many 1957, July 29, day; p =(6+7 +2) x lo-l3 gcmw3 causes such as discontinuities in the atmosphere 1958, Oct. 31, day; p=4*Ox 10-13gcm--3 at certain latitudes. For example, King-Hele (extrapolated) and Walker(40) insisted that near 30”N the effect 1958, Feb. 24, night; p=(1.3 kO.6) x lo-l3 of the irregularities was caused mainly by solar g cm-3 disturbances. In any event, the variations of it is clear that the median value corresponds to solar radiations at 20 cm and 10 cm @-iester( the value obtained from the satellite data, Jacchiac3Q) show clearly that solar emissions (4 * 2) x lo-l3 g cmv3. Furthermore, the value play a primary role in the variation of atmos- obtained at White Sands, of the order of pheric density. It should be noted here that it 1.4 x lo-l3 g crne3 at 200 km, corresponds to an is only possible to enter into a detailed discussion atmosphere, in 1951, for which the pressure of all the variations if the observational data was only 10m4mmHg at 100 km when it was are very precise and sufficient in number so as (3 + 1) x 10e4 mm Hg at Churchill. to be able to follow all the fluctuations as a Mikhnevich@l) indicating a density of function of altitude. 2.7 x lo-l3 g cm-3 at 200 km is still inside of the possible variation. However, he adoptP) 2. ANALYSIS OF OBSERVATIONAL the value of 2.1 x lo-l3 g crnm3 at 225 km for RESULTS an atmospheric model. 2.1. Mean values of the density It can be concluded that an average value of Before carrying out an analysis of the various the order of 4 x lo-l3 g crnws represents the variations of the density it is desirable to provide atmospheric density at 200 km during the sun- a description of the results as a whole. For this spot maximum in 1958-1959. Variations lead- reason we have summarized the main results as ing to (4 +2) x lo-l3 g cm-3 can be accepted, shown in Fig. 1. Extreme values between 1 and 7 x lo-l3 g cmw3 Before being able to determine which varia- are not representative of latitudinal, seasonal or tions modify the density we must decide on the diurnal variations at 200 km, but should be average conditions. The different determinations associated with the effect of solar activity if shown in Fig. 1 were made for different periods, they are not included in the possible errors of although most of them relate to the beginning measurement. of 1958. It should be noted that the rocket It must be pointed out that an analysis of results, for altitudes of the order of 200 km, the varying conditions at 200 km is to be related give variations which do not appear to agree to the analysis of conditions between 100 km with the results deduced from the acceleration and 150 km. For example, there is a variation of satellites. It appears, however, that the rocket of the density of molecular oxygen by a factor measurements of density carried out at about of 3 according to the measurements made by 200 km lead to values of (4 f2) x lo-l3 gem-‘, Byram et aZ.@)and Kupperian et aL’45). Like- STRUCTURE OF THE THERMOSPHERE

1 I I I

ATMOSPHERIC DENSITIES

Fig. 1. Density-altitude relation above 150 km from various determinations. The average curve represented by Groves’s data shows that the height variation of the density can only be explained by an increase of the scale height with altitude. Measurements made in 1957 and first months of 1958. wise considering the results obtained by Horo- the atmospheric structure above the later witz and L~Gow(‘~) at White Sands and by altitude. Horowitz et &.(25’ at Ft. Churchill it is clear The curve in Fig. 1 has been drawn following that there is a broad range of a factor 4 in the the determination of Groves@) and can be pressure and density data at 100 km. In other considered as an average distribution for the words if the value (2.5 + 1.5) x 10e4 mm Hg is first six months of 1958 corresponding to a accepted for the pressure at 100 km, the possi- certain sunlit atmosphere. The absolute values bility exists that the density at 200 km is near 200 km depend on the value which is subject to a variation of 50 per cent even if the assumed for the scale height at that altitude. structure of the atmosphere above 100 km is For example, the results of LidoP’) lead to essentially the same. Therefore, the data avail- values for p between 2.4 x lo-l3 g crnw3 to able on atmospheric density obtained by means 3.2 x lo-l3 g cm-3 if the scale heights are of rockets and satellites show that variations of 50 km and 30 km, respectively. El’Yasberg@) the density near 200 km must be connected with has adopted H= 25 km at 225 km. The average the atmospheric structure in the entire region value of GroveP) at 200 km is 46 km. Such between 100 and 200 km. A certain variation differences show that variations do occur in the of the density at 200 km must be explained by atmosphere above 200 km. But the main con- the boundary conditions near 100 km and by clusion to be drawn from the average values of 4 MARCEL NIcoLET

the density is that the vertical distribution must In using equation (2.2) we can see that H be explained by an increase of the scale height increases regularly with altitude between 150 km H with altitude. In fact the equation for a and 700 km. Thus the results of Grove@‘), perfect gas and the static equation indicate@‘) corresponding to a certain sunlit atmosphere in that the density can be expressed by the relation 1958, coincide with an average model presented dpg l+P dH by NicoleP). Subsequent calculations carried (2.1) out by NicoleP* w involving an analysis of the PET --P H physical conditions of an atmosphere in which where ,O=dH/dz is the gradient of the scale the temperature is constant above 220 km lead height and g is the gravitational acceleration. to the important conclusion that: the vertical The integration of equation (2.1) for a height interval sufficiently small so that j3 can be distribution of the density of the high atnws- phere can be explained if the atmosphere in considered practically constant leads to which the various constituents are subject to pg-peg, -exp (‘+‘)’ diflusion is isothermal above a certain level. [ - tW+HJ Such an atmospheric model shows that ultra- violet radiation is involved in the heating of {l+f(H~)‘+...}] (2.2) the atmosphere.

ISOTHERMAL ATMOSPHERES

400- IDIFFUSION) 7, * 11907(

Fig. 2. pHIla proportional to orbital acceleration of satellites in an isothermal atmosphere subject to diffusion. The density-altitude relations deduced from observational data can be followed. It is possible to fit the satellite observations of density, corresponding to a night- time atmosphere by an isothermal atmosphere. STRUCTURE OF THE! THERMOSPHERE 5

A recent analysis made by King-Hele and there is a and that its level is Walke?) leads to a night-time distribution in subject to a diurnal variation. Its altitude is 1959 shown in Fig. 2. This figure further shows maximum in a sunlit atmosphere and is mini- that an isothermal atmosphere at about 1200°K mum in a dark atmosphere. However, when with diffusion beginning at 150 km can represent the scale heights corresponding to isothermal the observations. The observational results do atmospheres in diffusion equilibrium are com- not differ from the model computed by pared (Fig. 3) with the empirical scale heights Nicold”‘). In the same way, an analysis of deduced by King-Hele and WalkefiA2) and by night-time conditions by Jacchia(3s) (see Fig. 2) Jacchia@‘) considerable differences are found. also shows the possibility of following the King-Hele and Walker have introduced a atmospheric distribution for high solar activity negative gradient below 250 km and Jacchia’s when a temperature of the order of 1400°K is curve corresponds to an important gradient even adopted for the isothermal layer. at 600 km. Such differences show that arbitrary The above results lead to the conclusion that atmospheric models can be made to follow

T2 DARK HEMISPHERE

x

SCALE HEIGHT

X JACCHIA A KING-HELE AND WALKER

THEORETICAL CURVES DIFFUSION

T,:1190-K T,= U25.K

I I I I I I I I I I , 50 60 70 80 90 100 SCALE HEIGHT (km)’ Fig. 3. Variations of the scale height with altitude. The variation of the scale height is associated with a variation of the mean molecular mass depending on diffusion. In this figure the scale height-altitude relations must be associated with the density distributions shown in Fig. 2. It is possible to deduce from observational data of pHIIs inconsistent values of the scale height. 6 MARCEL NICOLET

atmospheric densities deduced from satellite tudes and the diurnal variations are magnified observations. between 350 and 650 km. 2.2. Variations of the density The effect of the earth’s equatorial bulge is Jacchia(32) has shown that the amplitude of evident. Each transit at the equator of the fluctuations of the accelerations, propor- Explorer I corresponds to a maximum and the tional to pW2, increases with the altitude of the change in perigee height of Sputnik III leads perigee of the satellite. In fact, the important to a variation in the acceleration. fluctuations appear simultaneously at all alti- In Fig. 4 we consider data from satellite

