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Electron and nitrogen vibrational temperature in the E-region of the ionosphere
P&net. Space Sd. 1968. Vol. 16. pp. 321 to 327. Per@m~n Press. Printed in Northern &land
ELECTRON AND NITROGEN VIBRATIONAL TEMPERATURE IN THE E-REGION OF THE IONOSPHERE JAMBS C. G. WAIXBR* Aeronomy Branch, Goddard Space Flight Center, Greenbelt, Maryland (Received injinalform
17 October 1967)
Abstract-There is considerable evidence that electron temperatures in the E-region are greater than neutral gas temperatures by several hundred degrees. It is suggested that these temperatures rellect nitrogen vibrational temperatures of about 3100°K. Nitrogen vibrational energy may be provided by the reaction which quenches metastable ‘D oxygen atoms produced by photodissociation of oxygen in the Schumaru-Runge continuum. Vtbrational exchange collisions redistribute the energy leading to a Boltzmann vibrational distribution for the nitrogen molecules. Vibrational energy is lost mainly in collisions with the ambient electrons, and the lifetime of a vibrating molecule is about 5 x lo6 set in the E-region. 1. INTRODUCTION
probe measurements consistently yield electron temperatures in the E-region which exceed the neutral temperature by a factor of two or three (Boggess, Brace and Spencer, 1959; Spencer, Brace and Carignan, 1962; Brace, Spencer and Carignan, 1963; Spencer, Brace, Carignan, Taeusch and Niemann, 1965; Smith, Accardo, Weeks and McKinnon, 1965; Smith, Weeks and McKinnon, 1967). The high electron temperatures appear to be absent in radar backscatter data (Evans, 1967; Carru, Petit and Waldteufel, 1967) and the lack of a readily identitiable heat source for the electrons (Spencer, Brace, Carignan, Taeusch and NiemaM, 1965; Walker, 1966; Dalgarno, McElroy and Walker, 1967; Evans, 1967) has caused doubt concerning the validity of the Langmuir probe results at low altitudes. However, the Langmuir probe data are supported by measurements of electron collision frequency, and there exists, in addition, a plausible heat source for the electrons involving vibrationally excited nitrogen molecules. This heat source is described below. 2. ELECTRON COLLISION FBBQUENCIBS Collision frequencies deduced from the absorption of radio waves in the E-region exceed values deduced from scattering cross section data and model atmospheres (Schlapp, 1959; Shkarofsky, 1961; Beynon and Owen Jones, 1965; Thrane and Piggott, 1966), although agreement is excellent at lower altitudes. Thrane and Piggott (1966) suggest that this result may reflect the dissociation of oxygen in the E-region, but this suggestion may be dismissed on the basis of information on the atomic oxygen cross section (cf. Banks, 1966a; Breig and Lin, 1966; Garrett and Jackson, 1967; Henry, 1967). Because the electron collision frequency is nearly proportional to the electron temperature, Shkarofsky (1961) attributed the high collision frequencies to high E-region electron temperatures, and this suggestion has been reiterated by Beynon and Owen Jones (1965) and by Thrane and Piggott (1966). This interpretation of the collision frequency data yields electron temperatures comparable to the Langmuir probe results. Langmuir
* Now at Department of Geology, Yale University, New Haven, Connecticut. 321
6
322
JAMES C. G. WALKER
There is some evidence that the collision frequency in the E-region depends upon solar activity (Schlapp, 1959; Beynon and Owen Jones, 1965), and there may be a corresponding variation in E-region electron temperatures (cf. Smith, Weeks and McKinnon, 1967). 3. ELECTRONHEAT SOURCE The electron temperature in the E-region is not influenced by thermal conduction (Banks, 1966b; Dalgamo, McElroy and Walker, 1967) and presumably reflects local equilibrium between the electron heat source and the rate at which the electrons cool to the neutral molecules,* Cooling rates for NASA Flight 6.07 are given in Table 2, corresponding to the measured electron density and temperature (Spencer, Brace, Car&an, Taeusch and Niemarm, 1965) and the neutral atmosphere number densities and temperature (CIRA, 1965) appearing in Table 1. Cooling rates for other rocket flights are comparable. A heat TABLZ 1. NASA 6.07 DOWNLBO Altitude Oun)
n0ua) (cm-*)
n(O*) (cm-3
n(G) (cm-3
110
l-62(12)+ 4*00(11) 140(11) 6*27(10)
3*49(11) 7*50(10) 2.35(10) 960(9)
200(11) 760(10) 3.72(10) 218(10)
::
140
(z)
&
n(e) (cm-3
251 355 463 551
;zr 971 1029
* !z;; l-17(5) 1.350
* 1*62(12)a 1.62 x 1P’. TABLE 2
Aitihlde (km)
Elcctron.cc&lg rate (eV/cm*perset)
110 120 130 140
2::;; 24(4) l-3(4)
(& 3300 3100 ;z
O(lD) qucncbillgenergy (eV/cm*persee)
Quencbillgenergy
7*5(5) 4*0(5) 1*7(5) 9*2(4)
0.31 0.16 0.14 0.14
Coolingrate
