UV and IR auroral emission model for the outer planets: Jupiter and Saturn comparison

Icarus 213 (2011) 581–592

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UV and IR auroral emission model for the outer planets: Jupiter and Saturn comparison Chihiro Tao ⇑, Sarah V. Badman, Masaki Fujimoto Institute of Space and Astronautical Science (ISAS), Japan Aerospace eXploration Agency (JAXA), Yoshinodai 3-1-1, Chuo-ku, Sagamihara, Kanagawa 252-5210, Japan

a r t i c l e

i n f o

Article history: Received 7 January 2011 Revised 4 April 2011 Accepted 5 April 2011 Available online 12 April 2011 Keywords: Aurorae Jupiter, Atmosphere Saturn, Atmosphere Ionospheres

a b s t r a c t Planetary aurora display the dynamic behavior of the plasma gas surrounding a planet. The outer planetary aurora are most often observed in the ultraviolet (UV) and the infrared (IR) wavelengths. How the emissions in these different wavelengths are connected with the background physical conditions are not yet well understood. Here we investigate the sensitivity of UV and IR emissions to the incident precipitating auroral electrons and the background atmospheric temperature, and compare the results obtained for Jupiter and Saturn. We develop a model which estimates UV and IR emission rates accounting for UV absorption by hydrocarbons, ion chemistry, and Hþ 3 non-LTE effects. Parameterization equations are applied to estimate the ionization and excitation profiles in the H2 atmosphere caused by auroral electron precipitation. The dependences of UV and IR emissions on electron flux are found to be similar at Jupiter and Saturn. However, the dependences of the emissions on electron energy are different at the two planets, especially for low energy (<10 keV) electrons; the UV and IR emissions both decrease with decreasing electron energy, but this effect in the IR is less at Saturn than at Jupiter. The temperature sensitivity of the IR emission is also greater at Saturn than at Jupiter. These dependences are interpreted as results of nonLTE effects on the atmospheric temperature and density profiles. The different dependences of the UV and IR emissions on temperature and electron energy at Saturn may explain the different appearance of polar emissions observed at UV and IR wavelengths, and the differences from those observed at Jupiter. These results lead to the prediction that the differences between the IR and UV aurora at Saturn may be more significant than those at Jupiter. We consider in particular the occurrence of bright polar infrared emissions at Saturn and quantitatively estimate the conditions for such IR-only emissions to appear. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Aurorae are a phenomenon related to the plasma environments around a planet. Magnetospheric dynamics produce various field-aligned current systems which transfer energy and momentum between the planetary magnetosphere and the ionosphere–thermosphere. The aurorae are atmospheric emissions caused by precipitating particles which have often been accelerated by field-aligned potentials. Therefore, the aurora reflects both the magnetospheric conditions and the atmospheric parameters. Aurorae at the outer planets are emitted at infrared (IR), visible, ultraviolet (UV), X-ray, and radio wavelengths. The former three wavebands are related to the emissions from the main atmospheric component of the outer planets, molecular and atomic hydrogen. UV and visible emissions come from hydrogen directly excited by auroral electrons. IR wavelengths are emitted from thermally excited Hþ 3 which is produced from the ionization of ⇑ Corresponding author. Fax: +81 42 759 8456. E-mail addresses: [email protected] (C. Tao), [email protected] (S.V. Badman), [email protected] (M. Fujimoto). 0019-1035/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2011.04.001

atmospheric hydrogen by auroral electrons. Since UV and IR emissions are observable even on the dayside, a substantial number of observations have been obtained, from both ground- and spacebased instrumentation. Around the magnetic poles of Jupiter and Saturn, a bright main oval is observed both in the UV and IR, as well as polar emission at higher latitudes. At Jupiter, footprint aurorae of Galilean satellites are detected at lower latitudes. Statistical studies of the location of the main oval (UV) are available for Jupiter (e.g., Palllier and Prangé, 2001; Grodent et al., 2003) as well as for Saturn (Badman et al., 2006). The jovian main oval is considered to be magnetically conjugate to the magnetospheric closed field region (e.g., Hill, 1979; Cowley et al., 2005) and the polar region surrounded by the main oval covers both closed- and open-field regions. On the other hand, recent observations by Cassini suggest that Saturn’s main oval corresponds to the open-closed field line boundary (Bunce et al., 2008), at least on the dayside, although alternative models have been proposed (Sittler et al., 2006). Therefore, the entire polar region maps to open field lines at Saturn. Several features of both planets’ UV aurora and the corresponding magnetospheric phenomena have been characterized such as reconnection events