1 I , I I , I , , , , I I , I I , I , Y 30’ - VANGUARD I (1958 /3d

dp dt - . . d,dp x 10’days per day 5 L’ * *.a...... l. 4 - *..* ...... ‘. *...... *... 3 - . _. :*. 2 - *.. .*. . * . . *.*. 9. . . . 1 -

S s ~1022watts n?kycle/seci’ at 10.7 Fro 300 -

250

150 - I I I I I I , I I I I I I I _ 1959 JAN [ FEE [ MARCH [ APRIL [ MAY 1 JUNE 1 JULY 1 Fig. 4. Orbital acceleration of Vanguard I (1958 p2). -dP/dt CC pHIi (s). Perigee latitudes (y) and angular distance of the perigee from the subsolar point (@)(ss). The solar activity is represented by daily values of solar radiation at IO.7 cm (Ottawa, Covington) and the magnetic activity by the daily K values deduced from the three-hourly indices@). STRUCTURE OF THE THERMOSPHERE 7

1958 ;B 2 during the first half of 1959, obtained Such effects must be linked with disturbances. from the values determined by Jacchia(32) and The variations of @I2 at an altitude of Briggs”‘. The solar activity is represented by about 350 km, corresponding to the perigee of daily values of solar radiation at 10.7 cm as Explorer I (1958 a), are considerably smaller observed in Canada (National Research Council) than at an altitude of 650 km. From the and by the daily values deduced from the three- beginning of January 1959, when the angular hourly K indices provided by Bartels. It is distance of the sun reaches 180” until it reaches obvious, as Jacchia has shown(32), that there is 90” at the March equinox, the density decreases a very close correlation between the variations slightly in agreement with the diminution in of the density and those of the solar radiation solar flux. Between March and August 1959 as obtained using the electromagnetic radiation the increase in the acceleration occurs with the at 10.7 cm. As for a magnetic activity relation fluctuations clearly associated with the sequence to the corpuscular radiation, there is no general of perigees at the equator even if some associ- correspondence although, in certain cases, it is ation can be made with the solar activity. possible to see that corpuscular effects can Thus, at an altitude of 350 km, the effect of occur during important geomagnetic disturb- solar heating is evident and leads to a clear ances. It appears, however, that a greater diurnal variation. The effect of the earth’s resolution in the orbital acceleration is needed equatorial bulge is of the order of 10 per cent. to detect short-lived perturbations. When an analysis of the variations of the On April 30 the density has decreased (Fig. 4) density is carried out at altitudes less than 300 when the sun is at 90” (the angle at the centre km it is found that the diurnal effects are of the earth determined by the position of the greatly diminished. In the analysis of the density sun and of the perigee of the satellite); that is, deduced from the acceleration of 1958 E(‘~)the when the earth below the perigee is no longer diurnal effects that can be inferred for the period sunlit. Finally, on July 31 the nocturnal effect between July and November 1958 reach a is complete and the density is very low. These maximum of 20 per cent: at the same time, an data show that the atmosphere at an altitude apparent latitude effect, caused by a change in of 650 km is subject to a very important diurnal perigee height due to the earth’s equatorial variation and the different analyses of Jacchia@), bulge, is certainly of the order of 20 per cent. Wyatt(sG) and of Priester and Martino9) show The discontinuities in the density at 50”N and that the diurnal effect is the principal one. S cannot be attributed to a latitudinal variation This strong diurnal variation is confirmed by in air density. the observed accelerations of Vanguard II The analysis of the fluctuations of the 1959 G3), for which the diurnal variation of Sputniks by various authors already mentioned, pH’i2 is of the order of a factor of 5 between in particular King-Hele @*),have shown that the March and August 1959 (Fig. 5). It is therefore diurnal effect is generally masked by other necessary to consider that the altitude of the effects. In Fig. 6 the data given by Kozai(43) thermopause and the temperature of the iso- for 1958 6 2 are shown. It may be seen that therm1 atmosphere vary considerably between from January to November 1959 the maximum night and day. Under such conditions the variation is + 60 per cent. The main character normal heating of the upper atmosphere takes of this variation corresponds to a displacement place by electromagnetic radiation. It is, there- of the perigee from 24”s on 1 January 1959 to fore, not necessary to’ look for a corpuscular 65”S, at the beginning of June, and to less than effect(2l when investigating such a normal heating 10”s at the end of November 1959. Thus, the effect of the atmosphere, a hydromagnetic perigee was located in the Antarctic during effect(‘4”5) or any effect other than that of the winter. Because of this, the altitude of the electromagnetic radiation, because such effects perigee did not diminish with time(4g). In June cannot be associated with a diurnal variation its altitude, about 225 km, was a maximum and whose character is so’ pronounced at 650 km. it is necessary to consider an increase in altitude

STRUCTURE OF THE THERMOSPHERE 9

J

Fig. 6. Orbital acceleration of Sputnik Ill (1958 62). -dP/dt CC pH1/z(43). Other symbols, see Fig. 4. show that a limited resolution corresponding to 120” and the perigee latitudes were 30”N and several days may smooth the transient disturb- 15 “N, respectively. ances affecting the atmospheric density. Even if the observations of 1958 6 2 are However, if we consider the periods when the irregularly distributed three pronounced perigee was in a dark atmosphere (Q in Fig. 7) increases in the acceleration curve of Sputnik III we can see three other increases associated with (1958 6 2) can be seen (Fig. 6) for 27 March, the K indices (K > 5) even if the resolution is 29 June and 4 September. These are associated only 25 revolutions. They are 28-30 June, with geomagnetic disturbances which are repre- 24-26 September and 22-24 October, when the sented by the K indices@‘. It should be noted angular distance, KP,of the perigee from the sub- that these three remarkable increases in the solar point is greater than 90”. Again the atmospheric density were observed during the corresponding latitudes of the perigee are very three periods when the perigee was in the dark low; between 15”N and the equator from atmosphere. This shows again that the reactions September to October. of the atmosphere to a “corpuscular effect” are Taking again the Smithsonian data for Sputnik more clearly distinguishable when effects on a II (1957 P)(Z9), it can be shown (Fig. 8) that sunlit atmosphere can be eliminated. certain variations of the density can be associ- If we consider periods during which the ated with K 2 5 indices. Two remarkable atmosphere was sunlit (May, July, August) associations are found on l-2 January and important magnetic disturbances were also 9-l 1 February when the * angles were 80” and observed, but their associated effects do not 10 MARCEL NICOLET

SPUTNIK III

--

6- - f$ I 10'daysper day

Fig. 7. Orbital acceleration of Sputnik III (1958 61). -dP/dt CC pH1lz@l). Other symbols, see Fig. 4.

seem to be so disturbing to the behaviour of the associated with the maximum of the solar acceleration of satellite 1958 6 2. In particular, electromagnetic radiation. Similarly, the maxi- the magnetic storm of 12 May 1959 (see the K mum near 15 July at sunrise appears to be indices Fig. 6) observed by Ney et aZ.(54)in related to the electromagnetic solar radiation, association with cosmic radiation does not although the cosmic-ray bursts described by show, with the low resolution of the accelera- WinckleP5) are noteworthy. tion curves, a special effect on the acceleration Moreover, a comparison should be made of the satellite. The maximum in the accelera- between the magnetic storm of 16 August 1959 tion curve, about 8 May, is more closely and the recurrent storm of 4 September (during STRUCTURE OF THE THERMOSPHERE 11

I I I I I 1 1 I I I Y 30’- SPUTNIK II (1957 p_!

