Birge-Hopfield (LBH) bands (a liig_x 1y, g+) in the Earth's atmosphere is presented.

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. A8, PAGES 18,557-18,573, AUGUST 1, 2000 Modeling the Lyman-Birge-Hopfield bands in the dayglow: Including radiative and collisional cascading between the singlet states Richard W. Eastes Air Force Research Laboratory, Space Vehicles Directorate, Hanscorn Air Force Base, Massachusetts Abstract. A new model for the daytime airglow emissions from the N2 Lyman- Birge-Hopfield (LBH) bands (a liig_x 1y, g+) in the Earth's atmosphere is presented. This model gives good agreement, which other first principles models have been unable to obtain, with dayglow observations reporting increased vibrational popula- tions, relative to direct excitation, for v _ 1 of the N2 alii a state. The ability of the model to match the observations is due to the inclusion of radiative and collisional cascading between the singlet states. Such cascading was not included in previous first principles dayglow calculations for the singlet states. Not only does cascading improve the fit between the observed and modeled relative vibrational populations, it also increases the total emission from the LBH bands by a factor of due to the transfer of excitation from the a and w states to the a state, resulting in significantly greater emission than predicted by earlier models using the same excitation cross section for the a state. Such an increase in the total emission from the LBH bands is consistent with recent work by Budzien et al. [1994] and Link et al. [1994]. The coupling between the singlet states will have a significant impact on the interpretation of the LBH band emissions from the Earth's atmosphere. 1. Introduction rent first principles airglow models, the only variation The N2 Lyman-Birge-Hopfield (LBH) bands (a IIg - of the vibrational populations, due to a combination of X 1Eg +) are used for remote sensing on current satel- altitude-dependent variations of the photoelectron flux lite missions (e.g., the UV! experiment on the Polar and small differences in the excitation thresholds for satellite) and they will be used on future missions (e.g., different vibrational levels of the a state, is significantly SSUSI on DMSP and GUVI on TIMED). Uses of the smaller than the observed variationsø The relative vi- LBH emissions include determining the N2 densities relbrational populations of the N aliig state have been ative to atomic oxygen in the daytime and the energy derived from the N2 LBH band emissions in the Earth's deposition rates in the dayglow and aurora. An accudayglow and the aurora. In both, some observers have rate understanding of the LBH band emissions is necreported vibrational populations agreeing with theoretessary for reliable applications. However, discrepancies ical calculations for direct excitation (Xv=o - a) by between observations and calculations are seen in the electron impact [Conway, 1982; Meier et al., 1982; Morrelative vibrational populations and, according to some rison et al., 1990; and Tort et al., 1994], while others recent reports, also in the total brightness of the LBH leasres et al., 1985; Eastes and Sharp, 1987; Budzien bands. While the total brightness of the LBH band et al., 1994] report statistically significant departures. emissions from first principles airglow models [e.g., At- The earlier observations reporting vibrational populamospheric Ultraviolet Radiance Integrated Code (AUtions deviating from direct excitation have often been RIC) by Strickland et al. [1999] depends on the X - dismissed since the cross section measurements of Ajello a excitation cross section, the N2 density, and the elecand Shemansky [1985], which found less than 5% castron flux used in the calculation, the relative brightcade (indirect excitation) contribution to the a state, nesses of the emissions have almost no dependence on have often been interpreted as evidence that significant such changes. The relative brightnesse should be the cascading does not occur in the singlet system. How- This paper is not subject to U.S. copyright. Published in 2000 by the American Geophysical Union. Paper number 1999JA / 00 / 1999JA ,557 most reliable information from the observations. In cur- ever, that interpretation of the laboratory results is incorrect. The absence of cascading in their observations can be explained by the lifetimes of the states. The longer lived N species (a and w) can drift out of the field-of-view and collide with the walls before decaying (J. Ajello, personal communication, 1996).

2 18,558 EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW The observed departures from the direct excitation model can, in general, be characterized as enhancements at the lower vibrational levels relative to the higher ones. These enhancements indicate that direct excitation from and radiation to the ground state are not the only processes influencing the relative vibrational populations, as assumed in previous first principles dayglow models. The observations of Budzien et al. [1994], which are among the most recent, have significantly smaller statistical errors than earlier observations. The Budzien et al. [1994] observations, which clearly exhibit a relative enhancement of the lower vibrational levels, will be used in most of the comparisons with the calculations presented in this paper; however, the other observations will be addressed in the Discus- surements: collision-induced (CIET), for example, electronic transitions N (a 1II9) + M ++ N (a' 1 ) -I- M, (1) may significantly influence emissions from the LB H bands. According to their results, in the aurora CIET is more important than radiative transitions between singlet states, and a model including both processes is capable of better agreement with observations. Morrill and Benesch [1996] obtained similar results for a model of the triplet states of N2. However, in the Eastes and Dentamaro [1996] model, important rates for CIET transitions between the singlet state are extrapolated sion section. from similar transitions and consequently have large While the populations observed may not match direct uncertainties. Unfortunately, both CIET and radiative transitions are important in the aurora, where emissions (X -+ a) excitation, it is the only process included in the models which have been used for dayglow calculations. typically peak near 110 km, making it difficult to test Radiative cascade between the singlet states was in- the Eastes and Dentamaro [1996] model there. Fortucluded in the auroral modeling presented by Cartwright nately, observations from high altitudes (e.g., > 200 km) in the dayglow, where CIET will be insignificant due to [1978] and by Dashkevich et al. [1993], but both fail to match observations of the aurora or dayglow. Radiathe lack of collisions, provide a test of the radiative part tive cascade between singlet states should be significant of the model while at lower altitudes (m140 km) near the peak of the dayglow emission profile, CIET should based on the transition rate data, which indicate that be significant. The purpose of this paper is to present a radiative transitions between the singlet states of N2 model and calculations which include cascade processes are only a factor of - 5 slower than the a-+ X transiin the dayglow and to compare the results with relevant tions [e.g., Gilmore et al., 1992; MarineIll et al., 1989]. dayglow observations. Although radiative cascade has not been included in dayglow models for the Earth's atmosphere, it is nec- 2. Model essary in models for Jupiter where radiative cascading enhances the H2 Lyman band emissions [e.g., Ajello et The model calculations use the Jasperse [1976] photoal., 1998]. electron model to generate the direct volume excitation There is also the possibility of other types of transi- rates. Although excitation rates are calculated for all tions involving the N2 a state. Recently, a model and of the singlet states shown in Table 1, the excitation to auroral calculations by Eastes and Dentamaro [1996] the three lowest lying singlet states of N2 (the a liig, found that a mechanism observed in laboratory mea- a' 1E, and w lau states, which will be referred to as Table 1. Electron Impact Excitation Cross Sections Used for Excitation to the Lower Singlet States Threshold, E.,ax tr.,ax, Process ev ev 10-0 cm. Reference X -+ a IIg Ajello and Shemansky [1985] Cartwright et al. [1977] X -- a' E,, Cartwright et al. [1977] X-- w A,, Cartwright et al. [1977] X-+ b II, -+ a IIg a 0.07 a James et al. [1990] X -- b' 1 -] _.. a liig b Ajello et al. [1989] X -- c t 1E + -- aliia b'c Ajello et al. [1989] X-+ yliig-+ wla,, + a' 1E Allen et al. [1990] X -+ x E - - a' d Allen et al. [1990] Ratliff et at. [1991]. bbased on c[-a versus c t-x from Gilmore et al. [1992] and cross section for emission from state to ground state. cvaxiable tr., for t/---- O. dfifty percent to t#= 0.

