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Production of N2 Vegard–Kaplan and other triplet band emissions in the dayglow of Titan

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Production of N 2 Vegard–Kaplan and other triplet band emissions in the dayglow of Titan Anil Bhardwaj ⇑ , Sonal Kumar Jain Space Physics Laboratory, Vikram Sarabhai Space Centre, Trivandrum 695 022, India article info Article history: Received 1 August 2011 Revised 12 January 2012 Accepted 24 January 2012 Available online 9 February 2012 Keywords: Titan Ultraviolet observations Aeronomy abstract Recently the Cassini Ultraviolet Imaging Spectrograph (UVIS) has revealed the presence of N 2 Vegard– Kaplan (VK) band A 3 R þ u X 1 R þ g emissions in Titan’s dayglow limb observation. We present model cal- culations for the production of various N 2 triplet states (viz., A 3 R þ u ; B 3 P g ; C 3 P u ; E 3 R u ; W 3 D u , and B 3 R u ) in the upper atmosphere of Titan. The Analytical Yield Spectra technique is used to calculate steady state photoelectron fluxes in Titan’s atmosphere, which are in agreement with those observed by the Cassini’s CAPS instrument. Considering direct electron impact excitation, inter-state cascading, and quenching effects, the population of different levels of N 2 triplet states are calculated under statistical equilibrium. Densities of all vibrational levels of each triplet state and volume production rates for various triplet states are calculated in the model. Vertically integrated overhead intensities for the same date and light- ing conditions as reported by the UVIS observations for N 2 Vegard–Kaplan A 3 R þ u X 1 R þ g , First Positive B 3 P g A 3 R þ u , Second Positive (C 3 P u B 3 P g ), Wu–Benesch (W 3 D u B 3 P g ), and Reverse First Positive bands of N 2 are found to be 132, 114, 19, 22, and 22 R, respectively. Overhead intensities are calculated for each vibrational transition of all the triplet band emissions of N 2 , which span a wider spectrum of wavelengths from ultraviolet to infrared. The calculated limb intensities of total and prominent transi- tions of VK band are presented. The model limb intensity of VK emission within the 150–190 nm wave- length region is in good agreement with the Cassini UVIS observed limb profile. An assessment of the impact of solar EUV flux on the N 2 triplet band emission intensity has been made by using three different solar flux models, viz., Solar EUV Experiment (SEE), SOLAR2000 (S2K) model of Tobiska (Tobiska, W.K. [2004]. Adv. Space Res. 34, 1736–1746), and HEUVAC model of Richards et al. (Richards, P.G., Woods, T.N., Peterson, W.K. [2006]. Adv. Space Res. 37 (2), 315–322). The calculated N 2 VK band intensity at the peak of limb intensity due to S2K and HEUVAC solar flux models is a factor of 1.2 and 0.9, respectively, of that obtained using SEE solar EUV flux. The effects of higher N 2 density and solar zenith angle on the emission intensity are also studied. The model predicted N 2 triplet band intensities during moderate (F10.7 = 150) and high (F10.7 = 240) solar activity conditions, using SEE solar EUV flux, are a factor of 2 and 2.8, respectively, higher than those during solar minimum (F10.7 = 68) condition. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction The saturnian satellite Titan, the second biggest satellite in the Solar System, is in many ways the closest analogue to Earth. Like Earth, Titan’s atmosphere is dominated by N 2 . Hence, it is natural to expect that Titan’s airglow will be dominated by emissions of N 2 and its dissociation product N. In addition to N 2 , Titan also contains a few percent CH 4 in its atmosphere, with a mixing ratio of about 3% near 1000 km altitude (De La Haye et al., 2007; Strobel et al., 2009). The Voyager 1 Ultraviolet Spectrometer (UVS) provided the first ultraviolet (UV) airglow observation of Titan in the 53–170 nm band (Broadfoot et al., 1981). The extreme ultraviolet spectrum was dominated by emissions near 95–99 nm, which were attributed to N 2 Carroll–Yoshino (CY) c 01 4 R þ u X 1 R þ g (0, 0) and (0, 1) Rydberg bands (Strobel and Shemansky, 1982). Far ultraviolet emissions present were LBH bands of N 2 , and N and N + lines (Broadfoot et al., 1981; Strobel and Shemansky, 1982). By employ- ing multiple scattering model for CY band emissions, Stevens (2001) showed that CY (0–0) should be weak and undetectable, while CY (0–1) should be prominent emission at 981 nm and the features at 950 nm are N I lines. Thus, there is no need to invoke magnetospheric electron impact excitation (Stevens, 2001). After Voyager UVS, Cassini Ultraviolet Imaging Spectrograph (UVIS) provided the next observation of Titan’s airglow in the extreme ultraviolet (EUV, 56.1–118.2 nm) and far ultraviolet (FUV, 115.5–191.3 nm) wavelengths (Ajello et al., 2007, 2008). 0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2012.01.019 ⇑ Corresponding author. Fax: +91 471 2706535. E-mail addresses: [email protected], [email protected] (A. Bhardwaj), [email protected] (S.K. Jain). Icarus 218 (2012) 989–1005 Contents lists available at SciVerse ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus
Transcript

  • er

    Anil Bhardwaj , Sonal Kumar JainSpace Physics Laboratory, Vikram Sarabhai Space Centre

    a r t i c l e i n f o

    Article history:Received 1 August 2011Revised 12 January 2012Accepted 24 January 2012Available online 9 February 2012

    Keywords:TitanUltraviolet observationsAeronomy

    Earth, Titans atmosphere is dominated by N2. Hence, it is naturalto expect that Titans airglow will be dominated by emissions of N2and its dissociation product N. In addition to N2, Titan also containsa few percent CH4 in its atmosphere, with amixing ratio of about 3%near 1000 km altitude (De La Haye et al., 2007; Strobel et al., 2009).

    The Voyager 1 Ultraviolet Spectrometer (UVS) provided the rstultraviolet (UV) airglow observation of Titan in the 53170 nm

    emissions present were LBH bands of N2, and N and N lines(Broadfoot et al., 1981; Strobel and Shemansky, 1982). By employ-ing multiple scattering model for CY band emissions, Stevens(2001) showed that CY (00) should be weak and undetectable,while CY (01) should be prominent emission at 981 nm and thefeatures at 950 nm are N I lines. Thus, there is no need to invokemagnetospheric electron impact excitation (Stevens, 2001).

    After Voyager UVS, Cassini Ultraviolet Imaging Spectrograph(UVIS) provided the next observation of Titans airglow in theextreme ultraviolet (EUV, 56.1118.2 nm) and far ultraviolet(FUV, 115.5191.3 nm) wavelengths (Ajello et al., 2007, 2008).

    Corresponding author. Fax: +91 471 2706535.E-mail addresses: [email protected], [email protected]

    Icarus 218 (2012) 9891005

    Contents lists available at

    ru

    .e l(A. Bhardwaj), [email protected] (S.K. Jain).emission intensity are also studied. The model predicted N2 triplet band intensities during moderate(F10.7 = 150) and high (F10.7 = 240) solar activity conditions, using SEE solar EUV ux, are a factor of 2and 2.8, respectively, higher than those during solar minimum (F10.7 = 68) condition.

    2012 Elsevier Inc. All rights reserved.

    1. Introduction

    The saturnian satellite Titan, the second biggest satellite in theSolar System, is in many ways the closest analogue to Earth. Like

    band (Broadfoot et al., 1981). The extreme ultraviolet spectrumwas dominated by emissions near 9599 nm, which wereattributed to N2 CarrollYoshino (CY) c014 R

    u X1Rg (0,0) and

    (0,1) Rydberg bands (Strobel and Shemansky, 1982). Far ultraviolet+0019-1035/$ - see front matter 2012 Elsevier Inc. Adoi:10.1016/j.icarus.2012.01.019, Trivandrum 695 022, India

    a b s t r a c t

    Recently the Cassini Ultraviolet Imaging Spectrograph (UVIS) has revealed the presence of N2 Vegard

    Kaplan (VK) band A3Ru X1Rg

    emissions in Titans dayglow limb observation. We present model cal-

    culations for the production of various N2 triplet states (viz., A3Ru ; B

    3Pg ; C3Pu; E

    3Ru; W3Du , and B3Ru )

    in the upper atmosphere of Titan. The Analytical Yield Spectra technique is used to calculate steady statephotoelectron uxes in Titans atmosphere, which are in agreement with those observed by the CassinisCAPS instrument. Considering direct electron impact excitation, inter-state cascading, and quenchingeffects, the population of different levels of N2 triplet states are calculated under statistical equilibrium.Densities of all vibrational levels of each triplet state and volume production rates for various tripletstates are calculated in the model. Vertically integrated overhead intensities for the same date and light-

    ing conditions as reported by the UVIS observations for N2 VegardKaplan A3Ru X1Rg

    , First Positive

    B3Pg A3Ru

    , Second Positive (C3Pu B3Pg), WuBenesch (W3Du B3Pg), and Reverse First Positivebands of N2 are found to be 132, 114, 19, 22, and 22 R, respectively. Overhead intensities are calculatedfor each vibrational transition of all the triplet band emissions of N2, which span a wider spectrum ofwavelengths from ultraviolet to infrared. The calculated limb intensities of total and prominent transi-tions of VK band are presented. The model limb intensity of VK emission within the 150190 nm wave-length region is in good agreement with the Cassini UVIS observed limb prole. An assessment of theimpact of solar EUV ux on the N2 triplet band emission intensity has been made by using three differentsolar ux models, viz., Solar EUV Experiment (SEE), SOLAR2000 (S2K) model of Tobiska (Tobiska, W.K.[2004]. Adv. Space Res. 34, 17361746), and HEUVAC model of Richards et al. (Richards, P.G., Woods,T.N., Peterson, W.K. [2006]. Adv. Space Res. 37 (2), 315322). The calculated N2 VK band intensity atthe peak of limb intensity due to S2K and HEUVAC solar ux models is a factor of 1.2 and 0.9, respectively,of that obtained using SEE solar EUV ux. The effects of higher N2 density and solar zenith angle on theProduction of N2 VegardKaplan and othof Titan

    Ica

    journal homepage: wwwll rights reserved.triplet band emissions in the dayglow

    SciVerse ScienceDirect

    s

    sevier .com/locate / icarus

  • aru990 A. Bhardwaj, S.K. Jain / IcThese disk observations of Titan on 13 December 2004 showed thepresence of N2 LBH bands, atomic multiplets of NI and N+ lines, andfeatures at 156.1 and 165.7 nm reportedly from CI (Ajello et al.,2008). Recently, limb observation of Titan by UVIS obtained on22 June 2009 has revealed the presence of N2 VegardKaplan(VK) A3Ru X1Rg

    bands in the FUV spectrum (Stevens et al.,

    Fig. 1. Comparison of SEE, S2K, and HEUVAC solar EUV ux models on 23 June 2009at 1 AU. (top) SEE solar EUV ux compared with S2K. (bottom) SEE solar EUV uxcomparison with HEUVAC. The ratio of solar EUV uxes is also shown withmagnitude on right side Y-axis. Thin solid horizontal line depicts the S2K/SEE andHEUVAC/SEE solar ux ratio = 1.

    Fig. 2. Calculated photoelectron production spectrum at 1100 and 900 km atSZA = 60 using SEE solar EUV ux on 23 June 2009.s 218 (2012) 98910052011). Also, no CI emissions are reported to be observed. Stevenset al. (2011) showed that model emissions in the 150190 nmVK band are consistent with UVIS observations.