175 - V I I I I t I I I I I I 1957 NOV 1 DEC’ 1 1958 JAN 1 FEE 1 MARCH

Fig. 8. Orbital acceleration of Sputnik II (1957 p). -dP/dt CC pHllz(29). Other symbols, see Fig. 4.

the night for 1958 6 2). During the first 24 hr These different examples show that it should of the magnetic storm of 16 August, Arnoldy be possible to distinguish between all of the et al.(')found that about 3/4 of the particles in external effects by a detailed determination, with the outer Van Allen belt had been removed and sufficient resolution, of the acceleration of the had penetrated into the atmosphere. But satellites. In any event, the diurnal variation the effect of the “corpuscular” heating of the and the 28-day periodicity show that the absorp- atmosphere is probably not greater than the tion of solar electromagnetic radiation is the electromagnetic heating, whilst the exceptional primary process for heating the atmosphere effect observed on 4 September is clearly a above 100 km. The “corpuscular” radiation transient heating in the dark atmosphere. with its associated processes can easily affect the 12 MARCEL NICOLET nocturnal conditions but is more difhcult to increases with altitude necessitates an analysis detect in a sunlit atmosphere which is already of the variations of three parameters: the heated by an increased electromagnetic radia- temperature T, the mean molecular mass m and tion. Furthermore, the strong diurnal variations the acceleration due to gravity, g. at the higher altitudes can mask such effects. If the atmosphere above a certain altitude Finally, the penetration of energy below 100 km was in a state of complete dissociation, an has practically no influence on the structure of increase of N with altitude could only be the thermosphere in that the energy involved in explained by an increase of temperature with flares is not important compared with the total altitude. Above 300 km, we can neglect an kinetic energy of the atmosphere. The most important heating effect by ultra-violet radiation remarkable phenomenon near 200 km is the in that there is practically no absorption of such relation with the energy of the solar radiation radiations at very high altitudes. In this case, which varies in accordance with changes in the a very pronounced dissociation of molecular solar activity. This is the reason that several oxygen below 200 km, with a low pressure investigators have found correlations with (10m4 mm Hg) at 100 km, leads to an atomic various indices of solar activity. Such a oxygen atmosphere. To explain the gradient of variation at 200 km means that the atmosphere the scale height it is necessary to introduce a between 100 and 200 km is affected and must flux of external heat transported by conduction. correspond to a general increase of the scale Such an application has been made by height in the entire layer. NicoleP5, 5’) using Chapman’s theory of an The variations of the density as a function of extension of the solar corona. altitude demonstrate that the diurnal variation But an atmospheric model in which the is magnified with increasing height. It is the pressure at 100 km reaches 3 x 10m4 mm Hg, dominant factor at higher altitudes and must be with a small percentage of the oxygen dissoci- associated with the gradient of the scale height ated, represents more closely the atmospheric and altitude of the thermopause. conditions leading to a further understanding of The variation from one day to another is the thermosphere. An important temperature closely associated with solar activity and the gradient exists below 200 km and leads to a size of the variations of the density, increasing large abundance of molecular nitrogen at high with the altitude, depends on the energy of the altitudeP* ss? Since atomic nitrogen is a solar electromagnetic radiation which is avail- secondary ConstituenP~ 57) we may consider an able during a 27-day period. atmosphere whose constitution depends essen- A “corpuscular effect”* is evident at the time tially on the ratio NJO. of magnetic disturbances but it is only intro- In a general study, NicoleW has shown how duced sporadically and the energies which are the problem of the conditions in the thermo- involved are generally less than ultra-violet sphere can be analysed. Using as an example energies. Seasonal and latitude effects can only the following conditions at 100 km: be secondary in relation to the complex effects p=3 x 10-4mmHg; T=2OO”K; of the diurnal and solar variations. p=6-6 x 10-10gcm-3 (3.1) 3. THE CONSllTUTION OF THE corresponding to the concentrations (cm-“) THERMOSPHERE n (0,) = 2.2 x lo=, n (N,) = 1.1 x 10’3; The constitution of the thermosphere, that is iz (0) = l-4 x lOI and M =27-4 (3.2) to say of the atmosphere above 85 km, the conditions at higher altitudes can be deter- theoretically depends on the state of molecular mined if we fix the level for the beginning of dissociation at the highest altitudes. Indeed, diffusion and the gradient of the scale height. the essential observation that the scale height H In Fig. 9 are shown conditions such that diffusion begins at 120 km and at 150 km, and * “ Corpuscular effect ” means no direct electro- magnetic radiation effect. the scale height has large gradients of P = 1.0, STRUCJIJRE OF THE THERMOSPHERE 13

deduced from the satellite observations if we consider that there is a large temperature ATMOSPHERIC DENSITIES gradient between 100 and 200 km. Further- (11 (21 (31 more, the vertical distribution of the density and the absolute value at 200 km are practically independent of the exact value of the tempera- DIFFUSION ture gradient. An increase of the order of 50 - 120km --- 150km per cent in the density at 200 km would require an increase of the order of 1000°K in the TEMPERATURE AT )r 220km temperature. An increase of the density at 210 - 200 km should be caused mainly by its increase Ill 1560.K in the region of 120 km. -200 - (2) 2030.K A similar effect explains the differences in (3) 2560’K s the observations made with rockets at different &go - 3 periods at White Sands and Ft. Churchill. f 1160- Similarly, differences obtained at the same place of observation can only result from a change of 170 - temperature in the lower thermosphere. In other words, the structure of the thermosphere 160 - depends primarily on the conditions at the

150 - From 120 to 150 km limits applicable to the lower thermosphere dH/dZ I p (different densities at 100 km). Moreover the 140 - fact of having introduced diffusion at 120 km (11 p’l.0 or 150 km does not modify the above con- 130 - (21 p:1.5 clusions for the atmosphere at altitudes of less (31 P’2.0 than 250 km. 120 I I, I,!,,1 I I Illll 10“’ 2 5 lo-” * 5 ‘I We can therefore conclude that: the density DENSITV(gmcni’) of the high atmosphere is essentially dependent Fig. 9. Density-altitude relations above 120 km on the soZar energy absorbed below 200 km. for various gradients of temperature. The height variation of the density shows that any solution for This energy determines the temperature gradient an inadequately short range of altitudes is up to 400 km in a sunlit atmosphere and fixes arbitrary even if the beginning of the diffusion is the temperature of the isothermal atmosphere introduced at 120 km or 150 km. Boundary con- ditions being fixed at 120 km (T and p constant), up to the highest altitudes. variation of density at 200 km is small. Since various temperature gradients between 120 km (E-layer) and 200 km (F-layer) modify 1.5 or even 2-O between 120 and 150 km and only slightly the values of the density at 200 km, an arbitrary gradient of ,P= O-2 between 150 and if constant boundary conditions are taken at 220 km. In order to simplify the calculations it 120 km, the small variations in the densities was noted that these two gradients are almost deduced from satellite observations near 200 km equivalent to a variable gradient diminishing are easily explained. But it must be pointed with height until about 300 km. out that variations must occur in the E-layer Considering Fig. 9 we see that very different which modify the boundary conditions for the conditions do not modify to any great extent the whole thermosphere. The computations lead to vertical distribution of the density. For the following results: example, the density at 200 km only varies by 12Okm,p=3*26x 10-‘1gcm-3; T=262”K f 25 per cent from the mean value for the above range of variables. Consequently we can con- (3.3) clude that, for constant conditions at 100 km, 15Okm,p=(1~5+0~03)x 10-1agcm-5; it is easily possible to obtain the densities, 725°K G T d 1650°K (3.4) 14 MARaL NICOLET