3 EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18,559 Table 2. Geophysical Parameters Used for the Airglow Calculations sight for comparison with the observations of Budzien et al. [1994]. Parameter Value 2.1. Volume Excitation Rates Calculation F Average F Ap 5.O Geographic latitude, degrees 35.0 Geographic longitude (W), degrees 0.0 Date May 5, 1991 Time, UT 1100 Solar zenith angle, degrees 22.5 a, a, and w) dominates the calculations (as will be shown later). The geophysical conditions used for the cascade model calculations, shown in Table 2, were selected to match those for the observations of Budzien et al. [1994]. To determine where the excitation goes, an intrasystem cascade model based on that of Eastes and Dentamaro [1996] is used. This model calculates the vibrational populati6ns for the three lowest lying singlet states by solving the continuity equations describing the cascading between the a, a, and w states. Shown in Figure I are the lower energy levels of these states and the transitions (radiative and collision induced) which are included in the model. The resulting vibrational populations for the a state are integrated along the line of For the altitudes of the Budzien et al. [1994] observations, the photoelectron spectrum and consequently the volume excitation rates calculated using the Continuous Slowing Do.wn (CSD) code [Jasperse, 1976] are similar to those produced by more recent first principles codes such as AURIC [Strickland et al., 1999]. The emissions peak well below 300 km where transport, which is not included in the CSD code, plays a significant role [e.g., Lee et al., 1980a, b]. The neutral densities used were taken from the Mass Spectrometer Incoherent Scatter (MSIS) model [e.g., Hedin, 1991]. Shown in Figure 2a is the photoelectron spectrum calculated at 145 km and in Figure 2b is the electron density as a function of altitude. In addition to direct excitation of the a, a, and w states, the rate of excitation through radiative cascade from several higher singlet states (x, y, b, b, and c ) is also calculated. Although the list of higher states is not complete, it includes all the singlet states for which published emission cross sections were found (see Table 1). While the excitation cross sections for some of the higher singlet states in Table I are actually greater than those for the a, a, or w states, the effective cross sections for contributions to the a, a, and w states are 82 8O 78 E "' 72 z 7O 68 v=8 ELECTRON IMPACT EXCITATION FROM X STATE 5 RADIATIVE 6 RADIATIVE a', a a, ;w 4 5 a' a 4 a ;w CIET CIET 2 RADIATIVE a' --,' X STATE COLLISIONAL / 1 QUENCHING/ o COLLISIONAL/1 QUENCHING/ RADIATIVE a--,' X STATE a,lz - air wla u g u N 2 ELECTRONIC STATE Figure 1. Diagram of the radiative and collision-induced transitions used in the model calculations and the lowest energy levels for the a, a, and w states. Collision-induced electronic transitions (CIET) to slightly higher energy levels are possible due to the kinetic energy transfer during collisionsø

4 18,560 EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW ,,, I,,, I,,, I,,, I,,, ENERGY (ev) Figure 2a. The calculated photoelectron flux as a fi nction of energy at 145 km. The flux was calculated using the CSD model of Jasperse [1976] with the geophysical conditions shown in Table 2. The CSD approximation used for the calculation smooths out the features in the spectrum. small due to branching to the ground state and predissociation. In the dayglow the contributions of the higher states will be small due to the factor of _ 10 decrease in the photoelectron spectrum between - 15 ev, where the a, a, and w state cross sections peak, and ev where the cross sections of the higher states peak. Another effect which should be included at the altitudes of the Budzien et al. [1994] observations is excitation from Xv>0. A discussion of this issue and the electron impact excitation cross sections is given below Electron impact excitation cross sections. While there are significant uncertainties in the magnitudes of the excitation cross sections for the singlet states, (the a state, with measurements which vary by as much as a factor of two, is best known) the important issue for the cascade model is the relative cross sections. The validity of the calculations presented will not depend on the absolute magnitude of the cross sections but on the relative cross sections since most of the excitation to the a and w states cascades to the tional levels of the a state have the same shape but different excitation thresholds and magnitudes. The variation in the excitation thresholds, when combined with the photoelectron fluxes, produces vibrational populations with slightly greater excitation in the lower vibrational levels than is obtained from the ratios of the X-a Franck-Condon factors (FCFs). The source of these differences will be referred to as threshold effects. Due to a lack of measurements, threshold effects are not included for the a' and w states; instead, the vibrational distribution of the excitation is based on the FCFs from the ground (X) state. The cross sections for the a' and w states below 12 ev were taken from Cartwright et al. [1977], but they are scaled by the ratio of the Ajello and $hemansky [1985] to the Cartwright et al. measurements for the a state because at low en- ergies, Cartwright et al.'s cross sections are larger than more recent measurements. This scaling decreases the total excitation to the a' and w states by a factor of approximately 0.7. For excitation of the higher singlet states of N2, the sources of the cross sections and the magnitudes used are given in Table 1. However, for the b 1 IX u state the shape was based on Zipf and Gorman [1980]. While the x and y state cross sections referenced are emission cross sections for excitation of the lower singlet states (a' and w), the cross sections for c t, b', and b are for emission to the X state. The cross sections for the contributions from the c t, b', and b states to the lower singlet states were obtained from the published cross sections by assuming an X:a branching ratio of 93:1, based on Gilmore et al. [1992]. Due to predissociation, cascading from the b and b states is even smaller than Cartwright [1978] expected since he had only scattering cross sections rather than emission cross sections. Predissociation decreases the latter but not the former, and it is important for the a state. Therefore the cross sections for electron impact excitation of the a, a', and w states are taken from Cartwright et al. [1977] at energies _ 12 ev. At 12 ev and above their measurements for the a state are in 100 good agreement with more recent measurements [Ajello and $hemansky, 1985; Brunger and Teubner, 1990], and since Cartwright et al. [1977] used the same equipment to measure all three states, their relative cross sections should be more accurate than those from separate mea- ELECTRON DENSITY (cm-3) surements. Figure 2b. The electron density as a function of al- Below 12 ev the cross sections of Ajello and Sheman- titude. These electron densities were calculated by the sky [1985] are used for the a state. Their measurements CSD model of Jasperse [1976] with the geophysical conshow that the excitation cross sections for all the vibra- ditions shown in Table OO