    The N2 VK bands are a common feature in N2 atmospheres andhave been studied extensively on Earth (e.g., Cartwright, 1978;Meier, 1991; Broadfoot et al., 1997). The N2 VK bands have beenobserved recently on Mars by SPICAM aboard Mars Express(Leblanc et al., 2006, 2007; Jain and Bhardwaj, 2011). These

    Fig. 3. (top panel) Model calculated photoelectron ux at 1100 km using SEE,SOLAR2000 (S2K), and HEUVAC solar ux models. (bottom panel) Comparison ofmodel calculated photoelectron uxes using SEE solar EUV ux at 800, 900, and1100 km with those of Stevens et al. (2011).

    Fig. 4. Model calculated photoelectron ux on 5 January 2008 at an altitude of1100 km obtained by using SEE solar EUV ux compared with the Cassini CAPSobservation taken from Lavvas et al. (2011).

  • which has a wide spectral range 3005100 nm (Brown et al.,2004) and Imagining Science Subsystem (ISS, 2501100 nm) (Porcoet al., 2004), might be able to detect some of the bright emissionsof N2 triplet bands in the MUV, visible, and infrared wavelengthspredicted by our model. The model calculations presented in thepaper would also be useful for any N2-containing planetaryatmospheres.

    2. Model input

    The N2 density prole in our model is based on the observationmade by Huygens Atmospheric Structure Instrument (HASI) on-board Huygens probe (Fulchignoni et al., 2005). Following the ap-proach of Stevens et al. (2011), the density of N2 is reduced by afactor of 3.1 to bring the HASI N2 density at 950 km to the levelof measured density by Ion and Neutral Mass Spectrometer (INMS)(De La Haye et al., 2007) aboard the Cassini spacecraft. Since reduc-tion in N2 density affects the altitude of peak production of N2 trip-let bands, the effect of higher N2 density on emission intensities is

    Fig. 5. Calculated volume production rate of different triplet states of N2 due to

    A. Bhardwaj, S.K. Jain / Icarus 218 (2012) 9891005 991emission can also be observed on Venus by SPICAV onboard VenusExpress (Bhardwaj and Jain, 2012), but the bright sunlit limbcauses a problem in resolving the dayglow emission from scatteredlight from clouds.

    This paper presents a detailed model calculation for the produc-tion of N2 triplet band emissions on Titan, including the recentlyobserved N2 VK bands. The model includes interstate cascadingand quenching, and uses the Analytical Yield Spectra approachfor the calculation of electron impact excitation of triplet bands,and is similar to the model used for studying the N2 triplet emis-sions on Mars (Jain and Bhardwaj, 2011) and Venus (Bhardwajand Jain, 2012). We also present the overhead emission intensitiesof triplet bands, which lie in ultraviolet, visible, and infrared wave-lengths. The calculated limb prole of N2 VK 150190 nm emissionis compared with the Cassini UVIS observation. Impact on theintensity of N2 triplet emissions due to changes in the solar EUVux model, solar activity, and Titans N2 density are discussed.

    The N2 triplet band emissions span a wide spectrum of electro-magnetic radiation covering EUVFUVMUV, visible, and infrared(Jain and Bhardwaj, 2011; Bhardwaj and Jain, 2012). Major emis-sions in N2 VK band lie in the wavelength range 200400 nm,and a few signicant emissions in the visible. N2 triplet First Posi-tive (B? A), WuBenesch (W? B), and B0 ? B bands have promi-nent emissions in the infrared region. Thus, beside observations

    photoelectron impact at SZA = 60 for SEE solar EUV ux.of Titans dayglow by the Cassini UVIS in EUV and FUV region,the Cassini Visual and Infrared Mapping Spectrometer (VIMS),

    Fig. 6. Calculated relative vibrational population of the various triplet states of N2at an altitude of 1100 km at SZA = 60 using SEE solar ux.discussed in Section 4.3. Density of CH4 in our model is based onthe UVIS stellar occultation experiment reported by Shemanskyet al. (2005).

    Photoabsorption and photoionization cross sections of N2 andCH4 are taken from photo-cross sections and rate coefcients data-base (http://amop.space.swri.edu) (Huebner et al., 1992). Thebranching ratios for excited states of N2 and CH

    4 are taken from

    Avakyan et al. (1998). FranckCondon factors and transition proba-bilities required for calculating the intensity of a specicband m0 m00of N2 are taken fromGilmore et al. (1992). Inelastic cross sections forthe electron impact on N2 are taken from Jackman et al. (1977),except for the triplet states, which are taken from Itikawa (2006),and tted analytically for ease of usage in the model (Jackmanet al., 1977; Bhardwaj and Jain, 2009, 2012; Jain and Bhardwaj,2011). The tted parameters are given in Jain and Bhardwaj (2011).

    The solar EUV ux is a crucial input required in modelling theupper atmospheric dayglow emissions. The solar EUV ux directlycontrols the photoelectron production rate, and hence the intensityof emission in the planetary atmosphere that is produced by elec-tron impact excitation, like N2 triplet band emissions, since alltransitions between the triplet states of N2 and the ground stateare spin forbidden. We have used the solar irradiance measuredat Earth (between 2.5 and 120.5 nm) by Solar EUV Experiment(SEE, Version 10.2) (Woods et al., 2005; Lean et al., 2011) on 23

    Fig. 7. Volume emission rate of total N2 VK band along with the emission rates ofVK band in different wavelength regions calculated using SEE solar ux model atSZA = 60. N2 VK band emission rate of 130150 nm band is plotted after

    multiplying by a factor of 50. Emission rate proles for SOLAR2000 (S2K) andHEUVAC model solar uxes and in solar maximum condition (for SEE solar EUVux) are also shown.

  • June 2009 (F10.7 = 68) at 1 nm spectral resolution. The solar uxhas been scaled to the SunTitan distance (9.57 AU) to accountfor the weaker ux on Titan. To evaluate the impact of solar EUVux model on emission intensities we have also used solar EUVux from SOLAR2000 (S2K) v.2.36 model of Tobiska (2004) andHEUVAC solar EUV ux model of Richards et al. (2006) for the same

    Fig. 1 (bottom panel) shows the comparison of SEE solar EUVux with the solar ux calculated using HEUVAC model, with boththe daily F10.7 and the F10.781 days average values set to 68 (inunits of 1022 Wm2 Hz1 ), conditions appropriate for the date ofthe UVIS limb observations reported by Stevens et al. (2011). Sincethe HEUVAC model provides solar ux up to 105 nm only, the uxin the 105120.5 nm range is assumed the same as that in the SEEmodel. Since the solar ux at higher (>105 nm) wavelengths doesnot contribute to the photoelectron production, the inclusion ofSEE solar ux in the HEUVAC model at wavelengths higher than105 nm would not affect our calculation results. At wavelengthabove 30 nm HEUVAC solar uxes are smaller than those of SEEmodel, but at shorter (

  • Table 2Overhead intensities (in R) of N2 VegardKaplan A3Ru ! X1Rg band.

    m0 m00

    0 1 2 3 4 5 6 7 8 9

    0 1.4E5 1.9E2 2.5E1 1.2E+0 3.2E+0 5.6E+0 7.1E+0 6.8E+0 5.0E+0 2.9E+0(2010) (2109) (2216) (2334) (2463) (2605) (2762) (2937) (3133) (3354)

    1 3.1E3 1.1E2 2.8E1 1.1E+0 1.5E+0 7.9E1 1.7E7 1.2E+0 4.1E+0 6.0E+0(1954) (2047) (2148) (2258) (2379) (2511) (2657) (2819) (2998) (3200)

    2 3.2E2 3.0E3 9.1E2 2.8E1 7.4E2 2.0E1 1.3E+0 1.7E+0 5.3E1 1.2E1(1901) (1990) (2085) (2189) (2302) (2425) (2561) (2711) (2877) (3062)

    3 1.1E1 6.2E2 2.5E3 1.3E2 6.4E2 4.8E1 4.4E1 8.7E8 7.1E1 1.5E+0(1853) (1936) (2027) (2125) (2231) (2347) (2474) (2614) (2768) (2938)

    4 2.5E1 1.6E1 6.7E3 1.9E3 9.0E2 1.3E1 4.1E3 4.1E1 5.4E1 2.4E2(1808) (1887) (1973) (2065) (2166) (2275) (2394) (2524) (2668) (2826)

    5 4.3E1 2.3E1 5.7E3 1.8E4 2.4E2 5.2E4 1.3E1 2.2E1 1.3E4 3.6E1(1765) (1841) (1923) (2011) (2106) (2209) (2321) (2443) (2577) (2724)

    6 6.9E1 2.4E1 9.4E4 7.8E3 5.6E4 1.7E2 9.5E2 4.3E3 1.8E1 2.6E1(1726) (1798) (1876) (1960) (2050) (2147) (2253) (2368) (2494) (2632)

    7 1.1E+0 1.9E1 4.2E2 3.2E2 2.5E4 1.5E2 1.5E2 4.8E2 1.7E1 1.1E3(1689) (1758) (1833) (1912) (1998) (2090) (2191) (2299) (2418) (2547)

    8 1.0E+0 6.2E2 1.1E1 2.7E2 1.2E3 8.0E4 8.5E4 5.0E2 1.4E2 7.8E2(1655) (1721) (1792) (1868) (1950) (2038) (2133) (2236) (2347) (2469)

    9 5.9E1 2.7E3 9.6E2 4.7E3 7.2E3 3.1E4 1.9E3 8.4E3 4.2E3 4.5E2(1622) (1686) (1754) (1827) (1905) (1989) (2079) (2177) (2283) (2398)

    10 2.6E1 3.2E3 5.0E2 1.4E4 7.6E3 6.4E5 1.1E4 1.1E4 5.7E3 4.5E3(1592) (1653) (1718) (1788) (1863) (1943) (2030) (2122) (2223) (2332)

    11 1.2E1 9.3E3 2.0E2 2.7E3 4.1E3 1.7E4 7.8E5 7.4E5 1.5E3 3.8E5(1563) (1622) (1685) (1752) (1824) (1901) (1983) (2072) (2168) (2271)

    12 5.6E2 1.2E2 7.3E3 4.4E3 1.4E3 7.2E4 1.2E4 1.5E5 1.2E4 5.4E4(1536) (1593) (1654) (1719) (1788) (1861) (1940) (2025) (2116) (2215)

    13 2.7E2 1.0E2 1.8E3 4.0E3 1.7E4 8.9E4 1.8E5 1.2E5 3.1E7 2.9E4(1511) (1566) (1625) (1687) (1754) (1824) (1900) (1981) (2069) (2163)

    14 1.3E2 7.9E3 2.1E4 2.8E3 1.6E5 6.6E4 1.4E5 4.6E5 2.7E6 5.3E5(1487) (1541) (1597) (1658) (1722) (1790) (1863) (1941) (2024) (2114)

    15 6.7E3 5.7E3 8.5E6 1.7E3 2.0E4 3.4E4 8.7E5 3.5E5 7.1E7 1.8E6(1465) (1517) (1572) (1630) (1692) (1758) (1828) (1903) (1983) (2070)

    16 3.4E3 3.9E3 1.7E4 8.3E4 3.4E4 1.1E4 1.3E4 8.2E6 9.5E6 3.8E7(1444) (1494) (1548) (1604) (1664) (1728) (1796) (1868) (1945) (2028)