Thus, it is certain that varying conditions occur E-layer since convection and conduction are inside the E-layer. certainly involved. We can conclude therefore The total kinetic energy varies between 5 x lo4 that the E-layer is subject to varying conditions and 5 x lo5 ergs cru2 from about 120 km to depending on the coronal flux in the X-ray 100 km. If an energy of the order of 1 erg cmm2 spectrum and on the chromospheric and coronal secl is available for the heating of the E-layer, flux in the ultra-violet spectrum. it is clear that the boundary conditions at 120 At altitudes above the E-layer, from the km will be subject to variations resulting from beginning of the FI-layer, we must take into solar activity. In the same way, the region of the account the absorption of radiations of wave- El-layer where the total kinetic energy is less lengths longer than 200A. This corresponds than 5 x lo4 erg cm-2, will be strongly affected to the entire ultra-violet spectrum involving by an ultra-violet heating of the order of 1 erg helium lines at 304 A and 584A and also cm-2 se&. coronal lines of highly ionized atoms. An Below 100 km, at 85 km for example, the energy of the order of 1 erg cm-2 set-l can kinetic energy of a vertical column is of the produce temperature gradients of the order of order of 5 x 10” erg cn? and an equivalent 20°K per km. Such important gradients lead solar energy during one day of 12 hr would to very high temperatures above 200 km. require a total absorption of about 100 erg cm-2 If we consider a steady state for an overhead set-‘. We can therefore conclude that the sun, it is easy to show (see Section 5) that the entire thermosphere above 100 km is essentially energy E is distributed with height as follows dependent on the solar energy and its fluctua- tions if the energy available for heating is of the E=E,+Eu,(l-e-r) (4.1) order of 1 erg cm-2 set-I. Such an energy input in which E,,, denotes the energy flow at the top must be found in the X-ray and ultra-violet of the layer, E,, the ultra-violet solar energy radiations absorbed above 100 km. available at the top of the earth’s atmosphere for a certain spectral range and 7 is the optical 4. SOLAR RADIATION depth, which is defined by The diurnal variation of the atmospheric QI density above 250 km shows clearly that the r=K,, ndz (4.2) heating of the thermosphere depends mainly on I .z the electromagnetic radiation absorbed in the atmosphere above 100 km. Since the heating must be proportional to the Above 100 km the atmosphere absorbs radia- energy absorbed, it is evident that the tempera- tions with wavelengths of less than 1750A as ture gradient will decrease with height up to a a result of the dissociation of the oxygen mole- certain altitude where the optical depth is cules. The recombination of oxygen atoms negligible. mainly occurs below 100 km after a downward If there is no external heat flow, the sunlit transport and for this reason there is no atmosphere must be isothermal where there is important heating available from in situ recom- no absorption of solar radiation. Since X-rays binations. However, the energy available from and ultra-violet radiations are absorbed between the various monochromatic radiations between the E-layer and the F-layer the temperature 1500A and 1300A corresponds to about 3 ergs must increase continuously and no permanent cm-’ see-I, and the part transformed immedi- decrease can be expected in the whole thermo- ately into heat is about 0.5 erg cme2 set-l in the sphere. E-layer. Furthermore, the total energy from In order to study the variation of the short X-rays absorbed in the E-layer does not exceed ultra-violet radiations and of X-rays one refers 0.5 erg cmm2 set-l at the maximum of the solar to measurements of the centimeter or decimeter cycle. In addition, the heat flow from upper electromagnetic radiations emitted by the solar levels will lead to an important effect in the corona. NicoleP) has compared the results STRUCTURE OF THE THERMOSPHERE 1.5 obtained at various observatories from 3 to 30 radiation at 20 cm measured at Berlin. In fact, cm and has shown that the general behavior of during 1958, the relation between the extremes the solar activity is the same for the entire of radiation at 20 cm is of the order of 5 while spectral region. The mean daily solar fluxes that for 10.7 cm (which must be a maximum) from 8 to 15 cm are subject to identical varia- is only about 2. Since Priester and MartirW tions. The extremes of 3 cm and 30 cm differ and Jacchia(33) are able to follow the general from 10 cm by an extent which is much less variation of the atmospheric densities deduced than the fluctuations. In other words, the from satellite measurements by using the 1958 largest fluctuations of the solar radiation from measurements at 20 cm, it is quite strange that 3 cm to 30 cm are observed at about 10 cm such a good correlation has been obtained. although the complete spectrum varies, under There is no way to account for a special the same conditions, with the solar activity. behavior at 20 cm, with a variation of a factor Since Priester and MartirV, and JacchiaC33) of 5 in 1958, when the entire spectrum between after having used 10 cm(32), have based their 3 cm and 30 cm does not vary by more than a analysis of satellite accelerations on the solar factor of 2. energy of 20 cm wavelength observed at Berlin, Fig. 11 shows that, in 1959, the solar radia- it is important to compare the observational tions measured at 10.7 cm in Ottawa and at data at 10 cm and 20 cm. Fig. 10 shows that, 20 cm in Berlin are subject to the same general in 1958, the solar radiation at 10.7 cm measured variations and that the ratio Berlin/Ottawa of at Ottawa does not indicate a general variation the solar fluxes, taking as a unit the mean value which is as pronounced as that for the solar for 1959, does not vary by more than +20 per

SOLAR FLUX AT 10.7 cm and 20 cm in 1958

I II I, I I, I,, I,, I,, I /, I,, I,, I,, I., JAN FEB M*RCH APRIL MA” JUNE JULY AUG SW OCT NO” OEC

Fig. 10. Comparison between solar fluxes at IO-7 cm (Ottawa) and at 20 cm (Berlin) in 1958. While the difference between maximum and minimum corresponds to a factor of the order of 5 at Berlin, it is only of the order of a factor 2 at Ottawa. The real variation cannot be more than a factor of 2 and the flux ratio of 20 cm/IO cm cannot vary from l-5 to 0.4. 16 MARCElL NICOLET cent. The data on radio radiations at 20 cm, the basic radiation of the sun heating the upper therefore, introduce a systematic error when atmosphere the minimum value of the radio used in 1958 to compare the variations of the flux. Hence we may assume that from July to atmospheric density with that of the solar flux. November 1958 the basic radiation S at 10.7 cm In conclusion, when errors in calibrati of was never less than 220 units :[watts m-a (cycle- radio measurements have been eliminat $” one s@-’ x 10-22], while in 1959, from the begin- can say that in general the variations of the ning of September to the end of November, it activity are represented by all wavelengths was less than 220 reaching 150 at the begin- between 3 and 30 cm. The most pronounced ning of September. range of the variations is given by the spectral Such differences must correspond to varia- region centered on 10 cm. Thus the obser- tions of the solar emission in the ultra-violet vations at Ottawa at 10-7 cm, made during 1958 region and particularly in the X-ray spectrum. and 1959, and indicating a maximum variation It is evident that the variation in amplitude of of a factor 2.2, fix the maximum of the variation the radio emission cannot be directly propor- of the mean daily value for all the spectral tional to that of the entire ultra-violet spectrum region from 3 cm to 30 cm, i.e. of the slowly or of the spectrum at the shortest wavelengths. varying component of the sun’s radio-emission. The diflkulty of obtaining an exact relation Since the temperature and its vertical distri- between the optical and radio ranges is easy to bution in the chromosphere and corona remain understand since such radiations originate normal in the active regions emitting the deci- between the photosphere and corona, i.e. from meter radiations, it is convenient to consider as the lower and cooler part of the solar atmos-

