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Ionospheric electron densities and temperatures in aurora
Planet. Space Sci. 1968. Vol. 16, PP. 459 to 475. Pergamon Prcas. Printed in Northern Ireland
IONOSPHERIC
ELECTRON DENSITIES IN AURORA
AND TEMPERATURES
J. C. G. WALKER Department of Geology, Yale University, New Haven, Connecticut, U.S.A.
M. H. REES Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, U.S.A. (Received 16 November 1967)
Abstract--Electron density profiles corresponding to chemical equilibrium, and electron temperatures corresponding to heating of ambient electrons by auroral secondaries have been computed for five stable aurora1 arc systems with published height protiles of 123914volume emission rates. The maximum electron density varies approximately as the three-quarters power of the 23914 intensity while the maximum temperature varies remarkably little. For these five auroras the temperature maxima lie between 2920°K and 3511°K and occur at altitudes between 330 km and 390 km. 1. INTRODUCTION
During the large magnetic and aurora1 storm of 25 May 1967, the Langmuir probe on the Explorer 22 satellite measured an electron temperature of some 6500°K at 1000 km near Washington, D.C. (L. H. Brace, private communication), where an aurora was observed simultaneously. Less spectacular but highly significant was a recent measurement of the altitude profile of electron temperature on a rocket tied at night from Fort Churchill. An enhanced electron temperature was measured even in the absence of any visible aurora, reaching a value of 2000°K at 250 km (Walker and Brace, 1967). The physical mechanisms leading to high aurora1 electron temperatures are investigated in this paper. The electrons in a primary aurora1 stream lose energy as they penetrate into the atmosphere by a variety of processes. Ionization of the atmospheric gases is the dominant initial loss process (cf. Dalgarno, 1961; Rees, 1963) while production of bremsstrahlung X-rays accounts for a negligibly small loss when the electrons have an initial energy of 10 keV or less (Rees, 1964). Ionization occurs into electronically excited states of the ion as well as into the ground state. This is the origin of the Ns+ (1 N.G.) and Nsf (Meinel) bands, various bands of OS+, and atomic lines originating from 0+(2P) and 0+(20), all observable features in the visible, near-ultraviolet, and near-infrared aurora1 spectrum. The primary ionizations produce secondary electrons (which may be some 100 times as abundant as the primaries) which cause additional ionization, but lose energy principally in exciting
various
neutral
species to a host of electronic
states (cf. Stolarski
and Green,
1967). Once the energy of the secondaries (or tertiaries, etc.) is as low as 5 or 6 eV, energy loss to the ambient electron gas by elastic collisions becomes an important mechanism. The effect is to heat the electron gas and, with the large electron-electron energy transfer cross section, a Maxwellian distribution prevails which may be characterized by a temperature, T,. Above about 250 km the thermal electrons lose energy to the positive ions, providing a heat source for the ions which then attain a temperature, T,, higher than the neutral gas. The details of these processes are described below and the results of computations for five quiet aurora1 arc systems are presented. 4.59
460
J. C. G. WALKER
and M. H. REEIS
2. OBSERVATIONS
Five auroras have been selected for analysis ; they represent various types of arc systems, all of which persisted long enough to allow us to assume a steady state. These auroras were observed in February and March, 1960, from, College and Fort Yukon, Alaska. From these stations the height luminosity profiles in the 13914 radiation (N2+ 1 N.G.) were obtained by photometric triangulation. The details of the observational procedure and the deduction of the profiles are described by Belon, Romick and Rees (1966). We have chosen auroras representing a variety of physical parameters-various peak emission altitudes, a range of photon emission rates, and different widths. The salient parameters are summarized in Table 1. TABLE1. AURORAL ARC SYSTEMS
Date (1960) Time (AST) 2100 1939 2007 2207 2136
26 February 1 March 1 March 26 March 29 March
Geomagnetic latitude (“N.)
Maximum 13914 intensity at Fort Yukon (kR)
66.40 67.30 67.35 6633 67.31
30.6 13.0 22.0 34.7 7.2
Width (lo-@ 3: 26 :f
Altitude of max. emission rate (km) 120 133 103 110 142
3. ANALYSIS
3.1 The model atmosphere Jacchia’s (1964) formulae are used to arrive at a model appropriate to the time and place of the observations. The analytic formulation of Bates (1959) and Walker (1965) provides altitude proties for the temperature and density of all neutral constituents except atomic hydrogen. For the latter we use, as a guide, the review by Donahue (1966) to deduce an altitude profile appropriate to an exospheric temperature of 1200°K. Table 2 presents the atmospheric parameters. 3.2 The ion chemistry The cross sections for inelastic collisions between energetic electrons and atmospheric gases all exhibit similar dependence on electron energy and we take advantage of this observation to deduce the rates of production of various ionized and excited species from the volume emission rate of 13914. From the cross section for the process, e+Ns+e+N,++e+f3914
(1)
(McConkey and Latimer, 1965; McConkey, Woolsey and Bums, 1967), and the total ionization cross section for molecular nitrogen (Rapp and Englander-Golden, 1965) we deduce that q(Na+) + qcN+) = 17q(3914) (2) (cf. Dalgamo, Latimer and McConkey, 1965), where 7 (3914) is the volume emission rate of A3914, q(x) is the rate of production of species X, and we ignore production of multiply charged ions. * * The total ionization cross section measured by S&ram, Moustafa, Schutten and de Hcer (1966) is smaller than the cross section used here and leads to a ratio of 13 in (2). In the absence of further evidence we use 17 for this ratio.
461
ELEXXRON DENSITIES AND TEMPERATURES IN AURORA TABLE 2. W
Altitude (km) 350 542 690 804 893 961 1010 1050 1080 1110 1130 1140 1150 1160 1170 1180 1180 1180 1190 1190 1190 1200 1200 1200 1200 1200 1200 1200 1200
120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 350 400 450 500 550 600 650 700 750 800 * 4OO(-tll)
NEUTRAL ATMOSPHERE
n(K) (cm-3
n(G) (cm-*)
n(O) (cm-8)
n(He) (cm-3
4*00+11)* l-25(+11) 5*90(+10) 3.31(+10) 2.05(+10) 1*36(+10) 9*40(+9) 6.68(+9) 4.84( +9) 3.57(+9) 2.66(+9) 2.00(+9) 1.52(+9) 1*15(+9) 8.86(+8) 6*80(+8) 5.24(+8) 4*04(+8) 3.13(+8) 8.87(+7) 2*58(+7) 7.66(+6) Z31(+6) 7.14(+5) 2*23(+5) 7.11(+4) 2.30( +4) 7*57(f3) 2.52(+3)
7.50(+10) 2.12(+10) 9*27(+9) 4.90( +9) 2.89( +9) 1.82(+9) 1.20( +9) 8.17(+8) 5.69( +S) 4.03(+8) 2*88(+8) 2.09(+8) 1.52(+8) 1.11(+8) 8.25(+7) 6.10(+7) 4.53(+7) 3*37(+7) 2.51(f7) 5.96(+6) 1*45(+6) 3.63(+5)
7.60(+10) 3.25(+10) 1*9O(-tlO) l-28(+10) 9*33(-t9) 7*14(-t9) 5,64(-t-9) 456(+9) 3.75( +9> 3.12(-t9) 2.62(+9) 2*21(+9) 1.88(+9) 1.60(+9) 1.37( +9) l-18(+9) 1.01(+9) 8*75(+8) 7.55(+8) 3.66(+8) l-80(+8) g-03(+7) 4.56(+7) 2.32(+7) 1*19(+7) 6.23(+6) 3.26(+6) 1*73(+6) 9*25(+5)
3*40(+7) 2.36(+7) 1.89(+7) 1*62(+7) 1.45( +7) l-32(+7) l-22(+7) l-14(+7) 1.07(+7) l-02(+7) 9*71(+6) 9.27(+6) 8.87(+6) 8.50(+6) 8.16(+6) 7.84(+6) 7*54(+6) 7.26(+6) 6*99(+@ 5*82(+6) 488(+6) 4*1(X+6) 3.45(+6) 2.92(+6) 2.47(+6) 2*10(+6) 1*78(+6) 1.52(+6) l-30(+6)
ZZ:::; 6.39(+3) 1*72(+3) 4*75(+2) l-33(+2) 3.80(+1)
n(H) (cm-3
6+0(+5)
4.50(+5)
::FJ:; l-34(+5) 1*18(+5) 1.02(+5) 8.60(+4) 7*00(+4) 6.56(+4) 6.12(+4) 5*68(+4) 5.24(+4) 4.80( $4) 4=54(+4) 4*28(+4) 402( +4) 3*76(+4) 3*50(+4) 3.05(+4) 2.60( +4) 2.35(+4) 210(+4) 202(+4) l-95(+4) l-90(+4) 1*85(+4) 1*82(+4) 1.80(+4)
E 400 x lo+“.
We now distinguish
between the processes, e+N,-te+N,++e,
(3)
e+N,+e+N+N++e,
(4)
and
and utilize the cross section data reviewed by Kieffer and Dunn (1966) to arrive at q(Nz+) = 13.6 q(3914),
(5)
and q(N+) Similar
consideration
ionization
of ionization
of molecular
= 0.25 q(NZ+).
of atomic
(6>
and molecular
oxygen
and dissociative
oxygen yields, with cross sections from Kieffer and Dunn (1966), r(O,+)
= 0+3[17(N,+) +
dN+>I 3;
,
(7)
and v@+)
= @5~(0,+)
+ @5[rl(N,+)
where n(X) is the number density of species X.
+
r(N+)l$$
,
(8)
462
J.