    17 1.8E3 2.6E3 3.3E4 3.4E4 3.6E4 1.5E5 1.3E4 2.2E7 1.5E5 4.7E8(1425) (1473) (1525) (1580) (1638) (1700) (1765) (1835) (1910) (1990)

    18 9.5E4 1.7E3 4.0E4 1.1E4 3.0E4 1.3E6 9.0E5 9.3E6 1.1E5 8.0E7(1406) (1454) (1504) (1557) (1614) (1674) (1737) (1805) (1877) (1954)

    19 5.1E4 1.1E3 4.0E4 2.0E5 2.1E4 1.9E5 4.6E5 2.0E5 4.3E6 3.1E6(1389) (1435) (1484) (1536) (1591) (1649) (1711) (1777) (1846) (1921)

    20 2.8E4 6.9E4 3.6E4 5.0E8 1.4E4 3.8E5 1.8E5 2.5E5 4.1E7 4.5E6(1373) (1418) (1466) (1517) (1570) (1627) (1687) (1750) (1818) (1890)

    10 11 12 13 14 15 16 17 18 19 20

    0 1.4E+0 5.3E1 1.6E1 4.1E2 8.5E3 1.4E3 1.9E4 2.0E5 1.6E6 1.0E7 4.8E9(3604) (3890) (4221) (4606) (5062) (5608) (6274) (7106) (8171) (9584) (11,548)

    1 5.7E+0 3.8E+0 1.9E+0 7.5E1 2.3E1 5.6E2 1.1E2 1.7E3 2.0E4 1.8E5 1.3E6(3427) (3685) (3980) (4321) (4719) (5191) (5757) (6449) (7315) (8427) (9908)

    2 1.9E+0 4.0E+0 4.3E+0 3.1E+0 1.6E+0 5.9E1 1.7E1 3.9E2 6.8E3 9.2E4 9.4E5(3270) (3503) (3769) (4074) (4426) (4838) (5326) (5913) (6633) (7535) (8697)

    (continued on next page)

    A. Bhardwaj, S.K. Jain / Icarus 218 (2012) 9891005 993

  • 12(

    1(

    2(

    7(

    aruTable 2 (continued)

    10 11 12 13 14

    3 7.4E1 3.9E3 1.1E+0 2.6E+0 2.9E+0(3129) (3342) (3583) (3857) (4171)

    4 4.5E1 1.2E+0 5.9E1 2.0E3 7.7E1(3002) (3198) (3418) (3666) (3949)

    5 5.1E1 2.0E2 3.9E1 9.2E1 3.7E1(2887) (3068) (3270) (3497) (3753)

    6 3.9E4 4.0E1 4.4E1 1.0E3 4.6E1(2783) (2951) (3137) (3346) (3579)

    994 A. Bhardwaj, S.K. Jain / Ic/Z; E Z 100Wkl

    QZ; EUE; E0PlnlZrlTE

    dE0; 1

    where rlT(E) is the total inelastic cross section for the lth gas, at en-ergy E, nl(Z) is its density at altitude Z, Wkl is the threshold of kthexcited state of gas l, and U(E,E0) is the two-dimensional AYS, whichembodies the non-spatial information of electron degradation pro-cess. It represents the equilibrium number of electrons per unit en-ergy at an energy E resulting from the local energy degradation ofan incident electron of energy E0. For the N2 gas it is given as (Sing-hal et al., 1980)

    UE; E0 C0 C1Ek K=EM2 L2: 2Here C0, C1, K,M, and L are the tted parameters which are indepen-dent of the energy, and whose values are given by Singhal et al.

    7 2.7E1 2.6E1 2.0E2 5.1E1 3.3E1 2(2689) (2845) (3018) (3210) (3424) (

    8 1.4E1 5.2E3 2.6E1 1.2E1 7.2E2 3(2602) (2748) (2909) (3087) (3285) (

    9 1.3E3 7.0E2 5.1E2 2.4E2 1.4E1 1(2523) (2660) (2810) (2976) (3160) (

    10 8.2E3 2.1E2 1.3E3 4.0E2 7.0E3 2(2450) (2579) (2720) (2875) (3046) (

    11 5.8E3 5.5E4 8.7E3 5.6E3 5.3E3 1(2383) (2505) (2638) (2783) (2743) (

    12 1.2E3 7.7E4 3.6E3 1.8E4 6.3E3 4(2321) (2437) (2562) (2699) (2850) (

    13 2.6E5 1.0E3 2.6E4 1.5E3 1.1E3 1(2264) (2374) (2493) (2622) (2764) (

    14 4.2E5 3.5E4 6.1E5 8.2E4 1.4E5 1(2211) (2316) (2429) (2552) (2686) (

    15 5.5E5 4.0E5 1.9E4 1.3E4 3.0E4 3(2162) (2262) (2370) (2487) (2614) (

    16 2.0E5 4.0E7 1.1E4 5.3E7 2.3E4 2(2117) (2213) (2316) (2427) (2548) (

    17 2.5E6 8.0E6 2.8E5 3.1E5 6.5E5 5(2075) (2167) (2266) (2372) (2488) (

    18 2.1E10 6.2E6 1.9E6 3.3E5 3.3E6 6(2036) (2125) (2220) (2322) (2432) (

    19 1.3E7 1.8E6 3.6E7 1.5E5 2.8E6 3(2000) (2086) (2177) (2275) (2381) (

    20 4.0E9 1.5E7 1.3E6 3.6E6 7.8E6 6(1967) (2050) (2138) (2232) (2334) (

    Values in brackets show the band origin in .Calculations are made using SEE solar ux (F10.7 = 68) on 23 June 2009 and at SZA = 65 16 17 18 19 20

    .0E+0 9.7E1 3.5E1 9.2E2 1.8E2 2.8E34536) (4962) (5468) (6078) (6826) (7767)

    .8E+0 1.9E+0 1.2E+0 5.3E1 1.7E1 3.9E24274) (4650) (5092) (5617) (6250) (7030)

    .0E2 7.0E1 1.3E+0 1.2E+0 6.8E1 2.6E14065) (4381) (4771) (5229) (5773) (6432)

    .5E1 1.8E1 8.7E2 7.4E1 1.1E+0 8.2E13844) (4146) (4494) (4897) (5372) (5938)

    s 218 (2012) 9891005(1980). The term Q(Z,E) in Eq. (1) is the primary photoelectron pro-duction rate (cf. Bhardwaj and Singhal, 1990; Michael and Bhardwaj,1997; Bhardwaj, 2003; Jain and Bhardwaj, 2011). Fig. 2 shows thecalculated energy spectrum for photoelectron production at 900and 1100 km on 23 June 2009 at SZA = 60 using SEE solar EUV ux.Prominent peaks around 2426 eV are due to the ionization of N2 indifferent excited states by the solar He II Lyman-a line at 303.78 .Photoelectron energy spectrum below 25 eV at altitude of 900 kmis smaller than that at 1100 km, since electrons below 25 eV mainlyproduced by solar EUV photons > 30 nm which are attenuated athigher altitudes (>900 km). Higher energy photons can still pene-trate deeper in the atmosphere and attain unit optical depth at loweraltitudes (50 eV) is higher at 900 km compared toelectron spectrum at 1100 km.

    .2E2 6.0E1 6.1E1 4.6E2 2.3E1 8.3E13666) (3940) (4252) (4612) (5030) (5523)

    .9E1 1.1E1 9.3E2 4.6E1 2.5E1 1.2E33507) (3757) (4040) (4363) (4736) (5170)

    .6E2 8.7E2 1.6E1 6.8E3 1.0E1 1.9E13364) (3594) (3852) (4144) (4480) (4866)

    .8E2 4.6E2 2.3E4 5.6E2 3.8E2 2.9E33236) (3448) (3684) (3952) (4255) (4602)

    .6E2 1.6E5 2.0E2 8.9E3 5.6E3 2.5E23120) (3316) (3535) (3780) (4057) (4371)

    .1E4 6.4E3 4.3E3 2.3E3 9.8E3 3.7E43015) (3198) (3400) (3627) (3881) (4168)

    .2E3 2.7E3 2.7E4 4.1E3 2.6E4 3.3E32919) (3090) (3279) (3489) (3724) (3987)

    .3E3 4.3E5 1.5E3 4.9E4 1.1E3 1.5E32832) (2993) (3169) (3365) (3583) (3826)

    .1E4 2.9E4 6.0E4 1.4E4 9.4E4 2.2E62752) (2904) (3070) (3253) (3456) (3682)

    .2E7 3.5E4 1.3E5 4.2E4 8.0E5 3.8E42679) (2823) (2980) (3152) (3342) (3553)

    .6E5 1.1E4 6.5E5 1.7E4 4.8E5 2.5E42613) (2749) (2897) (3060) (3239) (3436)

    .8E5 4.8E6 1.0E4 9.4E6 1.3E4 2.2E52551) (2681) (2822) (2976) (3145) (3331)

    .2E5 7.7E6 4.8E5 1.2E5 9.4E5 1.2E52495) (2619) (2754) (2900) (3060) (3236)

    .4E6 1.9E5 7.5E6 3.0E5 8.6E6 4.0E52444) (2563) (2691) (2831) (2984) (3150)

    0.

  • Table 3Overhead intensities (in R) of N2 First Positive (B

    3Pg ! A3Ru ) band.

    m0 m00

    0 1 2 3 4 5 6 7 8 9

    0 1.1E+1 5.7E+0 1.7E+0 3.6E1 5.6E2 5.8E3 2.6E4 3.9E8 (10,469) (12,317) (14,895) (18,739) (25,084) (37,523) (72,916) (941,292)

    1 1.5E+1 6.7E2 2.8E+0 2.1E+0 7.8E1 1.9E1 2.9E2 2.4E3 3.0E5 (8883) (10,179) (11,878) (14,201) (17,569) (22,882) (32,502) (55,202) (173,933)

    2 6.9E+0 9.0E+0 1.7E+0 3.4E1 1.3E+0 8.4E1 3.0E1 6.8E2 9.2E3 4.1E4(7732) (8695) (9905) (11,471) (13,572) (16,538) (21,039) (28,671) (44,420) (95,828)

    3 1.4E+0 9.3E+0 2.4E+0 2.9E+0 7.6E2 3.6E1 5.6E1 3.1E1 1.0E1 2.0E2(6858) (7606) (8516) (9648) (11,092) (12,997) (15,624) (19,474) (25,651) (37,163)

    4 1.4E1 2.8E+0 7.1E+0 1.3E1 2.1E+0 5.3E1 1.3E2 2.3E1 2.2E1 1.0E1(6173) (6772) (7484) (8345) (9404) (10,739) (12,471) (14,807) (18,126) (23,207)

    5 6.4E3 3.5E1 3.2E+0 3.8E+0 1.4E1 8.9E1 6.7E1 4.5E2 4.1E2 1.1E1(5622) (6114) (6689) (7368) (8181) (9173) (10,408) (11,987) (14,072) (16,954)

    6 1.3E4 2.0E2 5.0E1 2.6E+0 1.5E+0 4.7E1 2.0E1 4.6E1 1.3E1 2.1E5(5168) (5582) (6057) (6608) (7255) (8025) (8954) (10,098) (11,539) (13,407)

    7 1.0E6 4.8E4 3.4E2 5.3E1 1.7E+0 4.0E1 4.9E1 9.0E3 2.2E1 1.3E1(4789) (5142) (5543) (6001) (6530) (7147) (7875) (8746) (9806) (11,124)

    8 1.0E9 3.9E6 9.2E4 4.1E2 4.4E1 9.6E1 5.5E2 3.3E1 1.1E2 6.7E2(4448) (4774) (5117) (5505) (5947) (6454) (7042) (7730) (8548) (9532)