source of the magnitude required by these data cannot be supplied by the absorption of solar ionizing radiation (Dalgamo, McElroy and Walker, 1967), and it appears that electric fields are too small to provide this much Joule heat to the electrons (Walker, 1966; Haerendel, Ltist and Rieger, 1967; Rees and Walker, 1968). Because of the large cross section for vibrational excitation of molecular nitrogen by electrons (Schulz, 1964), conversion of electron kinetic energy into nitrogen vibrational energy and vice versa is fairly rapid (Dalgarno, McElroy and Moffett, 1963) and the elevated E-region electron temperatures may be a result of high nitrogen vibrational temperatures in this region of the atmosphere. Vibrational temperatures appear to be high in some auroras (Clark and Belon, 1959; Valiance Jones and Hunten, 1960), and vibrating nitrogen molecules have been suggested as the souree of sodium excitation in auroras (Hunten, 1965) and in the nightglow (Starr, 1965). The thermal electron-nitrogen vibration energy exchange rate can be calculated from the cross sections of Chen (1964). For simplicity we ignore vibrational levels above the * At these altitudes the thermal electrons lose ene mainly in inelastic collisions with atomic 0 exciting the J = 1 and J = 0 levels of the ground term?yDaljpmcandDcggcs, 1968),byinclssticccU~ with molecular nitrogen, inducing rotation (Dalgamo an Henry, 1965), and by elasticcollisionswith molecularnitrogen(Banks,1966a).
323
TEMPEJUTURES IN THE E-REGION
grst and assume that the electron energy distribution is Maxwellian (cf. Megill and Cahn, 1964). Then the rate at which thermal electrons with temperature T”K gain energy from nitrogen with vibrational temperature T,“K is given by
Qe = l-5 x 10-l”Te-l/s (1 + &) -exp
[exp (9)
(F) [l + exp (~)]-‘n(e)n(N&
where n(e) cm-s and n(Ns) cm4 are By equating Qe to the tabulated vibrational temperature required to are given in Table 2. The differences and it appears that the data require independent of altitude.
eV/cmsper set,
(1)
the electron and nitrogen number densities. electron cooling rates we can calculate the nitrogen explain the measured electron temperatures. Results between the calculated temperatures are not sign&ant’ a vibrational temperature of about 31OO”K, nearly
4. NITROGEN VIBRATIONAL HFiAT SOURCE most abundant source of energy at Eregion altitudes is provided by the absorption of solar radiation in the Schumann-Runge continuum of molecular oxy&en (cf. Johnson and Wilkins, 1965). This process produces met&able oxygen atoms in the lD term and, at thealtitudes we are considering, these excited atoms are almost all quenched (Seaton, 1954; Zipf and Fastie, 1963; Dalgarno and Walker, 1964; Noxon, 1964; Wallace and McElroy, 1966) in collisions with molecular nitrogen (cf. Hunten and McElroy, 1966; McGrath and McGarvey, 1967; Snelling and Bair, 1967). The rate at which the quenching releases energy to the atmosphere is given in Table 2. These values correspond to the tabulated densities of molecular oxygen. It is. not known what fraction of the lD excitation energy is converted into vibrational energy of the nitrogen molecule by the quenching reaction, but experiments on the quenching of mercury atoms by CO and NO indicate that this fraction may be substantial (Polanyi, 1963; Karl and Polanyi, 1963; Karl, Kruus and Polar@, 1967; Karl, Kruus, Polanyi and Smith, 1967). The tabulated quenching energy therefore represents an upper limit on the nitrogen vibrational energy source. This upper limit exceeds the required electron heat source. Additional vibrational energy is provided by the reaction, The
N+NO-+Ns+O (2). (Phillips and Schiff, 1962; Morgan, Phillips and Schiff, 1962; Morgan and SchitI, 1963), and by collisions of non-thermal photoelectrons with a few electron volts of energy (Dalgamo, 1963; Dalgarno, McElroy and Moffett, 1963), but these processes are not likely to be competitive in the E-region. The quenching reaction may produce vibrating nitrogen molecules in any level up to tl = 7 (cf. Benesch, Vanderslice, Tilford and Wilkinson, 1965), but it appears from both theory and experiment (Lambert, 1962; Dalgamo, 1963; Rankin and Light, 1967; Schmeltekopf, Fehsenfeld, Gilman and Ferguson, 1967) that vibrational exchange collisions among nitrogen molecules redistribute the vibrational energy relatively rapidly, resulting in a Boltxmann distribution over vibrational levels. Phillips and Schiff (1962; Morgan, Phillips and S&it?‘, 1962) have measured a rate coefficient of 3.5 x 10-fe cms/sec for removal by nitrogen of molecules in vibrational levels above the third. The corresponding lifetimeof these levels at 110 km is about 3 x 109 set, much shorter than the lifetimes against
324
JAMES C. G. WALKER
collisions which convert vibrational energy to kinetic energy (see below). Moreover, Phillips and Schiff (1962) point out that their value for the rate coefficient may be too small because of uncertainty about the experimental vibrational distribution. Further indication of the rapidity of vibrational exchange collisions is provided by the theory of Rapp and Englander-Golden (1964). For nitrogen, the probability of a 1-O transition in a near resonance vibrational exchange collision is given by P = 3.7 x 10-8Tsecha (Rapp, 1965), where T‘K is the kinetic temperature and r/cm is the energy defect. This expression yields lifetimes against nitrogen vibrational exchange collisions of only about 10 set at 110 km. Since the vibrational distribution of the nitrogen molecules is Boltzmann the majority of the excited molecules are in the first vibrational level. The possibility that these molecules are quenched in collisions with the ambient neutral species must be considered. Vibrational exchange collisions between nitrogen molecules do not change the nitrogen vibrational energy content significantly but collisions with other atmospheric molecules represent a possible energy sink (White and Mill&an, 1964). From (3) the lifetime of nitrogen in the first vibrational level against exchange collisions with oxygen, Ns(u = 1) + O,(v = 0) + Ns(v = 0) + Os(u = 1)