C. G. WALKER and M. H. REES
The total ionization rate, s(e) = rl@&+) 4 VP+) + r(Os+) + rl(O+),
(9)
is shown in Fig. 1 for the five aurora1 arc systems. Many of the ions produced by electron impact ionization are electronically excited and contribute to aurora1 luminosity while some of the metastable levels are sufbciently longlived to influence the ion chemistry. We consider fist the reactions of ions in the ground state. -
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Molecular nitrogen ions are removed by the reactions, Nzf + 0, + O,+ + N,,
&r,,= 1 x lo-lo,
(10)
N$+O-+NO++N,
k,, = 2.5 x lo-lo
01)
(cf. Ferguson, 1967), and -l/S
N,-t+e+N+N,
k= = 2.9 x lo-’
$_,
(12) ( ) (cf. Biondi, 1967), where kais the rate coefficient of reaction s in ems se&. The rate coefficient of (10) does not depend on the temperature (Stebbings, Turner and Rutherford, 1966; Warneck, 1967), but there is evidence that the rate coefficient of (12) depends on the ion temperature (presumably the vibrational temperature) as well as on the electron temperature (cf. Biondi, 1967). The value given corresponds to an ion temperature of 300°K. Atomic nitrogen ions are removed by the reactions, N++O,+NOf+O,
k= = 5 x lo-l0 ,
(13)
k14 = 45 x lO- 10
(14)
and N++O,-+O,++N,
ELECTRON DENSITIES AND TEMPERATURES
IN AURORA
463
(cf. Ferguson, 1967; McElroy, 1967). Neither of these rate coefficients depends on the ion temperature (Stebbings, Turner and Rutherford, 1966). Molecular oxygen ions are removed by the reactions, O$ $1 N, + NO+ + NO,
(15)
for which we assume kls = 5 x lo-l6 (cf. Ferguson, 1967), and O,++e-+O+Q
k
(16)
(cf. Biondi, 1967). The temperature dependence of k,, has been measured only for ion temperature equal to electron temperature. Atomic oxygen ions are removed by the reactions, O++N,+NO++N,
kl, = 1.8 x lo-l2 ,
(17)
k18 = 2 x lO-11
(18)
and 0++0,-+0,++0,
(cf. Ferguson, 1967; Schmeltekopf, Fehsenfeld, Gilman, and Ferguson, 1967). The rate coefficient of (17) depends strongly on the nitrogen vibrational temperature and there is evidence that it is proportional to the ion temperature (Giese, 1966; Stebbings, Turner and Rutherford, 1966). We ignore these effects. The only reaction removing the NO+ ions produced by (1 l), (13), (15), and (17) is NO++e-+N+O,
k,, = 4.6 x lo-’
(19)
(cf. Biondi, 1967; Gunton and Shaw, 1965). This temperature dependence reflects measurements for equal ion and electron temperatures. In the absence of information on the rates of reaction of excited ions, any treatment of their effect on the ion chemistry must be approximate. Since the excited levels of N2+ are not metastable (cf. Dalgamo, McElroy and Moffett, 1963). these levels will not react chemically. The %’ and lD levels of N+ have long radiative lifetimes (cf. Chamberlain, 1961) and may react. In addition to Reactions (13) and (14) these ions can be removed by reactions with N2, N+~Dor?S’)+N2+N2f+N. (20) There is evidence that Reaction (14) is slower for excited N+ ions at impact energies of several tens of eV (Stebbings, Turner and Rutherford, 1966), but this behavior may not extend to thermal energies. We therefore assume that (13) and (14) are not affected by excitation of the nitrogen ion. There is no information on (20) but it is not likely to have a large effect on the ion chemistry. Accordingly we ignore metastable N+ ions altogether. Molecular oxygen ions in the a %rUstate are metastable and may be removed in reactions with N,, 0, and electrons, O$(a 4rTT,)+ N2 + I$+ + 0, o,+(a %T,) + 0 + O$(P?r,)
(21) + 0,
(22)
O$(a “vu) + e --t 02+(X2z-Q) + e.
(23)
and
464
J. C. G. WALKER
and M. H. REES
We assume that the rate coefficients of (21) and (22) are both lo-lo cm3 set-l, and that the rate coefficient of (23) is lo-’ cm3 SC&. There are other possible removal processes for these ions which we ignore. The number density of metastable O$ ions is therefore given by, (24) Metastable O+@‘) ions have a radiative lifetime of 5 set (Seaton and Osterbrock, and may be removed in the reaction with Nz, 0+(2P) + N, + 0 + N,+, for which we assume a rate coefficient of 10-l” cm3 se&, n(O+ 2P) =
1957) (25)
giving
m+ 2e
(26)
0.219 + k,,n(N,) ’
Other possible processes are ignored. For the very long-lived O+CO) level we consider removal by (17) with the rate coefficient equal to kI, (cf. Stebbings, Turner and Rutherford, 1966), by 0+(20) + N, + Ns+ + 0 with k2, = 1O-Qcm3 set-l (cf. Stebbings, Turner and Rutherford, McElroy, 1965), by electron quenching, 0+(20) + e --t O+(4s) + e,
(27) 1966; Dalgarno and
k,, = 3 x 10-s
(28)
(Seaton and Osterbrock, 1957) and by emission of radiation with a transition probability of 1.33 x lv set-l (Seaton and Osterbrock, 1957). These processes yield $@+ 20) + 0~171?2(0+2P) n(“+ 20) = (7% + k2&(N2) + k,n(e)
+ l-33 x 10-4 ’
(29
A useful discussion of the metastable ions and their removal processes has been given by Dalgarno and McElroy (1965). From the cross sections of Watson, Dulock, Stolarski and Green (1967) we deduce 11(02+a +,)
= @411(02+),
with allowance for cascading from O,+(b 42,-).
(30)
Seaton’s (1959) cross sections yield
q(o+ 2P) = 0*2[17(0+) - o*57j(02+)],
(31)
7j(Of2D) = @4[7(0+) - 0*5?7(0,+)],
(32)
and where cascading and possible contributions from dissociative ionization of 0, have been excluded. The chemical equilibrium ion densities corresponding to the reactions we have described have been derived for given electron temperatures, neutral number densities, and i13914 volume emission rate. Vertical diffusion of the ions becomes important above 250 km, limiting the usefulness of chemical equilibrium calculations to lower altitudes. At high altitudes the ion composition given by Taylor, Brace, Brinton and Smith (1963) has been
ELECTRON
DENSITIES
AND
TEMPERATURES
465
IN AURORA
TABLE 3. ION COMPOSITIONIN AIJRORALARC SYSTEMAT 2100 AST ON 26 FEBRUARY Altitude (W
loo 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 z 400 450 500 550 600 650 700 750 800
-n(O,+) n(e) 0.6848 0.4742 0.3208 0.2320 0.1713 0.1334 0.1091 0.0913 0.0775 0.0657 0.0553 0.0465 0.0386 0.0314 0.0249 0.0194 0.0146 0.0107 oaO74 0*0050 oaO3 1 oaoO2 0 0 0 0 0 0 0 0 0
* 3*397(+5)
WC+) n(e) 0.3148 05233 0.6641 0.7296 0.7638 0.7715 0.7599 O-7381 0.7050 0.6653 0.6206 0.5679 05123 0.4519 0.3871 0.3243 0.2627 0.2042 0.1497 0.1043 0.0675 oaO54 0.0053 oaO51 0 0 0 0 0 0 0
-n(C+) n(e)
_n(Na+) n(e)
n(N+) n(e)
0*0002 oaO15 oaO93 0.0268 0.0491 0.0760 0.1093 0.1470 0.1921 0.2423 0.2967 0.3575 0.4208 0.4885 0.5603 0.6296 0.6975 0.7620 0.8222 0.8728 0.9144 0.9887 0.9893 0.9898 0.990 0.965 0940 0.905 0.870 0.805 0.740
04000 oaOO1 OaOO4 oaO12 oaO21 0*0030 0.0041 0.0052 0.0064 0.0076 OaO88 0.0101 0.0112 0.0123 0.0133 0.0140 0.0144 0.0144 0.0140 0.0131 0.0119 0*0055 0.0054 oaO51 0 0 0 0 0
oaOo2 oaO1o 0.0053 0.0104 0.0138 0.0160 0.0176 0.0185 0*0190 0.0191 0.0187 0.0181 0*0171 0.0159 0.0145 0.0127 0.0108 OaO88 0.0067 OGO48 0.003 1 oaOO1 0 0 0 0 0 0 0 0 0
n(He+) - n(e) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oaO5 0.010 0.030 0050 0.075 0.100 0.150 0.200
n(H+) n(e) 0 0 0 0 0 : 0 0 0 0 0 0 0 0 0 0 0 0 0
x
0 0 0 oao5 0.010 0.020 0.030 0.045 0.060
n(e) (cm-3
2*460( +6) 2*470( +6) 2.520(+6) 2*580(+6) 2*500(+6) 2.414(+(F) 2.330(+6) 2*243(+6) 2.160(+6) 2.114(+6) 2.069( +6) 2.025( +6) 1.982(+6) 1.940(+6) 1*894(+6) 1*849(+6) 1.805(+6) l-762(+6) 1*720(+6) l-560(+6) 1.400(+6) l-260(+6) l-130(+6) 1*020(+6) 9.200(+5) S-300(+5) 7.400( t5) 6750(+5) 6*100(+5)
3 3.397 x 10+5.
adopted. The relative ion number densities for the aurora at 2100 AST on 26 February are given in Table 3, while the electron density, extrapolated to high altitude with an appropriate scale height, is shown in Fig. 2 for all five aurora1 arc systems. The results for the aurora at 2100 AST on 26 February may be compared with densities for the same aurora computed by Rees, Walker and Dalgamo (1967) using temperature independent rate coefficients and ignoring the effects of atomic nitrogen ions and metastable ions. In the chemical equilibrium region below 250 km the electron densities in Table 3 and Fig. 2 are about twice as large as the previously computed densities, reflecting principally the substantial reduction in dissociative recombination coefficients at high electron temperatures. The ionization rates in Fig. 1 are about the same as those previously computed below 250 km but are lower by a factor of about 2 at higher altitudes. This difference is not significant, arising simply from our extrapolation of the 13914 volume emission rate to high altitudes where photometric data are not available. The present electron densities are lower than the previous ones at high altitudes, principally because of lower electron and ion temperatures used in the extrapolation of the density above the chemical equilibrium region. 7
466
J. C. G. WALKER and M. H. REES 40Q
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3.3 Electron heating The deduction of the rate at which secondary electrons heat the ambient electron gas involves consideration of both continuous degradation of the energy of the secondary electron due to elastic collisions with the ambient plasma and discrete energy losses due to inelastic collisions with the ambient neutral particles (A. I. Stewart, private communication). For simplicity we assume that the inelastic processes can be adequately represented by a continuous energy loss and we assume, also, that all secondary electrons are produced with the same energy, E,,. The average amount of energy deposited by each secondary electron in the electron gas is therefore e(e) =
s
x0 r(e 1E) dE
0
r(T
eV,
(33)
1 E>
where r(e 1E) is the rate of energy loss resulting from elastic collisions with the ambient electrons (Butler and Buckingham, 1962), r(e I E) =
l-95 x lo-i2n(e) ev cm_l E
(cf. Dalgarno, McElroy, and Moffett, 1963), and r(T 1E) is the total energy loss rate. In the energy range considered here, r(T 1E) includes vibrational excitation of molecular nitrogen, excitation of 00 and O(lO), and elastic collisions with the ambient electrons (cf. Rees, Walker and Dalgarno, 1967). The value of E. is not critical, and may be taken as 5 or 6 eV with negligible difference in c(e). The average energy deposition per electron is, however, a function of altitude, and we list values of E in Table 4. The rate of heating of the electron gas by secondary electrons
ELECTICON DENSITIES AND TEMPERATURES
IN AURORA
467
TABLE4. AVERAGEENERGY DEPCXITED IN THE
AMBIENT ELECTRON GAS BY EACH SECONDARY BLSCTRON WITH INITIAL ENERGY, E. = 6~V(2100 AST 26 FEBRUARY)
Altitude (km)
(e&G
80 90 100 110 120 130 140 150 160 180
0.307 0.324 0.623 l-35 2.13 2.74 3.27 3-71 4.03 4.53 4*89 5-45 5.71 5.83 5.88 5.93 5.95
z 300 350 400 500 800
is given by &(z) = q(e)&(e) eV per ems se&.