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and associated plasma flow (e.g., Grodent et al., 2004; Radioti et al., 2008) and response to the solar wind (e.g., Clarke et al., 2009; Prangé et al., 2004). At infrared wavelengths, ground-based spectral observations have provided the emission location, Hþ 3 density, vibrational temperature, and ionospheric plasma velocity for both Jupiter (e.g., Lam et al., 1997; Satoh et al., 1996; Stallard et al., 2001, 2002, 2003) and Saturn (e.g., Stallard et al., 2007; Melin et al., 2007). Because the emissions at UV and IR wavelengths are produced via different mechanisms, it is important to compare the observations at different wavelengths to understand the underlying physics. Comparing the IR and UV data, Clarke et al. (2004) showed near-simultaneous observations of jovian UV and IR emissions. The UV and IR images were taken two minutes apart by the Hubble Space Telescope (HST) and Infrared Telescope Facility (IRTF), respectively. Clarke et al. (2004) reported differences in the intensity along the main oval, narrower UV emission on the dawn side relative to the broader IR, a longer Io auroral tail feature in the UV than the IR, and different fine structures in the polar region. Stallard et al. (2008) reported Saturn’s IR auroral structure, as observed by the Cassini Visual and Infrared Mapping Spectrometer (VIMS) experiment. Some features, i.e., a spiral feature and circular shape of the main oval, are common with those observed in UV (e.g., Clarke et al., 2005). In addition, recent statistical analysis has indicated that the UV and IR main oval aurorae typically lie at the same location and are thus driven by the same field-aligned current system (Badman et al., 2011). However, Stallard et al. (2008) also detected intense IR emission in the region poleward of the main oval. Similar UV aurora covering the polar region have not been observed so far. This IR emission is from the latitudes higher than the main oval which is expected to map onto plasma-depleted open field lines (e.g., Cowley et al., 2005; Bunce et al., 2008). Auroral emission models have been developed to explain the observed UV and IR emissions, relating their spatial and temporal variations to parameters such as auroral electron energy and flux, atmospheric temperature, and Hþ 3 density. Gérard and Singh (1982) estimated UV emission rates as a function of auroral electron energy flux and atmospheric hydrogen density at Jupiter and Saturn. Waite et al. (1983) developed a detailed model to obtain UV emission intensity caused by excitation due to solar EUV and auroral electrons. Grodent et al. (2001) used an estimated auroral electron spectrum to solve electron precipitation dynamics and thermal balance in Jupiter’s atmosphere, constrained by observed FUV and Hþ 3 and hydrocarbon IR emission profiles. They found the altitude of the maximum UV volume emission to be located at 200 km above the 1-bar level, lower than that of the IR peak at 350 km. Hydrocarbon molecules present at low altitudes absorb UV at shorter wavelengths <140 nm. Using this absorption behavior as well as the energy deposition characteristics of precipitating auroral electrons, the electron energy was estimated to be several 10s to a few 100s of keV from color-ratio observations at Jupiter (e.g., Gérard et al., 2003; Gustin et al., 2004a). Comparing UV spectral lines between models and observations at Jupiter, Gustin et al. (2004b) estimated both the precipitating electron energy and the hydrocarbon distribution in the atmosphere. The estimated auroral energy was in a similar range to that found by Gustin et al. (2004a). For Saturn, Gustin et al. (2009) inferred the electron energy and atmospheric temperature to fall in the ranges 4.4–342 keV and 500–900 K, respectively, using Cassini Ultraviolet Imaging Spectrograph (UVIS) and Far Ultraviolet Spectroscopic Explorer (FUSE) data. Modeling has also attempted to account for the departure of Hþ 3 populations from local thermal equilibrium (LTE), which acts to reduce the IR emission intensity. Melin et al. (2005) suggested the importance of non-LTE effects in Jupiter’s high altitude atmosphere

where reduced H2 density leads to a reduction in collisionally excited Hþ 3 , such that the LTE distribution is not achieved. They showed that the non-LTE effects become significant at altitude >1500 km and that the LTE assumption overestimates the emitted line intensity by a factor of 3 compared to the case when non-LTE effects are taken into account. We now consider the conditions that could lead to significant differences in IR and UV emissions, such as the bright IR polar emissions at Saturn discussed by Stallard et al. (2008). Although simultaneous UV images are not available for those events, the fact that the same structure has not been observed in the past extensive UV data led Stallard et al. (2008) to conclude that these emissions are an IR-dominated phenomenon. Candidate mechanisms that could produce such differences are as follows: (i) low energy electrons producing Hþ 3 at high altitude with a high temperature, so as to enhance IR emission, (ii) high energy electrons depositing their energy at low altitude where hydrocarbon absorption of the UV increases the IR/UV ratio, (iii) enhancement of the background temperature increasing IR emission selectively and efficiently. Which of these processes effectively contributes to the IR-dominant emission in the saturnian polar region? In order to answer this question, it is important to investigate the theoretical dependence of UV and IR emission intensities on auroral electron energy, flux, and atmospheric temperature. It should also be noted that an analogous jovian phenomena has not been observed, although transient polar emissions are commonly detected (e.g., Grodent et al., 2003). Can we explain the absence of IR-only polar emission at Jupiter using a similar model, but invoking differences in atmospheric components and/or temperature? In order to understand the similarities and differences of UV and IR emissions at Saturn and Jupiter in a systematic way, we develop a model that takes into account the dependence of these emissions on electron energy, flux, and atmospheric temperature. The structure of the paper is as follows. The emission model is described in Section 2. Emission altitude profiles and their dependences are presented in Section 3. In Section 4 we discuss the different characteristics of emissions at Jupiter and Saturn and estimate quantitatively how the IR-dominant polar emission observed at Saturn can be explained. Section 5 summarizes our results and conclusions. 2. Auroral emission model Our model provides UV and IR emission rates depending on the input parameters of a precipitating auroral electron energy

Fig. 1. Flowchart of our model. See details in the text.