SOLAR FLUX AT 10.7 cm and 20 cm in 1959

R.FLUX RATIO = R OTTAWA

1,11,11,11,,1,11111,,1111,1111111 JAN 1 FEB 1 MARCH 1 APRIL 1 MAV 1 JUNE 1 JULY 1 AUG 1 SEP I OCT I NOV I OEC

Fig. 11. Comparison between solar fluxes at IO.7 cm (Ottawa) and at 20 cm (Berlin) in 1959. The flux ratio 20 cm/IO cm varies’ only about +20 per cent and such a small variation indicates that 1958 results on 20 cm cannot be accepted. STRUCTURE OF THE THERMOSPHERE 17 phere up to the normal high temperature corona. with a temperature of the order of about 1000°K Nevertheless, it is true that the terrestrial and one at a high latitude with a temperature atmosphere between 100 km and 200 km is of about 2000°K. has little plausibility. subject to the variable heating resulting from An inflow of 2 x lO*l electrons cm-* set-’ the absorption of ultra-violet radiation and leading to a heat source Q=4 x 1O1Ocal crns3 X-rays. The implication is that the thermo- set-’ at 300 km, as mmputed by Jastrow’S5), sphere is heated by all radiations for which the corresponds to an injection into the thermo- absorption cross-section is greater than IO-l9 sphere which is not observed even during cm=. There is no particular terrestrial layer auroras. Meredith(s”) has given a specific above 100 km which is especially heated, since example of a flux between 2 and 6 x 10’ the energy is distributed with height according electrons cm-Z secl of about 10 keV inside to (4.1). a diffuse aurora. Such an example shows that Sources of heating other than electromagnetic normaI heating of the atmosphere by corpus- radiation depend on the energy which is avail- cular radiation must be excluded. However. able. The use of the energy of the radiation sporadic conditions corresponding to geomag- belt in one form or another is limited by the netic storms and leading to energies of lO22ergs total energy available. This, according to may lead to appreciable transient heating since Dessler and Vestine(‘s), is 6 x 102* erg and is it corresponds to 05 erg cmm2 see-1 for the about a factor of 10 greater than the energy entire earth during one hour or about one- involved in a magnetic storm; 10Z2ergs accord- twentieth of the earth’s surface during 24 hours. ing to Chapman and Bartels(“). On the other Dessler(“‘) has put forward the view that the hand, Arnoldy et al.“’ have observed, during normal heating of the thermosphere is due to the first phase of a geomagnetic storm, a loss hydromagnetic heating. Against this view it can of about two-thirds of the energy of the outer be stated that the diurnal variation of the tem- belt. Such energies place limits on the energy perature of the thermosphere cannot be which would be immediately available from the explained by this process. But the increased radiation belt and we agree with Bates”) that orbital acceleration of satellites observed during the time period would be too short if “corpus- geomagnetic storms at any latitude does not cular” energy must pass through the radiation exclude a direct heating of the atmosphere out- belt. side the aurora1 zone. The hydromagnetic With a total of 6 x lo’? ergs, the maximum heating, therefore, must be kept among the energy available for the earth’s atmosphere hypotheses needed to explain a heating at very cannot be more than 10’ erg cn?. An energy low latitudes during geomagnetic storms. A supplied to the atmosphere of the order of 1 erg final decision cannot be reached until the crne2 set-‘. which would be given by electrons variations of the atmospheric density are of the order of 10 keV according to Kras- properly explored by using physical parameters sovsky(“), will lead to the total energy of the such as the temperature and pressure in addition radiation belt in about 3 hr. The hypothesis to the density and the scale height. put forward by Krassovski”‘) is very difficult to accept since the energy of the radiation 5. TRANSPORT OF HEAT BY CONDUCTION should be renewed several times a day. Conse- quently, various suggestions of the normal 5.1. The equationsof conduction heating of the upper atmosphere or of the The solar radiation heats the thermosphere creation of a heated atmosphere in a definite at various altitudes, according to the values of region of the aurora1 zone by the channelling of the coefficients of absorption which range from charged particles through the radiation belt can- 1O-1o cm2 to IO-‘* cm2. It is. therefore, appro- not be accepted. Hence the deduction of priate to investigate the behavior of the atmos- Jastrow(S5) that two atmospheres can exist phere under the effect of the conduction of heat simultaneously, i.e. a low latitude atmosphere depending on the gradient of temperature. 18 MARCEL NICOLET

The flux density of heat, E, can be written leading to the following relation, by using (5.7).

E= -h,gradT (5.1) e= 2TS’2-T;/2 l-112 (5.12) where T is the temperature and h, is the thermal 3 2 conductivity. If E is expressed in erg cm-* Using (5.7) and (5.12) equation (5.1) can now se&, h, is given in erg cm-l set-’ deg-l and is be written as related to the coefficient of viscosity, p, by the equation~l” E= - AT:I’grad 9 (5.13) A, = fW” (5.2) The continuity equation is written as follows where c, is the specific heat at constant volume and f represents a numerical value equal to pcVag+divE=P-L (5.14) about 2.5 for spherical molecules (monatomic gas) and can be equal to I.9 for diatomic mole- in which P denotes the production of heat per cules. unit of time, per unit of volume and L the loss The viscosity ,u can be expressed as of heat per unit of time and volume. Consider- ing the heat capacity per unit of volume, PC,, (5.3) where p is the density, equation (5.14) can be written as where v is the atomic radius, k Bohzmann’s "!3i7ze+(P-L)~^ constant and m the atomic mass. This formula ae (5.15) at= pc, z ? can be used in the high atmosphere(5B*E”), and the values used are, for atomic hydrogen, where the coefficient AT1/*/pco is the thermal a=2.0x 10-8cm, diffusivity which, if n is the atomic concen- tration, can be written ,u (H)=6.8 x IO-“T”” (5.4) a(T,n)=A,T”2/n (5.16) atomic oxygen, u = 2.4 x 1O-8 cm, where A, is a constant which has the following p (0) = 1.9 x 1O-JT1’2 (5.5) values (cm-l set’ deg-‘12) molecular nitrogen and oxygen, u = 3.3 x 1Om8cm A,(H) = 1.0 x lOI (5.17) ,u (I$., 0,) = 1.3 x 10-5T”2 (5.6) A, (0) = 1.75 x 10’8 (5.18) In using equations (5.2) and (5.3) the thermal A, (Nz. 0,) =5*3 x 10” (5.19) conductivity can be denoted by As a result, the differential equation (5.15) h c =AT’IZ (5.7) for the conduction becomes: where A is a constant, depending on the atmos- phere constituents. The numerical value of this constant is (in erg cm-’ see-’ deg-S’2): By using the variable T instead of introducing A(H) =2.1 x 103 (5.8) the temperature parameter 8, equation (5.20) A (0) =3.6x lo2 (5.9) would be non-linear. In fact the problem can A (Oz. NJ = 1.8 x lo2 (5.10) always be studied by considering a condition at the limits 8, = 0 for all fixed values of T = T2. Since h, is a function of the temperature, we If ae/at=o, equation (5.20) becomes introduce a new variable defined by Poisson’s equation which can be applied to the steady state (5.11) P-L (5.21) % v2e+ AT;‘” =’ STRUCTURE OF THE THERMOSPHERE 19