(4)
is 2 x 108 set at 110 km and the lifetime against the reaction with nitric oxide is 109 set for n(N0) = 3.5 x 10’ cm-s (Barth, 1966). Exchange collisions with molecular hydrogen are even less effective in quenching nitrogen vibration for the hydrogen densities given by Patterson (1966). Since the lifetime, derived from (l), against quenching in collisions with electrons is 5 x 105 set, none of these exchange collisions are important. Collisions which convert vibrational energy into kinetic energy have been extensively studied both theoretically (cf. Benson and Berend, 1966; Calvert and Amme, 1966; Shin, 1966) and experimentally. Millikan and White (1963) have correlated a wide range of vibrational relaxation data by means of the expression log,, @TV>= 5.0 x lo-$r’W’s(T-~~
- 0.015$‘4) - 8.0
(5)
where TVseconds is the lifetime of the relaxing species with vibrational quantum temperature 6°K against quenching in collisions with a species at pressurep atm, p atomic mass units is the reduced mass of the colliding particles, and T”K is the kinetic temperature. Expression (5) yields quenching times for collisions with N,, 02, 0, He, and H which are all greater than log set in the II-region, so these processes are negligible compared with electron quenching. A further potential quenching mechanism is provided by atom-atom interchange in collisions with atomic nitrogen (Bates and Moiseiwitsch, 1956; Dalgarno, 1963; Dalgamo, McElroy and Moffett, 1963), N + Ns(u) + N.& < a) + N,
(6)
but the rate coefficient of this reaction is not known and neither is the density of atomic nitrogen. Accordingly, we ignore this mechanism and assume that vibrating nitrogen molecules in the ®ion are quenched only by the ambient electrons.
TEMPERATURES
IN THE EREGION
325
This means that the lifetime of the excited molecules is about 5 x 105 set and, consequently, that vertical transport processes redistribute nitrogen vibrational energy. In spite of the complications which transport introduces we can obtain an indication of the fraction of the 0 (‘D) excitation energy which is converted by quenching into nitrogen vibrational energy by dividing the electron cooling rate by the quenching energy. The results in Table 1 indicate that this fraction is about 0.2. If we assume a constant value for this fraction, independent of altitude, and calculate the nitrogen vibrational temperature which would result from local equilibrium between the rate at which the molecules gain energy in quenching collisions and the rate at which they lose energy to the electrons, we find that the temperature increases rapidly with altitude in the region we are considering. The nearly constant vibrational temperature deduced from the electron temperature data presumably reflects the action of vertical transport in carrying vibrational energy downwards from higher altitudes. 5. DISCUSSION Because of the long lifetime of the vibrating nitrogen molecules, enhanced vibrational temperatures will-probably persist through the night. Electron temperatures in the nocturnal Eregion comparable to daytime temperatures have, in fact, been measured on a recent rocket flight (Brace, 1965). Moreover, the sodium vapour trail observations of Bedinger, Manring and Ghosh (1958) could be the result of a nocturnal vibrational temperature as low as 2400°K at 140 km, provided sodium excitation occurs at the gas kinetic rate (Mentall, Krause and Fite, 1967). On the other hand, most auroras do not show high nitrogen vibrational temperature (Hunten and Shepherd, 1955; Broadfoot, 1967), and this may reflect rapid quenching of vibration as a result of enhanced aurora1 electron densities or of enhanced atomic nitrogen densities. While the nitrogen vibrational temperature depends upon the electron density, the electron temperature at a given altitude resulting from the vibrational heat source does not. Eclipse observations (Smith, Accardo, Weeks and McKinnon, 1965; Smith, Weeks and McKinnon, 1967) confirm this property of E-region electron temperatures. Enhanced nitrogen vibrational temperatures can be expected at higher altitudes in the atmosphere also, where energy is .provided by photoelectron impact and by reaction (2). Thus electron temperatures may be affected in the E-region as well as in the E-region. Enhanced vibrational temperatures will also influence the rate of removal of atomic oxygen ions by the reaction, O++N,-+NO++N (7) (Thomas and Norton, 1966; Schmeltekopf, Fehsenfeld, Gilman and Ferguson, 1967), the rate being increased by a factor of about 10 in the E-region. AcknowZe&ertzentsLE. C. Zipf and T. M. Donahue stimulated my interest in nitrogen vibrational temperatures in the upper atmosphere, and A. I. Stewart pointed out a major error in my interpretation of vibratmnal relaxation data. L. H. Brace provided helpful advice concerning Langmuir probe results, and D. M. Hunten clarikd the aurora1 observations and commented on the manuscript. A. Dalgamo made several helpful suggestions and kindly provided me with values of the electron-oxygen cooling rate before publication. I am grateful to the National Academy of Sciences-National Research Council for a Postdoctoral Resident Research Associateship supported by the National Aeronautics and Space Administration. RRPRRRNCRS BANKS,P. M. (1966a). Planet. Space Sci. 14, 1085. BANKS,P. M. (1966b). Annls Gdophys. 22,577. BARTH,C. A. (1966). Planet. Space Sci. 14,623.