C. Tao et al. / Icarus 213 (2011) 581–592

spectrum and the atmospheric temperature and composition structure. Fig. 1 shows a flowchart of the model, which we now describe. Auroral electrons collide with and excite atmospheric molecules and atoms. The UV aurora is emitted from electron-excited H2 and H when it de-excites to its ground state. Considering absorption of UV by hydrocarbon molecules, we generate a height-integrated transmitted spectrum. Auroral electrons also ionize molecular hydrogen, which can undergo various chemical reactions to produce ions including Hþ 3 . Following collisions with background H2 under high thermospheric temperature, Hþ 3 is excited vibrationally. Some excited Hþ ions de-excite by IR emission 3 to generate the aurora of interest in this study. Our model estimates the population of excited Hþ 3 under non-LTE conditions caused by this efficient IR emission. For the different planets, Jupiter and Saturn, we use the same model code with different inputs. We focus on steady state output in this study. Details are described in the following sections. 2.1. Background atmosphere Fig. 2 shows the assumed atmospheric temperature and density profiles for Jupiter and Saturn. The exospheric temperature in the high-latitude region is enhanced due to auroral electrons and Joule heating effects. For Jupiter, we refer to the temperature profile in Grodent et al. (2001) constructed by using several observations. Neutral mixing ratios of H and He are taken from Perry et al. (1999) based on solutions involving diffusive equilibrium and detailed chemistry. Neutral mixing ratios of CH4, C2H2, and C2H4 are from a detailed hydrocarbon chemistry study by Gladstone et al. (1996). For Saturn, we use the high-latitude temperature model proposed by Gérard et al. (2009) following analysis of both auroral limb images and spectral observations. Neutral mixing ratios of H, He, and hydrocarbons are taken from those in Moses and Bass (2000) and Moses et al. (2000). They solved detailed photochemistry to obtain results comparable with observations. Mixing ratios of H2O originating from the planetary rings and moons are taken from the observation-based results of Moore et al. (2009).

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The electron temperature is assumed to be equal to the neutral temperature (Waite et al., 1983). This one-dimensional model has 80 altitude layers at a resolution of 0.3 pressure scale heights. 2.2. Auroral precipitation The altitudinal distribution of ionization rates in an H2 atmosphere caused by electron precipitation is obtained using a parameterized equation (Hiraki and Tao, 2008; Tao et al., 2009). Though the parameterization equation is based on results from a Monte Carlo simulation solving auroral electron precipitation into the jovian atmosphere, the equation itself is applicable to an arbitrary initial energy spectrum of precipitating electrons and an arbitrary density profile of an H2-dominant atmosphere (Hiraki and Tao, 2008). Here we apply it to Saturn in addition to Jupiter. The auroral electrons are assumed to form a Maxwellian distribution with variable mean energy and flux. Hereafter the quoted electron energy e0 is equal to half the mean energy of the distribution, and the electron temperature is e0/kB. We assume auroral electrons precipitate into the atmosphere vertically for simplicity. 2.3. Solar EUV In addition to auroral electrons, solar EUV radiation also ionizes the upper atmosphere. To obtain the solar EUV flux at the top layer of the atmosphere, we use the EUVAC (solar EUV flux model for aeronomic calculations) model (Richards et al., 1994), which is based on the reference spectra derived from sounding rocket observations. We assume low solar activity conditions of F10.7 = 80  1022 W m2 Hz1 in this study. Because this model gives the solar flux at the Earth, i.e., at a distance of 1 AU from the Sun, the flux value is divided by a factor 5.22 (9.62) for the case of Jupiter (Saturn) located at 5.2 (9.6) AU from the Sun. The photoþ þ ionization and absorption rates for Hþ 2 ; CH4 , and C2 H2 from H2, CH4, and C2H2 are calculated using appropriate cross sections (Schunk and Nagy, 2000; after Kim and Fox, 1994). We fix the solar zenith angle vsun as 75° and neglect daily variations. This angle

(a)

(b)

(c)

(d)

Fig. 2. Vertical profiles assumed in this study: (a) temperature and (b) neutral number densities for Jupiter and (c) temperature and (d) neutral number densities for Saturn. Legends for the lines representing neutral species in (b) and (d) are shown in the right side of each figure.