5 EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18,561 higher singlet states. This predissociation of c, b, and b states is included in the cross sections shown in Table 1. Other singlet states for which even stronger predissociation has been reported include the a" state [Karn and Pipkin, 1991], the o II state [Walter et al., 1994; Allen et al., 1990; James et al., 1990], and the cxii state [Walter et al., 1994; James et al., 1990]. These measurements indicate that cascading from the a", o, and c states to the lower lying singlet states should be negligible due to predissociation. Since the cascading from the x, y, c, b, and b states is the only contribution expected from all the higher states listed above, a list which includes most of the singlet states listed by Lofthus and Krupenie [1977], it is assumed to be a significant fraction of the total radiative cascading from the higher singlets, and it will be used to show that cascading from the higher states is not important. For the lower lying singlets, predissociation of the a state above v = 6, j = 13 is taken into account by assuming that only 0.88 (based on the sum of FCFs from Xv=o to av<6) of the direct excitation to the a _ state is seen in emission. Although the a v>7 and Wv>5 vibrational levels lie above the lowest dissociation limit (N(4S)-}-N( 4 S)) dissociation energy of q ev [Roncin et al., 1984], predissociation of these states would have to proceed by a different mechanism than it does for the a state due to inversion symmetry [van der Karnp et al., 1994]. Approximately half of the direct excitation to the d and w states goes to these higher levels, but there are no reports of predissociation Excitation from X(v > 0). Excitation from v > 0 is included in the model since at high altitudes (e.g., > 200 km) in the daytime a significant fraction of the N2 can be in v > 0, which produces a different vibrational distribution for the a state than that produced from v = 0. From v > 0, more of the excitation goes to the lower vibrational levels of the a, a, and w states, according to the Franck-Condon factors. All of the molecules are assumed to be in the three lowest vibrational levels and to follow a Boltzmann distribution. At 200 km approximately 6% of all N2 molecules in X(v > 0) assuming a Boltzmann distribution at an ambient neutral temperature (Tn = 1150 K) appropriate for Budzien et al. [1994], but < 0.1% of the molecules are in v > 3. of the upper state, by symmetry, it should not change with the vibrational level of the lower state Intrasystem Cascade Calculations The intrasystem cascade model, a modified version of the Eastes and Dentamaro [1996] model, calculates the equilibrium excitation rates and vibrational populations for the a, a, and w states from the volume excitation rates produced by the photoelectrons. To do this, the model solves the equations describing the statistical equilibrium between the a, a, and w states [e.g. Cartwright et al., 1971; Morrill and Benesch, 1996]. These coupled equations, all of the same form as (2) below, include the processes (excitation by electron impact and relaxation by radiation and collisions) which have a significant influence on the populations of the three lowest lying singlet states. A schematic of the transitions included is shown in Figure 1. For a given vibrational level v = j, in a given state 3, the relative number density (n /nn ) at statistical equilibrium is described by where K ;j a,/, i,j, k K ;j electron impact excitation rate (per N2) of vibrational level v - j in state ; collision induced electronic transition rate from c (v - i) to/ (v -j); transition probability from c (v - i) to/ (v --j); electronic states; vibrational levels; total quenching rate from (v - j), The rate coefficients for collisional processes are based on the available laboratory measurements but significant extrapolation is necessary. The following is a brief overview and a discussion of the minor changes from the model presented by Eastes and Dentamaro [1996] Radiative' processes. Radiative transition rate data are readily available for the three lowestlying singlet states. The rates tabulated by Gilmore et In addition to the vibrational populations, the electron in/pact excitation cross section for each vibrational al. [1992] were used for a a, w a, and a -+ X. level of the X state is needed to determine the effects of These values reflect recent measurements of the radiaexcitation from Xv>o, but the measured cross sections are for Xv=o - a. It is assumed that the cross section for Xv= a each have the same magnitude and shape as the Xv=o -+ a cross section. This assumption is an extrapolation from the a state measurements of tive decay lifetimes. For the a -+ X transition, a 17 ms lifetime [Casassand Golde, 1979] was used. Although longer lifetimes have been measured [Marinelli et al., 1989], the Casassa and Golde [1979] measurement is consistent with the longer lifetimes, and it gives a more Ajello and $hemansky [1985]. They measured the cross conservative assessment of CIET relative to radiation. sections from Xv=o to the different vibrational levels of the a state and found that the shapes of all the cross sections are the same (within 5%). Since the shape of It is assumed that the w state makes transitions only to the a state (no w -+ X) since transitions between the w xa and a x Z states are doubly forbidden by dipole the cross section did not change the vibrational level selection rules and X w transitions are also strongly