If, on the other hand, there is no loss or if the temperatures T, at 300 km are 900°K production of heat at the centre of the volume and 1600”K, respectively. being studied then (5.20) corresponds to the These numerical data show how the tempera- Laplace equation ture would vary if an external heating were VV=O (5.22) involved. However, since no direct determin- ation of the temperature can be obtained from When there is cooling by conduction with no satellite data, it is necessary to consider (5.1) production or loss of heat inside of the volume, when the scale height H is used instead of T. equation (5.20) should be written With (5.9) and (5.10), the equations are (5.23) E (0) = -0.817 x 1O-s (g/900)3’2H’~‘;$ (5.27) in which, for ease of calculation, we can take a for atomic oxygen, and mean value of A,T112 and, thus, the thermal conduction depends, essentially, upon the value E (Nz, 0,) = - 0.945 x 1O-3(g/900)3/2H’12 ‘g of the concentration n. (5.28) 5.2. Steady state with no source or loss of heat for air, when g=900 cm set-’ is adopted for an inside the volume altitude of 280 km. In a sphere where the temperature is a If we consider the night-time data of function only of the radius r, the solution of JacchiatS3) between 600 and 700 km, it is clear (5.20) is that the energy which is required to maintain (5.24) such a gradient according to (5.27) and (5.28), is E (600-700 km)night= (0.28 f 0.02) erg cm-’ see-l if o2 =0 at a distance r=r, from the center of (5.29) the sphere and 8, at r=rl. According to (5.12), the distribution of the temperature becomes, However, it has been shown (see Fig. 2) that at (5.24), the highest levels it is possible to interpret the satellite observations concerned with atmos- (T312- T;P)/(T;P -c/“)= = ‘-$ F (5.25) 1 2 pheric drag in terms of an isothermal atmos- phere subject to difEusion. The heat flow E, is therefore (5.13) and (5.25), As far as the daytime data are concerned, Jacchia(33) has deduced a more pronounced Ercr:$A A(T3/2-c/2)/(r-rZ) (5.26) gradient which leads, in the same range of altitudes, to An immediate application is a night-time atmosphere where there is no heating by ultra- E (600-700 km)day 3 1 erg cm-’ set-l (5.30) violet radiation at a sufliciently high altitude. As a matter of fact, such a deduction corres- In an atomic oxygen atmosphere if the heat flow ponds to an increase of E with altitude, since has the following values at 500 km near 600 km EN 1 erg cmS2 se& and near 0.1 0.2 O-5 erg cnP set-‘, 700 km E > 1.3 erg cmSa se&. If at 700 km, a ditference of about 1 erg cmA2 the corresponding values of the temperatures set-l distinguishes the difference between a obtained at 700 km are sunlit and dark atmosphere (5.29) and (5.30), it 1250°K; AT = 350 1550°K; AT = 650 would be necessary to assume that electro- magnetic radiation can be absorbed at such high 2300°K; AT = 1400 altitudes. The maximum possible total number 1850°K; AT=250 2100°K; AT=500 of atoms in a vertical column, in using Jacchia’s 2900°K: AT = 1300 datatS3), cannot be more than 8 x 1Ol4 cmm2. 20 MARCEL NICOLET

Since any absorption cross-section cannot be (0.80 kO.06) erg cmm2 set-’ and a downward more than lo-l6 cm2, the optical depth cannot heat flow of (l-15 50.08) erg cme2 set-‘, i.e. a be more than 0.08 and the ultra-violet energy heat loss of about 2 erg cnP set-’ for a layer needed would be more than 125 erg cm-’ set-‘. of thickness less than 10 km. The total energy Furthermore, since the absorption cross-section lost in one hour by such a layer would be more must be less than lo-l6 cm2, the ultra-violet than its total kinetic energy. This shows that radiation required should be more than 50 erg such a discontinuity cannot be a permanent cmb2 set-l and such an energy will lead to feature in the thermosphere. We shall see later temperature gradients below the unit optical that such an artificial gradient would have a depth of more than 500°K per km. very short lifetime. In any case, it can be In fact, the gradients of temperature for shown (see Fig. 3) that the vertical distribution 400”Km, radiation and loss by infra-red radiation for an undissociated atmosphere. The scale In a steady state with one dimension the height gradients, ,B, are under the same con- equation (5.21) is ditions, respectively (5.35) ~(0)=(0~51+0~10)E (5.33) and or aE /3(N2,0,)=(0~46+0~10)E (5.34) z +P=L (5.36) It is clear that E cannot be very different between day and night at highest altitudes since Considering an atmosphere subject to a it would require a higher ultra-violet energy heating by several radiations, the production of than is available from the sun. A corpuscular heat P (cm-” set-l) is effect will not lead to a difference between day and night, and any external heating cannot P = BnKE,,, exp ( - j”,,,,) dz = ZE,,e-rdr explain such a difference. It must be concluded, I therefore, that there is no physical process to be (5.37) found to explain an increase of the temperature at such altitudes. An increase of the scale in which K is the appropriate absorption cross- height gradient can be found only where the section of the radiation E,, of wavelength h by laws of diffusion can be employed, in fact at atoms of concentration it. 7 is the optical depth very high altitudes the gradient decreases and defined by finally the scale height becomes constant. dr = - nKdz_ (5.38) leading to Another aspect of a special behavior deduced ccl from observational data is the gradient of the scale height (see Fig. 3) adopted by King-Hele (5.39) and WalkeP2) near 200 km. The gradient is z negative between 210-220 km, /3= -0.3; it is In the thermosphere, the principal infra-red positive between 200-210 km, p= + 0.4. Using radiator is atomic oxygen, according to Bates’s formulas (5.27) and (5.28), a thin layer near process@) 200 km should lead to an upward heat flow of 0 (“P,) --f 0 (“P,) + hv (A = 63~) (5.40) STRUClWRE OF THE THERMOSPHERE 21 since molecular nitrogen and oxygen have no dipole. The loss of heat (cm-’ set-‘) is there- fore (in erg cm” set-‘) EUT L=Rn(O)=n(O) + 27 Uog~o - Ei ( - 7,) + 0.577221 (1.68 x 10-1*e--22*~~/(1+0.6 x e--228/T+ + 0.2 x e--325.3/T) (5.41) - &, (0) H, (0) - n (0) H 01 (5.45) leading to where A is the constant of (5.27) or (5.28). L (E-layer) = (5 f 1) x 10-lg n (0) erg crnTs set-’ Adopting rO= 1, near the absorption peak, (5.42a) the effect of the ultra-violet radiation on the L (F-layer) = (8 f 05) x 10-19n(0) erg cms3 set-’ scale height can be shown by the following (5.42b) examples: Using (5.37) and (5.40), integration of (5.36) If H, =40 km (r= l), H, has the values (+ 7 leads to per cent) E=E,+E,,(l-e-r)+Rn(O)H(O)(g/~ H =6Okm 84km 113km 145km (5.43) when E,,,= 1 2 3 4 erg cmV2set-’ in which Em denotes the external heat available for the layer, and R’ and 2 are mean values. If H, = 50 km (7 = l), H, reaches the values Since the absorption cross-section in the ultra- H =72km 99km 129km 164km violet range is K 3 10-l’ cm2 and R < 10-l’ erg when set-‘, E,,= 1 2 3 4 erg cm-2 se& E,, (1 - e-r) > & (0) H (0) (5.44) In other words, the scale height varies by a and above the unit optical depth, it is clear that factor of 2 between the absorption peak and the radiation loss is also negligible. A loss of the beginning of the isothermal layer when the heat of the order of 1 erg cme2 see-’ requires ultra-violet energy available for heating is of 2 x 1Ol8 cmm2 atoms of oxygen, i.e. a layer of the order of 2 erg cm-2 set-l. Since diffusion 10 km with concentration of 2 x 1012atoms cm-3 is also involved, it is evident that scale heights which corresponds to an altitude of the order of greater than 100 km can be reached if the ultra- 100 km. It can be concluded that the loss of violet energy is of the order of 1 erg cme2 see-l. heat at 63~ occurs mainly inside the E-layer, Evidence favouring an important gradient of where the radiation is certainly of the order of temperature in a sunlit atmosphere is shown by 1 erg crnm2 scP. In the F-layer the total loss the occurrence of pronounced diurnal variations of a vertical column would be of the order of of the density. An exact vertical distribution 0.1 erg crne2 set-‘: thus the loss of heat by of the temperature cannot be obtained since the radiation may be neglected in a sunlit atmos- solar spectrum in the ultra-violet must be known phere above the E-layer when the ultra-violet in all the details and also the exact, varying, energy available is at least 1 erg cm-* XX-~. On ratio N,/O. However, the diminution in the the other hand, any ultra-violet energy of the temperature gradient should be indicated by a order of 0.1 erg cmV2 sc& absorbed above law of the form the level of the Fl peak is of the order of the dT heat loss by atomic oxygen since K N 10R. z CTZE,, (I- emr) (5.46) The integration of (5.43) with the use of (5.27) and (5.28) may lead to a determination of the for an overhead sun. possible increases of the scale height (&J up It is possible to obtain some idea of the to the isothermal layer. The result can be conditions which are required to reach the written as follows (neglecting the variation of g): observed densities at 200 km and scale heights 22 MARCEL NICOLET deduced from (5.45). If we assume, for As was said before (see equation 3.4). the example, that below the specific level of density remains almost constant at 150 km for 150 km (see equation 3.4), the effect of con- any gradient 0.50 d P d 1.50. The energy vection is such that the energy E follows the necessary for such gradients varies according to following law (5.48) from 0.7 erg cm-* se4P to 3.3 erg cm-* so.? (see Fig. 12). The solar energy which (5.47) must be available for the heating cannot be determined if the absorption cross-section is not where H,, corresponds to 150 km, H < H,, and known. Let us assume for example a mean ‘U is the kinetic energy. The scale height value of 2 x 10-l’ cm2 which corresponds to the gradient is, according to (5.28) most important part of the ultra-violet spectrum. p=Eh/AH;/2=1*058 x 10J (EJH:,“) (5.48) In such a case, the following ultra-violet energies