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corresponds to a typical auroral/polar region at equinox. We do not include Saturn ring shadowing effects. 2.4. Ion chemistry and diffusion Our model solves a simplified set of neutral-ion chemical reacþ + + tions (see Table 1) for 13 ions (H+, Hþ 2 ; H3 , H2O , H3O , þ þ þ þ þ þ þ þ CH3 ; CH4 ; CH5 ; C2 H2 ; C2 H3 ; C2 H5 ; C3 Hn ; C4 Hn , where the latter two symbols represent classes of ions) and six fixed neutral species (H2, H, CH4, C2H2, C2H4, H2O; see Fig. 2). The most significant production and loss reactions are selected from the detailed ion chemical model presented by Kim and Fox (1994) to describe the fundamental ionospheric structure and conductance. In order to apply it to Saturn, H2O ions are added. Two important loss processes of H+ are dissociative recombination with H2O and reactions with vibrationally excited H2(v P 4). We assume the H2(v P 4)

Table 1 Ion chemical reactions and rates used in this study. References: 1, Hiraki and Tao (2008); 2, Schunk and Nagy (2000); 3, Kim and Fox (1994); 4, e.g., Majeed et al. (1991); 5, Anicich (1993); 6, Perry et al. (1999); 7, Millar et al. (1997). Te denotes the electron temperature. The unit of measurement for the rates is cm3 s1. Reactions H2 + e⁄ H + hv H2 + hv CH4 + hv

C2H2 + hv H+ + H2 (v 6 4) H+ + CH4 H+ + H2O H+ + H2 H+ + CH4 H+ + C2H2 H+ + C2H4 Hþ 2 þ H2 O CHþ 3 þ CH4 CHþ 4 þ H2 CHþ 5 þ C2 H2 CHþ 5 þ H2 O C2 Hþ 2 þ H2 C2 Hþ 3 þ CH4 C2 Hþ 3 þ C2 H2 C2 Hþ 3 þ C2 H4 C2 Hþ 5 þ C2 H2

 ! CHþ 4e  ! C2 H þ 2 þe ! Hþ 2 þH

! CHþ 3 þ H2 ! CHþ 4 þH ? H2O+ + H þ ! H3 þ H ! CHþ 5 þ H2 ! C2 H þ 3 þ H2 ! C2 H þ 3 þ 2H2 ! C2 H þ 5 þ H2 ? H3O+ + H ! C2 H þ 5 þ H2 ! CHþ 5 þH ! C2 H þ 3 þ CH4 ? H3O+ + CH4 ! C2 H þ 3 þH ! C3 H5 þ þH2

H2O+ + H2 H+ + e

! C4 H þ 3 þ H2 ! C2 H þ 5 þ C2 H2 ! C3 H þ 3 þ CH4 ! C4 H þ 5 þ H2 ? H3O+ + H ? products

 Hþ 3 þe

? products

 CHþ 3 þe

? products ? products

 CHþ 4 þe  CHþ 5 þe

Rates

 ! Hþ 2 þe þe ? H+ + e  ! Hþ 2 þe ? H+ + e + products  ! Hþ 2 þ e þ products ? H+ + e + products  ! CHþ 3 þ e þ products

? products

 C2 Hþ 2 þe

? products

 C2 Hþ 3 þe  C2 Hþ 5 þe  C3 Hþ n þe  þ e C4 Hþ n H2O+ + e H3O+ + e

? ? ? ? ? ?

products products products products products products

References 1 2 2 2 2 2 3 3

2  109

3 4

3.4  109

5

7.4  1010 8.2  109 2  109 2.4  109 3.2  109 2.03  109 8.7  1010 5.3  109 1.10  109

5 5 6 6 5 5 5 5 5

3  1011 1.56  109

6 3

3.7  109 1.8  1012 2.00  1010 2.16  1010 9.30  1010 6.84  1011 1.22  1010 7.6  1010 3.5  1012 (300/ Te)0.75 1.15  107 (300/ Te)0.65 3.5  107 (300/Te)0.5 3.5  107 (300/Te)0.5

5 After 6 3 3 3 3 3 5 7

2.78  107 (300/ Te)0.52 2.71  107 (300/ Te)0.5 4.5  107 (300/Te)0.5 7.5  107 (300/Te)0.5 7.5  107 (300/Te)0.5 7.5  107 (300/Te)0.5 3.6  107 (300/Te)0.5 1.0  106 (300/Te)0.5

6

6 7 7

6 7 7 6 6 7 7

density based on the vibrational temperature (e.g., Moses and Bass, 2000). The vibrational temperatures for Jupiter and Saturn are simply assumed to be 900 K and 1500 K, respectively, larger than their neutral temperatures inferred from detailed vibrational chemistry models (Cravens, 1987; Majeed et al., 1991). Fig. 3 shows ionization profiles caused by auroral electrons and solar EUV described in Sections 2.2 and 2.3. Ionization caused by auroral electrons increase with increasing electron initial energy, where energies of 0.1, 1, 10, and 100 keV have been shown. Solar + EUV provides Hþ 2 (dashed lines), H (dot-dashed) and hydrocarbon (dotted) ions in our model. We take into account ambipolar diffusions of H+ and Hþ 3 as follows:

dni =dt ¼ Q i  Li þ cosðvÞd=dzfD dni =dz þ ðni D=TÞdT=dz  ðDni mi GÞ=ð2kB TÞg;