6 18,562 EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW forbidden [e.g., Lofthus and Krupenie, 1977]. Transitions involving the higher states are omitted since their contributions to the lower singlet states are negligible Collisional processes. Two collisional processes, CIET and quenching are included in the model. Quenching of the electronic states [e.g., Katayama et al., 1994] was not included in the Eastes and Dentamaro [1996] model. Eastes and Dentamaro [1996] assumed that part (0.33 of the total) of the CIET due to collisions with atomic oxygen is lost from the singlet system, but in this work the only collision-induced losses from the singlet system are through quenching. A third process, v -+ v- n transitions or vibrational redistribution, is not expected to have a significant influence on the calculations Collision-induced electronic transi- tions (CIET): Based on dipole selection rules, collision-induced electronic (CIET) transitions for both a a and w a are included in the model but a' w transitions are not. According to laboratory measure- ments [e.g., Katayama and Dentamaro, 1986], selection rules apply for CIET transitions just as they do for radiative transitions, but while radiative transition rates increase as the energy gap increases between the initial and final states, the CIET rates decrease with energy gap. Also, endothermic transitions are allowed by CIET because translational to vibrational energy transfer can occur in collisions. While a theoretical understanding of CIET is incomplete, empirical models (based on laboratory observations) have recently been presented by Eastes and Dentamaro [1996] for the N2 singlet system and by Morrill and Benesch [1996] for the N2 triplet system. Details of the CIET model used can be found in the Eastes and Dentamaro [1996] paper. It should be noted that important rates for CIET transitions between the singlet state are extrapolated from similar transitions and consequently have large uncertainties. Eastes and Dentamaro's [1996] work demonstrated that CIET is most important for the lower vibrational levels of the a and a' states because the radiative transition rates to either the a or X states are slow from the lower vibrational levels of the a' state. In the lower thermo- sphere, CIET can provide a significantly faster decay channel than radiation Quenching: Collisions with atoms or molecules can also remove molecules from the singlet system by quenching, which changes the electronic state. While there are measurements of quenching rates for the triplet states, the N (a'v-0) + N2 measurement of Dreyer and Perner [1972] was the only one found for the singlet states. Therefore, based on the rationale presented by Cartwright [1978], the quenching rates for the singlet states are extrapolated from the Morrill and Benesch [1996] rates for the triplet state and the Dreyer and Perner [1972] measurement for N2 a'v=o. For v > 0 in the a' state, the rates are extrapolated from the v -- 0 measurements by assuming that the a' rates vary in parallel with the B rates, and for both the a and w states, quenching is assumed to proceed at the same rate as for the N2 B3IIg state. Based on the available information for similar collisional rates, it is assumed that quenching by O2 is an order of magnitude faster than quenching by N2 and that quenching by atomic oxygen (O) is 2 orders of magnitude faster than by N2. The resulting quenching rates are approximately an order of magnitude slower than the CIET rates for the singlet states Vibrational redistribution (v -4 v- n): Vibrational redistribution due to collision-induced vibrational transitions (v -4 v-n) is possible, but the rates are expected to be insignificant in the dayglow. For the singlet states, v -4 v-1 transitions involving either Na or Oa (the most likely recipients of the vibrational energy since the amount of energy to be ex- changed is large for vibrational to translational energy transfer) require substantial energy input, making significant transition rates unlikely. However, v -4 v-2 and v -4 v-3 are energetically allowed. Such v > 1 transitions are seen in the A 3Eu+ state, but the rates [Dreyer et al., 1974; Morrill and Benesch, 1996] are a factor of 10 slower than the quenching rates (which are in turn a factor of.. 10 less than the CIET rates). All of the vibrational energy transfer rates for the A state are small, but those for the lower vibrational lev- els are the slowest. The poor match between the Xv_-O - Xv: energy gap and the vibrational energy gaps in the A state are responsible. Similarly, in the singlet states the vibrational energy gaps do not match the X _-0 - X _ gap. Consequently, the vibrational redistribution rates for the singlet states should also be slow relative to either quenching or CIET. Examination of the laboratory measurements used to determine the CIET rates [e.g., Katayama et al., 1994] indicates that v -4 v- I transitions within an electronic state are orders of magnitude weaker than the CIET transitions to other states, and that v -4 v-n transitions are < 0.1 of the CIET rates (A. Dentamaro, personal communication, 1997). This is consistent with vibrational redistribution rates in the triplet states. Although Marinelli et al. [1988] reported v -+ v- 1 transition rates of approximately the same order of magnitude as the CIET rates used here, their observations were not state specific, and their omission of collision induced transitions other than v -+ v- n is inconsistent with state specific measurements of the a state. 3. Results Using the model discussed in the previous section, the brightness (relative to direct excitation) and relative vibrational populations of the N2 LBH bands are calculated for comparison with Budzien et al.'s [1994] observations. Good agreement is seen in both comparisons. These comparisons and additional information, about the volume excitation rates and the vibrational populations at lower tangent altitudes, will be presented.

7 EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18, z O 1.2 n 1 o.8 0.6,, CARTWRIGHT [1978] [] o BUDZIEN, et al. [1994] - A MODEL (200 km TANGENT ALTITUDE) V MODEL WITH 0.9 SCALING OF RADIATIVE RATES _ [] DIRECT EXCITATION AT 200 km (X--*a) I I I I I I I Figure 3. Comparison of the relative vibrational populations from the cascade model calculations and the observations. The observations of Budzien et al. [1994] are shown as diamonds with + I (r statistical error bars. Results from the cascade model when using the published radiative rates from Gilmor et al. [1992](triangles) and when scaling their rates by 0.9 (inverted triangles) agree well with the observations. The viewing geometry (200 km tangent altitude) and geophysical conditions (see Table 2) for the model calculations match those for the observations. Also shown are the populations calculated by Cartwright [1978] for the aurora (asterisks) and the direct excitation rates (squares) calculated at 200 km (using the same geophysical conditions as the cascade model) Comparison With Observations model and the observations. The resulting populations As shown in Figure 3, the relative vibrational pop- are shown in Figure 3 as inverted triangles connected ulations calculated using the cascade model (triangles) by a solid line. This scaling factor, which is used for agree well with the observations of Budzien et al. [1994] the rest of the calculations presented, was selected by (diamonds with + I a error bars). The calculated vi- inspection. A more sophisticated fitting technique is brational populations are for observations from 270 km not justified due to the omission of threshold effects along a line of sight with a tangent altitude of 200 for the a and w states (which will be addressed in the km. This tangent altitude is used because Budzien Discussion section). et al. [1994] used observations with tangent altitudes The relative vibrational populations from the cascade _ 200 km when determining the vibrational popula- model agree better with the Budzien et al. [1994] obsertions, and for such observations the greatest contributions are from the lowest altitude, 200 km. The large vations than either the Cartwright [1978](asterisks) or direct excitation (squares) models which are also shown tangent altitude simplifies comparisons of observations in Figure 3. The direct excitation rates shown in Figand calculations since photoabsorption by O2 and self- ure 3 are for the same geophysical conditions as the absorption by N2 are not significant at 200 km [e.g., cascade model calculations, but they are the popula- Conway, 1982]. The comparison further simplified by tions calculated for an altitude of 200 km (with excitathe lack of significant collisional effects at 200 km and tion from Xv>0) rather than a line of sight sum. One above. While there is a large deviation for v-6 due might expect Cartwright's [1978] results, which depend to a systematic error in the analysis of Budzien et al. [1994; S. Budzien, personal communication, 1996], the agreement between the observations and calculations is good at v- 3-5, and the calculated populations are slightly higher at v _ 2. All of the data plotted in Figure 3 are also shown in Table 3. Since the calculated populations are consistently higher for v_ 2, the radiative rates for transitions between the singlet states [Gilmore et al., 1992] were scaled by a factor of 0.90 to improve the agreement between the primarily on radiative transitions, to agree with the observation since CIET is negligible for tangent altitudes _ 200 km. However, the radiative transition rates assumed by Cartwright are significantly larger (by factors of ) than the rates [Gilmore et al., 1992] used in the cascade model. The total brightness of the a state emissions from the cascade model also agrees with Budzien et al.'s [1994] conclusion that the LBH bands were (1.48 average) times brighter than their first principles calcu-