    9 3.0E12 4.0E9 8.5E6 1.3E3 4.3E2 3.3E1 4.8E1 5.3E5 1.7E1 3.6E2(4192) (4460) (4758) (5092) (5468) (5894) (6380) (6940) (7592) (8358)

    10 1.3E13 3.5E11 8.0E9 1.3E5 1.5E3 3.7E2 2.2E1 2.0E1 1.1E2 6.7E2(3953) (4190) (4453) (4744) (5068) (5432) (5842) (6309) (6843) (7459)

    11 7.4E15 5.6E14 7.8E11 1.1E8 1.5E5 1.4E3 2.7E2 1.2E1 7.2E2 1.8E2(3744) (3956) (4189) (4446) (4729) (5045) (5397) (5792) (6239) (6748)

    12 8.4E14 7.7E15 8.0E13 1.3E10 1.1E8 1.4E5 1.1E3 1.7E2 5.8E2 1.9E2(3560) (3751) (3960) (4188) (4439) (4716) (5022) (5363) (5744) (6172)

    13 2.1E14 3.0E14 1.0E13 3.3E12 2.0E10 9.2E9 1.1E5 7.3E4 9.6E3 2.6E2(3396) (3570) (3758) (3963) (4187) (4433) (4702) (5000) (5329) (5696)

    14 4.4E16 4.2E14 9.2E14 7.2E13 8.5E12 2.8E10 7.7E9 9.2E6 5.3E4 5.8E3(3250) (3409) (3580) (3766) (3968) (4187) (4427) (4690) (4978) (5297)

    15 5.5E15 6.1E15 6.9E14 3.7E13 1.7E12 1.6E11 3.6E10 6.7E9 8.2E6 4.2E4(3119) (3265) (3422) (3591) (3774) (3972) (4188) (4422) (4678) (4958)

    16 1.2E15 1.4E16 3.0E14 1.4E13 6.7E13 3.1E12 2.9E11 4.2E10 5.5E9 6.9E6(3001) (3136) (3280) (3436) (3603) (3783) (3978) (4188) (4417) (4666)

    17 2.4E16 6.2E17 5.1E15 2.9E14 1.8E13 9.8E13 4.0E12 3.3E11 3.4E10 3.3E9(2894) (3020) (3153) (3296) (3450) (3615) (3792) (3983) (4190) (4413)

    18 8.0E16 3.0E16 2.1E16 4.0E15 3.9E14 2.3E13 9.6E13 3.9E12 3.1E11 2.3E10(2797) (2914) (3039) (3171) (3313) (3465) (3627) (3802) (3989) (4191)

    19 3.9E16 5.6E16 2.5E17 4.7E16 9.4E15 5.5E14 3.0E13 1.2E12 4.8E12 3.8E11(3709) (2818) (2935) (3058) (3190) (3330) (3480) (3641) (3812) (3996)

    20 5.7E18 7.3E17 4.4E17 1.3E17 1.0E15 7.5E15 5.2E14 2.5E13 9.6E13 4.2E12(2628) (2731) (2840) (2956) (3079) (3209) (3348) (3496) (3654) (3823)

    10 11 12 13 14 15 16 17 18 19 20

    3 2.0E2 1.9E3 (66,117) (274,786)

    4 3.0E2 4.8E3 2.3E4 (31,941) (50,449) (115,737)

    5 7.8E2 3.2E2 7.7E3 8.7E4 6.2E6 (21,186) (27,999) (40,761) (73,199) (311,787)

    (continued on next page)

    A. Bhardwaj, S.K. Jain / Icarus 218 (2012) 9891005 995

  • 15

    1.1E(117

    2.3E(42,

    4.8E(25,

    1.7E(18,

    6.3E(14,

    4.9E(12,

    2.3E(10,

    aruTable 3 (continued)

    10 11 12 13 14

    6 3.1E2 4.2E2 2.5E2 8.6E3 1.7E3(15,923) (19,487) (24,916) (34,172) (53,448)

    7 1.5E2 2.9E3 1.5E2 1.5E2 7.4E3(12,802) (15,009) (18,036) (22,434) (29,394)

    8 8.9E2 2.8E2 7.5E4 3.0E3 6.3E3(10,737) (12,248) (14,192) (16,781) (20,392)

    9 1.1E2 4.4E2 2.6E2 4.8E3 2.3E5(9272) (10,377) (11,739) (13,456) (15,683)

    10 3.8E2 4.6E5 1.5E2 1.7E2 6.4E3(8178) (9025) (10,038) (11,268) (12,789)

    11 1.9E2 2.5E2 1.8E3 3.1E3 7.6E3(7330) (8004) (8791) (9720) (10,831)

    12 1.5E2 1.8E3 1.2E2 3.1E3 1.5E4(6656) (7207) (7838) (8568) (9420)

    996 A. Bhardwaj, S.K. Jain / IcDuring the degradation of photoelectrons in the atmosphere ofTitan we have not considered CH4 since N2 is the dominant species.Contribution of CH4, which is having a mixing ratio of 3% near1000 km, to the photoelectron ux is less than 10% (Stevenset al., 2011). The effect of omitting the CH4 contribution in thephotoelectron production rate is less than 5% in our calculation.Stevens et al. (2011) also have stated that neglecting the CH4 con-tribution in the calculation of photoelectron production rate re-sults in only less than 5% enhancement in the EUV and FUVvolume production rates for the UVIS observation conditions.

    Fig. 3 (top panel) shows the steady state photoelectron ux ataltitude of 1100 km and solar zenith angle of 60. Around 6 eV, pho-toelectron ux is maximum with a value of few 108 cm2 s1 eV1.Due to the degradation of electrons in the atmosphere, the photo-electron ux is smoother compared to the photoelectron produc-tion energy spectrum (cf. Fig. 2); still prominent peaks can beseen in the ux, e.g., peak at 24 eV is present in the photoelectronux. Photoelectron uxes calculated by using S2K and HEUVAC so-lar EUV uxes are also shown in Fig. 3. As discussed in Section 2,due to higher solar EUV ux in the S2K model, the photoionizationyield is slightly higher compared to that in the SEE model, which isresponsible for the higher photoelectron ux when S2K model is

    13 4.2E3 8.6E3 1.1E4 4.3E3 2.5E3 8.3E(6106) (6566) (7087) (7678) (8355) (913

    14 1.2E2 6.4E4 4.7E3 9.9E5 1.4E3 1.6E(5650) (6042) (6479) (6970) (7524) (815

    15 3.9E3 6.2E3 1.8E5 2.5E3 3.5E4 3.6E(5265) (5604) (5979) (6394) (6857) (737

    16 3.2E4 2.5E3 3.0E3 4.9E5 1.2E3 4.4E(4938) (5234) (5560) (5917) (6312) (674

    17 4.4E6 1.8E4 1.2E3 1.1E3 1.1E4 3.6E(4655) (4918) (5204) (5516) (5857) (623

    18 1.9E9 2.6E6 9.8E5 5.5E4 3.4E4 1.0E(4409) (4644) (4899) (5174) (5473) (579

    19 2.1E10 1.5E9 2.2E6 7.4E5 3.5E4 1.4E(4194) (4406) (4634) (4880) (5145) (543

    20 3.3E11 1.4E10 9.7E10 1.4E6 4.3E5 1.7E(4003) (4196) (4403) (4624) (4862) (511

    Values in brackets show the band origin in .Calculations are made using SEE solar ux on 23 June 2009 and at SZA = 60.16 17 18 19 20

    4 ,886)

    3 3.5E4 7.7E6 028) (71,926) (229,296)

    3 2.1E3 5.8E4 6.7E5 1.2E7 765) (34,576) (51,601) (98,056) (718,231)

    3 2.4E3 1.6E3 6.5E4 1.6E4 1.4E5679) (22,912) (29,322) (40,124) (62,048) (129,839)

    4 1.4E4 7.7E4 8.4E4 5.2E4 2.1E4713) (17,219) (20,605) (25,412) (32,758) (45,186)

    3 1.3E3 5.4E5 1.1E4 3.0E4 2.9E4181) (13,849) (15,958) (18,697) (22,383) (27,577)

    3 2.5E3 1.2E3 2.4E4 1.4E6 5.0E5424) (11,623) (13,072) (14,855) (17,091) (19,962)

    s 218 (2012) 9891005used. Whereas at energies below 60 eV, photoelectron ux calcu-lated using HEUVAC model is lower than that calculated usingSEE solar EUV ux, but at higher energies (>60 eV) photoelectronux calculated using HEUVAC model is higher than that calculatedusing both SEE and S2K models. Higher photoelectron ux at high-er energies (>60 eV) for HEUVAC model is due to the higher solarEUV ux at shorter wavelengths (cf. Fig. 1).

    Fig. 3 (bottom panel) shows the steady state photoelectronuxes at three different altitudes along with the calculated photo-electron uxes of Stevens et al. (2011). At and below 6 eV, our cal-culated photoelectron ux is higher than that of Stevens et al.(2011). This is due to the lack of electronelectron collision lossconsideration in our model, which is an important electron energyloss process below 10 eV (Bhardwaj et al., 1990; Bhardwaj andRaghuram, 2012). Between 6 and 15 eV, calculated photoelectronuxes of Stevens et al. (2011) are higher than our calculated valuesat all altitudes. At 1100 km, our calculated photoelectron ux be-tween 15 and 25 eV is higher than that of Stevens et al. (2011). Thisdifference in the photoelectron ux between two model calcula-tions may be due to the slightly different treatment of the altitudedependence of electron degradation in both models. In our model,the AYS approach used for the calculation of photoelectron ux is

    5 4.3E4 9.5E4 7.2E4 2.8E4 4.6E56) (10,043) (11,108) (12,369) (13,881) (15,717)

    3 3.1E4 2.5E5 2.9E4 3.6E4 2.2E41) (8866) (9685) (10,630) (11,728) (13,012)

    4 9.0E4 3.9E4 1.5E5 5.8E5 1.5E44) (7955) (8608) (9347) (10,185) (11,140)

    4 4.4E5 4.1E4 3.2E4 6.9E5 9.3E77) (7230) (7765) (8312) (9026) (9768)

    4 2.9E4 7.5E7 1.1E4 1.6E4 7.1E50) (6639) (7089) (7582) (8124) (8721)

    4 8.6E5 1.5E4 1.4E5 2.0E5 6.0E58) (6150) (6534) (6951) (7404) (7896)

    4 1.0E4 2.0E5 8.9E5 2.6E5 1.5E61) (5739) (6072) (6430) (6816) (7231)

    4 4.2E5 6.3E5 1.3E6 3.6E5 2.1E56) (5389) (5681) (5993) (6327) (6683)

  • 2 u g

    0 00

    5

    3.5E(466

    1.3E(426

    1.5E(394

    3.3E(367

    4.7E(344

    15

    1.3E(13,9

    4.6E(10,9

    6.3E(901

    3.4E(770

    9.4E(677

    carum m0 1 2 3 4

    0 6.5E+0 4.4E+0 1.8E+0 5.5E1 1.5E1(3370) (3576) (3804) (4058) (4343)

    1 1.7E+0 8.3E2 7.8E1 7.0E1 3.4E1(3158) (3338) (3536) (3754) (3997)

    2 2.0E1 5.0E1 3.9E2 8.4E2 2.0E1(2976) (3135) (3309) (3499) (3709)

    3 7.5E3 1.0E1 8.5E2 4.1E2 1.6E3(2818) (2961) (3115) (3284) (3468)

    4 5.2E5 4.9E3 3.4E2 1.1E2 1.4E2(2684) (2812) (2952) (3102) (3266)

    10 11 12 13 14

    0 1.3E5 2.4E6 4.2E7 6.9E8 1.0E8(7181) (7992) (8985) (10,228) (11,828)

    1 1.5E4 3.3E5 7.1E6 1.4E6 2.7E7(6281) (6893) (7619) (8495) (9571)

    2 8.5E4 2.2E4 5.5E5 1.3E5 3.0E6(5599) (6080) (6638) (7293) (8071)

    3 1.9E3 6.2E4 1.8E4 5.1E5 1.4E5(5067) (5458) (5904) (6416) (7011)

    4 2.2E3 8.8E4 3.2E4 1.0E4 3.2E5(4648) (4974) (5342) (5758) (6233)Table 4Overhead intensities (in R) of N Second Positive (C3P ? B3P ) band.