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JAMES C. G. WALKER
BATES.D. R. and Moraarwrrscu, B. L. (1956). J. atmos. terr. Phys. 8,305. B~DIN~ER,J. F., -Q, E. R. and Gx-xoati,S. N. (1958). J. geq+s. Res. 63,19. Bamwcpr, W., VANLXXZICZ,J. T., Tmwmu, S. G. and WILKINXI N, P. G. (1965). Astrophys. J. 142, 1227. Ba~ao~, S. W. and B-ND, G. C. (1966). J. them. Phys. 44,470. &iEYNON, W. J. G. and OWBNJONPS,E. S. (1965). J. atmos. terr. Phys. 27,761. BOOOR+ R L., BRACE,L. H. and SPENCER,N. W. (1959). J.geophys. Res. 64,1627. BRACB,L. H. (1965). Paper presented at 2nd Conf. on Direct Aeronomic Meusurements in the Lower Ionosphere, Urbana, Illinois. Bluca, L. II., SPBNCXR,N. W. and CARIGNAN,G. R. (1963). J. geophys. Res. 68,5397. BREIO,E. L. and Lm, C. C. (1966). Phys. Rev. 151,67. BROALXQOT, A. L. (1967). J. atmos. terr. Phys. 30,151. CALVBRT,J. B. and AMMO,R. C. (1%6). J. them. Sot. 45,471O. CARRu, H., Pmrr, M. and WALDTBUPBL, P. (1967). J. atmos. terr. Phys. 29,351. C&EN,J. C. y. (1964). J. &em. Phys. 40,3513; 41,3263. CIRA 1965, COSPAR Interndtional Reference Atmosphere 1965, Committee on Spae6 Research. NorthHolland, Amsterdam. CLARK,K. C. and BELoN, A. E. (1959). J. atmos. terr. Phys. 16,205. DALOARNO,A. (1963). Planet. Space Sci. 10,19. DALC+ARNO, A. and D~aam, T. P. (1968). Planet. Space Sci. 16,125. DALUA~NO,A. and HENRY,R. J. W. (1965). Proc. R. Sot. A288,521. DALO~, A., MCBLROY,.M. B. and Mopwrr, R J. (1963). Planet. S’ Scf. 11,463. DALOARNO,A., MclQxo~, M. B. and WALICER, J. C. G. (1967). Planet. S’S&. 15,331. DALOARNO,A. and WALlCaR,J. C. G. (1964). J. utmos. Sci. 21,463. EVANS,J. V. (1967). J. geophys. Ret. 72,3343. Gmr’r, W. R and JAQCSON,H. T. (1967). Phys. Reu. 153,28. HAERENDEL, G., ,Ltfs~, R. and Rmmm, E. (1967). Planet. Space Sci. l&l. HENRY,R. J. W. (1967). Phys. Reu. 162,56. Hursra~, D. M. (1965). J. utmos. terr. Phys. 27,583. HUNTW, D. M. and MCELROY,M. B, (1966). Rev. Geophys. 4,303. HUNTEN, D. M. and Srm~pran~, G. G. (1955). J. atmos. terr. Phys. 6,64. JOHNSON,F. S. and WILKINS,E. M. (1965). J. geophys. Res. 70,128l. Kku, G., KRWS, P. and POLANM,J. C. (1967). J. them. Phys. 46,224. K.uu, G., KRWS, P., POLAR, J. C. and SMITH,I. W. M. (1967). J. them. Phys. 46,244. KARL, G. and POLANYI,J. C.