8 18,564 EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW Table 3. Relative Populations of N2 a xiia State Vibrational Levels Shown in Figure 3 v Model Cartwright Budzienb Model c Rates Scaled Direct With :l: I :t: :k :t: :t: :t: :l: a Cartwright [1978]. bbudzien et al. [1994]. CTangent altitude = 200 kin. titangent altitude = 200 km and radiative rates between the singlet states scaled by 0.9. eat 200 km altitude. lations which used only direct excitation. Their calculations were based on the X - a cross sections of Ajello and Shemansky [1985] and the N2 densities from the MSIS model atmosphere [Hedin, 1991]. They could achieve agreement between their calculations and the observed altitude profiles for six strong LBH features (their Figure 10) by either of two alternatives. One was to scale (increase) either the N densities or the X- a excitation cross sections, but scaling did not allow them to match the relative vibrational populations observed. They could match both the relative vibrational populations and the total brightness observed if they assumed a contribution having the relative populations calculated by Cartwright [1978](i.e., assume radiative cascading from the a and w states). The cascade model, which is based on cross sections and N densities from the same sources as those used by Budzien et al. [1994], gives a similar brightness enhancement to that observed. The expected brightness change as a function of altitude is shown in Figure 4 by the final (equilibrium) volume excitation rate curve since the brightness and the a state production rate are proportional. In Figure 4 all of the curves are for av < 6, and the rates for both radiative and CIET cascade to the / i I loo RADIATION CIET DIRECT FINAL (EQUILIBRIUM) (X-.a), [, I,,,, J,,, I I J, N 2 a STATE VOLUME EXCITATION RATES (RELATIVE) Figure 4. The final (equilibrium) a state excitation rate relative to the direct (X - a) excitation rate. Also shown are the rates of contribution through the radiative and CIET channels. Since cascading out of the a state is not included in the individual rates, their sum is greater than the final production rate. Radiative and collisional cascading from a and w states are responsible for the difference between direct excitation and the final excitation rate. The greatest effects are seen above 200 km where the final (equilibrium) excitation rate reaches 1.67 times the direct excitation (X- a) source.

9 EASTES' N: LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18,565 a state and the equilibrium excitation rate are plotted relative to the direct excitation rate. The contributions to the a state are greater than the final volume excitation rate, due to cascading between the singlet states (primarily a d). At the lower, near auroral, altitudes ( km) the enhancement of the LBH bands is smallest but has the greatest variation with altitude. Near the peak of the dayglow, which has the greatest influence on the scaling factors Budzien et al. [1994] derived from their altitude profiles, the final (equilibrium) volume excitation rate is a factor of 1.55 greater than the direct excitation to v i 6 of the a state, which is in good agreement with the observations. However, one cannot conclude that the calculated enhancement of the LBH bands is correct on the basis of the agreement between the model and the Budzien et al. [1994] observations. Another possiblexplanation for the factor of 1.55 difference between their observa- tions and calculations is a combination of uncertainties Their O I brightness was 9% less than calculated, while the LBH observations were a factor of 1.5 greater than calculated. The agreement with the O I nm emis- sion strengthens the argument that the N2 LBH excess is real. Also, the analysis of other observations by Link et al. [1994] requires a similar enhancement in the LB H emission (R. Link, personal communication, 1998). The two independent results provides greater confidence that the amount of enhancement calculated is in agreement with observations Volume Excitation Rates Shown in Figure 5 is the altitude dependence of the X -+ a, X -+ w and X -+ a volume excitation rates. These rates are used by the cascade model when calculating the equilibrium excitation rates and vibrational populations. For each vibrational level of the a state the contributions are summed from 270 km along a line of sight with a tangent altitude of 200 km. in the absolute magnitude of the a state cross section, the N2 densities, and the observations. To fit their observations, Budzien et al. [1994] made significant modifications to the model atmosphere used. They lowered the exospheric temperature predicted by MSIS for their flight by 175 K in order to fit their altitude profiles. Variations in the a:a :w ratio produced by direct excitation are responsible for most of the variation in the final (equilibrium) production rates for the a state, which are shown in Figure 4. The differences between the thresholds and shapes of the excitation cross sections for the a, a, and w states, combined with the altitude de- This is a large adjustment given the low geomagnetic pendent variations in the photoelectron spectrum, proactivity and moderate solar activity conditions of the duce the variations in the relative volume excitation observations. This adjustment decreases N2 above 200 km; consequently, their calculations produce less LBH emission. However, in their modeling, both O I nm and the N2 LBH band emissions were modeled simultaneously. Consequently, the retrieved temperature rates. While the vibrational populations of the a state which are produced by direct excitation can vary with altitude due to threshold effects, the variation is small. This can be seen from Figure 6 where the vibrational level dependence of the a state relative populations prodescribes not just the N2 density, but O and 02 also. duced direct excitation at 145 and 200 km are shown as t FINAL (EQUILIBRIUM) a STATE DIRECT a STATE (X--* a) \,... DIRECT w STATE (X--,w) i..'\ DIRECT a' STATE (X--* a') - ¾'.. \... (x+y) x 10--,(a' or w)...\,... (b+b'+c, )xlo-,a , I, I I, I VOLUME EXCITATION RATES (MOLECULE cm '3 s -1) Figure 5. The altitude dependence of the volume excitation rates for the a, a, and w states. The direct excitation rates from the X state to the a, a, and w states are shown as well as contributions from the higher singlet states (x, y, c[, b, and b ). The final (equilibrium) volume excitation rate for the a state is also shown.