(35)
Cole (1967) has recently pointed out that the electron gas can also be heated by joule dissipation of the reverse current corresponding to the directed flux of electrons at each location. Assuming that the directed and omnidirectional fluxes are similar in magnitude he finds that this heat source is comparable to heating by elastic collisions. Only primary electrons, however, contribute significantly to the directed flux, and the joule heat source is negligible compared with heating by the secondaries described above. 3.4. The electron temperature We evaluate the electron temperature by solving the steady state heat conduction equation for the electron gas with allowance for local heating, Qe(z) eV per cm3 set-l, and local cooling, L(z 1 Te) eV cm-3 se+ (cf. Dalgarno, McElroy and Walker, 1967), = QeW - J% 1 Tel,
(36)
where K is the thermal conductivity of the electron gas (Spitzer and HBrm, 1953), /C=
7.7 x 108 sin21 T,512
= KT,S/2 eV cm-l set-l degr.
(37)
In (37) I is the geomagnetic dip and the second term in the denominator represents the reduction in the conductivity resulting from electron-neutral collisions (Banks, 1966b; Dalgarno, McElroy and Walker, 1967). It is small at high altitudes where conduction is important. In (37) the summation is over all neutral species, j; the electron-neutral momentum transfer cross section, 9,(i) cm2, is given by Banks (1966a). Our expression differs from the expression given by Banks (1966b) who assumed that electron-neutral collisions yield the same thermal diffusion coefficient as electron-ion collisions.
J. C. G. WALKER and M. H. REES
468
In addition to the electron cooling terms discussed by Dalgamo, McElroy and Walker (1967) we have included cooling due to elastic collisions with atomic hydrogen (Banks, 1966a), but we have not included cooling due to collisions which excite the fine structure levels of the ground term of atomic oxygen (Dalgamo and Degges, 1968; Tohmatsu, 1965). The conduction Equation (36) has been solved using a simple relaxation approach (cf. Hildebrand, 1952). The altitude range is divided into M - 1 small segments (generally 10 km high) and an index, m, associated with each altitude point. The lower boundary is at zl = 120 km and the upper boundary is at Z~ = 800 km. Writing T, for the electron temperature at z, we replace (36) with the finite difference equation, Q&J
- L(zm 1 T,J + +KTz2B2 + 2KTz2A
= 0,
(38)
where
T&m - zm-3 + Pm - Tmdzm - z,n+,) %3h+1 - %a) kn+1 - %dG-1 - GJ ’
-
(39)
and T m+l
A=
-
Tm
Tm-
Tm-I WI
hn+1-
%a-&,+1
-
4
+
bn+1-
.Gn4kn-1-
%J
*
In (38) we have ignored a negligibly small term involving dK/dz. The expression (38) represents a set of M - 2 coupled non-linear algebraic equations which must be solved for the values of T, at all interior points. The boundary values, Tl and TM, are handled differently. At the lower boundary we assume that conduction is negligible and determine Tl from the expression, Uz, 1 q) = Q&A
(41)
while at the upper boundary we specify the temperature gradient,
1
-dTe = s. [ dz z= Thus, TM is given by the equation, Qe(z&
-
L(zM 1 TM) + gKTa2S2 TM--~
’ = (zj,_l
-
TM
-
zj,f)2 -
(42)
+ 2KTa2C
= 0,
(43)
S (z&&1 - ZM) ’
(44)
In the absence of information on temperature gradients at high altitudes in aurora we set S = 0. We now solve (41) for Tl using an iterative procedure and guess a set of values for T,,,, 2 < m Q M. Leaving Tl and T3 tied we solve (38) for T2; then, leaving T, and T4 tied we solve (38) for T3. In this way we work through the grid, finally solving (43) for TM. We now go back to z, and repeat the whole procedure again and again, until the values of T, no longer change significantly at any altitude. In practice we Cnd that the relaxation is quite stable, but very slow, frequently requiring more than a hundred passes. A more sophisticated relaxation procedure (cf. Allen, 1954) would be faster. 3.5. The ion temperature Banks (1966c; 1967) has shown that thermal conduction in the ion gas affects ion temperatures when the electron density is low. At aurora1 densities this effect is not likely
ELECTRON
DENSITIES AND TEMPERATURJ%
469
IN AURORA
to be significant and we ignore it. The ion temperature is therefore determined by the balance between the rate at which the ions are heated in elastic collisions with the ambient electrons, i;l(e)(T, - &) eV crnm3 set-l, and the rate at which the ions cool in elastic collisions with the neutrals, R(n)(Z’, - Z’,) eV cmA3 se+.
BOO2100 700
FEBRUARY
7.6
-
600-
g500Y w,4003 I;300-I .z 200-
100 -
I*,_J 400
800
I 1200
*,,,.I 1800
* 2000
2400
L 2800
s
t. 3200
I 3600
*
I. 4000
I
b
I,
f’Kf
TEMPERATURE
FIG.3. ALWUDE PROFILESOF ELECIXON TEXPERATURB,To, ION TBWERATWRE, T&,ANJJ NINTRAL GAS TTMPJSRAW, T,, FOR m AURORA AT 2100AST ON 26 FEBRUARY. T,’ is the electron temperature calculatedwithout thermal conduction.
Equating these two rates and solving for Tf we obtain T.
*
WW, + Rle)T~
=
R(n)+
where R(e) =
R(e)
’
7.7 x 10-%(e) TeSt%
(45)
(46)
(Spitzer, 1956), and R(n) = 3k 2 n(i) 2 p!%i?! i
n
%
(47)
(cf. Banks, 1966d). Here A, is the ion mass in a.m.u., k is the Boltzmann constant, mt and m, are the ion and neutral masses in g, y,, is the reduced mass, Pi* =
wm, m, i- m, ’
(48)
vtn is the ion-neutral collision frequency used by Rees and Walker (1968), and the summations are taken over all neutrals, n, and ions, i.
470
J. C. G. WALKER and M. H. REES 4. RESULTS AND DISCUSSION
Electron temperatures computed without heat conduction, Te’, and including conduction, Te, are shown for the aurora at 2100 AST on 26 February in Fig. 3, together with the ion temperature, T,, computed from Equation (45), and the neutral gas temperature, T,,. The calculated value of Te’ is very sensitive to the heating rate and electron density and the zig-zags in this profile are caused by rounding off these quantities. The zig-zags are not significant and, indeed, Te’ is plotted only because it shows where thermal conduction becomes important. Because of the large heating rates and electron densities in this aurora conduction is not important below 450 km.
600
70
I
600I Y -
500-
: 3 c 4005 4 JOO-
zoo-
IOO-
ELECTRON FIG.
4. THE EFFECT
ON
THE
ELECTRON
TEMPERATURE
TEMPERATURE
POSITIONS
IN
THE
OF
ASSIJMING
(OKI DIFFJXIINT
ION
COM-
TOPSIDE.
The temperatures in Fig. 3 may be compared with the values calculated by Rees, Walker and Dalgamo (1967) for the same aurora. Below about 350 km the two temperature profiles are almost identical in spite of the difference in the electron density profiles at low altitude (see Section 3.2). At low altitudes the aurora1 secondaries share their energy between the ambient plasma and the neutral particles (see Equation (33) and Table 4) so the rate of heating of the ambient electrons is nearly proportional to electron density. Since the thermal electrons at these altitudes cool largely to the neutral particles the cooling rate is also proportional to the electron density, so the electron temperature which results from a given ionization rate is approximately independent of electron density. At altitudes above 350 km the electron temperatures which we calculated previously are considerably higher than the temperatures shown in Fig. 3. This is a result of our reduction in the extrapolated value of the i13914 volume emission rate (see Section 3.2). This extrapolation is uncertain and the temperature at high altitudes reflects this uncertainty. Uncertainty in the high altitude temperature profile leads to uncertainty in topside electron
ELECTRON DENSITIES AND TEMPERATURES
IN AURORA
471
densities also. However, the intensity of the oxygen red line is not greatly affected because the rate of excitation of OPD) by thermal electrons peaks at about 200 km (Rees, Walker and Dalgarno, 1967). Topside electron temperatures are also sensitive to the ion composition and this introduces additional uncertainty. It was noted in Section 3.2 that the aurora1 ion composition was derived below 250 km, but above this altitude the composition measured by Taylor, Brace, Brinton, and Smith (1963) was adopted. The corresponding temperatures are shown f
‘1’
I
-
1 *
/
1 /
z
I
’
I
/.
*
,
*
“
/
/
r,
i
*
800 -
100
1939
MARCH
I
600 -
,500Y 400iii 2 ;300-I 4. zoo-
IOO-
r
*
1
400
*
8.1
800
*
1200
1
*
1
-
1
I600 2000 2400 TEMPERATURE
FIG.~. ALTITUDE
PRO~LES
*
‘r’s
2800
1
3200
1
3600
1.K)
OF THE TBMPERATURES 1 MARCH.