SOLAR ULTRAVIOLET ENERGY gg

3.0 - HEAT FLOW AT 150 km

p=1.06~103Eh/Hlh/2

2.5 - kv=Eh/l-•q

20 -

7:

2 -

P -ts- $3 B iTI _

ln-

Fig. 12. Heat flow and scale height with constant scale height gradient. The effect of thermal conductivity at 150 km is shown by a curve relating the scale height gradient and the energy necessary to maintain a certain gradient. Assuming an absorption cross- section of the order of 2x10-17 cm* the ultra-violet energy necessary at the top of earth’s atmosphere E,, Is deduced. STRUCTURE OF THE THERMOSPHERE 23

E,, at the top of the earth’s atmosphere would scquently, certain that the variations in the be necessary: thermosphere above 100 km can be associated fl 05 0.75 1.00 1.25 1.50 with the variations of the solar energy and that .?& 0.9 1.4 2.0 2.7 3.4 ergcm-z St-z1 the variations of the temperature and its gradient and the corresponding temperatures ‘at 150 km are closely associated with the absorption (see Fig. 13) would be: processes below 200 km. The temperature at T 725 960 1190 1425 1650°K the thermopause depends strongly on its Such scale height gradients and temperatures gradient below 200 km. But the level of the would correspond to real parameters since the thermopause must be subject to a diurnal varia- total kinetic energies which are involved in the tion according to the laws of cooling after atmosphere above 150 km are between lo4 erg sunset. crnm2 and 6 x IO4 erg crne2 corresponding to 5.4. Cooling of the atmosphere after sunset E,, from O-9 erg cm-2 set-’ to 3.4 erg cm-* The application of equation (5.23). after SC’, respectively. In other words, the solar sunset, in the following form energy which is used during one day of 12 hr is of the same order as the kinetic energy of the vertical column above 150 km. It is, con- $j;= (A,T'/2/n) x (i328/i3z2) (5.47)

1700

1600 TEMPERATURF AT 150 km VERSUS 1500 ULTRAVIOLET ENERGY

lb00

1300

; 2 1200

5

2 1100 a” : - 1oocI-

90( I- EuV= E(lSOkm)/l-ir

En I- E = AT”dT/dz

ABSORPTION COEFFICIENT : 2 xlli”c16’

701I-

6M I-

Fig. 13. Temperature at 150 km and ultra-violet energy available at the top of the earth’s atmosphere. From the abscissae re resenting the ultra-violet energy, may be deduced the temperature at 150 t m If. the absorption cross- section Is assumed. 24 MARCEL NICOLET corresponding to an initial atmosphere with a and the variation of the temperature below certain vertical gradient leads to the following 200 km. results. As a consequence, the heat transport by Let us consider, as an example, an atmos- conduction associated with the gradient of phere* giving approximately the vertical distri- temperature that results from the absorption of bution of the observed density and corres- solar ultra-violet radiation explains the diurnal ponding to a heat flow of about 0.3 erg cm-* variation of the density of the thermosphere set-’ through atomic oxygen. If the variation deduced from the variation of the acceleration is very small at 200 km, it is of the order of a of the satellites. We must also conclude that factor of 10 near 650 km in about 12 hr. There the diurnal variation of the temperature of the is a clear indication that the atmosphere isothermal region is of the order of 500°K and becomes rapidly isothermal at the highest alti- that the temperature gradient is certainly subject tudes and the isothermy extends with time to to a variation down to 150 km. lower levels. It must be pointed out that pHII* Lastly, we must realize that the heating during at highest altitudes decreases rapidly during the magnetic storms will have an effect during a first hours, and it is interesting to note that the time of the order of one day since the effect of variation is very small between 12 and 24 hr the solar electromagnetic radiation leads to a compared with the variation during the first strong diurnal variation. Consequently, any 12 hr. sporadic effect, if energetic enough, will modify In fact. the tendency to isothermy is very the atmospheric structure only during its own rapid when the density is less than 5 x lo-l5 lifetime and its role will be more or less g crnwS or concentrations less than lo8 cm-s. effective if it occurs in a dark or sunlit atmos- Equation (5.47) shows that if a temperature phere, respectively. gradient corresponding to a heat flow of the order of 0.3 erg crne2 set-l exists in an atomic 5.5. Times of conducrion oxygen atmosphere, it disappears in less than The application of equation (5.47) to the 30 min between 450 km and 750 km. Such a problem of the cooling of the atmosphere after result shows that it is not possible to consider sunset indicates that the time required for the a dark atmosphere with a temperature gradient transport of heat varies greatly with altitude above 300-350 km. Moreover, the temperature and distance. Actually, the time of conduction of the isothermal atmosphere decreases in a is proportional to the concentration, n, and to continuous way following a decrease in the the square of the distance. temperature gradient between 200 km and In order to provide order of magnitudes for 300 km. times of conduction, we apply equation (5.47) The absolute value of the decrease, being to very simple examples. Let us consider two obviously a function of the initial gradient, the infinite regions of the atmosphere where the behavior of the variation depends upon the conditions are such that the temperatures are vertical distribution of the ultra-violet radiation initially T, (x < 0) and T, (x > 0). The redistri- absorbed in the sunlit atmosphere. Nevertheless, bution of the temperature (isothermy) is given it is clear that the variation of the temperature by the solution of (5.47): of the isothermal layer between r =30 min and 8/8,=1-#(P) (5.48) r =2 hr is of the same order as that between when T, is kept constant (T +- T,) and x > c) r =2 hr and r = 12 hr. In other words, after a or rapid tendency towards isothermy at highest ~P,=tIl+~wl (5.49) altitudes, the temperature of the isothermal if T-+-)(T,+T,) and -~<(x<+oo. Tn layer decreases according to the rapidity with (5.48) and (5.49), which the isothermal layer extends downwards I(

* Such an atmosphere does not represent real con- (5.50) ditions and has been chosen as a working model. STRUCTURE OF THE THERMOSPHERE 25

diurnal variations which are important accord- ing to the results of the analysis made in P”= &-&iiJ (5.51) Section 5.4. If we consider that horizontal layers of a where t denotes the time; A, is given by (5.18) certain thickness x occur with different tempera- or (5.19). tures T, and T,. it is possible to consider the By using (5.12), we can write the relation time of conduction which ought to be taken into between the temperatures if we adopt a definite account to reach isothermy. For example, value for 3 0. Since # 01) =0.2 leads to con- King-Hele and Walker”“’ in their atmospheric ditions near to isothermy, such a value is model have introduced a peak in the scale height adopted and introduced in (5.48) and (5.49). at 210 km (H=47 km) and a minimum at With (5.48). the solutions are: 250 km (H=40 km). For a molecular nitrogen If T,JT,=0.5, TJT,=0*91, . . ., if T,/T,=0.9. atmosphere, equation (5.47) shows that T/T,=0*98. and with (5.49). (5.58) if T, JT, =0*5. T/T, =0*80, . . ., if Tt JT, =0.9, e/e, =t$0 where T/T, =0*95. ,u*=a2n/A,T1h (5.59) It is, therefore, possible to define a time of conduction related to the concentration (see if a is the thickness of the layer with initial 5.51) and the distance x. Using the constants temperature T, (x < a) and initial temperature from the formulas (5.17), (5.18) and (5.19). we T2 for -a