10 18,566 EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW o. l //"--- ' X-. a, AT 200 km r // [] x-. a' AT 145 km and 200 km - x X-. w AT 145 km and 200 km LU 0.6 ' o o lo Figure 6. The relative vibrational distributions for direct excitation to the a, a, and w states at 145 and 200 km are shown. The a state populations at 145 and 200 km are shown as asterisks and triangles respectively. The relative populations of the a state (squares) at both altitudes are set equal. The relative populations shown for the w state are an average of those at 145 and 200 km. Actual values are a factor of higher at 200 km and commensurately lower at 145 km. The populations at 145 km are normalized such that 1.0 corresponds to an excitation rate of 156 molecules cm -3 s -. The relative populations at 200 km are normalized such that 1.0 corresponds to an excitation rate of 79 molecules cm -3 s -. The relative vibrational distribution for the a and w states are based on the Franck-Condon factors from the X state, but the a state populations use separate cross sections for each vibrational level. asterisks and triangles respectively. The relative vibrational distributions of excitation to the a and w states are also shown, but their populations are based on the Franck-Condon factors from the X state rather than 3.3. Excitation Transfer Channels The details of how the excitation to the a and w states is transferred to the a state through radiative and collisional cascading are worth examining. Near the dayglow peak the transfer of excitation by CIET appears to be less important than transfer by radiation (see Figure 4), but CIET has a strong vibrational level dependence and for some of the vibrational levels it is equally important. This can be seen in Figure 7 where the vibrational level dependence of the excitation chan- separate cross sections for each vibrational level. The relative populations for the a state (shown as squares) at both altitudes are set equal. For the w state, due to the similarity of the populations at 145 and 200 km, the relative populations shown are an average. Actual values are a factor of higher at 200 km and commensurately lower at 145 km. nels at the dayglow peak (145 km) are shown for the Also shown in Figure 5 is the excitation contributed a state. The contributions to each of the vibrational to the lower singlet states (a, a, and w) from the higher levels, v- 0-6, are shown, and a relative population of singlets (x, y, b, b, and c ). To make them more legible, 1.0 corresponds to an excitation rate of 156 molecules the contributions from the higher singlets have been multiplied by 10. For the lower singlets the ratio of the cm -s s -1. The vibrational populations as well as the four contributions, direct excitation (X - a), w- a radirect to the radiative cascade contributions from the diative, a - a radiative, and a - a CIET, are shown. higher singlets is 6.1:0.005 at the dayglow peak (- 145 The w - a CIET contribution is not shown since it is km). Even if all the excitation from the b, b, c, x, and y states went to one vibrational level of the a state, the contribution would be < 10% of the total excitation to < 0.01 for any vibrational level. Clearly, CIET is as important as radiative cascade for the lower vibrational levels (v_< 2) of the a state. that vibrational level. Since the contributions shown in In Figure 8 the vibrational level dependence of the vi- Figure 5 are expected to be a significant fraction of the total excitation cascading from the higher singlets, the brational populations and the contributing sources for the a state are shown. As in Figure 7, Figure 8 is for calculations are simplified by omitting the contributions an altitude of 145 km and a relative population of 1.0 from the higher states. corresponds to 156 molecules cm -s s -1. The radiative

11 _ EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18, E a STATE FINAL m "J :-' : '... e, ':f-' " " '' -- I I '... a'--, a R D IATIV.% CASCADE - a'-, a CIET CAS( AOE' '. " Figure 7. The final (equilibrium) relative populations and the contributions to vibrational each level of the a state, v - 0-6, at 145 km. The w - a CIET contribution is not shown since it is < 0.01 for any vibrational level. A relative population of 1.0 corresponds to 156 molecules cm S. and CIET cascade channels which are shown in Figure 8 for the a state are sinks for the a state. For the w state the vibrational populations are not shown because they are not significantly different from the direct populationshown in Figure 6 (the energy gaps are sufficiently large that CIET to the w state is small at 145 km and radiation is even smaller), but for the a state the differences between the equilibrium and the direct vibrational populations are significant. The lower vibrational levels of the a state are populated primarily by radiative and CIET transitions from the a state. Most of this excitation is, of course, transferred back to the a state but frequently to a lower vibrationalevel than it came from / \., ' Figure 8. The final (equilibrium) relative populations and the contributions to each vibrational level of the a state at 145 km. As in Figure 7, relative population of 1.0 corresponds to 156 molecules cm -3 s -1.

12 18,568 EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW z _0 1.2 n I II. 0.2 V 200 km TANGENT ALTITUDE,x 14,5 km TANGENT ALTITUDE o 11,5 km TANGENT ALTITUDE I I I I I I! 0 I Figure 9. The relative populations of the a state for dayglow observations tangent altitudes of 145 km and 115 km as well as 200 km (which was shown earlier in Figure 3). All of the calculations are for observations from 270 km assuming the geophysical parameters in Table Tangent Altitude Dependence of the Relative Vibrational Populations For observations from 270 km the expected vibrational populations at tangent altitudes of 145,115,and 200 km are shown in Figure 9 and Table 4. The 200 km calculation was shown earlier in Figure 3. At the lower tangent altitudes, the relative populations of the lower vibrational levels decrease due to two effects: CIET and a decrease in the amount of excitation to the a s and w states relative to the a state. As the amount of excita- tion to the a s and w states decreases, direct excitation (X - a) becomes more important and the relative popu!ations become more similar to the populations produced by direct excitation. CIET is also important. It changes. the distribution of excitation cascading from the d and w states, and it is responsible for approximately half of the difference between the 145 and 115 km calculations. Table 4. Relative Populations of N2 a liig State Vibrational Levels Calculated for Different Tangent Altitudes Tangent Altitude, km v I ! The relative vibrational populations shown in Figure 9 for a tangent altitude of 115 km should not be confused with the auroral populations from 115 km. For the dayglow calculations at 115 km tangent altitude, much of the emission actually comes from higher altitudes where CIET effects are small. By contrast, in the aurora, where the emission typically peaks below 125 km, most of the emission comes from altitudes where the effects of CIET are more significant. 4. Discussion The vibrational populations from the model calculations agree well with the only observations [Budzien et al., 1994] which have been shown, but there are other daytime observations of the LBH bands, some of which reportedly match direct (X - a) excitation. The following discussion will show that the cascade model is in good agreement with all but one set of observations. Some issues which influence the results of the model presented in the previous section will also be addressed Additional Observations The dayglow measurements reported by Eastes et al. [1985] and analyzed in the companion paper by Meier et al. [1985], also show enhancements of the relative populations in the lower vibrational levels. However, Conway [1982], Morrison et al. [1990], and Tort et al. [1994] have reported agreement with direct excitation in the dayglow. If their observations have statistically significant differences from the cascade model, it could indicate problems in either the cascade model or the observations.