FOR THE AURORA
AT 1939AST
ON
as Case B in Fig. 4. If, instead, we assume that the topside ionosphere is composed entirely of oxygen ions the resulting temperature profile (Case A) is indistinguishable. If, on the other hand, we use the results of Hoffman (1967) yielding a very low mean ion mass at high altitudes we obtain somewhat lower electron temperatures (Case C), The light ions are much more effective in cooling the electrons, as shown by Equation (46). Using the Taylor ion composition we have calculated electron and ion temperatures for the other four arc systems in Table 1. The results in Figs. 5-8, together with Fig. 3, show surprisingly little variation in electron temperature profiles in view of the marked differences between auroras in intensity, ionization rate, electron density, and altitude of peak emission. All of the temperature profiles exhibit maxima between 2920°K and 3511°K at altitudes between 330 km and 390 km. In the region of the temperature m~mum the electrons cool mainly to the ions and the cooling rate varies as the square of the electron density [Equation (46)]. The electron heating rate, on the other hand, is proportional to the ionization rate since most of the secondary electron energy at these altitudes is given to the ambient electrons (Table 4). Since the electron density is nearly proportional to the square root of the ionization rate (compare Fig. 1 and Fig. 2), the electron temperature is nearly independent of the ionization rate.
J, C. G. WALKER and M. H. RJ?ES
472
80O-
Tn,.
2007 MARCH
,)
70O-
60 o-
‘o-
lo-
IO-
I
I
IO-
O-
I
*
400
.I.
I
800
I.
1200
I600
I.
2000
L
I
I
2400
2800
TEMPERATURE
FIG.6.hITlVL%
PRO-
*
I
3200
*
I.
3600
3.
I
4000
s
I
4400
t*K)
OF THE TRMPERA~
AT 2007AST
FOR THE AURORA
ON
1 MARCH.
2207
i
*
I
400
L
I
800
I
I
1200
*
8
1800
*
1 2000
’
I
2400
*
1 2800
TEMPERATURE
FIG. 7. Acmmm
PROFILES OF THE TEMPERATURES
26 STARCH.
*
1 3200
*
1 3600
MARCH
*
’
4OCQ
26
)
’
4400
f-K)
FOR THB AURORA
AT 2207AST
ON
ELECTRON
DENSITIES
AND TEMPERATURES
IN AURORA
473
The explanation is different at lower altitudes. Here the electrons cool principally to the neutral particles and the cooling rate is a rapidly increasing function of electron temperature. This serves to stabilize the temperature, and the results show, for example, that T, - T, varies approximately as the fifth root of the ionization rate at 150 km. The variation would be approximately linear at this altitude if the cooling rate were linear in the electron temperature. Because the temperature profiles in the different auroras are so similar there is little variation, between auroras, in the dissociative recombination coefficients at a given I
r
I
1 400
*
“““I. 800
c I
I
’
I
’
I
’
I,
I
’
I
’
I
’
I
-
I
600
7
6
5 Y
500
w 2 400 IL < 300
200
100
~
,
)
1200
I600
2000
““““I 2400 TEMPERATURE
I 2800
3200
3600
4000
(OK)
FIG. 8. ALTTIVDE PROFILESOF THE TEMPERATURES FOR THE AURORA AT 2136 AST 29 MARCH.
ON
altitude. Thus, at 150 km, the electron density varies almost exactly as the square root of the ionization rate. On the other hand, the maximum electron density in these five auroras varies approximately as the cube root of the maximum ionization rate. This is an altitude effect. In our sample the intense auroras peak at low altitude where recombination coefficients are large while the weak auroras peak at higher altitudes where temperatures are higher and recombination coefficients lower. Variability in the altitude profile of the volume emission rate, in the width of the arc system, and in the location of the observer relative to the arc system precludes any attempt to deduce a general relationship between observed aurora1 intensities and aurora1 electron densities and temperatures from the five auroras we have studied. For these five auroras, however, results are summarized in Table 5. These results may be compared with Dalgarno’s values (Dalgarno, 1965; Dalgarno, Latimer and McConkey, 1965). Dalgarno’s ionization rates exceed the ionization rates in Table 5 for A3914 intensities corresponding to his IBC I and II designations and are smaller at higher intensities. His electron densities are smaller by about a factor of 2.5 over the range of intensities in Table 5. From Table 5 it appears that the value of 6500°K for the electron temperature measured
474
J. C. G. WALRER and M. II. REES
TABLE5
Date 1960 Time AST 2100 1939 2007 2207 2136
Maximum i13914 intensity at Fort Yukon (kR)
Maximum ionization rate (cm-a/sec-1)
Maximum electron density (cm-*)
Maximum electron temperature (OR)
30.6 13.0 22.0 347 7.2
516(+5) 6*12(+4) l-23(+5) 4-56(-t-5) 2+30(+4)
2.58(+6) l-13(+9 l-29(46) l-77($-6) 7*66(+5)
3511 3118 3420 3469 2920
26 February I March 1 March 26 March 29 March
by Explorer 22 near Was~gton, D. C. (L. H. Brace, private ~o~~ication~ could not have been caused by aurora1 electron bombardment in stable arc systems such as we have considered in this paper. Ack~~~e~g~#ts-We are pleased to acknowledge the wn~ibutions of Sandra Fuller to the pro~~ug and computational aspects of the research. Advice concerning metastable ion chemistry was provided by M. B. McElroy. This work has been supported in part (M. H. R.) by grants from the National Science Foundation (GA-1238) and the National Aeronautics and Space Administration (NGr-06-003-052). Part of the work was performed while one of us (J. C. G. W.) held a National Research Council Postdoctoral Research Associateship supported by the National Aeronautics and Space Administration.
ALLaN,D. N. DEG. (1954). Reluxution ~eth~.
McGraw-~, New York. BANK%P. M. (1966a). Collision freouencies and enerav transfer. Electrons. Planet. Sauce Sci. 14.1085-1103. BANK& P. M.‘(l966b). Charged particle tempera&&s and electron thermal wkductivity h the upper atmosphere, Ads. Gdophys. 22,577-587. BANK%P. M. (1966c). Thermal conduction and ion temneratures in the ionosuhere. I i ~Earth Planet. Sci. fRtt; 1,27&275. BANKS,P. M. (1966d). Collision frequencies and energy transfer. Ions, PA-met.Space Sci. 14,1105-1122. BANKS,P. M. (1967). Ion temnerature in the unner atmosnhere. J. aeoohvs. Res. 72.3365-3385. BATF&D. R. (1959). Some prbblems concern&g the term&al atm&pheie above about the 100 km level, Proc. R. Sot. A2!53,451-462.
BELON,A. E., ROMKXC, G. J. and REES,M. H, (1966). The energy spe&um of primary auroral electrons determined from aurora1 luminosity profiles, P&net. Space Sci. 14,597-61X BIONDI, M. A. (1967). Recombination chap. 11.
processes (charged particles), DASA Reaction Rate Hundbook,
BUTLER,S. T. and BUCKINGHAM, M. J. (1962). Energy loss of a fast ion in a plasma, Phys. Reu, 126, l-4. CHAMBERLAIN, J. W. (1961). Physics of the Auroru and Airgow. Academic Press, New York. Co=, IL D. (1967). A new facet of the heating of ambient electrons by energetic charged particle streams, Pianet. Space Sci. 15,873-879.
DALOARNO, A. (1961). Charged particles in the upper atmosphere, Annls G6ophys. 17, 16-49. DALGARNO, A. (1965). Interaction of energetic charged particles with the atmosphere, in AurorulPhenomenu. Experiments and Theory (Ed. M. Walt), pp. 39-45. Stanford Univ. Press, Palo Alto. DAL~AIZNO, A. and DEGGBS,T. P. (1968). Electron cooling in the upper atmosphere, Planet. Space Sci. 16,125-127.
DALGARNO,A. and MCELROY,M. B. (1965). The fluorescence of solar ionizing radiation, &net. Sci. 13,947-957. DALGARNO,A., LATIME~,I. D. and MCCONKEY,J. W. (1965). Corpuscular bombardment radiation, Planet. Space Sci. 13,1008-1009.
Space
and NI+
DALGARNO, A., MCELROY,M. B. and Morwrn-r, R. J. (1963). Electron temperatures in the ionosphere, Planet. Space Sci. 11,463-484.
DALGARNO,A., MCELROY,M. B. and WALKER,J. C. G. (1967). The diurnal variation of ionospheric temperatures, Planet. Space Sci. l&331-345.
DONAHUFX, T. M. (1966). The problem of atomic hydrogen, Am& GPophys. 22,175~188. FERGUSON, E. I?. (1967). Ionospheric ion-molecule reaction rates, Rev. Geophys. 5,305-327. Gmsa, C. F. (1966). The reaction O+ + NI -+ NO+ + N, A&
Chem. 58,20-27.