8m I I I I I

ISOTHERMAL ATMOSPHERES

550 -

ISOBARIC LEVEL VERSUS TEMPERATURE 500 -

150 -

LOO - ii s ; X JACCHIA 1” C A KING-HELE AND WALKER

2 350 -

TOTAL DENSITY . C5xl#5gm cm? p(O,.N,l. ~101 n(O). 16*10’c+? n~N,~.C1*lO’c~’ 250 - n10,).3.3.10scni3

200 I I I I I 5w 750 1000 1250 1500 1750 200 0 TEMPERATURE~?4l

Fig. 14. Temperature-altitude relation for a total density p=43x lo-15 gm cm-s where p (02, Ns)=p (0) in an Isothermal atmosphere. The know- ledge of the altitude of the isobaric level leads to a determination of the temperature and therefore of the vertical distribution of the density.

Fig. 16 shows the vertical distribution of the It is clear that the preceding determination of density for which the constant density defined night-time conditions of the isothermal layer by (5.67) corresponds to the equality of the does not give a complete answer since it depends density of molecules and atoms. As was shown on boundary conditions for diffusion and tem- before (Fig. 2) the curves leading to (5.66) at perature. The atmospheric model is consistent 400 km and 450 km are not far from the night- in the use of all physical parameters: however, it time densities deduced by King-Hele and represents only a guide to the study of atmos- WalkeP) and Jacchia@“). respectively. pheric behavior. In order to show how small STRUCTURE OF THE THERMOSPHERE 29

IOOC

9oc

w TEMPERATURE

soaI-

700

; 600 t k!l z 2 500

X JACCHIA A KING-HELE AND WALKER

SCALE HEIGHT VERSUS HEIGHT

I I I I I I I I 50 w 70 e3 90 1Od SCALE HEIGHT (km1 Fig. 15. Scale height-altitude relations for various isothermal atmos heres. Scale height values deduced by Jacchla ’ (38) and King-Hele and Wa Pker(dz) are shown with thelr different vertical distribution. differences in physical conditions can modify the of density for various temperatures are shown conclusions, instead of (5.66). we assume in Fig. 16 where it is interesting to compare the results represented by the dotted curves with the P(O,. o)=Po (5.69) data shown by continuous curves. corresponding again for all temperatures to a Computation shows that the condition (5.69) constant density. The expression (5.69) leads is obtained where the total density has the to a different distribution of the density, even definite value if the concentration of atomic oxygen, p = (4.75 * 025) x lo-l5 g cm-S (5.70) n(0) =8*5 x 10’ cm-s, remains the same at the This thermo-isobaric relation leads to the thermo-isobaric level. The vertical distribution results of Table 2. 30 MARCEL NICOLET

Fig. 16. Densities in isothermal atmospheres. The absolute values of density are determined by conditions p (Os, Ns)=p 0) at an isobaric level p=4.5x lo-15 g cm-3 and p (0s. 0)= p (Ns) at an isobaric level 4.7 k x10-15 g cm- 3 leading to densities at 220 km corresponding to observed values and to remarkable differences at highest altitudes.

- Table 2. Table 3(a) Altitude in km Temperature (“K) Density at Isothermal Atmosphere ofp(N,)=p(O,, 0) I 220 km 10-13 g cm-3 (OK) TI (OK) Ta --- (1) 0.32 - 805 (2) 0.85kO.5 725 1050 (3) 1.7 *to*1 958 1285 (4) 2.5 kO.1 1190 1515 (5) 3.2 &to.1 1424 1745 The main conclusions are given in Tables 3(a) (6) 3.9 *O-l 1657 1975 and 3(b). S-l-RUCXURE OF THE THERMOSPHERE 31

Table 3(b) These various values will serve as a guide in ----, the analysis of night-time conditions in the iono- PI= PI = PZ= sphere, of airglow and auroras keeping in mind 4.45x IO-‘5 4.7spxz+ 8.5 x JO-” 1.25 x JO-‘& Altitude Altitude ( Altitude ( Altitude that in a normal dark atmosphere during maxi- (km) I otm) Otm) (km) mum sunspot conditions the temperature of the isothermal atmosphere may reach values (1) 300 - 450 between 1200°K and 1400°K. However, values (2) 300 350 450 550 of the order of 1000°K can be easily accepted. (3) 350 550 650 z 650 750 The problem of the sunlit atmospheres must :; 2 750 850 be studied under various conditions depending :: 850 950 on the ultra-violet solar radiation available and (@ ;: I M= M- M- on the vertical distribution of its absorption. 20.33fO.O3~20*95f0*05 16.5OkO.03 16.80+0.02 -.--- e -=z= AcknowledgmenrJ--The research reported in this work has been sponsored by the Geophysical Research The main conclusions are given in Tables 3(a) Directorate of the Air Force Cambirdge Research and 3(b). Center, Air Research and Development Command, under Contract AF 19 (604)-4563. Starting from thermo-isobaric levels leading The author is grateful to the Astrophysical Obser- to 4.5x lo-l5 g cm-s and 4.75x lo-‘” g vatory of the Smithsonian Institution for supplying the satellite data. cmU3, corresponding to p(O,.N,)=p(O) and REFERENCES ~(0,. 0) =p(N,), respectively, i.e. mean mole- 1. R. ARNOLDY, R. HOFFMAN,and J. R. WINCKLER, cular masses M =20.33 and M =20.95, the same Proc. COSPAR Symposium, Nice, p. 877. North altitudes are obtained if the temperatures dBer- Holland Company, Amsterdam (1960). ence is of the order of 100°K. An altitude 2. J. BARTER, Nururwiss. 45, 181 (1959). difference of 50 km corresponds to isothermal 3. D. R. BAT& The Eurth us u Planet (Edited by G. P. KUIPER). Chanter 12. Univ. of Chicago Press. atmospheres for which the temperatures differ Chicago’(l954j. from each other by about 300°K. In such a 4. D. R. BATES,Proc. Roy. Sot. London, 253,451 (1959). case they lead to the same density at 220 km; 5. R. E. BRIGGS, Smith. Astrophys. Obs. Sp. Rep. 30, at the highest altitudes, a difference of more 9 (1959). 6. E. T. BYRAM,T. A. CHUBB and H. FRIEDMAN,The than 100 km is required to reach the same Threshold of Space (Edited by M. ZELIKOFF),p. 211. density. Pergamon, London (1957). Such large differences show that the structure 7. K. W. CHAMPIONand R. A. MINZNER,Plane: Space of the high atmosphere is very sensitive to Sci. 1, 259 (1959). 8. S. CHAPMAN,Smith. Contr. Astrophys. 2, 1 (1957). diffusion and there is a possibility of finding 9. S. CHAPMAN,Annales Giophys. 15, 434 (1959). physical conditions which can represent the JO. S. CHAPMANand J. BARTELS,Geomagnetism, p. 897. conditions of a dark atmosphere. From the pre- Oxford Univ. Press (1940). ceding table and from satellite data, the 11. S. CHAPMANand T. G. COWL~G, The Mathematical Theory of Non Uniform Gases. Cambridge Univ. following data may be taken as a guide (see pre- Press (1939). ceding table): ~(220 km) = (2.5 kO.7) x 10-ls for 12. K. D. CQLE, Nafure 186,874 (1960). 96O”K

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