Corresponding author: J. L. Fox, Department of Physics, Wright State University, Dayton, OH 45435, USA. (email@example.com)
 The first N2 emissions in the Martian dayglow were detected by the SPICAM UV spectrograph on board the Mars Express spacecraft. Intensities of the (0,5) and (0,6) Vegard-Kaplan bands were found to be about one third of those predicted more than 35 years ago. The Vegard-Kaplan band system arises from the transition from the lowest N2 triplet state () to the electronic ground state (). It is excited in the Martian dayglow by direct electron-impact excitation of the ground N2(X) state to the A state and by excitation to higher triplet states that populate the A state by cascading. Using revised data, we compute here updated intensities of several of the bands in the N2 triplet systems and those involving the a1Πg state, the upper state of the Lyman-Birge-Hopfield bands. We find that the predicted limb intensities for the (0,5) and (0,6) Vegard-Kaplan bands are consistent with the measured values.
 The (0, 6), (0, 5), and possibly the (0,7) bands of the N2 Vegard-Kaplan (VK) system () were detected for the first time from the Martian atmosphere by the SPICAM (Spectroscopy for Investigations of the Characteristics of the Atmosphere of Mars) UV spectrograph on board the Mars Express (MEX) spacecraft [Leblanc et al., 2006, 2007]. The solar activity at the time of the measurements, which were carried out from late 2004 to late 2005, was fairly low; F10.7 at earth varied from ∼89 to ∼117. The integrated overhead intensities derived from the limb scans were about one third of those predicted for low solar activity conditions by Fox et al.  and Fox and Dalgarno  (hereafter FD79). In the last 35+ years, however, there have been several updates to the electron-impact cross-sections and to the molecular parameters that determine the emission rates. We report here integrated overhead intensities of a number of band systems between states in the N2 triplet manifold and those between the lowest three singlet states that are connected to the ground state by dipole forbidden transitions. In addition, we report computed limb intensity profiles for the three Vegard-Kaplan bands that were detected by SPICAM.
2 Modeling Approach
 We have constructed thermospheres/ionospheres of Mars here for both low and high solar activities that are similar to those we have presented earlier, with minor updates to the rate coefficients and cross-sections [e.g., Fox, 2004; Fox and Hać, 2009]. The low solar activity model is based on the Viking neutral in situ measurements [e.g., Nier and McElroy, 1977]; the high solar activity model is based on the MTGCM of Bougher et al. [2000, 2009]. For the high solar activity model, we have doubled the O mixing ratio, so that it would be larger than that of the low solar activity model. The models include 12 background species: CO2, N2, O, Ar, CO, O2, NO, N, C, He, H, and H2. Although our background models extend from 80 to 700 km, the computations of the overhead and limb intensities of the N2 band systems extend from 80 to 300 km.
 We have adopted the solar photon fluxes from 1 to 2000 Å from the Solar 2000 v1.24 models of Tobiska [2004, and private communication] in “Hinteregger” format, that is, at 1 Å intervals in the continuum and as delta functions at the strong solar lines. For the low solar activity model, we have adopted the solar fluxes for day 200 of 1976, when the F10.7 parameter was 70; for the high solar activity model, we have adopted the solar fluxes for day 178 of 1999, when the F10.7 parameter was 214. The solar zenith angle is assumed to be 60°.
 Using these models, we have computed the electron-impact excitation rates of the following states of N2: , B3Πg, W3Δu, , C3Πu, , , a1Πg, , and w1Δu. We have adopted most of the electron-impact excitation cross-sections from the critical compilation of Itikawa . For the state, we have adopted the cross-sections from Filipelli et al. . We have assumed that the vibrational levels of the excited states are populated by electron impact in proportion to the Franck-Condon factors between the ground vibrational levels and the (v′) levels of the excited states. We have adopted the Franck-Condon factors reported by Gilmore et al. . We have further assumed that the vibrational levels of the N2 ground state are thermally distributed with a temperature of 1000 K. At sufficiently high altitudes, the vibrational levels of the ground state are probably not in local thermodynamic equilibrium, and this assumption is a possible source of uncertainty in the model.
 We have computed the energies of the vibrational levels using the vibrational constants of Laher and Gilmore . We have included vibrational levels from v=0 to v=21 for the X, A, B, B′, W, a, and a′ states, from v=0 to v=15 for the wstate, from v=0 to v=4 of the C state, two levels (v=0,1) of the Estate, and one level (v=0) for the D state. None of the vibrational levels that we include here, except for the D(v=0) state at 12.84 eV and the a(v=21) state at 12.175 eV, is above the N2 predissociation threshold of 12.14 eV. States with energies higher than this value are assumed to be predissociated.