ELECTRON
DENSITIES
AND TEMPERATURES
IN AURORA
475
GUNTON, R. C. and SHAW, T. M. (1965). Electron-ion recombination in nitric oxide in the temperature range 196 to 358”K, Phys. Rev. 14OA, 756-763. HILDEBRAND,F. B. (1952). Methods of Applied Mathematics, Prentice-Hall, Englewood Cliffs, N.J. HOFFMAN,J. H. (1967). A mass spectrometric determination of the composition of the nighttime topside ionosphere, J. geophys. Res. 72,1883-1888. JACCHIA,L. G. (1964). Static diffusion models of the upper atmosphere with empirical temperature profiles, Res. in Space Sci., Smithsonian Astrophys. Obs. Spec. Rpt. 170,53p. KIEFFER,L. J. and DUNN, G. H. (1966). Electron impact ionization cross section data for atoms, atomic ions, and diatomic molecules: I. Experimental data, Rev. mod. Phys. 38, l-35. MCCONKEY, J. W. and LATIMER,I. D. (1965). Absolute cross sections for simultaneous ionization and excitation of N* by electron impact, Proc. phys. Sot. 86,463-466. MCCONKEY, J. W., WOOLSEY,J. M. and BURNS, D. J. (1967). Absolute cross section for electron impact excitation of 3914 A N,+, Planet. Space Sci. 15, 1332-1334. MCELROY, M. B. (1967). Atomic nitrogen ions in the upper atmosphere, Planet. Space Sci. 15,457-462. RAPP, D. and ENGLANDER-GOLDEN, P. (1965). Total cross sections for ionization and attachment in gases by electron impact. I. Positive ionization, J. them. Phys. 43,1464-1479. REES, M. H. (1963). Aurora1 ionization and excitation by. incident eneretic electrons, Planet. Smxe Sci. a 11;1209-12‘18. REES,M. H. (1964). Ionization in the Earth’s atmosphere by aurorally associated bremsstrahhmg X-rays, Planet. Space Sci. 12, 1093-1108. Ress, M. H. and WAL&R, J. C. G. (1968). Ion and electron heating by auroral electric fields, AnnIs Gkophys. (in press). REES, M. H., WALKER, J. C. G. and DALGARNO,A. (1967). Aurora1 excitation of the forbidden lines of atomic oxygen, Planet. Space Sci 15, 1097-I 110. SCHMF~LTEKOPF, A. L., FEHSENFELQF. C., GILMAN, G. I. and FERGUSON,E. E. (1967). Reaction of atomic oxygen ions with vibrationally excited nitrogen molecules, Planet, Space Sci. 15,401406. SCHRAM,B. L., MOUSTAFA,H. R., SCHUTT~N,J. and DEHEER, F. J. (1966). Ionization cross sections for electrons (100-600 ev) in noble and diatomic gases, Physicu, Eindhoven. 32,734-740. SEATON,M. J. (1959). Electron impact ionization of Ne, 0, and N, Phys. Rev. 113,814. SEATON,M. J. and OSTERBROCK,D. E. (1957). Relative [011] intensities in gaseous nebulae, Astrophys. J. 125,66-83.
SPITZER, L. (1956). Physics of FuIly Ionized Gases, Interscience, New York. SP~TZER,L. and HjcRM, R. (1953). Transport phenomena in a completely ionized gas, Phys. Rev. 89, 977-981. STEBBINGS,R. F., TURNER, B. R. and RUTHERFORD,J. A. (1966). Low-energy collisions between some atmospheric ions and neutral particles, J. geophys. Res. 71,771-784. STOLARSKI,R. S. and GREEN, A. E. S. (1967). Calculations of aurora1 intensities from electron impact, J. geophys. Res. 72,3967-3974. TAYLOR,H. A., BRACE,L. H., BRINTON,H. C. and Shnrn, C. R (1963). Direct measurement of helium and hydrogen ion concentration and total ion density to an altitude of 940 km, J.geophys. Res. 68,5339-5348. TOHMATSU,T. (1965). Photoelectronic excitation of atomic oxygen 1300 A triplet emission in the day airglow-II. The line intensity ratio, Rep. Zonosph. Space Res., Japan 19, 509-514. WALKER, J. C. G. (1965). Analytic representation of upper atmosphere densities based on Jacchia’s static diffusion models, J. Atmos. Sci. 22, 462-463. WALKER, J. C. G. and BRACE, L. H. (1967). Langmuir probe evidence for a nocturnal E-region ionization source at Fort Churchill, paper presented at COSPAR Symposium, London, July. WARNECK,P. (1967). Studies of ion-neutral reactions by a photoionization mass-spectrometer technique. I., J. them. Phys. 46,502-512. WATSON, C. E., DULOCK, V. A., STOLARSKI,R. S. and GREEN, A. E. S. (1967). Electron impact cross sections for atmospheric species, 3. Molecular oxygen, J. geophys. Res. 72, 3961-3966.
IONOSPHERIC
ELECTRON DENSITIES IN AURORA
AND TEMPERATURES
J. C. G. WALKER Department of Geology, Yale University, New Haven, Connecticut, U.S.A.
M. H. REES Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, U.S.A. (Received 16 November 1967)
Abstract--Electron density profiles corresponding to chemical equilibrium, and electron temperatures corresponding to heating of ambient electrons by auroral secondaries have been computed for five stable aurora1 arc systems with published height protiles of 123914volume emission rates. The maximum electron density varies approximately as the three-quarters power of the 23914 intensity while the maximum temperature varies remarkably little. For these five auroras the temperature maxima lie between 2920°K and 3511°K and occur at altitudes between 330 km and 390 km. 1. INTRODUCTION
During the large magnetic and aurora1 storm of 25 May 1967, the Langmuir probe on the Explorer 22 satellite measured an electron temperature of some 6500°K at 1000 km near Washington, D.C. (L. H. Brace, private communication), where an aurora was observed simultaneously. Less spectacular but highly significant was a recent measurement of the altitude profile of electron temperature on a rocket tied at night from Fort Churchill. An enhanced electron temperature was measured even in the absence of any visible aurora, reaching a value of 2000°K at 250 km (Walker and Brace, 1967). The physical mechanisms leading to high aurora1 electron temperatures are investigated in this paper. The electrons in a primary aurora1 stream lose energy as they penetrate into the atmosphere by a variety of processes. Ionization of the atmospheric gases is the dominant initial loss process (cf. Dalgarno, 1961; Rees, 1963) while production of bremsstrahlung X-rays accounts for a negligibly small loss when the electrons have an initial energy of 10 keV or less (Rees, 1964). Ionization occurs into electronically excited states of the ion as well as into the ground state. This is the origin of the Ns+ (1 N.G.) and Nsf (Meinel) bands, various bands of OS+, and atomic lines originating from 0+(2P) and 0+(20), all observable features in the visible, near-ultraviolet, and near-infrared aurora1 spectrum. The primary ionizations produce secondary electrons (which may be some 100 times as abundant as the primaries) which cause additional ionization, but lose energy principally in exciting
various
neutral
species to a host of electronic
states (cf. Stolarski
and Green,
1967). Once the energy of the secondaries (or tertiaries, etc.) is as low as 5 or 6 eV, energy loss to the ambient electron gas by elastic collisions becomes an important mechanism. The effect is to heat the electron gas and, with the large electron-electron energy transfer cross section, a Maxwellian distribution prevails which may be characterized by a temperature, T,. Above about 250 km the thermal electrons lose energy to the positive ions, providing a heat source for the ions which then attain a temperature, T,, higher than the neutral gas. The details of these processes are described below and the results of computations for five quiet aurora1 arc systems are presented. 4.59
460
J. C. G. WALKER
and M. H. REEIS
2. OBSERVATIONS
Five auroras have been selected for analysis ; they represent various types of arc systems, all of which persisted long enough to allow us to assume a steady state. These auroras were observed in February and March, 1960, from, College and Fort Yukon, Alaska. From these stations the height luminosity profiles in the 13914 radiation (N2+ 1 N.G.) were obtained by photometric triangulation. The details of the observational procedure and the deduction of the profiles are described by Belon, Romick and Rees (1966). We have chosen auroras representing a variety of physical parameters-various peak emission altitudes, a range of photon emission rates, and different widths. The salient parameters are summarized in Table 1. TABLE1. AURORAL ARC SYSTEMS
Date (1960) Time (AST) 2100 1939 2007 2207 2136
26 February 1 March 1 March 26 March 29 March
Geomagnetic latitude (“N.)
Maximum 13914 intensity at Fort Yukon (kR)
66.40 67.30 67.35 6633 67.31
30.6 13.0 22.0 34.7 7.2
Width (lo-@ 3: 26 :f
Altitude of max. emission rate (km) 120 133 103 110 142
3. ANALYSIS
3.1 The model atmosphere Jacchia’s (1964) formulae are used to arrive at a model appropriate to the time and place of the observations. The analytic formulation of Bates (1959) and Walker (1965) provides altitude proties for the temperature and density of all neutral constituents except atomic hydrogen. For the latter we use, as a guide, the review by Donahue (1966) to deduce an altitude profile appropriate to an exospheric temperature of 1200°K. Table 2 presents the atmospheric parameters. 3.2 The ion chemistry The cross sections for inelastic collisions between energetic electrons and atmospheric gases all exhibit similar dependence on electron energy and we take advantage of this observation to deduce the rates of production of various ionized and excited species from the volume emission rate of 13914. From the cross section for the process, e+Ns+e+N,++e+f3914
(1)
(McConkey and Latimer, 1965; McConkey, Woolsey and Bums, 1967), and the total ionization cross section for molecular nitrogen (Rapp and Englander-Golden, 1965) we deduce that q(Na+) + qcN+) = 17q(3914) (2) (cf. Dalgamo, Latimer and McConkey, 1965), where 7 (3914) is the volume emission rate of A3914, q(x) is the rate of production of species X, and we ignore production of multiply charged ions. * * The total ionization cross section measured by S&ram, Moustafa, Schutten and de Hcer (1966) is smaller than the cross section used here and leads to a ratio of 13 in (2). In the absence of further evidence we use 17 for this ratio.