    A. Bhardwaj, S.K. Jain / Ibased on the Monte Carlo model (cf. Singhal et al., 1980; Singhaland Bhardwaj, 1991; Bhardwaj and Singhal, 1993; Bhardwaj andMichael, 1999a,b; Bhardwaj and Jain, 2009), while in the AURICmodel (Strickland et al., 1999) it is based on the solution of Boltz-mann equation. Above 25 eV, the photoelectron ux calculated byStevens et al. (2011) is consistent with our model values. The peakstructures in our calculated photoelectron ux are slightly differ-ent than the photoelectron ux of Stevens et al. (2011). This differ-ence is due to the different branching ratios used in the twomodels. In our model, stable branching ratios taken from Avakyanet al. (1998) are used, whereas in AURIC model branching ratios arewavelength dependent.

    To compare the calculated photoelectron ux with Cassiniobservations we have run our model taking the HASI N2 densityand SEE solar EUV ux on 5 January 2008 (F10.7 = 79.7) atSZA = 37. Fig. 4 shows the model calculated photoelectron uxat 1100 km along with the photoelectron ux observed by theCAPS instrument (energy resolution DE/E = 16.7%) on-boardCassini taken from Lavvas et al. (2011). Model calculated photo-electron ux agrees well with the observed ux between 7 and20 eV. Above 20 eV model predicted photoelectron ux is slightlyhigher than the observation. At higher energies (>60 eV) the calcu-lated photoelectron ux starts decreasing sharply compared to theobserved ux. Lavvas et al. have also observed similar differencesin their calculated and the observed photoelectron ux at energies>60 eV, which they attributed to the instrument artifact (Lavvaset al., 2011; Arridge et al., 2009).

    3.2. Volume emission rates

    Using the photoelectron ux /(Z,E) obtained in Eq. (1), thevolume excitation rate for N2 emissions is calculated as

    Values in brackets show the band origin in .Calculations are made using SEE solar ux on 23 June 2009 and at SZA = 60.6 7 8 9

    2 7.7E3 1.6E3 3.3E4 6.7E55) (5032) (5452) (5938) (6507)

    1 3.9E2 1.1E2 2.8E3 6.6E48) (4573) (4317) (5309) (5759)

    1 7.7E2 3.0E2 1.0E2 3.0E32) (4200) (4489) (4813) (5180)

    2 4.3E2 2.9E2 1.4E2 5.6E31) (3894) (4140) (4415) (4722)

    4 3.8E3 8.9E3 7.9E3 4.7E35) (3641) (3856) (4093) (4355)

    16 17 18 19 20

    9 1.3E10 7.4E12 5.7E16 2.6E13 7.6E1462) (16,944) (21,403) (28,779) (43,302) (84,991)

    14 6.8E09 7.6E10 4.4E11 2.3E14 2.2E1221) (12,665) (15,000) (18,285) (23,236) (31,536)

    7 1.2E7 2.1E8 2.9E9 2.4E10 1.8E121) (10,166) (11,618) (13,495) (16,014) (19,563)

    6 8.1E7 1.8E7 3.5E8 5.7E9 7.1E109) (8539) (9541) (10,771) (12,317) (14,315)

    6 2.6E6 7.0E7 1.7E7 3.7E8 7.1E98) (7412) (8155) (9037) (10,101) (11,406)

    s 218 (2012) 9891005 997ViZ nZZ EEth

    /Z; EriEdE 3

    where n(Z) is the density of N2 at altitude Z and ri(E) is the electronimpact cross section for the ith state at energy E, for which thethreshold is Eth. Fig. 5 shows the volume excitation rates for N2 trip-let states (A, B, C, W, B0, and E ) by photoelectron impact excitation.The production rates for all the states peak around 1025 km, whichis 25 km higher than the calculated peak altitude of 1000 km ofStevens et al. (2011). This difference in height of peak productionmight due to the different treatment of altitude dependence of pho-toelectrons in the two models.

    The N2 triplet E, C,W, and B0 states populate the B state, which inturn radiate to the state A (First Positive band). Further the inter-state cascading B3PgA3Ru and B3Pg W3Du are also importantin populating the B level (Cartwright et al., 1971; Cartwright, 1978;Jain and Bhardwaj, 2011; Bhardwaj and Jain, 2012). To calculatethe total population of different vibrational levels of state A, wesolve the equations for statistical equilibrium based on the formu-lation of Cartwright (1978). Contributions of cascading from highertriplet states and interstate cascading and quenching by atmo-sphere constituents are included in the calculation. At a speciedaltitude, for a vibrational level m of a state a, the population isdetermined using the statistical equilibrium equation

    Vaq0m Xb

    Xs

    Abasm nbs Kaqm

    Xc

    Xr

    Aacmr

    ( )nam 4

    where Va is electron impact volume excitation rate (cm3 s1 ) ofstate a; q0m is FranckCondon factor for the excitation from groundlevel to m level of state a; Abasm is transition probability (s

    1 ) fromstate b(s) to am; Kaqm is total electronic quenching frequency (s1)of level m of state a by all the gases dened as:

    PlK

    aqlm nl, where,

  • Table 5Overhead intensities (in R) of N2 WuBenesch (W3Du? B3Pg) band.

    m0 m00

    0 1 2 3 4 5 6 7 8 9

    0 1.6E1 (1,361,044)

    1 4.5E1 (64,311)

    2 6.5E1 7.3E2 (33,206) (76,556)

    3 5.6E1 4.9E1 9.0E3 (22,505) (36,522) (94,180)

    4 3.5E1 8.5E1 2.4E1 1.9E4 (17,092) (24,124) (40,502) (121,693)

    5 1.9E1 7.9E1 7.5E1 8.8E2 1.8E4 (13,825) (18,090) (25,962) (45,362) (170,594)

    6 8.0E2 5.2E1 9.8E1 4.9E1 1.8E2 1.6E4 (11,639) (14,521) (19,193) (28,067) (51,426) (281,484)

    7 3.0E2 2.7E1 7.9E1 8.6E1 2.3E1 8.7E4 1.1E5 (10,075) (12,165) (15,281) (20,421) (30,501) (59,196) (774,629)

    8 1.0E2 1.2E1 4.8E1 8.7E1 5.9E1 8.3E2 5.4E4 (8900) (10,493) (12,732) (16,112) (21,794) (33,343) (69,497)

    9 3.3E3 4.5E2 2.4E1 6.2E1 7.5E1 3.3E1 1.9E2 1.5E3 (7986) (9246) (10,941) (13,347) (17,024) (23,339) (36,704) (83,791)

    10 9.8E4 1.6E2 1.0E1 3.5E1 6.2E1 5.3E1 1.5E1 1.6E3 1.2E3 (7255) (8280) (9614) (11,424) (14,014) (18,030) (25,088) (40,735) (104,922)

    11 2.8E4 5.2E3 4.0E2 1.7E1 4.0E1 5.2E1 3.1E1 5.1E2 2.1E4 5.4E4(6658) (7511) (8592) (10,009) (11,943) (14,742) (19,145) (27,084) (45,654) (139,282)

    12 7.9E5 1.6E3 1.5E2 7.2E2 2.1E1 3.8E1 3.7E1 1.6E1 1.2E2 1.3E3(6160) (6883) (7781) (8925) (10,432) (12,505) (15,536) (20,386) (29,381) (51,783)

    13 2.2E5 4.9E4 4.9E3 2.8E2 1.0E1 2.3E1 3.1E1 2.3E1 6.7E2 1.4E3(5740) (6363) (7122) (8069) (9281) (10,886) (13,114) (16,408) (21,774) (32,050)

    14 6.2E6 1.5E4 1.7E3 1.1E2 4.6E2 1.3E1 2.3E1 2.4E1 1.4E1 2.5E2(5380) (5924) (6577) (7376) (8375) (9661) (11,376) (13,776) (17,369) (23,337)

    15 1.5E6 4.1E5 5.0E4 3.6E3 1.7E2 5.5E2 1.2E1 1.7E1 1.4E1 6.1E2(5069) (5549) (6118) (6803) (7645) (8702) (10,070) (11,905) (14,497) (18,431)

    16 3.8E7 1.1E5 1.5E4 1.2E3 6.4E3 2.3E2 6.0E2 1.1E1 1.2E1 8.3E2(4798) (5225) (5727) (6323) (7044) (7932) (9052) (10,509) (12,478) (15,286)

    17 9.2E8 3.1E6 4.5E5 3.9E4 2.3E3 9.4E3 2.8E2 5.9E2 8.6E2 8.1E2(4559) (4943) (5390) (5915) (6541) (7300) (8238) (9427) (10,982) (13,100)

    18 2.0E8 7.8E7 1.3E5 1.2E4 7.9E4 3.6E3 1.2E2 2.9E2 5.1E2 6.3E2(4347) (4695) (5096) (5564) (6114) (6772) (7572) (8565) (9830) (11,493)

    19 3.9E9 1.8E7 3.4E6 3.7E5 2.6E4 1.3E3 4.9E3 1.3E2 2.8E2 4.1E2(4159) (4476) (4839) (5259) (5748) (6325) (7018) (7863) (8916) (10,263)

    20 5.5E10 3.8E8 8.7E7 1.1E5 8.3E5 4.6E4 1.9E3 5.8E3 1.4E2 2.4E2(3990) (4281) (4612) (4991) (5430) (5943) (6550) (7280) (8174) (9292)

    10 11 12 13 14 15 16 17

    12 1.4E4 (204,814)

    13 1.5E3 1.5E5 (59,621) (378,656)

    14 1.7E5 1.1E3 4.9E8 (35,186) (69,984) (2,189,094)

    998 A. Bhardwaj, S.K. Jain / Icarus 218 (2012) 9891005

  • 541)

    40)

    42)

    67)

    caruKaqlm is the quenching rate coefcient cm3 s1 of level m of state aby the gas l of density nl; A

    acmr is transition from level m of state a to

    vibrational level r of state c; n is density (cm3); a, b, and c are elec-tronic states; and s and r are source and sink vibrational levels,respectively.

    While calculating the cascading from C state we have accountedfor predissociation. The C state predissociates approximately halfthe time (this is an average value for all vibrational levels of theC state; excluding m = 0,1, which do not predissociate at all) (cf.Daniell and Strickland, 1986). In Earths airglow the N2(A) levelsget effectively quenched by atomic oxygen and the abundance ofO increases with increase in altitude. Titan atmosphere is N2 dom-inated with small amount of CH4. The quenching rates for differentvibrational levels of N2 triplet states by N2 are adopted fromMorrill and Benesch (1996) and by CH4 is taken from Clark and Set-ser (1980).