ð1Þ

where ni is the ion density; t is time; z is altitude; Qi and Li are production and loss rates due to ion chemistry; v is the angle between the magnetic field and the vertical (here simplified to cos(v)  1); mi is ion mass; T is temperature; G is the magnitude of gravitational acceleration (25 ms2 for Jupiter and 10 ms2 for Saturn); kB is the Boltzmann constant. D ¼ 2kB T=mi v iH2 is the ambipolar diffusion coefficient, where v iH2 is the collision frequency of ions and H2 taken from Chapman and Cowling (1970). We solve the ion composition equations using the implicit method in Shimazaki (1985). This method requires knowledge of the density at the upper boundary of the model, but this has not been constrained by observations. We simply assume the same reduction ratio of the density with the neighboring altitude below, i.e.,

ni at K ¼ n2iat K1 =ni at K2 ;

ð2Þ

where K indicates the layer of the upper boundary. For simplicity, we do not take into account transport by winds. The ion chemistry model has a time resolution of 1000 s and reaches a quasi-steady state after a time integration of 100 rotation periods (41 Earth-days). The results at 100 rotations are shown hereafter. 2.5. IR emission estimation 2.5.1. Non-LTE effect We consider the non-LTE populations of the Hþ 3 vibrational states. According to the method of Melin et al. (2005), we calculate the detailed balance between 17 vibrational levels up to v2 = 4. This balance calculation formula was originally proposed by Oka and þ Epp (2004) for Hþ 3 rotational states. H3 vibrational levels at each altitude are determined from the balance between collisional excitation and de-excitation with H2 and IR emission. The transition probability is taken from Dinelli et al. (1992). The time step is set as a function of altitude depending on the H2 density (Melin et al., 2005). The calculation runs until the time variation of the densities becomes lower than a threshold value, (dni/dt)/ni 6 107. This calculation does not alter the input temperature profiles. Fig. 4 shows the altitude profile of the LTE fraction for the different Hþ 3 excited states, where the LTE fraction is the ratio of the density including non-LTE effects to the density determined in LTE, i.e., gðzÞ ¼ nHþ3 nonLTE =nHþ3 ;LTE . For both Jupiter (Fig. 4a) and Saturn (Fig. 4b), the LTE fractions decrease in the high altitude regions, except for the ground state (dashed line) which remain P1. In this study we focus on the strong emission fundamental line, which is shown by the black lines. Departure from LTE becomes large at 1000–2000 km for Jupiter and at 2000–3000 km for Saturn. The LTE fraction is a function of background temperature and H2 density, as shown in Fig. 5a. The LTE fraction increases with

C. Tao et al. / Icarus 213 (2011) 581–592

(a)

585

(b)

Fig. 3. Altitude profiles of ionization rates caused by auroral electrons (black lines) and solar EUV (gray lines) on (a) Jupiter and (b) Saturn. Ionization rates caused by auroral electrons increase with increasing electron initial energy, where energies of 0.1, 1, 10, and 100 keV have been shown. Dashed, dot-dashed, and dotted lines show the þ production rates of Hþ 2 ; H , and hydrocarbon ions due to solar EUV, respectively.

increasing H2 density (lower y-axis) and/or with smaller temperature (left side of x-axis). The former effect can be attributed to the fact that low H2 density reduces collisional excitation. The latter effect occurs since high temperature increases emission efficiency, thus decreasing the LTE fraction. The atmosphere temperature– density profiles of Jupiter and Saturn are shown by diamonds and pluses, respectively. In the constant temperature region, the LTE fraction is <0.1 for Jupiter and varies from 0.9 to <0.1 depending on H2 density for Saturn. The LTE fraction is estimated independently of the time variation of the ion chemistry. The Hþ 3 vibrational density in non-LTE is estimated from the density in LTE multiplied by the LTE fraction. This process is appropriate if the relaxation time is shorter than ion chemical time constants. This relaxation time is also plotted in Fig. 5b as a function of temperature and H2 density. Under the atmospheric conditions of Jupiter and Saturn, this time decreases from several tens of seconds at high altitude to lower values at lower altitude. These results are not largely affected by the initial conditions, e.g., whether the vibrational levels are distributed under LTE conditions or concentrated in the ground states. 2.5.2. IR emission intensity þ Using the Hþ 3 ion density NH3 estimated in Section 2.4, the LTE fraction g, and the atmospheric temperature T, we obtain the IR emission strength of the fundamental line as follows:

IIR ðxif ; zÞ ¼ N Hþ gðzÞgð2J þ 1Þhcxif Aif exp ðEf =kB T Þ=Q ðTÞ; 3

ð3Þ

where IIR is the emission intensity; xif = 2529.5 cm1 is the wavenumber; g = 4 is the nuclear spin weight; J = 1 is the rotational quantum number of the upper level of transition; h is the Planck constant; c is the light velocity; Aif is the Einstein coefficient of 129 s1; Ef is the energy of the upper level of the transition 2616.5 cm1; kB is the

(a)