461
ELEXXRON DENSITIES AND TEMPERATURES IN AURORA TABLE 2. W
Altitude (km) 350 542 690 804 893 961 1010 1050 1080 1110 1130 1140 1150 1160 1170 1180 1180 1180 1190 1190 1190 1200 1200 1200 1200 1200 1200 1200 1200
120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 350 400 450 500 550 600 650 700 750 800 * 4OO(-tll)
NEUTRAL ATMOSPHERE
n(K) (cm-3
n(G) (cm-*)
n(O) (cm-8)
n(He) (cm-3
4*00+11)* l-25(+11) 5*90(+10) 3.31(+10) 2.05(+10) 1*36(+10) 9*40(+9) 6.68(+9) 4.84( +9) 3.57(+9) 2.66(+9) 2.00(+9) 1.52(+9) 1*15(+9) 8.86(+8) 6*80(+8) 5.24(+8) 4*04(+8) 3.13(+8) 8.87(+7) 2*58(+7) 7.66(+6) Z31(+6) 7.14(+5) 2*23(+5) 7.11(+4) 2.30( +4) 7*57(f3) 2.52(+3)
7.50(+10) 2.12(+10) 9*27(+9) 4.90( +9) 2.89( +9) 1.82(+9) 1.20( +9) 8.17(+8) 5.69( +S) 4.03(+8) 2*88(+8) 2.09(+8) 1.52(+8) 1.11(+8) 8.25(+7) 6.10(+7) 4.53(+7) 3*37(+7) 2.51(f7) 5.96(+6) 1*45(+6) 3.63(+5)
7.60(+10) 3.25(+10) 1*9O(-tlO) l-28(+10) 9*33(-t9) 7*14(-t9) 5,64(-t-9) 456(+9) 3.75( +9> 3.12(-t9) 2.62(+9) 2*21(+9) 1.88(+9) 1.60(+9) 1.37( +9) l-18(+9) 1.01(+9) 8*75(+8) 7.55(+8) 3.66(+8) l-80(+8) g-03(+7) 4.56(+7) 2.32(+7) 1*19(+7) 6.23(+6) 3.26(+6) 1*73(+6) 9*25(+5)
3*40(+7) 2.36(+7) 1.89(+7) 1*62(+7) 1.45( +7) l-32(+7) l-22(+7) l-14(+7) 1.07(+7) l-02(+7) 9*71(+6) 9.27(+6) 8.87(+6) 8.50(+6) 8.16(+6) 7.84(+6) 7*54(+6) 7.26(+6) 6*99(+@ 5*82(+6) 488(+6) 4*1(X+6) 3.45(+6) 2.92(+6) 2.47(+6) 2*10(+6) 1*78(+6) 1.52(+6) l-30(+6)
ZZ:::; 6.39(+3) 1*72(+3) 4*75(+2) l-33(+2) 3.80(+1)
n(H) (cm-3
6+0(+5)
4.50(+5)
::FJ:; l-34(+5) 1*18(+5) 1.02(+5) 8.60(+4) 7*00(+4) 6.56(+4) 6.12(+4) 5*68(+4) 5.24(+4) 4.80( $4) 4=54(+4) 4*28(+4) 402( +4) 3*76(+4) 3*50(+4) 3.05(+4) 2.60( +4) 2.35(+4) 210(+4) 202(+4) l-95(+4) l-90(+4) 1*85(+4) 1*82(+4) 1.80(+4)
E 400 x lo+“.
We now distinguish
between the processes, e+N,-te+N,++e,
(3)
e+N,+e+N+N++e,
(4)
and
and utilize the cross section data reviewed by Kieffer and Dunn (1966) to arrive at q(Nz+) = 13.6 q(3914),
(5)
and q(N+) Similar
consideration
ionization
of ionization
of molecular
= 0.25 q(NZ+).
of atomic
(6>
and molecular
oxygen
and dissociative
oxygen yields, with cross sections from Kieffer and Dunn (1966), r(O,+)
= 0+3[17(N,+) +
dN+>I 3;
,
(7)
and v@+)
= @5~(0,+)
+ @5[rl(N,+)
where n(X) is the number density of species X.
+
r(N+)l$$
,
(8)
462
J.
C. G. WALKER and M. H. REES
The total ionization rate, s(e) = rl@&+) 4 VP+) + r(Os+) + rl(O+),
(9)
is shown in Fig. 1 for the five aurora1 arc systems. Many of the ions produced by electron impact ionization are electronically excited and contribute to aurora1 luminosity while some of the metastable levels are sufbciently longlived to influence the ion chemistry. We consider fist the reactions of ions in the ground state. -
42 IO
I
8
I1111
I
I
IL1111,
+3 IO
/hlTUDE
-
--
-
2 IO0
FEBRUARY
I939
MARCH
PROFILES
26 I
2007
MARCH
I
-.*-‘*
2 2 07
MARCH
26
-*-•-
2 I 36
MARCH
29
I
I
I
I11111
1
I1111‘1,
+5 IO
d4
IONIZATION Fb3.1.
-.-
IO
+6
RATE (CM-*/SEC)
OF THE IONIZATXON
RATB IN FIVE AURORAL
ARC
SYSTEMS.
Molecular nitrogen ions are removed by the reactions, Nzf + 0, + O,+ + N,,
&r,,= 1 x lo-lo,
(10)
N$+O-+NO++N,
k,, = 2.5 x lo-lo
01)
(cf. Ferguson, 1967), and -l/S
N,-t+e+N+N,
k= = 2.9 x lo-’
$_,
(12) ( ) (cf. Biondi, 1967), where kais the rate coefficient of reaction s in ems se&. The rate coefficient of (10) does not depend on the temperature (Stebbings, Turner and Rutherford, 1966; Warneck, 1967), but there is evidence that the rate coefficient of (12) depends on the ion temperature (presumably the vibrational temperature) as well as on the electron temperature (cf. Biondi, 1967). The value given corresponds to an ion temperature of 300°K. Atomic nitrogen ions are removed by the reactions, N++O,+NOf+O,
k= = 5 x lo-l0 ,
(13)
k14 = 45 x lO- 10
(14)
and N++O,-+O,++N,
ELECTRON DENSITIES AND TEMPERATURES
IN AURORA
463
(cf. Ferguson, 1967; McElroy, 1967). Neither of these rate coefficients depends on the ion temperature (Stebbings, Turner and Rutherford, 1966). Molecular oxygen ions are removed by the reactions, O$ $1 N, + NO+ + NO,
(15)
for which we assume kls = 5 x lo-l6 (cf. Ferguson, 1967), and O,++e-+O+Q
k
(16)
(cf. Biondi, 1967). The temperature dependence of k,, has been measured only for ion temperature equal to electron temperature. Atomic oxygen ions are removed by the reactions, O++N,+NO++N,
kl, = 1.8 x lo-l2 ,
(17)
k18 = 2 x lO-11
(18)
and 0++0,-+0,++0,
(cf. Ferguson, 1967; Schmeltekopf, Fehsenfeld, Gilman, and Ferguson, 1967). The rate coefficient of (17) depends strongly on the nitrogen vibrational temperature and there is evidence that it is proportional to the ion temperature (Giese, 1966; Stebbings, Turner and Rutherford, 1966). We ignore these effects. The only reaction removing the NO+ ions produced by (1 l), (13), (15), and (17) is NO++e-+N+O,
k,, = 4.6 x lo-’
(19)
(cf. Biondi, 1967; Gunton and Shaw, 1965). This temperature dependence reflects measurements for equal ion and electron temperatures. In the absence of information on the rates of reaction of excited ions, any treatment of their effect on the ion chemistry must be approximate. Since the excited levels of N2+ are not metastable (cf. Dalgamo, McElroy and Moffett, 1963). these levels will not react chemically. The %’ and lD levels of N+ have long radiative lifetimes (cf. Chamberlain, 1961) and may react. In addition to Reactions (13) and (14) these ions can be removed by reactions with N2, N+~Dor?S’)+N2+N2f+N. (20) There is evidence that Reaction (14) is slower for excited N+ ions at impact energies of several tens of eV (Stebbings, Turner and Rutherford, 1966), but this behavior may not extend to thermal energies. We therefore assume that (13) and (14) are not affected by excitation of the nitrogen ion. There is no information on (20) but it is not likely to have a large effect on the ion chemistry. Accordingly we ignore metastable N+ ions altogether. Molecular oxygen ions in the a %rUstate are metastable and may be removed in reactions with N,, 0, and electrons, O$(a 4rTT,)+ N2 + I$+ + 0, o,+(a %T,) + 0 + O$(P?r,)
(21) + 0,
(22)
O$(a “vu) + e --t 02+(X2z-Q) + e.
(23)
and
464
J. C. G. WALKER
and M. H. REES
We assume that the rate coefficients of (21) and (22) are both lo-lo cm3 set-l, and that the rate coefficient of (23) is lo-’ cm3 SC&. There are other possible removal processes for these ions which we ignore. The number density of metastable O$ ions is therefore given by, (24) Metastable O+@‘) ions have a radiative lifetime of 5 set (Seaton and Osterbrock, and may be removed in the reaction with Nz, 0+(2P) + N, + 0 + N,+, for which we assume a rate coefficient of 10-l” cm3 se&, n(O+ 2P) =
1957) (25)
giving
m+ 2e
(26)
0.219 + k,,n(N,) ’
Other possible processes are ignored. For the very long-lived O+CO) level we consider removal by (17) with the rate coefficient equal to kI, (cf. Stebbings, Turner and Rutherford, 1966), by 0+(20) + N, + Ns+ + 0 with k2, = 1O-Qcm3 set-l (cf. Stebbings, Turner and Rutherford, McElroy, 1965), by electron quenching, 0+(20) + e --t O+(4s) + e,
(27) 1966; Dalgarno and
k,, = 3 x 10-s
(28)
(Seaton and Osterbrock, 1957) and by emission of radiation with a transition probability of 1.33 x lv set-l (Seaton and Osterbrock, 1957). These processes yield $@+ 20) + 0~171?2(0+2P) n(“+ 20) = (7% + k2&(N2) + k,n(e)
+ l-33 x 10-4 ’
(29
A useful discussion of the metastable ions and their removal processes has been given by Dalgarno and McElroy (1965). From the cross sections of Watson, Dulock, Stolarski and Green (1967) we deduce 11(02+a +,)
= @411(02+),
with allowance for cascading from O,+(b 42,-).