-(1963). J. them. Whys. 38,271. LAMBERT, J. D. (1962). Atomic and Molecular Process (Ed. D. R. Bates), p. 783. Academic Press, New York. MCGRATH,W. D. and M~GARVEY,J. J. (1967). Planet. Space Sci. 15,427. MCGILL,L. R. and C&N, J. H. (1964). J.geophys. Res. 69,504l. MENTALL,J. E., KRAUSE,H. F. and Frrz, W. L. (1967). Disc. Faraday. Sot., Toronto, September. M~LLIKAN,R. C. and Wm-rz, D. R. (1963). J. &em. Phys. 39,3209. MORGAN, J. E., PHILLIPII, L. F. and Scmpp, H. I. (1%2). Disc. Fur&y Sot. 33,118. MORG~, J. E. and !Ictiq H. I. (1963). Can. J. Chem. 41,903. NOXON,J. F. (1964). J. geophys. Res. 69,3245. PATI’ZIWN, T. N. L. (1966). Planet. Space Sci. 14,417. hnuIps, L. F. and Scamp, H. I. (1962). J. them. Phys. 36,3283. PO-, J. C. (1963). J. quan. Spectros. & radiat. lkzn.$3,471. RANKIN,C. C. and LIGHT,J. C. (1967). J. them. Phys. 46,1305. UP, D. (1965). J.&em. Phys. 43,316. RAPP,D. and ENGLANLWR-GOLDEN, P. (1964). J. &em. Phys. 40,573; 40,312O. REIB,M. H. and WALKER,J. C. G. (1968). Annls Gdophys. (in press). S-P, D. M. (1959). J. atmos. terr. Phys. 16,340. S~HMEL,~OPF,A. L.. FHHSE~LD, F. C., GIL&UN,G. I. and FERGUS~N, E. E. (1967). P&met. Space Scf. 15,401. Scmnz, G. J. (1964). Phys. Rev. 135, A988. SEATON, M. J. (1954). J. atmos. terr. Phys. 4,295. SHIN,H. (1966). Adu. Chem. 58,44. SHKAROFSKY,I. P. (1961). Proc. I. R. E. 49,1857. l&rut, L. G,, Accxauo, C. A., WEEKS,L. H. and McKINNoN, P. J. (1965). J. atmos. terr. Phys. 27,803. SMITH,L. G., WEEKS,L. H. and MCKINNON, P. J. (1967). Paper presented at COSPAR, London, July. SNELLING,D. R. and BAIR, E. J. (1967). J. them. Phys. 47,228. SPBNC~R, N. W., BRAG, L H. and CARIGNAN, G. R. (1962). J. geophys. Res. 67,157. SPENCER, N. W., BRACE,L. H., CARIQNAN, G. R., TAEUSCH, D. R. and NIBMANN,H. (1965). J. geophys.
Res. 70,2665.
TEMF’ERATUBES IN THE E-REGION STARR, W. L. (1965). J. them. Phys. 43,73. THOMAS,L. and NORTON, R B. (1966). J. geophys. Z&s. 71,227. THRANE,E. V. and Pmxm, W. R. (1966). J. atmos. Yew. Phys. 28,721. VN.LANCEJam, A, and Humm, D. M. (1960). Can.J. Phys. 38,458. WALKER,J. C. G. (1966). Planet. S’ce Sci. 14,987. WALLXE, L. and MCELROY,M. B. (1966). Planet. Space Sci. 14,677. Wm, D. R and -, R. C. (1964). AZAA Jni 2,1844. ZIPF,B. C. and FASTXE, W. G. (1963). J. geophys. Res. 68,6208.