P Boltzmann constant; Q = i(2J + 1)gi exp(Ei/kBT) is the partition function (Neale and Tennyson, 1995). We confirm that the dependence on electron energy, flux, and atmospheric temperature of other emission lines in the 4 lm range as similar to that of the fundamental line. We focus on the fundamental line as representative of IR emission in this study. 2.6. UV emission estimation Ultraviolet emissions mainly consist of H Lyman a and H2 Lyman and Werner bands excited by precipitating electron impacts. Here we consider only H2 band emissions because the contribution of H Lyman-a emission to the total UV emission is small (e.g., <10%, Perry et al., 1999). In H2, the excitation rates to the B and C states are directly related to the strength of the Lyman and Werner bands, respectively. Here we obtain a UV spectrum from excited B and C states whose cross sections are large. Since the altitude profiles of ionization (qion) and excitation rates (qexB, qexC) are almost proportional, the parameterization function for the excitation rates may be described by multiplying the ionization rate qion by a certain factor for simplicity; i.e., qexB(e0, z) = gB(e0)qion(e0, z) and qexC(e0, z) = gC(e0)qion(e0, z). e0 is the initial electron energy. qion(e0, z) is obtained from the parameterization equation in Hiraki and Tao (2008) as mentioned in Section 2.2. The coefficients are also obtained from Monte Carlo simulations (Hiraki and Tao, 2008) as follows:

gB ðe0 Þ ¼ 0:499 þ 0:310log10 e0 þ 0:152ðlog10 e0 Þ2 ; gC ðe0 Þ ¼ 0:396 þ 0:228log10 e0 þ 0:081ðlog10 e0 Þ2 ;

ð4Þ ð5Þ

with e0 in keV. We confirm that this simplified formula provides an excitation profile in good correspondence with simulation results.

(b)

Fig. 4. Departure from the thermal population of the Hþ 3 vibrationally excited states for (a) Jupiter and (b) Saturn. Gray lines are all levels considered in this estimation and black lines show that of the v2 level of our interest. Dashed lines indicate the ground states.

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(a)

(b)

Fig. 5. Contour maps of (a) LTE fraction and (b) time constants as a function of temperature and H2 density. Parameters for Jupiter and Saturn are shown by diamonds and pluses, respectively, in (a).

The small effect of the quenching of B and C states (Gérard and Singh, 1982) is ignored in this estimation. The emission intensity of the transition band from the upper v0 to the lower v00 state, IW v 0 ;v 00 , in the Werner system is given by X!C C!X IW v 0 ;v 00 ¼ Ic qv 0 ;o Av 0 ;v 00 =

X

Av 0 v 00 ;

ð6Þ

v 00

where Ic is the total intensity of the C state; qX!C v 0 ;0 represents the Frank–Condon factors for the excitation rate of the C state into the v0 level (Spindler, 1969a); AC!X v 0 v 00 is the Einstein coefficient for the transition from v0 to v00 (Allison and Dalgarno, 1970). The fracP tion AC!X v 0 v 00 = v 00 Av 0 v 00 corresponds to the branching ratio for the line. The emission intensity of a v0 ? v00 transition band in the Lyman system, ILv 0 v 00 is given by

(

L

Iv 0 ;v 00 ¼

IB qX!B v 0 ;0

þ

IE;F qX!E;F v 0 ;0

X v 00

,

E;F!X

Av 0 v 00

, X B!X ðAv 0 v 00 þ Dv 0 v 00 Þ;  Av 0 v 00 v 00

,

B!X  1:25IB qX!B v 0 ;0 Av 0 v 00

X

X

!)

Av v

0 00

v 00

ð7aÞ

Av 0 v 00 ;

ð7bÞ

v 00

X!E;F where IB and IE,F are the total emission intensities. qX!B v 0 ;0 and qv 0 ;0 represent the Frank–Condon factors of the B (Spindler, 1969b) and E, F states, respectively. AB!X v 0 v 00 is the transition probability for a band from the B state to the ground state (Allison and Dalgarno, 1970). L AE;F!X v 0 v 00 is that for a band from the E or F states to the B state. Dv 0 v 00 is the dissociation probability of a particular band. The second term in the brackets is the contribution of cascading from the E or F states. This contribution rate, 25% (Gérard and Singh, 1982), is incorporated into Eq. (7b) for simplicity in this estimation. UV auroral emissions are absorbed by hydrocarbon molecules existing at low altitude. Using absorption cross sections rCHs summarized in Parkinson et al. (2006), the transmitted spectrum is obtained as

Iobs ðkÞ ¼ I0 ðkÞ exp 

Z X

!

rCHs NCHs ðzÞ= cosðvsun Þdz ;