(30)
Seaton’s (1959) cross sections yield
q(o+ 2P) = 0*2[17(0+) - o*57j(02+)],
(31)
7j(Of2D) = @4[7(0+) - 0*5?7(0,+)],
(32)
and where cascading and possible contributions from dissociative ionization of 0, have been excluded. The chemical equilibrium ion densities corresponding to the reactions we have described have been derived for given electron temperatures, neutral number densities, and i13914 volume emission rate. Vertical diffusion of the ions becomes important above 250 km, limiting the usefulness of chemical equilibrium calculations to lower altitudes. At high altitudes the ion composition given by Taylor, Brace, Brinton and Smith (1963) has been
ELECTRON
DENSITIES
AND
TEMPERATURES
465
IN AURORA
TABLE 3. ION COMPOSITIONIN AIJRORALARC SYSTEMAT 2100 AST ON 26 FEBRUARY Altitude (W
loo 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 z 400 450 500 550 600 650 700 750 800
-n(O,+) n(e) 0.6848 0.4742 0.3208 0.2320 0.1713 0.1334 0.1091 0.0913 0.0775 0.0657 0.0553 0.0465 0.0386 0.0314 0.0249 0.0194 0.0146 0.0107 oaO74 0*0050 oaO3 1 oaoO2 0 0 0 0 0 0 0 0 0
* 3*397(+5)
WC+) n(e) 0.3148 05233 0.6641 0.7296 0.7638 0.7715 0.7599 O-7381 0.7050 0.6653 0.6206 0.5679 05123 0.4519 0.3871 0.3243 0.2627 0.2042 0.1497 0.1043 0.0675 oaO54 0.0053 oaO51 0 0 0 0 0 0 0
-n(C+) n(e)
_n(Na+) n(e)
n(N+) n(e)
0*0002 oaO15 oaO93 0.0268 0.0491 0.0760 0.1093 0.1470 0.1921 0.2423 0.2967 0.3575 0.4208 0.4885 0.5603 0.6296 0.6975 0.7620 0.8222 0.8728 0.9144 0.9887 0.9893 0.9898 0.990 0.965 0940 0.905 0.870 0.805 0.740
04000 oaOO1 OaOO4 oaO12 oaO21 0*0030 0.0041 0.0052 0.0064 0.0076 OaO88 0.0101 0.0112 0.0123 0.0133 0.0140 0.0144 0.0144 0.0140 0.0131 0.0119 0*0055 0.0054 oaO51 0 0 0 0 0
oaOo2 oaO1o 0.0053 0.0104 0.0138 0.0160 0.0176 0.0185 0*0190 0.0191 0.0187 0.0181 0*0171 0.0159 0.0145 0.0127 0.0108 OaO88 0.0067 OGO48 0.003 1 oaOO1 0 0 0 0 0 0 0 0 0
n(He+) - n(e) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 oaO5 0.010 0.030 0050 0.075 0.100 0.150 0.200
n(H+) n(e) 0 0 0 0 0 : 0 0 0 0 0 0 0 0 0 0 0 0 0
x
0 0 0 oao5 0.010 0.020 0.030 0.045 0.060
n(e) (cm-3
2*460( +6) 2*470( +6) 2.520(+6) 2*580(+6) 2*500(+6) 2.414(+(F) 2.330(+6) 2*243(+6) 2.160(+6) 2.114(+6) 2.069( +6) 2.025( +6) 1.982(+6) 1.940(+6) 1*894(+6) 1*849(+6) 1.805(+6) l-762(+6) 1*720(+6) l-560(+6) 1.400(+6) l-260(+6) l-130(+6) 1*020(+6) 9.200(+5) S-300(+5) 7.400( t5) 6750(+5) 6*100(+5)
3 3.397 x 10+5.
adopted. The relative ion number densities for the aurora at 2100 AST on 26 February are given in Table 3, while the electron density, extrapolated to high altitude with an appropriate scale height, is shown in Fig. 2 for all five aurora1 arc systems. The results for the aurora at 2100 AST on 26 February may be compared with densities for the same aurora computed by Rees, Walker and Dalgamo (1967) using temperature independent rate coefficients and ignoring the effects of atomic nitrogen ions and metastable ions. In the chemical equilibrium region below 250 km the electron densities in Table 3 and Fig. 2 are about twice as large as the previously computed densities, reflecting principally the substantial reduction in dissociative recombination coefficients at high electron temperatures. The ionization rates in Fig. 1 are about the same as those previously computed below 250 km but are lower by a factor of about 2 at higher altitudes. This difference is not significant, arising simply from our extrapolation of the 13914 volume emission rate to high altitudes where photometric data are not available. The present electron densities are lower than the previous ones at high altitudes, principally because of lower electron and ion temperatures used in the extrapolation of the density above the chemical equilibrium region. 7
466
J. C. G. WALKER and M. H. REES 40Q
I
350-
-2100 -.---I939 ----2007 ----2207 -2136
I
I
I11111 FE8 26 MARCH MARCH MARCH MARCH
I I 26 29
300-
22505 : GOO5 c < 150-
_.---
100-
._._
I
5,$4
I
*-.-
I
I111111
I
ELECTRON
Fro. 2.
ALTITUDE
I1111111
I
+5 IO
PROFILES
4
11!11/
l6 IO CONCENTRATION
OF THE ELECTRON
Kf’
(Chi3,
CONCENTRATION
IN
FIVE AURORAL
ARC
SYSTEMS.
3.3 Electron heating The deduction of the rate at which secondary electrons heat the ambient electron gas involves consideration of both continuous degradation of the energy of the secondary electron due to elastic collisions with the ambient plasma and discrete energy losses due to inelastic collisions with the ambient neutral particles (A. I. Stewart, private communication). For simplicity we assume that the inelastic processes can be adequately represented by a continuous energy loss and we assume, also, that all secondary electrons are produced with the same energy, E,,. The average amount of energy deposited by each secondary electron in the electron gas is therefore e(e) =
s
x0 r(e 1E) dE
0
r(T
eV,
(33)
1 E>
where r(e 1E) is the rate of energy loss resulting from elastic collisions with the ambient electrons (Butler and Buckingham, 1962), r(e I E) =
l-95 x lo-i2n(e) ev cm_l E
(cf. Dalgarno, McElroy, and Moffett, 1963), and r(T 1E) is the total energy loss rate. In the energy range considered here, r(T 1E) includes vibrational excitation of molecular nitrogen, excitation of 00 and O(lO), and elastic collisions with the ambient electrons (cf. Rees, Walker and Dalgarno, 1967). The value of E. is not critical, and may be taken as 5 or 6 eV with negligible difference in c(e). The average energy deposition per electron is, however, a function of altitude, and we list values of E in Table 4. The rate of heating of the electron gas by secondary electrons
ELECTICON DENSITIES AND TEMPERATURES
IN AURORA
467
TABLE4. AVERAGEENERGY DEPCXITED IN THE
AMBIENT ELECTRON GAS BY EACH SECONDARY BLSCTRON WITH INITIAL ENERGY, E. = 6~V(2100 AST 26 FEBRUARY)
Altitude (km)
(e&G
80 90 100 110 120 130 140 150 160 180
0.307 0.324 0.623 l-35 2.13 2.74 3.27 3-71 4.03 4.53 4*89 5-45 5.71 5.83 5.88 5.93 5.95
z 300 350 400 500 800
is given by &(z) = q(e)&(e) eV per ems se&.
(35)
Cole (1967) has recently pointed out that the electron gas can also be heated by joule dissipation of the reverse current corresponding to the directed flux of electrons at each location. Assuming that the directed and omnidirectional fluxes are similar in magnitude he finds that this heat source is comparable to heating by elastic collisions. Only primary electrons, however, contribute significantly to the directed flux, and the joule heat source is negligible compared with heating by the secondaries described above. 3.4. The electron temperature We evaluate the electron temperature by solving the steady state heat conduction equation for the electron gas with allowance for local heating, Qe(z) eV per cm3 set-l, and local cooling, L(z 1 Te) eV cm-3 se+ (cf. Dalgarno, McElroy and Walker, 1967), = QeW - J% 1 Tel,
(36)
where K is the thermal conductivity of the electron gas (Spitzer and HBrm, 1953), /C=
7.7 x 108 sin21 T,512
= KT,S/2 eV cm-l set-l degr.
(37)
In (37) I is the geomagnetic dip and the second term in the denominator represents the reduction in the conductivity resulting from electron-neutral collisions (Banks, 1966b; Dalgarno, McElroy and Walker, 1967). It is small at high altitudes where conduction is important. In (37) the summation is over all neutral species, j; the electron-neutral momentum transfer cross section, 9,(i) cm2, is given by Banks (1966a). Our expression differs from the expression given by Banks (1966b) who assumed that electron-neutral collisions yield the same thermal diffusion coefficient as electron-ion collisions.
J. C. G. WALKER and M. H. REES
468
In addition to the electron cooling terms discussed by Dalgamo, McElroy and Walker (1967) we have included cooling due to elastic collisions with atomic hydrogen (Banks, 1966a), but we have not included cooling due to collisions which excite the fine structure levels of the ground term of atomic oxygen (Dalgamo and Degges, 1968; Tohmatsu, 1965). The conduction Equation (36) has been solved using a simple relaxation approach (cf. Hildebrand, 1952). The altitude range is divided into M - 1 small segments (generally 10 km high) and an index, m, associated with each altitude point. The lower boundary is at zl = 120 km and the upper boundary is at Z~ = 800 km. Writing T, for the electron temperature at z, we replace (36) with the finite difference equation, Q&J
- L(zm 1 T,J + +KTz2B2 + 2KTz2A
= 0,
(38)
where
T&m - zm-3 + Pm - Tmdzm - z,n+,) %3h+1 - %a) kn+1 - %dG-1 - GJ ’
-
(39)
and T m+l
A=
-
Tm
Tm-
Tm-I WI
hn+1-
%a-&,+1
-
4
+
bn+1-
.Gn4kn-1-
%J
*
In (38) we have ignored a negligibly small term involving dK/dz. The expression (38) represents a set of M - 2 coupled non-linear algebraic equations which must be solved for the values of T, at all interior points. The boundary values, Tl and TM, are handled differently. At the lower boundary we assume that conduction is negligible and determine Tl from the expression, Uz, 1 q) = Q&A
(41)
while at the upper boundary we specify the temperature gradient,
1
-dTe = s. [ dz z= Thus, TM is given by the equation, Qe(z&
-
L(zM 1 TM) + gKTa2S2 TM--~
’ = (zj,_l
-
TM
-
zj,f)2 -
(42)
+ 2KTa2C
= 0,
(43)
S (z&&1 - ZM) ’
(44)
In the absence of information on temperature gradients at high altitudes in aurora we set S = 0. We now solve (41) for Tl using an iterative procedure and guess a set of values for T,,,, 2 < m Q M. Leaving Tl and T3 tied we solve (38) for T2; then, leaving T, and T4 tied we solve (38) for T3. In this way we work through the grid, finally solving (43) for TM. We now go back to z, and repeat the whole procedure again and again, until the values of T, no longer change significantly at any altitude. In practice we Cnd that the relaxation is quite stable, but very slow, frequently requiring more than a hundred passes. A more sophisticated relaxation procedure (cf. Allen, 1954) would be faster. 3.5. The ion temperature Banks (1966c; 1967) has shown that thermal conduction in the ion gas affects ion temperatures when the electron density is low. At aurora1 densities this effect is not likely
ELECTRON
DENSITIES AND TEMPERATURJ%
469
IN AURORA
to be significant and we ignore it. The ion temperature is therefore determined by the balance between the rate at which the ions are heated in elastic collisions with the ambient electrons, i;l(e)(T, - &) eV crnm3 set-l, and the rate at which the ions cool in elastic collisions with the neutrals, R(n)(Z’, - Z’,) eV cmA3 se+.