    Fig. 6 shows the population of different vibrational levels of trip-let states of N2 relative to the ground state at 1100 km. We foundthat the effect of quenching is negligible on the vibrational popula-

    Table 5 (continued)

    10 11 12 13 14

    15 6.0E3 5.4E4 5.2E4 (25,109) (38,919) (84,300)

    16 2.5E2 8.6E4 7.9E4 2.0E4 (19,612) (27,132) (43,431) (105,325)

    17 4.3E2 8.8E3 2.4E6 6.6E4 5.5E(16,153) (20,931) (29,461) (48,989) (139,1

    18 4.9E2 2.0E2 2.4E3 1.4E4 4.1E(13,778) (17,109) (22,413) (32,169) (55,99

    19 4.2E2 2.7E2 8.3E3 4.0E4 2.8E(12,047) (14,519) (18,167) (24,089) (35,35

    20 3.0E2 2.6E2 1.3E2 2.9E3 9.9E(10,731) (12,649) (15,332) (19,345) (25,99

    Values in brackets show the band origin in .Calculations are made using SEE solar ux on 23 June 2009 and at SZA = 60.

    A. Bhardwaj, S.K. Jain / Ition. Stevens et al. (2011) have calculated the vibrational popula-tion of VK band up to 10 vibrational levels and the population ofvibrational level 11 is taken as 44% of that for m0 = 10. In our model,the vibrational population is considered up to m0 = 20 levels. Ourcalculated population for m0 = 11 level is 40% of the m0 = 10 level.

    After calculating the steady state density of different vibrationallevels of excited triplet states of N2, the volume emission rate V

    abm0m00

    of a vibration band m0 ? m00 can be obtained using

    Vabm0m00 nam0 Aabm0m00 cm3 s1 5

    where nam0 is the density of vibrational level m0 of state a, and Aabm0m00 is

    the transition probability (s1 ) for the transition from the m0 level ofstate a to the m00 level of state b.

    Fig. 7 shows the volume emission rates for the VK band. The N2VK band span wavelength range from FUV to visible, and sometransitions even emit at wavelength more than 1000 nm. Fig. 7 alsoshows the emission rates of VK bands in FUV and visible wave-lengths. Volume emission rates for VK bands in the wavelengthrange 400800, 300400, 200300, and 150200 nm are 22%,38%, 35%, and 4.5%, respectively, of the total VK band emission rate.Contribution of VK band emissions in the 130150 nm wavelengthrange is very small (0.02%). In the visible and near infrared range(400800 nm), the main contribution comes from the emissionsbetween 400 and 500 nm, which comprises around 73% of the VKvisible emission band. Our calculated total VK band volume emis-sion rate is in good agreement with that of Stevens et al. (2011).

    Fig. 8 shows the prominent VK band transition in ultraviolet re-gion. VK (0,5), (0,6), and (0,7) bands (between 200 and 300 nm)have been observed on Mars by SPICAM/Mars Express (Leblancet al., 2006, 2007). In the 150200 nm region, VK (5,0), (6,0),(7,0), (8,0), and (9,0) bands are reported for the rst time in thedayglow of Titan (Stevens et al., 2011). The emission rates in thesetwo wavelength band regions, 150200 and 200300 nm, differ byabout an order of magnitude but the altitude of peak production(1025 km) remains the same for all the VK band emissions (Fig. 7).

    The volume emission rates are vertically-integrated to calcu-late the overhead intensities. Table 1 shows the total overheadintensity for VegardKaplan (A? X), First Positive (B? A), SecondPositive (C? B ), HermanKaplan (E? A), E? B, Reverse First Po-sitive (A? B), and E? C triplet bands of N2 at SZA = 60. Sincethe VK band spans a wide range of electromagnetic spectrum,from FUV to visible wavelengths, we also present in Table 1 theoverhead intensities in different wavelength regions of VK bands.

    15 16 17

    1.0E5 (202,357)

    2.1E4 9.5E7 (65,067) (362,190)

    2.7E4 8.6E5 5.7E9(39,142) (77,278) (1,546,312)

    s 218 (2012) 9891005 999Emissions in the 300400 nm constitute a major fraction of thetotal VK band emission followed closely by emissions in the200300 nm band, with contributions of around 38% and 35%,respectively. The 150200 nm emission band contributes around4.5% to the total VK band intensity. Contribution of visible wave-length region (400800 nm) is also signicant (22%) in the totalVK band intensity, in which wavelength region 400500 nm con-tributes 16% of the total VK band intensity or 73% of total visibleband emission.

    Table 2 shows the overhead intensity for all the vibrational lev-els of N2 VK bands calculated using SEE solar EUV ux on 23 June2009 at SZA = 60. The VK (0,6) emission (at 276.2 nm) is the stron-gest emission in the VK band system having an overhead intensityof7 R, which is around 5% of the total VK band intensity and com-prises around 15% of VK band emissions in the 200300 nm range.The VK (0,6) band has been observed on Mars (Leblanc et al., 2007;Jain and Bhardwaj, 2011). In the dayglow spectrum of Titan VK(7,0) transition is the strongest emission observed by Cassini UVIS.For the VK (7,0) band the model calculated overhead intensity is1.1 R, which is 0.8% of the total VK band intensity.

    The calculated overhead intensities of N2 First Positive (1P)transitions are presented in Table 3. Prominent transitions in thisband lie above 600 nm. The 1P (1,0) emission at 888.3 nm is thebrightest followed by (0,0) emission at 1046.9 nm, which contrib-ute around 13% and 9%, respectively, to the total 1P emission.

  • uxes at shorter wavelength would cause higher photoelectronux at higher energies (>60 eV) (see Fig. 3).

    aruEmissions between 600 and 800 nm wavelength consist of about50% of the total 1P band system. The calculated overhead intensi-ties of Second Positive (2P) band transitions are presented in Ta-ble 4. Major portion of 2P band emission lies in wavelengthsbetween 300 and 400 nm, which is more than 90% of the total2P band overhead intensity. Prominent emissions in the 2P bandsystem are (0,0), (0,1), (0,2), and (1,0) transitions, having over-head intensities of around 6.5, 4.5, 1.8, and 1.7 R, thus contribut-ing around 34, 24, 9, and 9%, respectively, to the total 2Pemission.

    Tables 5 and 6 show the calculated overhead intensities ofWuBenesch (W? B) and B0 ? B band emissions, respectively.Most of the emissions in W? B band are in infrared region with alittle or negligible contribution from emissions below 800 nm. Sim-ilar is the case in B0 ? B band system. Table 7 shows the calculatedoverhead intensities of HermanKaplan (E? A), E? B, and E? Cbands of N2, and Table 8 shows the overhead intensities of ReverseFirst Positive (R1P) band emissions. Prominent emissions in the R1Pband system are in infrared region, with (9,0) emission being thestrongest having the overhead intensity of 1.9 R, which is around9% of the total R1P emission.

    Stevens et al. (2011) suggested that N2 VK (8,0) emission near165.4 nm and (11,0) band near 156.3 nm could have been misi-dentied as CI 165.7 and 156.1 nm emissions by Ajello et al.(2008). Also, the VK (10,0) band could be the emission near159.2 nm, which is reported as mystery feature by Ajello et al.(2008). We calculated the overhead intensities of CI 165.7 and156.1 nm emissions due to electron impact dissociative excitationof CH4 by using the emission cross sections from Shirai et al.(2002). The model calculated overhead intensities of CI 156.1and 165.7 nm emissions are 1.6 103 and 3.7 103 R, respec-tively, which are about two orders of magnitude lower than theVK (8,0) and VK (11,0) bands intensities (see Table 2). We alsoestimated the solar scattered intensities for CI 165.7 and156.1 nm using the density of atomic carbon from the model ofKrasnopolsky (2010) and g-factor values of 7.21 106 and2 105 s1, respectively, at 1 AU. The overhead intensities of CI156.1 and 165.7 nm due to solar uorescence are an order ofmagnitude lower (1.98 104 and 5.5 104 R, respectively)than that due to photoelectron excitation. The difference of 23orders of magnitude between intensities of (8,0) and (11,0) VKbands and CI line emissions suggest that bands near 156.1 and165.4 nm might have been misidentied by Ajello et al. (2008),as reported by Stevens et al. (2011).

    The calculated band emission rate is integrated along the lineof sight at a projected distance from the centre of Titan to obtainlimb prole. Fig. 9 shows the calculated limb intensities of theprominent VK band emissions in ultraviolet region. Limb intensi-ties of VK bands in different wavelength regions are also shownin Fig. 9. The altitude of maximum limb intensity is around950 km for all the transitions, slightly higher than the calculatedN2 VK peak of Stevens et al. (2011) of 928 km. Fig. 10 shows thelimb intensity of total VK band, which peaks at 950 km, with avalue of around 1.1 kR. Limb intensities calculated at different so-lar zenith angle are also shown in Fig. 10. The main effect of SZAis on the altitude of peak limb intensity and intensity at the peak;lower the value of SZA, the deeper the peak of the limb prolewith higher intensity, which is due to the penetration of solarEUV at lower altitudes in the atmosphere. For SZA = 0, the calcu-lated peak limb intensity is 2.2 kR at an altitude of 892 km,whereas at SZA = 80, the peak limb intensity is 0.4 kR at analtitude of 1050 km. Above 1200 km the effect of solar zenith an-gle is not seen in the limb intensities.

    1000 A. Bhardwaj, S.K. Jain / IcAs mentioned earlier, N2 VK bands were observed for the rsttime in the dayglow of Titan by Cassini UVIS in the 150190 nmwavelength band (Stevens et al., 2011). For comparing our calcu-Volume emission rates of total VK band calculated using S2Kand HEUVAC solar ux models are shown in Fig. 7. The emissionrate calculated using S2K model is 23% higher than that calcu-lated using SEE solar EUV ux. At the emission peak and above, vol-ume emission rate calculated using HEUVAC model is around 14%smaller than that calculated using SEE solar ux. However, belowthe emission peak, the volume emission rate calculated using HEU-VAC model becomes higher than that calculated using SEE modeldue to the larger photoelectron uxes at higher energies (cf.Fig. 3). At the lower peak, volume emission rate calculated usingHEUVAC model is around 2.5 times higher than that calculatedusing SEE solar EUV ux.

    Figs. 10 and 11 show the limb intensity of VK band calculatedusing S2K and HEUVAC solar ux models. Limb intensities calcu-lated using S2K solar EUV ux model are slightly higher than theobserved values whereas intensities calculated using SEE and HEU-VAC solar uxes and model predicted intensity of Stevens et al.(2011) are lower than the observed values; but all model calcula-tions are in good agreement with the observation within the obser-vation and model uncertainties. The height of peak emission rate(Fig. 7) and the altitude of peak limb intensity (Figs. 10 and 11)are unaffected by the change in the input solar EUV ux model.lated limb proles with UVIS observation we have run our modelat the solar zenith angle of 56. Stevens et al. (2011) in their calcu-lation assumed that VK bands in the 150190 nmrange correspondsto 5% of total VK band emission. Fig. 11 shows the calculated limbintensity of VK bands in the 150190 nm region by taking 5% ofthe total VK band intensity, and also by adding the individual bandswhich lie in the 150190 nm wavelength region. The calculatedlimb intensity of Stevens et al. (2011) is also shown in Fig. 11 alongwith the Cassiniobserved limb intensity of VK band in 150190 nmregion taken from Stevens et al. (2011). We found that VK bandemission in the wavelength region 150190 nm corresponds to4.5% of the total VK band intensity (see Table 1). Our calculated limbintensity is in good agreementwith theUVIS observation. The calcu-lated altitude of peak VK emission also agrees well with the obser-vation within the observational uncertainty of 15% (Stevens et al.,2011). Our calculated limb intensities are slightly higher (10%)than those calculated by Stevens et al. (2011). Altitude of emissionpeak is in good agreement in both calculations and is consistentwith that of the observed emission peak. Overall good agreementbetween calculated and observed emission shows that the VK bandintensity can be explained by taking the photoelectron impact exci-tation source alone.