 For the transitions among the states, we have adopted the Einstein A factors and the wavelengths of the band origins from Gilmore et al. . In addition to the VK bands, we have included the following transitions among the N2 triplet states: the (B−A) first positive bands, the (A−B) reverse first positive bands, the (B′−B) bands, the reverse (B−B′) bands, the (W−B) Wu-Benesch bands, the reverse (B−W) bands, the (C−B) second positive bands, the (D−B) fourth positive v′=0 progression, the (E−A) Herman-Kaplan bands, the (E−C) bands, and the (E−B) bands. In the singlet manifold, we have included only transitions involving the first three states that are connected to the ground state by dipole forbidden transitions: the (a−X) Lyman-Birge-Hopfield (LBH) bands, the (a−a′) bands, the reverse (a′−a) bands, the (w−a) bands, and the reverse (a−w) bands. Since the v=0 level of the a′state is the lowest level of the excited singlet states, we have included, as a loss process for this state, the (0,0) band of the Ogawa-Tanaka-Wilkinson-Mulligan (a′−X) system, with a transition probability of 10 s−1 [e.g., Golde, 1975]. The results of this study are not sensitive to the A value assigned to this transition.
 Only the VK and LBH bands are found in the ultraviolet. The second positive bands range from the near UV to the visible; the first positive and Wu-Benesch bands are in the infrared, but they are important in populating the A state by cascading. The E−A, E−B, and E−C bands range from the near UV to the infrared, but the intensities are small, as are those for the v′=0 progression of the D−B bands, which also appears in the near UV. The a−a′and w−abands are in the visible to infrared, and they are found to play a minor role in determining the intensities of the LBH bands.
 The state is metastable with a lifetime against radiation of about 2 s for vibrational levels v′=0–8, and quenching by background species in the atmosphere of Mars is possible. The calculations of FD79 did not include this process because the rate coefficients for quenching of N2(A) by CO2 are small, of the order of 2×10−14 cm3 s−1for the first vibrational level. By contrast, quenching by O is efficient, with coefficients that increase from 2.8×10−11 to 7.5×10−11 cm3 s−1as the vibrational level increases from v=0 to v=7. The small quenching coefficients for CO2 are interpreted as evidence for the presence of a reaction barrier in the quenching process [Herron, 1999]. Since vibrational energy can be used at least partly to overcome this barrier, the quenching coefficients for N2(A) by CO2 (and other species) are found to increase with increasing vibrational level. We have adopted the recommended quenching coefficients from the critical compilation of Herron . We include here quenching by CO2, O, O2, NO, CO, N2, H2, and H, and we have assumed that the relaxation process is electronic rather than vibrational.
 The background thermosphere models include vertical diffusion, but the calculations of the densities of the N2 excited states assume photochemical equilibrium. We find that this is a valid approximation up to at least 250 km, by comparing the time constants against radiation to those for transport for the longest-lived species. Of the N2 excited states that we consider here, those with the longest lifetime against radiation are the first eight vibrational levels of the metastable A(v′) state, for which the lifetime is in the range ∼2–2.4 s. The value for the binary diffusion coefficient Db of the N2(A) state through the ground N2(X) state has been measured several times. Haydon et al.  showed that values of Db at ∼300 K measured by a number of investigators differ only slightly from each other and from that of the self-diffusion coefficient Ds of N2. Boushehri et al.  computed the temperature dependent self-diffusion coefficients of N2. From their values of Ds for N2 at 200 and 300 K, we derive a fit to the usual expression Ds=A′Ts/n cm2 s−1, where T is the ambient temperature in Kelvins and n is the total number density of N2 in cm−3. We find that a′ is ∼6.4×1016 and s is ∼0.77. The binary diffusion coefficients of ground state N2 through CO2 and O are similar: a′is ∼4×1016 and s is ∼0.8 for N2 diffusion through CO2 [e.g., Bzowski et al., 1990]; a′ is in the range (7.8−9.6)×1016 and sis in the range (0.77−0.81) for N2 diffusion through O [e.g., Morgan and Schiff, 1964; Banks and Kockarts, 1973]. One would expect that the binary diffusion coefficient of an excited state would be somewhat smaller than that of the ground state. If so, the average value of the binary diffusion coefficient Db of the N2(A;v′) states through the species in the Mars atmosphere should be ∼5×1016T0.8/n cm2 s−1, to within a factor of ∼2. The diffusion lifetime is usually approximated as τD=H2/Db, where H is the atmospheric scale height. The value of τD in the low solar activity model in the range 220–250 km minimizes at about 20 s. This is much longer than the time constant against radiation of all the excited states that we consider here. Thus, photochemical equilibrium appears to be a fairly good approximation up to quite high altitudes.