BOO2100 700
FEBRUARY
7.6
-
600-
g500Y w,4003 I;300-I .z 200-
100 -
I*,_J 400
800
I 1200
*,,,.I 1800
* 2000
2400
L 2800
s
t. 3200
I 3600
*
I. 4000
I
b
I,
f’Kf
TEMPERATURE
FIG.3. ALWUDE PROFILESOF ELECIXON TEXPERATURB,To, ION TBWERATWRE, T&,ANJJ NINTRAL GAS TTMPJSRAW, T,, FOR m AURORA AT 2100AST ON 26 FEBRUARY. T,’ is the electron temperature calculatedwithout thermal conduction.
Equating these two rates and solving for Tf we obtain T.
*
WW, + Rle)T~
=
R(n)+
where R(e) =
R(e)
’
7.7 x 10-%(e) TeSt%
(45)
(46)
(Spitzer, 1956), and R(n) = 3k 2 n(i) 2 p!%i?! i
n
%
(47)
(cf. Banks, 1966d). Here A, is the ion mass in a.m.u., k is the Boltzmann constant, mt and m, are the ion and neutral masses in g, y,, is the reduced mass, Pi* =
wm, m, i- m, ’
(48)
vtn is the ion-neutral collision frequency used by Rees and Walker (1968), and the summations are taken over all neutrals, n, and ions, i.
470
J. C. G. WALKER and M. H. REES 4. RESULTS AND DISCUSSION
Electron temperatures computed without heat conduction, Te’, and including conduction, Te, are shown for the aurora at 2100 AST on 26 February in Fig. 3, together with the ion temperature, T,, computed from Equation (45), and the neutral gas temperature, T,,. The calculated value of Te’ is very sensitive to the heating rate and electron density and the zig-zags in this profile are caused by rounding off these quantities. The zig-zags are not significant and, indeed, Te’ is plotted only because it shows where thermal conduction becomes important. Because of the large heating rates and electron densities in this aurora conduction is not important below 450 km.
600
70
I
600I Y -
500-
: 3 c 4005 4 JOO-
zoo-
IOO-
ELECTRON FIG.
4. THE EFFECT
ON
THE
ELECTRON
TEMPERATURE
TEMPERATURE
POSITIONS
IN
THE
OF
ASSIJMING
(OKI DIFFJXIINT
ION
COM-
TOPSIDE.
The temperatures in Fig. 3 may be compared with the values calculated by Rees, Walker and Dalgamo (1967) for the same aurora. Below about 350 km the two temperature profiles are almost identical in spite of the difference in the electron density profiles at low altitude (see Section 3.2). At low altitudes the aurora1 secondaries share their energy between the ambient plasma and the neutral particles (see Equation (33) and Table 4) so the rate of heating of the ambient electrons is nearly proportional to electron density. Since the thermal electrons at these altitudes cool largely to the neutral particles the cooling rate is also proportional to the electron density, so the electron temperature which results from a given ionization rate is approximately independent of electron density. At altitudes above 350 km the electron temperatures which we calculated previously are considerably higher than the temperatures shown in Fig. 3. This is a result of our reduction in the extrapolated value of the i13914 volume emission rate (see Section 3.2). This extrapolation is uncertain and the temperature at high altitudes reflects this uncertainty. Uncertainty in the high altitude temperature profile leads to uncertainty in topside electron
ELECTRON DENSITIES AND TEMPERATURES
IN AURORA
471
densities also. However, the intensity of the oxygen red line is not greatly affected because the rate of excitation of OPD) by thermal electrons peaks at about 200 km (Rees, Walker and Dalgarno, 1967). Topside electron temperatures are also sensitive to the ion composition and this introduces additional uncertainty. It was noted in Section 3.2 that the aurora1 ion composition was derived below 250 km, but above this altitude the composition measured by Taylor, Brace, Brinton, and Smith (1963) was adopted. The corresponding temperatures are shown f
‘1’
I
-
1 *
/
1 /
z
I
’
I
/.
*
,
*
“
/
/
r,
i
*
800 -
100
1939
MARCH
I
600 -
,500Y 400iii 2 ;300-I 4. zoo-
IOO-
r
*
1
400
*
8.1
800
*
1200
1
*
1
-
1
I600 2000 2400 TEMPERATURE
FIG.~. ALTITUDE
PRO~LES
*
‘r’s
2800
1
3200
1
3600
1.K)
OF THE TBMPERATURES 1 MARCH.
FOR THE AURORA
AT 1939AST
ON
as Case B in Fig. 4. If, instead, we assume that the topside ionosphere is composed entirely of oxygen ions the resulting temperature profile (Case A) is indistinguishable. If, on the other hand, we use the results of Hoffman (1967) yielding a very low mean ion mass at high altitudes we obtain somewhat lower electron temperatures (Case C), The light ions are much more effective in cooling the electrons, as shown by Equation (46). Using the Taylor ion composition we have calculated electron and ion temperatures for the other four arc systems in Table 1. The results in Figs. 5-8, together with Fig. 3, show surprisingly little variation in electron temperature profiles in view of the marked differences between auroras in intensity, ionization rate, electron density, and altitude of peak emission. All of the temperature profiles exhibit maxima between 2920°K and 3511°K at altitudes between 330 km and 390 km. In the region of the temperature m~mum the electrons cool mainly to the ions and the cooling rate varies as the square of the electron density [Equation (46)]. The electron heating rate, on the other hand, is proportional to the ionization rate since most of the secondary electron energy at these altitudes is given to the ambient electrons (Table 4). Since the electron density is nearly proportional to the square root of the ionization rate (compare Fig. 1 and Fig. 2), the electron temperature is nearly independent of the ionization rate.
J, C. G. WALKER and M. H. RJ?ES
472
80O-
Tn,.
2007 MARCH
,)
70O-
60 o-
‘o-
lo-
IO-
I
I
IO-
O-
I
*
400
.I.
I
800
I.
1200
I600
I.
2000
L
I
I
2400
2800
TEMPERATURE
FIG.6.hITlVL%
PRO-
*
I
3200
*
I.
3600
3.
I
4000
s
I
4400
t*K)
OF THE TRMPERA~
AT 2007AST
FOR THE AURORA
ON
1 MARCH.
2207
i
*
I
400
L
I
800
I
I
1200
*
8
1800
*
1 2000
’
I
2400
*
1 2800
TEMPERATURE
FIG. 7. Acmmm
PROFILES OF THE TEMPERATURES
26 STARCH.
*
1 3200
*
1 3600
MARCH
*
’
4OCQ
26
)
’
4400
f-K)
FOR THB AURORA
AT 2207AST
ON
ELECTRON
DENSITIES
AND TEMPERATURES
IN AURORA
473
The explanation is different at lower altitudes. Here the electrons cool principally to the neutral particles and the cooling rate is a rapidly increasing function of electron temperature. This serves to stabilize the temperature, and the results show, for example, that T, - T, varies approximately as the fifth root of the ionization rate at 150 km. The variation would be approximately linear at this altitude if the cooling rate were linear in the electron temperature. Because the temperature profiles in the different auroras are so similar there is little variation, between auroras, in the dissociative recombination coefficients at a given I
r
I
1 400
*
“““I. 800
c I
I
’
I
’
I
’
I,
I
’
I
’
I
’
I
-
I
600
7
6
5 Y
500
w 2 400 IL < 300
200
100
~
,
)
1200
I600
2000
““““I 2400 TEMPERATURE
I 2800
3200
3600
4000
(OK)
FIG. 8. ALTTIVDE PROFILESOF THE TEMPERATURES FOR THE AURORA AT 2136 AST 29 MARCH.
ON
altitude. Thus, at 150 km, the electron density varies almost exactly as the square root of the ionization rate. On the other hand, the maximum electron density in these five auroras varies approximately as the cube root of the maximum ionization rate. This is an altitude effect. In our sample the intense auroras peak at low altitude where recombination coefficients are large while the weak auroras peak at higher altitudes where temperatures are higher and recombination coefficients lower. Variability in the altitude profile of the volume emission rate, in the width of the arc system, and in the location of the observer relative to the arc system precludes any attempt to deduce a general relationship between observed aurora1 intensities and aurora1 electron densities and temperatures from the five auroras we have studied. For these five auroras, however, results are summarized in Table 5. These results may be compared with Dalgarno’s values (Dalgarno, 1965; Dalgarno, Latimer and McConkey, 1965). Dalgarno’s ionization rates exceed the ionization rates in Table 5 for A3914 intensities corresponding to his IBC I and II designations and are smaller at higher intensities. His electron densities are smaller by about a factor of 2.5 over the range of intensities in Table 5. From Table 5 it appears that the value of 6500°K for the electron temperature measured
474
J. C. G. WALRER and M. II. REES
TABLE5
Date 1960 Time AST 2100 1939 2007 2207 2136
Maximum i13914 intensity at Fort Yukon (kR)
Maximum ionization rate (cm-a/sec-1)
Maximum electron density (cm-*)
Maximum electron temperature (OR)
30.6 13.0 22.0 347 7.2
516(+5) 6*12(+4) l-23(+5) 4-56(-t-5) 2+30(+4)
2.58(+6) l-13(+9 l-29(46) l-77($-6) 7*66(+5)
3511 3118 3420 3469 2920
26 February I March 1 March 26 March 29 March
by Explorer 22 near Was~gton, D. C. (L. H. Brace, private ~o~~ication~ could not have been caused by aurora1 electron bombardment in stable arc systems such as we have considered in this paper. Ack~~~e~g~#ts-We are pleased to acknowledge the wn~ibutions of Sandra Fuller to the pro~~ug and computational aspects of the research. Advice concerning metastable ion chemistry was provided by M. B. McElroy. This work has been supported in part (M. H. R.) by grants from the National Science Foundation (GA-1238) and the National Aeronautics and Space Administration (NGr-06-003-052). Part of the work was performed while one of us (J. C. G. W.) held a National Research Council Postdoctoral Research Associateship supported by the National Aeronautics and Space Administration.
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and NI+
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ELECTRON
DENSITIES
AND TEMPERATURES
IN AURORA
475
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