    4. Effect of various model input parameters

    4.1. Effect of solar EUV ux model

    To access the effect of solar EUV ux on the calculated limbintensity we use the solar EUV ux on 23 June 2009 from SO-LAR2000 (S2K) v.2.36 model of Tobiska (2004) and HEUVAC modelof Richards et al. (2006). As discussed in Section 2, the solar ux atwavelengths below 60 nm is higher in the S2K model (cf. Fig. 1).The effect of higher ux at shorter wavelengths is clearly seen inthe photoelectron ux calculations, where the ux calculated usingS2K model is higher than that calculated using SEE solar EUV ux(cf. Fig. 3). While the HEUVAC solar ux is smaller than the SEE so-lar ux at wavelengths higher than 15 nm, at wavelengths below15 nm the HEUVAC solar ux is higher than SEE ux. Higher EUV

    s 218 (2012) 9891005By changing the solar EUV ux in the model, maximum varia-tion at peak intensity is around 40%. Since uncertainty in varioussolar EUV ux models itself varies differently for different solar

  • Table 6Overhead intensities (in R) of N2 B

    03Ru ! B3Pg band.

    m0 m00

    0 1 2 3 4 5 6 7 8 9

    0 1.2E2 3.4E3 2.5E4 3.4E6 (15,280) (20,664) (31,616) (65,977)

    1 6.2E2 2.9E3 1.1E2 1.7E3 3.1E5 (12,442) (15,793) (21,479) (33,241) (71,941)

    2 1.0E1 8.6E2 3.2E3 1.3E2 4.1E3 1.0E4 (10,520) (12,820) (16,329) (22,337) (34,981) (78,778)

    3 9.4E2 2.2E1 4.7E2 2.5E2 7.5E3 6.1E3 1.9E4 (9132) (10,816) (13,212) (16,887) (23,237) (36,843) (86,653)

    4 5.9E2 2.6E1 2.4E1 5.9E3 4.8E2 1.7E3 6.4E3 2.4E4 (8083) (9375) (11,123) (13,618) (17,468) (24,181) (38,831) (95,765)

    5 2.9E2 2.0E1 3.8E1 1.6E1 4.0E3 5.2E2 3.0E5 5.3E3 2.5E4 (7262) (8289) (9626) (11,440) (14,040) (18,072) (25,169) (40,949) (106,355)

    6 1.2E2 1.1E1 3.3E1 3.6E1 6.4E2 2.8E2 3.9E2 1.8E3 3.6E3 2.1E4(6603) (7441) (8501) (9886) (11,769) (14,476) (18,699) (26,201) (43,199) (118,707)

    7 4.3E3 5.0E2 2.2E1 4.0E1 2.6E1 1.0E2 4.8E2 2.2E2 4.4E3 2.0E3(6062) (6761) (7625) (8721) (10,154) (12,107) (14,927) (19,349) (27,275) (45,581)

    8 1.4E3 2.0E2 1.1E1 2.9E1 3.6E1 1.4E1 5.4E4 5.2E2 8.8E3 5.7E3(5610) (6204) (6924) (7815) (8947) (10,430) (12,457) (15,392) (20,021) (28,389)

    9 4.2E4 7.0E3 4.8E2 1.7E1 3.1E1 2.6E1 5.1E2 1.1E2 4.3E2 2.2E3(5227) (5739) (6350) (7092) (8011) (9180) (10,714) (12,817) (15,872) (20,712)

    10 1.2E4 2.3E3 1.8E2 8.1E2 2.0E1 2.7E1 1.6E1 1.1E2 2.3E2 2.8E2(4890) (5345) (5872) (4500) (7264) (8213) (9419) (11,007) (13,187) (16,364)

    11 3.4E5 7.1E4 6.6E3 3.4E2 1.1E1 2.0E1 2.0E1 7.6E2 1.3E4 2.6E2(4614) (5008) (5467) (6008) (6655) (7442) (8420) (9666) (11,308) (13,566)

    12 9.2E6 2.1E4 2.2E3 1.3E2 4.9E2 1.2E1 1.7E1 1.3E1 2.9E2 2.4E3(4365) (4716) (5121) (5592) (6149) (6815) (7625) (8633) (9919) (11,616)

    13 2.5E6 6.2E5 7.0E4 4.7E3 2.0E2 5.8E2 1.1E1 1.2E1 6.9E2 7.2E3(4145) (4460) (4821) (5236) (5721) (6294) (6979) (7817) (8853) (10,179)

    14 6.5E7 1.8E5 2.2E4 1.6E3 7.9E3 2.6E2 6.0E2 9.1E2 8.2E2 3.2E2(3950) (4235) (4559) (4929) (5356) (5854) (6443) (7148) (8007) (9078)

    15 1.7E7 4.9E6 6.5E5 5.3E4 2.9E3 1.1E2 3.0E2 5.5E2 6.8E2 4.8E2(3775) (4035) (4328) (4660) (5040) (5479) (5991) (6596) (7322) (8206)

    16 4.4E8 1.4E6 1.9E5 1.7E4 1.0E3 4.3E3 1.3E2 2.9E2 4.5E2 4.6E2(3619) (3857) (4123) (4424) (4765) (5155) (5606) (6132) (6754) (7500)

    17 1.1E8 3.7E7 5.6E6 5.2E5 3.4E4 1.6E3 5.4E3 1.4E2 2.6E2 3.4E2(3477) (3696) (3940) (4214) (4522) (4872) (5273) (5737) (6277) (6917)

    18 2.8E9 9.9E8 1.6E6 1.6E5 1.1E4 5.6E4 2.1E3 6.2E3 1.3E2 2.1E2(3349) (3552) (3776) (4027) (4308) (4624) (4984) (5395) (5871) (6427)

    19 6.6E10 2.6E8 4.5E7 4.8E6 3.6E5 2.0E4 8.1E4 2.6E3 6.3E3 1.2E2(3232) (3420) (3629) (3859) (4116) (4404) (4729) (5099) (5521) (6010)

    20 1.4E10 6.4E9 1.2E7 1.4E6 1.1E5 6.6E5 3.0E4 1.0E3 2.8E3 5.9E3(3125) (3301) (3495) (3708) (3945) (4209) (4504) (4838) (5217) (5651)

    10 11 12 13 14 15 16 17 18 19 20

    7 1.5E4 (133,152)

    8 9.6E4 9.9E5 (48,087) (150,065)

    9 5.7E3 3.8E4 5.9E5 (29,540) (50,709) (169,831)

    (continued on next page)

    A. Bhardwaj, S.K. Jain / Icarus 218 (2012) 9891005 1001

  • 15

    aruTable 6 (continued)

    10 11 12 13 14

    10 1.1E4 4.6E3 1.2E4 3.2E5 (21,422) (30,723) (53,427) (192,800)

    11 1.6E2 1.9E4 3.3E3 2.5E5 1.7E5(16,868) (22,148) (31,929) (56,215) (219,162)

    1002 A. Bhardwaj, S.K. Jain / IcEUV ux, e.g., for SEE observations uncertainty is around 1020%(Woods et al., 2005), uncertainty in HEUVAC model depends onthe uncertainties in the F74113 reference spectrum and it couldbe 1530% (Richards et al., 2006). Hence, based on the calculationscarried out in the present paper, it is difcult to suggest a preferredsolar ux model. However, since HEUVAC and S2K depend on var-ious proxies, while SEE solar EUV ux is based on actual observa-tion and is available online (http://lasp.colorado.edu/see/l3_data_page.html) it is preferable to use SEE solar EUV ux.

    12 2.3E2 7.3E3 7.6E4 2.1E3 1.4E6 8.5E(13,955) (17,383) (22,886) (33,152) (59,037) (24

    13 6.6E3 1.7E2 2.8E3 1.1E3 1.3E3 9.9E(11,932) (14,352) (17,907) (23,633) (34,378) (61

    14 6.0E4 8.5E3 1.0E2 7.9E4 1.1E3 7.2E(10,446) (12,255) (14,756) (18,437) (24,383) (35

    15 1.3E2 2.2E4 8.1E3 5.9E3 1.2E4 9.8E(9308) (10,718) (12,584) (15,166) (18,972) (25

    16 2.5E2 3.6E3 1.3E3 6.3E3 3.0E3 1.2E(8410) (9545) (10,996) (12,918) (15,581) (19

    17 2.8E2 1.2E2 5.6E4 2.1E3 4.4E3 1.3E(7683) (8619) (9786) (11,280) (13,258) (15

    18 2.4E2 1.6E2 4.7E3 1.3E9 2.2E3 2.7E(7084) (7872) (8834) (10,033) (11,568) (13

    19 1.6E2 1.5E2 8.2E3 1.5E3 1.9E4 1.9E(6581) (7255) (8065) (9052) (10,284) (11

    20 9.6E3 1.1E2 8.9E3 3.8E3 3.2E4 4.2E(6153) (6739) (7432) (8262) (9276) (10

    Values in brackets show the band origin in .Calculations are made using SEE solar ux on 23 June 2009 and at SZA = 60.

    Table 7Overhead intensities (in R) of E3Rg ! A3Ru , E3Rg ! B3Pg , and E3Rg ! C3Pu bands of N2.

    m0 m00

    0 1 2 3 4

    E3Rg ! A3Ru0 8.9E3 2.8E2 4.5E2 5.0E2 4.1E2

    (2173) (2243) (2316) (2392) (2472)1 2.7E3 6.2E3 7.0E3 4.8E3 2.2E3

    (2074) (2138) (2204) (2273) (2345)

    E3Rg ! B3Pg0 7.5E3 1.1E2 9.2E3 5.7E3 2.9E3

    (2742) (2877) (3022) (3181) (3353)1 5.6E4 2.0E4 1.0E6 5.8E5 1.2E4

    (2587) (2707) (2835) (2974) (3124)

    E3Rg ! C3Pu0 1.3E1 1.1E2 4.1E4 2.6E6

    (14,713) (20,824) (34,947) (101,275) 1 2.3E3 2.3E3 5.5E4 3.9E5 7.4E7

    (11,134) (14,312) (19,816) (31,522) (71,884)

    Values in brackets show the band origin in .Calculations are made using SEE solar ux on 23 June 2009 and at SZA = 60.16 17 18 19 20

    s 218 (2012) 98910054.2. Effect of solar cycle

    The N2 VK band emissions reported by Stevens et al. (2011) arefor low solar activity condition (F10.7 = 68, on 23 June 2009). To cal-culate the emission intensity during solar maximum we have runour model for solar EUV ux on 30 January 2002 (F10.7 = 245) mea-sured by SEE, at solar zenith angle of 60. Model atmosphereremains the same for the solar maximum calculation. Fig. 7 showsthe volume emission rate of total N2 VK band for solar maximum

    6 8,754)

    7 4.2E6 ,844) (280,746)

    4 4.4E6 2.1E6 ,595) (64,575) (313,255)