13 - _. _ - _ -. - _. EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18, I _ ß DIRECT EXCITATION AT [ 145 km X TORR,etal. [1994] (>190) km) _. BUDZIEN, etal. [1994] _ z 2 - A MEIER, et al. [1985] - [] MORRISON, et al. [1990] V CASCADE MODEL a_ 1.5 o m 1 > n,, I I I I I I I 6 Figure 10. The dayglow observations which report relative vibrational populations for the LBH bands versus the direct and cascade model calculations. The populations reported by Meier et al. [1985], Morrison et al. [1990], Budzien et al. [1994] and Tort et al. [1994](190 km) are shown as Triangles, squares, diamonds, and crosses respectively. All the observations are normalized to 1.0 at v = 4, and the errors from v = 4 are propagated into the other levels (for clarity some of the data points are offset horizontally). For the Morrison et al. [1990] data the original errors are shown by the inner set of error bars. Also shown are the populations from the coupled singlet states (inverted triangles) and direct excitation (asterisks) models. Both model calculations are based on the geophysical parameters shown in Table 2. The direct excitation model calculation is for an altitude of 145 km, the peak of the dayglow, while the coupled states calculation is for observations a tangent altitude of 200 km (as in Figure 3). The dayglow observations for which a state vibrational populations have been presented are shown in Figure 10. The observations reported by Meier et al. tion models, respectively). As presented by Morrison et al. [1990], the relative populations for the lower vibrational levels (v < 3) appear to match direct excitation. [1985], Morrison et al. [1990], Budzien et al. [1994], and However, their errors for the higher levels (v = 3-6) Tort et al. [1994](altitude _ 190 km) are shown as are large, making the populations of the lower levels triangles, squares, diamonds, and crosses respectively. relative to the higher ones uncertain, which makes it Each set of observations has been normalized to 1.0 at difficult to distinguish between the two models. v - 4, and the errors from v - 4 are propagated into the According to least squares fits of the calculations other levels (for clarity some of the data points are offset and observations shown in Figure 10, the Tort et al. horizontally). For Morrison et al.'s [1990] observations, [1994] observations are the only ones which clearly agree the original error bars are also shown as an additional, best with direct excitation. This is surprising since the inner set of error bars. Aiso shown in Figure 10 are Budzien et al. [1994] observations agree well with the calculations from the direct excitation (asterisks) and cascade calculations. Less than a year separated the two cascade (inverted triangles) models. The direct excita- sets of observations, and as shown in Table 6, both have tion populations are calculated for an altitude of 145 km using the geophysical conditions in Table 2, and they are approximately equal to the direct populations used in the papers originally reporting the observations. The cascade model calculations were shown earlier in Figure 3 as inverted triangles. The values for all of the relative populations shown in Figure 10 are given in Table 5. similar tangent altitudes and geophysical conditions. Significant differences do exist in the amount of temporal and spatial averaging in the Tort et al. [1994] and Budzien et al. [1994] observations. Budzien et al. [1994] summed the data from 261 separate 10.8 s scans taken on four separate orbits when determining the vibrational populations; consequently, they would not be From Figure 10 it is clear that Morrison et al.'s [1990] expected to observe short-term temporal or small-scale observations have such large errors that the agreement spatial variations. By contrast, Tort et al. [1994] used with either excitation model, direct or cascade, is similar. This is confirmed by least squares fitting (X and 7.5 for the fits to the cascade and direct excitadata from the 190 km tangent altitude observations during a shuttle roll sequence; therefore the observations cover significantly less time and space. In the more

14 18,570 EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW Table 5. Relative Populations of N2 a liig State Vibrational Levels With Errors From v - 4 Propagated to the Other Levels Direct 145 km Budzien" Meier b Morrison c Torr a Cascade Model (Rates Scaled) e :k: abudzien et al. [1994]. b Meier et al. [1985]. ½Morrison et al. [1990]. a Tort et al. [1994]. etangent altitude km and radiative rates between the singlet states scaled by 0.9. temporally and spatially limited sample of data used by Conway [1982] also reported agreement with direct Torr et al. [1994], there is a greater chance of deviations excitation; however, he did not present the relative vifrom the average conditions presumed by current day- brational populations from his analysis. In his paper the glow models. The neutral density and solar flux models only comparisons of data and calculations are plots of used in the model calculations are based on averages; emission versus altitude, and they all involve emissions hence the results are more appropriate for averages of observations, such as Budzien et al.'s [1994]. from the higher (v >_ 4) vibrational levels, for which no significant differences between observations and cal- There are also differences between the instruments culations have been seen. Also, a statistical analysis used for the two sets of observations which can affect of the vibrational populations would be inconclusive, the error analysis and therefore the conclusions. Instru- based on comparisons with the rocket observations rements similar to that used by Budzien et al. [1994] have ported by Eastes et al. [1985]. Their observations were been proven on many previous flights, while Tort et al.'s also from a rocket, and the emissions were significantly [1994] instrument is significantly more complex and less brighter (and consequently have better signal-to-noise) proven. The instrument used by Budzien et al. [1994] than those used by Conway [1982]; however, the Eastes operated in a pulse counting mode, allowing a good de- et al. [1985] data do not provide statistically conclutermination of the statistical errors, while the Tort et al. sive evidence of an enhancement of the lower vibrational [1994] observations were taken with an intensified CCD, for which statistical errors are less certain. Because of levels. Consequently, while data analyzed by Conway [1982] may be consistent with direct excitation, they the spatial, temporal, and instrumental considerations, should not be expected to distinguish between excitathe Budzien et al. [1994] data are expected to be more tion models. appropriate for comparisons with the model than those of Tort et al. [1994]. In summary, although there are several reports [Conway, 1982; Morrison et al., 1990; Tort et al., 1994] of Table 6. Comparison of the Conditions for Recent Observations Parameter Budzien" Tort b F10.7 (daily) F 10.7 (90 day average) Ap 5 Geographic latitude, degrees 60 to-60 Geographic longitude (W), degrees 75 to 270 Date May 5-6, 1991 Time, UT A 0+ to 2+ Tangent altitude, km _> March 29, abudzien et al. [1994]. b Torr et al. [1994].