327
ELECTRON AND NITROGEN VIBRATIONAL TEMPERATURE IN THE E-REGION OF THE IONOSPHERE JAMBS C. G. WAIXBR* Aeronomy Branch, Goddard Space Flight Center, Greenbelt, Maryland (Received injinalform
17 October 1967)
Abstract-There is considerable evidence that electron temperatures in the E-region are greater than neutral gas temperatures by several hundred degrees. It is suggested that these temperatures rellect nitrogen vibrational temperatures of about 3100°K. Nitrogen vibrational energy may be provided by the reaction which quenches metastable ‘D oxygen atoms produced by photodissociation of oxygen in the Schumaru-Runge continuum. Vtbrational exchange collisions redistribute the energy leading to a Boltzmann vibrational distribution for the nitrogen molecules. Vibrational energy is lost mainly in collisions with the ambient electrons, and the lifetime of a vibrating molecule is about 5 x lo6 set in the E-region. 1. INTRODUCTION
probe measurements consistently yield electron temperatures in the E-region which exceed the neutral temperature by a factor of two or three (Boggess, Brace and Spencer, 1959; Spencer, Brace and Carignan, 1962; Brace, Spencer and Carignan, 1963; Spencer, Brace, Carignan, Taeusch and Niemann, 1965; Smith, Accardo, Weeks and McKinnon, 1965; Smith, Weeks and McKinnon, 1967). The high electron temperatures appear to be absent in radar backscatter data (Evans, 1967; Carru, Petit and Waldteufel, 1967) and the lack of a readily identitiable heat source for the electrons (Spencer, Brace, Carignan, Taeusch and NiemaM, 1965; Walker, 1966; Dalgarno, McElroy and Walker, 1967; Evans, 1967) has caused doubt concerning the validity of the Langmuir probe results at low altitudes. However, the Langmuir probe data are supported by measurements of electron collision frequency, and there exists, in addition, a plausible heat source for the electrons involving vibrationally excited nitrogen molecules. This heat source is described below. 2. ELECTRON COLLISION FBBQUENCIBS Collision frequencies deduced from the absorption of radio waves in the E-region exceed values deduced from scattering cross section data and model atmospheres (Schlapp, 1959; Shkarofsky, 1961; Beynon and Owen Jones, 1965; Thrane and Piggott, 1966), although agreement is excellent at lower altitudes. Thrane and Piggott (1966) suggest that this result may reflect the dissociation of oxygen in the E-region, but this suggestion may be dismissed on the basis of information on the atomic oxygen cross section (cf. Banks, 1966a; Breig and Lin, 1966; Garrett and Jackson, 1967; Henry, 1967). Because the electron collision frequency is nearly proportional to the electron temperature, Shkarofsky (1961) attributed the high collision frequencies to high E-region electron temperatures, and this suggestion has been reiterated by Beynon and Owen Jones (1965) and by Thrane and Piggott (1966). This interpretation of the collision frequency data yields electron temperatures comparable to the Langmuir probe results. Langmuir
* Now at Department of Geology, Yale University, New Haven, Connecticut. 321
6
322
JAMES C. G. WALKER
There is some evidence that the collision frequency in the E-region depends upon solar activity (Schlapp, 1959; Beynon and Owen Jones, 1965), and there may be a corresponding variation in E-region electron temperatures (cf. Smith, Weeks and McKinnon, 1967). 3. ELECTRONHEAT SOURCE The electron temperature in the E-region is not influenced by thermal conduction (Banks, 1966b; Dalgamo, McElroy and Walker, 1967) and presumably reflects local equilibrium between the electron heat source and the rate at which the electrons cool to the neutral molecules,* Cooling rates for NASA Flight 6.07 are given in Table 2, corresponding to the measured electron density and temperature (Spencer, Brace, Car&an, Taeusch and Niemarm, 1965) and the neutral atmosphere number densities and temperature (CIRA, 1965) appearing in Table 1. Cooling rates for other rocket flights are comparable. A heat TABLZ 1. NASA 6.07 DOWNLBO Altitude Oun)
n0ua) (cm-*)
n(O*) (cm-3
n(G) (cm-3
110
l-62(12)+ 4*00(11) 140(11) 6*27(10)
3*49(11) 7*50(10) 2.35(10) 960(9)
200(11) 760(10) 3.72(10) 218(10)
::
140
(z)
&
n(e) (cm-3
251 355 463 551
;zr 971 1029
* !z;; l-17(5) 1.350
* 1*62(12)a 1.62 x 1P’. TABLE 2
Aitihlde (km)
Elcctron.cc&lg rate (eV/cm*perset)
110 120 130 140
2::;; 24(4) l-3(4)
(& 3300 3100 ;z
O(lD) qucncbillgenergy (eV/cm*persee)
Quencbillgenergy
7*5(5) 4*0(5) 1*7(5) 9*2(4)
0.31 0.16 0.14 0.14
Coolingrate
source of the magnitude required by these data cannot be supplied by the absorption of solar ionizing radiation (Dalgamo, McElroy and Walker, 1967), and it appears that electric fields are too small to provide this much Joule heat to the electrons (Walker, 1966; Haerendel, Ltist and Rieger, 1967; Rees and Walker, 1968). Because of the large cross section for vibrational excitation of molecular nitrogen by electrons (Schulz, 1964), conversion of electron kinetic energy into nitrogen vibrational energy and vice versa is fairly rapid (Dalgarno, McElroy and Moffett, 1963) and the elevated E-region electron temperatures may be a result of high nitrogen vibrational temperatures in this region of the atmosphere. Vibrational temperatures appear to be high in some auroras (Clark and Belon, 1959; Valiance Jones and Hunten, 1960), and vibrating nitrogen molecules have been suggested as the souree of sodium excitation in auroras (Hunten, 1965) and in the nightglow (Starr, 1965). The thermal electron-nitrogen vibration energy exchange rate can be calculated from the cross sections of Chen (1964). For simplicity we ignore vibrational levels above the * At these altitudes the thermal electrons lose ene mainly in inelastic collisions with atomic 0 exciting the J = 1 and J = 0 levels of the ground term?yDaljpmcandDcggcs, 1968),byinclssticccU~ with molecular nitrogen, inducing rotation (Dalgamo an Henry, 1965), and by elasticcollisionswith molecularnitrogen(Banks,1966a).