    4 3.9E4 6.2E6 1.1E6 ,131) (36,786) (67,157) (343,066)

    0 7.5E4 2.0E4 6.2E6 6.4E7 ,507) (25,869) (37,932) (69,506) (365,813)

    3 4.0E5 5.2E4 1.0E4 5.1E6 4.0E7,997) (20,039) (26,589) (39,011) (71,531) (376,997)

    3 5.3E4 8.8E5 3.4E4 5.0E5 3.8E6,600) (16,414) (20,564) (27,283) (40,001) (73,141)

    3 1.6E3 1.8E4 1.1E4 2.2E4 2.4E5,859) (13,944) (16,829) (21,077) (27,939) (40,875)

    4 1.4E3 8.4E4 4.7E5 1.0E4 1.3E4,539) (12,154) (14,289) (17,238) (21,572) (28,548)

    5 6 7 8 9 10

    2.8E2 1.6E2 7.7E3 3.3E3 1.2E3 3.9E4(2555) (2643) (2734) (2830) (2930) (3035)5.6E4 3.9E5 2.0E5 8.6E5 1.0E4 7.8E5(2420) (2498) (2580) (2665) (2754) (2846)

    1.3E3 5.6E4 2.2E4 8.3E5 3.0E5 1.0E5(3542) (3749) (3978) (4230) (4511) (4826)1.2E4 8.0E5 4.6E5 2.3E5 1.1E5 4.6E6(3288) (3465) (3660) (3872) (4107) (4365)

  • caruTable 8Overhead intensities (in R) of N2 Reverse First Positive (A

    3Ru ! B3Pg ) band.

    m0 m00

    A. Bhardwaj, S.K. Jain / Icondition. At the altitude where emission rate peaks, the calculatedemission rate for solarmaximumcondition is a factor of2.8 higherthan that for solar minimum condition. Altitude of peak emissionrate remains the same for both low and high solar activity conditionsince the model atmosphere is same. Overhead intensities of

    0 1 2 3 4

    8 1.5E+0 (88,467)

    9 1.9E+0 7.0E1 (42,771) (158,042)

    10 8.2E1 2.3E+0 8.5E3 (28,438) (55,215) (741,757)

    11 2.5E1 1.5E+0 1.2E+0 (21,436) (33,788) (77,920)

    12 7.7E2 6.9E1 1.6E+0 3.1E1 (17,292) (24,523) (41,640) (132,578)

    13 2.2E2 2.5E1 9.5E1 9.9E1 7.9(14,555) (19,361) (28,664) (54,305) (4

    14 6.3E3 8.7E2 4.5E1 9.0E1 3.9(12,617) (16,076) (22,007) (34,521) (7

    15 1.9E3 3.0E2 1.9E1 5.5E1 6.3(11,175) (13,806) (17,964) (25,513) (4

    16 5.7E4 9.9E3 7.3E2 2.8E1 5.1(10,063) (12,148) (15,254) (20,373) (3

    17 1.8E4 3.4E3 2.8E2 1.3E1 3.1(9181) (10,886) (13,316) (17,057) (2

    18 5.8E5 1.2E3 1.1E2 5.5E2 1.7(8468) (9897) (11,865) (14,747) (1

    19 1.9E5 4.1E4 4.0E3 2.3E2 8.3(7880) (9103) (10,763) (13,052) (1

    20 6.5E6 1.5E4 1.5E3 9.8E3 4.0(7390) (8456) (9852) (11,761) (1

    Values in brackets show the band origin in .Calculations are made using SEE solar ux on 23 June 2009 and at SZA = 60.

    Fig. 9. Limb proles of prominent transitions of N2 VK bands calculated using SEEsolar ux model at SZA = 60. Limb proles of N2 VK band in different wavelengthregions (130150, 200300, 300400, and 400800 nm) are also shown.s 218 (2012) 9891005 1003individual transition in various triplet states are also a factor of2.82.9 higher for the solarmaximumcondition (cf. Table 1). Similarincrease of around a factor of 2.8 can be seen in limb intensity of

    5 6 7 8

    E3 48,147)

    E1 8,216)

    E1 7.1E2 3,455) (140,462)

    E1 3.0E1 5.0E4 0,393) (58,790) (710,500)

    E1 3.6E1 8.3E2 3,560) (37,662) (91,328)

    E1 2.8E1 1.9E1 6.8E3 9,370) (27,985) (49,675) (207,470)

    E2 1.8E1 2.0E1 6.1E2 6,548) (22,452) (34,558) (73,390)

    E2 1.0E1 1.6E1 1.0E1 8.3E34,525) (18,884) (26,773) (45,371) (142,399)

    Fig. 10. Limb proles of total N2 VK bands at three different solar zenith angles (0,60, and 80) calculated using SEE solar EUV ux model. Limb proles calculatedusing S2K and HEUVAC models, and in solar maximum condition (for SEE solar ux)are shown for SZA = 60. Limb intensity prole calculated using HASI N2 density andSEE solar EUV ux is also shown for SZA = 60.

  • aruHuygens Atmospheric Structure Instrument (HASI) measuredthe density prole of N2 in Titans atmosphere (Fulchignoni et al.,2005). In our calculations we have used the density prole of N2observed by HASI, but reduced by a factor of 3.1 to be consistentwith N2 densities measured by Ion and Neutral Mass Spectrometer(INMS) (De La Haye et al., 2007) at 950 km. This reduction is alsorequired for the better agreement in the UVIS-observed and calcu-total N2 VKband for solarmaximumcondition (see Fig. 10).Wehavealso run our model for the moderate solar activity condition usingthe SEE solar EUV ux for 20 June 2002 (F10.7 = 150) at SZA = 60.Model atmosphere remains the same. Table 1 shows the calculatedoverhead intensities of various triplet states during the moderatesolar activity condition,which are a factor of 2 higher than those cal-culated during solar minimum condition.

    4.3. Effect of model atmosphere

    Fig. 11. Calculated limb proles of N2 VK 150190 nm wavelength range emissionson 23 June 2009 for SEE, S2K, and HEUVAC solar EUV ux models at SZA = 56, alongwith the Cassini UVIS observed limb intensity and model prole of Stevens et al.(2011). Model limb prole obtained by taking 5% of the total N2 VK band intensityfor SEE EUV solar ux is also shown.1004 A. Bhardwaj, S.K. Jain / Iclated emission peak altitudes. To see the effect of higher N2 densityon emission intensities, we have run our model using the originalunscaled HASI N2 density prole keeping the other model inputparameters same. Fig. 10 shows the limb prole of N2 VK band cal-culated using HASI N2 density. The altitude of the peak emission issituated at 1052 km with a value of 1.12 kR when HASI N2 den-sity prole is used. Thus, the calculated altitude of peak emissionis around 100 km higher than that calculated by using reduced(by a factor of 3.1) N2 density, but the intensity of emission atthe peak remains the same (1.11 kR).

    5. Summary

    A model for the production of N2 triplet band emissions in thedayglow of Titan is developed. We have used the Analytical YieldSpectra technique to calculate the steady state photoelectron ux,which is compared with the Cassini CAPS observed photoelectronux. The calculated photoelectron ux is in good agreement withthe observed spectrum in the 660 eV energy range. Volume pro-duction rates of various triplet states of N2 have been calculated.Population of any given level of triplet states has been calculatedconsidering direct electron impact excitation and quenching as wellas cascading from higher triplet states in statistical equilibrium con-dition. Volume emission rates are calculated and vertically-integratedto calculate the overhead intensities of N2 VegardKaplan band invarious wavelength regions, viz., 130150, 150200, 200300,300400, and 400800 nm, which are given in Table 1. In addition,the vertical-integrated intensities of First Positive, Second Positive,WuBenesch, B0 ? B, E? C, E? B, E? A, and Reverse First Positivebands of N2, are also calculated and presented in Table 1 along withtheir contributions in different wavelength regions. Vertically-integrated overhead intensities of various vibrational transitionsin triplet states are presented in Tables 28.

    The calculated volume emission rates are integrated along theline of sight to calculate the limb intensity of total VK band. Limbproles of various prominent transitions of VK band are also calcu-lated and presented in Fig. 9. The VK band in the wavelength region200400 nm contribute around 73% of the total VK band intensity,followed by the VK band in visible region (400800 nm) whichcontributes around 22%. The calculated limb intensity prole ofVK 150190 nm band is in good agreement with the recent CassiniUVIS-observed prole. We found that the observed intensity of VKbands can be explained by the photoelectron impact excitationalone (Stevens et al., 2011). The effect of change in solar zenith an-gle is seen in the altitude of peak emission as well as intensity atthe emission peak. Variation in the SZA from 0 to 80 resulted in18% upward shift in the altitude of emission peak, while the limbintensity at the peak decreased by a factor of 5.5. Our calculationsuggests that intensity of CI 156.1 and 165.7 nm emissions dueto photoelectron impact dissociative excitation of CH4 and uores-cence scattering of solar lines by carbon in Titans atmosphere are afew orders of magnitude smaller than the N2 VK 110 (156.3 nm)and 80 (165.4 nm) emission intensities, respectively.

    We have also made a detailed study on the effect of solar EUVux models on the N2 triplet band emission intensities which isa step further to the calculations of Stevens et al. (2011). Emissionintensities calculated by using the S2K model are around 23% high-er than that calculated using the SEE solar ux. The limb intensityat peak calculated using the HEUVAC model is around 13% smallerthan that calculated using SEE solar ux. The calculated intensitiesfor moderate (F10.7 = 150) and high (F10.7 = 240) solar activityconditions are about a factor of 2 and 2.8, respectively, higher thanthose calculated during solar minimum (F10.7 = 68) condition. Cal-culations are also carried out taking the HASI-observed N2 densityin the model atmosphere. Due to higher N2 density in the HASIobservation by a factor of 3.1, the altitude of peak emission shiftedupwards by 100 km; however, the intensity at the peak remainedthe same.

    The calculations presented in this paper will help in under-standing the production of N2 VK and other triplet band dayglowemissions on Titan as well as in other N2-containing planetaryatmospheres.

    Acknowledgment

    Sonal Kumar Jain was supported by Senior Research Fellowshipof ISRO during the period of this work.

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    Production of N2 VegardKaplan and other triplet band emissions in the dayglow of Titan1 Introduction2 Model input3 Results and discussion3.1 Photoelectron flux3.2 Volume emission rates

    4 Effect of various model input parameters4.1 Effect of solar EUV flux model4.2 Effect of solar cycle4.3 Effect of model atmosphere

    5 SummaryAcknowledgmentReferences


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Transportation here we live, vegard ) (1)

Education

Meeting Point N2

Meeting Point N2

Documents

Jism v1 n2

Jism v1 n2

Health & Medicine

rup n2 part.pdf

rup n2 part.pdf

Documents

Triplet correctors specifications

Triplet correctors specifications

Documents

Triplet Extinction Coefficients, Triplet Quantum Yields, and (mainly) Laser Flash Photolysis

Triplet Extinction Coefficients, Triplet Quantum Yields, and (mainly) Laser Flash Photolysis

Documents

N2 Energie Presentation

N2 Energie Presentation

Documents

N2 Portfolio

N2 Portfolio

Documents

Vegard Heide

Vegard Heide

Documents

Ostracon v9 n2

Ostracon v9 n2

Documents

Design of a Cooke Triplet

Design of a Cooke Triplet

Documents

Inner Triplet Supports

Inner Triplet Supports

Documents

Digital Portfolio N2

Digital Portfolio N2

Documents