15 EASTES: N. LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW 18,571 vibrational populations which match direct excitation, only the observations reported by Torr et al. [1994] exhibit significantly better agreement with the direct excitation model than with the cascade model presented. The other observations reporting agreement with direct excitation in the dayglow [Conway, 1982; Morrison et al., 1990] lack statistical conclusivehess, and as demonstrated for the Morrison et al. [1990] observations, exhibit similar agreement with both models. The dayglow observations of Budzien et al. [1994], which are thought to be reliable and appropriate for comparisons with the cascade model, exhibit significantly better agreement with the cascade model calculations. vibrational levels is unclear. However, good information about the vibrational level dependence of the cross section is available for the a state, for which comparison of the excitation calculated (including threshold effects) with FC Factor ratios indicates that the difference for any vibrational level is approximately 10% or less. Since the excitation thresholds for all three states (a, a, and w) are similar, including threshold effects for the a and w states is expected to introduce a similar (- 10% or less) change in the vibrational populations of the a and w states. Such a small change would not significantly alter the agreement between the model calculations and the observations Model Issues There is some uncertainty about the collisional reaction rates and the electron impact excitation cross 5. Conclusions The model presented produces relative vibrational sections. These uncertainties and their effect on the populations which are in good agreement with the dayresults of the cascade model will now be examined. glow observations of Budzien et al. [1994], Morrison et Collisional reaction rates. Rate coef- al. [1990], and Eastes et al. [1985](as analyzed bymeier ficient data are incomplete for the two collisional processes used in the model: CIET and quenching. The most important of the two is CIET. Due to a lack et al. [1985]). The enhancement observed in the relative populations of the lower vibrational levels is reproduced by including cascading between the singlet states. At of measurements, the N (singlets) -b O rate coe cient the higher altitudes (e.g., the observations of Budzien (the dominant one in the cascade calculations) is extrapolated from data for N (a)+ N2 and N2 triplets. A et al., 1994) the cascading is primarily due to radiative transitions, but CIET is significant at the dayglow change in the CIET rates would not affect the compari- emission peak (- 145 km) and below. The model does son at high altitudes (_ 200 kin). But, at lower tangent not agree as well with the observations of Tort et al. altitudes, where CIET is important, the relative populations in the dayglow would be affected. Since the radiative part of the calculation appears to be correct, [1994], which are best fit by direct excitation; however, they used a less proven instrument design and had limited spatial and temporal coverage, factors which could based on the comparisons near 200 km, comparisons contribute additional, nonstatistical errors. at lower altitudes should be valuable in addressing the The cascading which enables the model to obtain accuracy of the CIET rate coe cients, but such obser- agreement with the observed relative vibrational popuvations have not been published. Although the data are lations also increases the emission from the LBH bands also incomplete for quenching, it is slower than CIET relative to direct excitation alone. At the peak of the by a factor of - 10 according to the available data [e.g., dayglow emission (- 145 km), the calculated emission Morrill and Benesch, 1996]; therefore the effects of er- a factor of 1.55 greater than expected from direct exrors in the rates should be negligible to the final result citation alone. This extra emission is consistent with in the dayglow. both the observations of Budzien et al. [1994] who Electron impact excitation cross sec- found a factor of 1.48 more LBH emission than pretions. As discussed earlier, changes in the electron dicted by model calculations using only direct excitaimpact excitation cross sections for any of the three lowest singlet states could change both the total amount of tion, and with the results of Link et al. [1994] whose analysis found a similar discrepancy in the LB H emisemission from the LB H bands and the relative vibra- sions observed from sounding rockets. Cascading from tional populations. Due to the omission of threshold the a and w states is the source of the extra emission; effects for the a and w states, the actual cross sections consequently, any changes in the a and w state cross differ from those used in the calculations, and including threshold effects would change the relative popusections will produce a proportional change in the total emission calculated. Although the observed and calculations. Since threshold effects increase excitation to lated enhancements in the emission agree well, better cross section data are needed because there are significant uncertainties in the excitation cross sections of the lower vibrational levels at the expense of the upper vibrational levels, the populations of the lower vibrational levels of the a and w states would be increased, which would in turn increase the relative excitation of the lower vibrational levels of the a state. The available cross sections for the a and w states are actually convolutions of the cross sections for all the vibrational levels, and the shape of the cross section for individual both states. This extra LB H band emission is a problem. for first principles models of the dayglow, especially previous ones which, when using the same electron impact excitation cross sections, have reported good agreement with the total brightness of not only the N LBH bands

16 18,572 EASTES: N2 LYMAN-BIRGE-HOPFIELD BANDS IN THE DAYGLOW but also with other UV emissions. If the omission of a third of the total LBH emission could be obscured by adjustment of the solar EUV fluxes, neutral densities, and the excitation cross sections, the accuracy and reliability of dayglow models is less than desired for remote sensing applications. The LBH bands have been used to remotely sense the N2 density because the excitation mechanism has been assumed to be simple. However, these results indicate that not only does the total brightness of the LBH bands differ from direct excitation but it also varies significantly with altitude. Errors in interpreting the LBH band emissions can also affect the densities for other species such as 02 which are often retrieved simultaneously from altitude profiles of atmospheric emissions. The results also have implications for auroral remote sensing. Clearly, cascading needs to be considered when deriving energy deposition rates from auroral data since cascading would increase the auroral emission brightnesses. But, the amount of increase can vary. The dayglow calculations presented indicate that the brightness of emissions from auroral altitudes ( km) are enhanced by a factor of , and the amount of enhancement is altitude dependent, which makes it dependent on the particle energies in an aurora. Acknowledgments. Tt, e author thanks both D. Decker and A. Dentamaro for their comments on this paper. He is further indebted to D. Decker for providing a copy of the CSD photoelectron model and patiently answering numerous questions about it. The author thanks the reviewers for their comments. Janet G. Luhmann thanks Scott Budzien and Joseph M. Ajello for their assistance in evaluating this paper. References Ajello, J.M., and D.E. 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