323
TEMPEJUTURES IN THE E-REGION
grst and assume that the electron energy distribution is Maxwellian (cf. Megill and Cahn, 1964). Then the rate at which thermal electrons with temperature T”K gain energy from nitrogen with vibrational temperature T,“K is given by
Qe = l-5 x 10-l”Te-l/s (1 + &) -exp
[exp (9)
(F) [l + exp (~)]-‘n(e)n(N&
where n(e) cm-s and n(Ns) cm4 are By equating Qe to the tabulated vibrational temperature required to are given in Table 2. The differences and it appears that the data require independent of altitude.
eV/cmsper set,
(1)
the electron and nitrogen number densities. electron cooling rates we can calculate the nitrogen explain the measured electron temperatures. Results between the calculated temperatures are not sign&ant’ a vibrational temperature of about 31OO”K, nearly
4. NITROGEN VIBRATIONAL HFiAT SOURCE most abundant source of energy at Eregion altitudes is provided by the absorption of solar radiation in the Schumann-Runge continuum of molecular oxy&en (cf. Johnson and Wilkins, 1965). This process produces met&able oxygen atoms in the lD term and, at thealtitudes we are considering, these excited atoms are almost all quenched (Seaton, 1954; Zipf and Fastie, 1963; Dalgarno and Walker, 1964; Noxon, 1964; Wallace and McElroy, 1966) in collisions with molecular nitrogen (cf. Hunten and McElroy, 1966; McGrath and McGarvey, 1967; Snelling and Bair, 1967). The rate at which the quenching releases energy to the atmosphere is given in Table 2. These values correspond to the tabulated densities of molecular oxygen. It is. not known what fraction of the lD excitation energy is converted into vibrational energy of the nitrogen molecule by the quenching reaction, but experiments on the quenching of mercury atoms by CO and NO indicate that this fraction may be substantial (Polanyi, 1963; Karl and Polanyi, 1963; Karl, Kruus and Polar@, 1967; Karl, Kruus, Polanyi and Smith, 1967). The tabulated quenching energy therefore represents an upper limit on the nitrogen vibrational energy source. This upper limit exceeds the required electron heat source. Additional vibrational energy is provided by the reaction, The
N+NO-+Ns+O (2). (Phillips and Schiff, 1962; Morgan, Phillips and Schiff, 1962; Morgan and SchitI, 1963), and by collisions of non-thermal photoelectrons with a few electron volts of energy (Dalgamo, 1963; Dalgarno, McElroy and Moffett, 1963), but these processes are not likely to be competitive in the E-region. The quenching reaction may produce vibrating nitrogen molecules in any level up to tl = 7 (cf. Benesch, Vanderslice, Tilford and Wilkinson, 1965), but it appears from both theory and experiment (Lambert, 1962; Dalgamo, 1963; Rankin and Light, 1967; Schmeltekopf, Fehsenfeld, Gilman and Ferguson, 1967) that vibrational exchange collisions among nitrogen molecules redistribute the vibrational energy relatively rapidly, resulting in a Boltxmann distribution over vibrational levels. Phillips and Schiff (1962; Morgan, Phillips and S&it?‘, 1962) have measured a rate coefficient of 3.5 x 10-fe cms/sec for removal by nitrogen of molecules in vibrational levels above the third. The corresponding lifetimeof these levels at 110 km is about 3 x 109 set, much shorter than the lifetimes against
324
JAMES C. G. WALKER
collisions which convert vibrational energy to kinetic energy (see below). Moreover, Phillips and Schiff (1962) point out that their value for the rate coefficient may be too small because of uncertainty about the experimental vibrational distribution. Further indication of the rapidity of vibrational exchange collisions is provided by the theory of Rapp and Englander-Golden (1964). For nitrogen, the probability of a 1-O transition in a near resonance vibrational exchange collision is given by P = 3.7 x 10-8Tsecha (Rapp, 1965), where T‘K is the kinetic temperature and r/cm is the energy defect. This expression yields lifetimes against nitrogen vibrational exchange collisions of only about 10 set at 110 km. Since the vibrational distribution of the nitrogen molecules is Boltzmann the majority of the excited molecules are in the first vibrational level. The possibility that these molecules are quenched in collisions with the ambient neutral species must be considered. Vibrational exchange collisions between nitrogen molecules do not change the nitrogen vibrational energy content significantly but collisions with other atmospheric molecules represent a possible energy sink (White and Mill&an, 1964). From (3) the lifetime of nitrogen in the first vibrational level against exchange collisions with oxygen, Ns(u = 1) + O,(v = 0) + Ns(v = 0) + Os(u = 1)
(4)
is 2 x 108 set at 110 km and the lifetime against the reaction with nitric oxide is 109 set for n(N0) = 3.5 x 10’ cm-s (Barth, 1966). Exchange collisions with molecular hydrogen are even less effective in quenching nitrogen vibration for the hydrogen densities given by Patterson (1966). Since the lifetime, derived from (l), against quenching in collisions with electrons is 5 x 105 set, none of these exchange collisions are important. Collisions which convert vibrational energy into kinetic energy have been extensively studied both theoretically (cf. Benson and Berend, 1966; Calvert and Amme, 1966; Shin, 1966) and experimentally. Millikan and White (1963) have correlated a wide range of vibrational relaxation data by means of the expression log,, @TV>= 5.0 x lo-$r’W’s(T-~~