ð8Þ

s

where I0 is the spectrum before absorption and vsun is the solar zenith angle. 3. Results 3.1. Jupiter Fig. 6 shows the ion density and emission profiles vs. altitude obtained for Jupiter. The input auroral electron energy is varied

between 0.1 (dot-dashed line), 1 (dashed), 10 (dotted), 100 keV (solid) with a fixed flux of 9.375  1011 m2 s1 corresponding to 0.15 lA m2. Fig. 6a shows that H+ (orange line) is the dominant ion at high altitude >2000 km. Hþ 2 (purple line) produced by auroral þ electrons and solar EUV reacts with H2 to form Hþ 3 . H3 (red line) is the dominant ion in the altitude range of 500–1500 km. At lower altitude, the main ionized species becomes hydrocarbon ions which are produced by solar EUV and dissociative recombination of Hþ 3 with hydrocarbons located at low altitude <500 km. The higher energy electrons can precipitate deep into the atmosphere, which can clearly be seen in the UV emission altitude profile (blue line) peaking at 300 km in Fig. 6b. The altitude profile of the UV emission is similar to the ionization profile in Fig. 3a except for below 300 km where hydrocarbon absorption becomes significant. The peak altitude of Hþ 3 density decreases with increasing electron energy. The density has a small local minimum at the H+ peak altitude, 2200 km. This relates to relatively rapid ion recombination of Hþ 3 with enhanced electron densities there. The local maximum of these ion densities around 1600 km is caused by ionization by solar EUV radiation. The altitude profile of IR emitted from Hþ 3 shown by the red lines in Fig. 6b reflects the density profile of Hþ 3 , except for the rapid decrease at high altitude compared to the Hþ 3 density and UV emission where non-LTE effects become significant. The dependence of altitude-integrated values of UV and IR emissions on electron energy, flux, and exospheric temperature is shown by black diamonds and crosses in Fig. 7. They are normalized by the value for the case with 10 keV, 0.15 lA m2, and 1200 K, respectively. The reference values for this case are 38.1 kR for the UV emission rate in the 117–174 nm wavelength range and 33.0 lW m2 str1 for the IR fundamental line Q(0, 1). Though the reference energy and flux are the lower end of the ranges estimated from observations, 10–150 keV and 0.04– 0.4 lA m2 (e.g., Gustin et al., 2004a,b), we select these values for comparison with the Saturn case later. UV emission increases directly with the electron energy at 0.1– 100 keV. The energy dependence of IR emission at <0.5 keV is small, because for these energies Hþ 3 is mainly produced by solar EUV. IR emission also increases with energy at 0.5–10 keV, while it decreases with increasing energy at >20 keV. This is explained by considering electrons with high energy which penetrate to low altitude where the atmospheric temperature is low. Low temperature reduces IR excitation efficiency. IR emission from perfect LTE conditions is shown by triangles, indicating that the non-LTE effect works effectively for low electron energies, reducing IR emission by factors of the order 10%. The dependences of UV and IR emissions on electron energy without hydrocarbons are shown by gray diamonds and crosses. Absorption of UV and loss of Hþ 3

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(a)

(b)

Fig. 6. Vertical profiles of Jupiter’s (a) ion density and (b) volume emission rate for precipitating electrons with initial energy 0.1 (dot-dashed), 1 (dashed), 10 (dotted), and þ 100 keV (solid). Orange, purple, red, and green lines in (a) show Hþ ; Hþ 2 ; H3 , hydrocarbon ions, respectively. In (b), blue lines show the UV emission rates in the 117–174 nm wavelength range, and red lines show the IR emission rates of the Q(1, 0) line. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(b)

(a)

(c)

Fig. 7. Dependence of Jupiter’s IR and UV emission rates on (a) energy, (b) number flux, and (c) exospheric temperature normalized by those in the 10 keV, 0.15 lA m2, and 1200 K cases. IR emission rates in non-LTE and LTE conditions are shown by black diamonds and gray triangles, respectively, and UV rates are shown by black crosses. IR and UV results from the case excluding hydrocarbons are shown by gray diamonds and gray crosses, respectively.

through dissociative recombination by hydrocarbons reduce the UV and IR rates, respectively, for higher energy electrons. The dependence of UV emissions on electron flux, plotted in Fig. 7b, is more sensitive than that of the IR. The former is directly proportional to the electron flux, while the latter is proportional to the square root of the flux, as will now be shown. The IR dependence indicates that the peak Hþ 3 density is mainly determined by the Hþ 3 production rate P (itself almost proportional to the electron flux) and the loss by ion recombination, as follows:

dn =dt ¼ P  kn n Hþ 3

Hþ 3

e

P

2 knHþ 3

) 0;

ð9Þ

where nHþ is Hþ 3 density; P is the production rate; k is the ion recom3 bination coefficient. In the steady state, the left-hand side becomes negligible. Since the production rate P is almost proportional to the flux over the certain energy range capable of ionizing hydrogen, then we obtain

nHþ ¼ 3

qffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P=k / ðfluxÞ=k:

ð10Þ

IR emission is directly related to the Hþ 3 density and thus to the square root of the flux. At the IR peak altitude, Hþ 3 is dominant, and the above loss assumption is valid. If other ions, such as H+ and/or H2O+ + H3O+, exist at the same altitudes, the assumption nHþ ¼ ne in Eq. (9) must be modified by increasing the electron 3 density ne above the value of nHþ . In the extreme case, where ne 3  is kept constant, we obtain nþ H3  P=ðkne Þ, i.e., it is directly related to the electron flux. The shallower slope seen in <0.005 lA m2 is due to the prevalence of solar EUV photoionization.