 In Table 1, we list the overhead integrated total production rates of the various N2 states for the low and high solar activity models, compared to those computed by FD79, and those for the A, B, W, B′, and Cstates computed with the present low solar activity atmospheric model using the electron-impact cross-sections for N2 recommended by Majeed and Strickland . We find that there are major differences between the production rates using the latter cross-sections only for the W and C states. The ratio of the production rates computed with the cross-sections of Itikawa  to those computed with the cross-sections of Majeed and Strickland  are 0.7 and 1.4 for the W and C states, respectively. According to Itikawa , however, the accuracy of the recommended cross-sections is in the range 30–40%, so the difference is not significant.
Table 1. Integrated Production Rates of Various States of N2(106 cm−2 s−1)
From Fox and Dalgarno  for Viking conditions, that is, very low solar activity.
Computed with the cross-sections recommended by Majeed and Strickland .
 In Table 2, we present the total integrated overhead intensities for the 15 band systems that we model. Although we state the predicted intensities to two significant figures, the accuracy of the modeled emissions is limited by the accuracy of the electron-impact cross-sections, that is, to ∼35%. Although the LBH bands are in the FUV, we have not included absorption by CO2 in the integrated intensities presented in Table 2. We have included absorption by CO2 in the calculations of the intensities only for the most important LBH bands: those that originate from v′=0−5 of the a1Πg state and emit to v′′=0−5 of the ground state. The total integrated overhead intensity of this subset of bands at low solar activity is 30 R including absorption, and 31 R without absorption; at high solar activity, the total intensity is 83 R including absorption and 86.5 R without absorption.
Table 2. Predicted Total Integrated Overhead Intensities of Band Systems of N2(R)
 The predicted integrated overhead intensities of the most intense bands of the VK, First Positive, Wu-Benesch, and Second Positive Bands for the low and high solar activity models are reported in Table 3, along with those of FD79. For the low solar activity model, the most intense bands of the VK system are the (0,5), (0,6), and (0,7) bands, for which the low solar activity predicted intensities are 6 R, 8 R, and 8 R, while FD79 predicted intensities of 16 R, 20 R, and 20 R, respectively. At high solar activity, our predicted values for all the bands are larger by factors of ∼2.7–2.8 than those for low solar activity. This ratio is in very good agreement with that of 2.8 predicted by Leblanc et al.  for the F10.7 range of 70 to 210. The present computed intensities at low solar activity are smaller by factors of 2.5–2.6 than those predicted by FD79 and are in substantial agreement with the SPICAM measured values [Leblanc et al., 2007]. The ratio of the measured VK (0,6) to (0,5) limb intensity between 120 and 170 km is reported as 0.9±0.3, in fairly good agreement with our computed overhead intensity ratio of ∼1.27, which is equal to the ratio of the adopted transition probabilities for the two emissions. The VK (0,7) band is predicted to have about the same intensity as the (0,6) band, and, although it was marginally detected, its intensity could not be ascertained reliably. The VK (0,7) band origin lies at about 2937 Å, which is between the ultraviolet doublet at 2883 and 2896 Å, and the O(1S)→O(3P) line at 2972 Å.
Table 3. Computed Overhead Intensities of N2 Emission Bands
Fox and Dalgarno , for very low solar activity.
Wu-Benesch W3Δu→B3Πg xx-xx
Second Positive C3Πu→B3Πg xx-xx
 We have computed the limb profiles for the VK (0,5), (0,6), and (0,7) bands numerically, and the results are shown in Figure 1 for both the low and the high solar activity models. The predicted maximum limb intensities appear at 124 km for the low solar activity model with values of 114, 145, and 138 R for the (0,5), (0,6), and (0,7) VK bands, respectively; for the high solar activity model, the limb intensities peak near 129 km, with values of 270, 344, and 327 R, respectively. Our computed Ilimb/Inadir ratio is a factor of 16–18. The measured limb profiles are noisy, with an estimate for the maximum limb intensity of 180 R for solar zenith angles near 45° for the VK(0,6) band [Leblanc et al., 2007]. Using our computed factor of 18 for the maximum limb to nadir ratio, we obtain a value of 10 R for the nadir intensity of the VK (0,6) band, as measured by SPICAM. Our model predictions for this intensity as shown in Table 3are 8 R at very low solar activity and 22 R at high solar activity.
 The intensities in all the bands of the triplet and singlet systems are smaller than those predicted by FD79. For example, the predicted intensities of the first positive bands presented in Table 3 are a factor of ∼2.4–2.8 smaller than those of FD79. The Wu-Benesch bands are factors of about 10 smaller. This could partially be explained if FD79 included a smaller number of vibrational levels of the W state in their calculation. The total intensity of this band system is spread out over a large number of bands because the Franck-Condon factors between the N2X(v″=0) ground state and the N2W(v′) levels maximize between v′=7 and v′=8 with values of about 0.1 and fall off slowly for smaller and larger values of v′.