- 0.015$‘4) - 8.0
(5)
where TVseconds is the lifetime of the relaxing species with vibrational quantum temperature 6°K against quenching in collisions with a species at pressurep atm, p atomic mass units is the reduced mass of the colliding particles, and T”K is the kinetic temperature. Expression (5) yields quenching times for collisions with N,, 02, 0, He, and H which are all greater than log set in the II-region, so these processes are negligible compared with electron quenching. A further potential quenching mechanism is provided by atom-atom interchange in collisions with atomic nitrogen (Bates and Moiseiwitsch, 1956; Dalgarno, 1963; Dalgamo, McElroy and Moffett, 1963), N + Ns(u) + N.& < a) + N,
(6)
but the rate coefficient of this reaction is not known and neither is the density of atomic nitrogen. Accordingly, we ignore this mechanism and assume that vibrating nitrogen molecules in the ®ion are quenched only by the ambient electrons.
TEMPERATURES
IN THE EREGION
325
This means that the lifetime of the excited molecules is about 5 x 105 set and, consequently, that vertical transport processes redistribute nitrogen vibrational energy. In spite of the complications which transport introduces we can obtain an indication of the fraction of the 0 (‘D) excitation energy which is converted by quenching into nitrogen vibrational energy by dividing the electron cooling rate by the quenching energy. The results in Table 1 indicate that this fraction is about 0.2. If we assume a constant value for this fraction, independent of altitude, and calculate the nitrogen vibrational temperature which would result from local equilibrium between the rate at which the molecules gain energy in quenching collisions and the rate at which they lose energy to the electrons, we find that the temperature increases rapidly with altitude in the region we are considering. The nearly constant vibrational temperature deduced from the electron temperature data presumably reflects the action of vertical transport in carrying vibrational energy downwards from higher altitudes. 5. DISCUSSION Because of the long lifetime of the vibrating nitrogen molecules, enhanced vibrational temperatures will-probably persist through the night. Electron temperatures in the nocturnal Eregion comparable to daytime temperatures have, in fact, been measured on a recent rocket flight (Brace, 1965). Moreover, the sodium vapour trail observations of Bedinger, Manring and Ghosh (1958) could be the result of a nocturnal vibrational temperature as low as 2400°K at 140 km, provided sodium excitation occurs at the gas kinetic rate (Mentall, Krause and Fite, 1967). On the other hand, most auroras do not show high nitrogen vibrational temperature (Hunten and Shepherd, 1955; Broadfoot, 1967), and this may reflect rapid quenching of vibration as a result of enhanced aurora1 electron densities or of enhanced atomic nitrogen densities. While the nitrogen vibrational temperature depends upon the electron density, the electron temperature at a given altitude resulting from the vibrational heat source does not. Eclipse observations (Smith, Accardo, Weeks and McKinnon, 1965; Smith, Weeks and McKinnon, 1967) confirm this property of E-region electron temperatures. Enhanced nitrogen vibrational temperatures can be expected at higher altitudes in the atmosphere also, where energy is .provided by photoelectron impact and by reaction (2). Thus electron temperatures may be affected in the E-region as well as in the E-region. Enhanced vibrational temperatures will also influence the rate of removal of atomic oxygen ions by the reaction, O++N,-+NO++N (7) (Thomas and Norton, 1966; Schmeltekopf, Fehsenfeld, Gilman and Ferguson, 1967), the rate being increased by a factor of about 10 in the E-region. AcknowZe&ertzentsLE. C. Zipf and T. M. Donahue stimulated my interest in nitrogen vibrational temperatures in the upper atmosphere, and A. I. Stewart pointed out a major error in my interpretation of vibratmnal relaxation data. L. H. Brace provided helpful advice concerning Langmuir probe results, and D. M. Hunten clarikd the aurora1 observations and commented on the manuscript. A. Dalgamo made several helpful suggestions and kindly provided me with values of the electron-oxygen cooling rate before publication. I am grateful to the National Academy of Sciences-National Research Council for a Postdoctoral Resident Research Associateship supported by the National Aeronautics and Space Administration. RRPRRRNCRS BANKS,P. M. (1966a). Planet. Space Sci. 14, 1085. BANKS,P. M. (1966b). Annls Gdophys. 22,577. BARTH,C. A. (1966). Planet. Space Sci. 14,623.
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