 In Table 4, we present the predicted intensities of the most intense LBH bands and the (a′−a) and (w−a) bands. The latter two transitions play minor roles in determining the intensities of the LBH bands. The predicted integrated overhead intensities of the LBH bands shown in this table do include absorption by the CO2 layer above the emitting altitudes. The intensities are smaller than those presented by FD79 by factors of 1.3–1.6. The reason for the difference is not apparent. FD79 did include absorption by CO2 in determining the LBH intensities but did not include the a′or w singlet states in the calculation. In any case, even the most intense of the LBH bands are predicted to be too faint to be observed, especially at low solar activity.
Table 4. Integrated Overhead Intensities of N2 Emission Features
 The differences between the predicted intensities of the bands of FD79 and the present results is not obvious, and, since the original documentation of the calculation is not available, a comparison of all the relevant effects is not possible. FD79 employed the cross-sections of Cartwright et al.  for the triplet states. A comparison of the cross-sections from the latter source to those used here shows that the peak values of the cross-sections that we use are substantially smaller only for the Wstate. The shapes of the excitation functions are, however, significantly different, with the current adopted cross-sections peaking at different energies and falling off faster with increasing energy.
 Although we include electronic quenching of the A(v′) levels in the current calculation, the effect is small for the v=0 level. The quenching altitude for both the high and low solar activity models is about 100 km for this vibrational level. Including quenching decreases the integrated overhead intensities of the VK bands originating in v′=0 by about 10%, but it decreases the total intensities in the band system by ∼20%. FD79 did not include quenching in their calculation.
 The Mars nitrogen VK band intensities have also been modeled recently by Jain and Bhardwaj . Their computed intensities for all the bands are significantly larger than ours. For Viking conditions, they predict intensities of 21, 26, and 25 R for the VK (0,5), (0,6), and (0,7) bands, respectively; for their solar maximum model, they predict 52, 66, and 63 R, respectively, for the same VK bands. The difference between their calculations and ours is difficult to understand. They employ the same cross-sections, those of Itikawa , but fit them to an analytical functional form. The assumption of a solar zenith angle (SZA) of 45° should not produce significantly different results from those of our assumed SZA of 60°. They include only five species, CO2, N2, O, CO, and O2, compared to our 12 species model. The additional seven species are, however, relatively minor. Other characteristics of their models are not readily comparable to ours. Jain and Bhardwaj  assert that their results indicate that the N2 mixing ratio in the Martian thermosphere should be reduced by a factor of ∼3 to 1.1–1.4% at 120 km. Leblanc et al.  suggest that the differences between the SPICAM measured intensities and those predicted by FD79 are due to modifications to the molecular data and parameters used in the latter study.
 The mixing ratios of N2 at the lowest altitude of our low and high solar activity models, 80 km, are about 2.6%, equal to that measured in the lower thermosphere by the Viking neutral mass spectrometer [e.g., Nier and McElroy, 1977]. At 120 km, the mixing ratios of N2 are 3.0% and 2.6% for our low and high solar activity models, respectively. The mass spectrometer on the first Viking lander measured a mixing ratio for N2 of 2.7% at the surface [e.g., Owen et al., 1977].
 We have predicted the integrated overhead (nadir) intensities of 15 band systems of electron-excited N2 in the Martian thermosphere. The results for specific bands are smaller than those of FD79 by factors in the range ∼1.4–10. Our predicted nadir intensities of the (0,5) and (0,6) Vegard-Kaplan bands are 6 and 8 R, respectively. These values are smaller than those of FD79 by factors of 2.5–2.7. The maximum limb intensities of these two bands are 114 and 145 R, in substantial agreement with those measured at slightly higher solar activity by the SPICAM on MEX [Leblanc et al., 2007]. Jain and Bhardwaj  modeled the emission rates of the VK bands and found values that are in agreement with FD79 and are substantially larger than the present results. They also concluded that the Viking N2 mixing ratio should be reduced by a factor of 3. Our predicted intensities of the VK (0,5) and (0,6) bands in the current model are consistent with the measured intensities and do not require substantial modification of the N2 mixing ratio. Recently, the N2 mixing ratio in the Martian lower atmosphere has been measured by the Sample Analysis at Mars (SAM) quadrupole mass spectrometer on Curiosity [Mahaffy et al., 2013], and a mixing ratio of N2 at the surface of 1.89% was reported, which, if applicable to the thermosphere, would reduce the predicted emission intensities by about 25%. Since the uncertainties in the intensities are in the range 35–40%, our computed intensities could accommodate such a reduction but do not require it.
 This work has been supported by grant NNX09AB70G from the National Aeronautic and Space Administration to Wright State University. The Solar 2000 research grade irradiances are provided courtesy of W. Kent Tobiska and SpaceWx.com. These historical irradiances have been developed with funding from the NASA UARS, TIMED, and SOHO missions.
 The Editor thanks Francois Leblanc and an anonymous reviewer for their assistance in evaluating this paper.