Fig. 7c shows that the IR emission increases by one order for an exospheric temperature enhancement from 800 to 2000 K. The dependence in the case with non-LTE effects included is less sensitive than in the LTE case (gray line). The UV emission rate exhibits no temperature dependence. 3.2. Saturn Altitude profiles of ion densities and emission rates for Saturn are shown in Fig. 8. Compared to the jovian case, water-ions H2O+ and H3O+ (light-blue) produced from H2O are also included, and dominate at 800–1300 km altitude. The other main features are similar to those at Jupiter: H+ is dominant at high altitudes at >2600 km, Hþ 3 is dominant at 1300–2600 km, and hydrocarbon ions are dominant at low altitude 500–800 km. An energy dependence is also seen in the Hþ 3 density profiles. A smaller peak density of Hþ 3 is obtained for 100 keV electrons (solid line) compared to 10 keV electrons (dotted line) because water ions directly and indirectly (through electron density enhancement) decrease the number of Hþ 3 ions. The UV and IR emission profiles shown in Fig. 8b are related to the auroral electron penetration altitude and Hþ 3 density, respectively, as described for Jupiter. Fig. 9 shows the dependence of altitude-integrated emission rates of UV (black crosses) and IR (black diamonds) on electron energy, flux, and exospheric temperature. They are normalized to the values obtained under the nominal conditions 10 keV, 0.15 lA m2, 420 K, respectively. The reference emission rate values for Saturn are 37.3 kR for the UV emission over the wavelength

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(a)

(b)

Fig. 8. As Fig. 6 except for Saturn. Light-blue lines in (a) show H2O+ + H3O+ density. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

(a)

(b)

(c)

Fig. 9. As Fig. 7 except for Saturn normalized by rates in the 10 keV, 0.15 lA m2, and 420 K cases.

range 117–174 nm and 0.530 lW m2 str1 for the IR emission at the fundamental line Q(0, 1). The dependences of emission rates on electron energy for Saturn are similar to those at Jupiter: UV emission rate increases with energy, a local maximum in the IR emission is present at around 10 keV, the hydrocarbon effect reduces UV emission for high energy electrons, and the non-LTE effect on the IR emission rate arises at low electron energy. This non-LTE effect at Saturn is less sensitive than that at Jupiter. The IR emission dependence on energy in the range 0.3–6 keV at Saturn is smaller than the Jupiter case. The smaller IR reduction at high energy is related to the existence of H2O and its ions dominating above hydrocarbon altitudes. The UV emission rate shown in Fig. 9b is directly related to the electron flux as seen for Jupiter, while the dependence of the IR emission on the electron flux is steeper than the square root of the flux. This is explained by the existence of water ions at lower altitudes affecting the Hþ 3 density and IR emission profile as previously discussed in Section 3.1. The temperature dependence of IR emission shown in Fig. 9c varies by almost three orders of magnitude over the temperature range 340–860 K. The difference between this relationship and that observed at Jupiter is discussed in the following section. 4. Discussion 4.1. Jupiter and Saturn comparison The different dependence of emission rates on electron energy and temperature between the Jupiter and Saturn models seen in the previous section is summarized as two main points: (1) the temperature-dependent variability of IR emissions for Saturn

(three orders of magnitude, Fig. 9c) is larger than that for Jupiter (one order of magnitude, Fig. 7c) and (2) the electron energy dependence of IR emission for Saturn (Fig. 9a) has a smaller slope in the energy range of 0.5–5 keV than that for Jupiter (Fig. 7a). In this section we will discuss the cause of these differences. For the temperature dependence of IR emissions, the difference is related to the difference in the sensitivity of non-LTE effects related to the temperature variability. We focus on the dependence of LTE fraction rates on temperature in Fig. 5a at the H2 density of 1012 cm3 where an auroral electron with 10 keV contributes to the ionization peak (see Figs. 2 and 3). The LTE fraction at this H2 density does not change with variation of the exospheric temperature by several hundred K at Jupiter, while the LTE fraction changes considerably for a similar relative temperature variation at Saturn. The IR emission rate for Jupiter is plotted in Fig. 10 over the same exospheric temperature range (300–900 K) previously shown for Saturn. The emission varies over almost three orders of magnitude for a 340–860 K variation as in the Saturn case (Fig. 9c), i.e., if Jupiter’s exospheric temperature was similar to Saturn’s then the same large increase in IR emission rate for a given temperature increase would be observed. Next we consider the different energy dependences of the IR emission rates between the two planets, which are plotted in Figs. 7a (Jupiter) and 9a (Saturn). Jupiter’s IR emission has a larger slope in the energy range of 0.5–5 keV. Different conditions for Saturn are illustrated: without H2O, high exospheric temperature of 860 K, and the combined cases are shown by black triangles, pluses, and squares, respectively, in Fig. 11. For all conditions, IR emission decreases for low energy electrons and increases for high energy electrons compared to the original conditions, with the largest changes seen in the combined case. The high temperature results in a steeper slope in the low electron energy case.

C. Tao et al. / Icarus 213 (2011) 581–592

Fig. 10. As Fig. 6c, except that temperature varies from 420 K to 860 K.

Fig. 11. Dependence of Saturn’s IR and UV emission rates on energy normalized by those in the 10 keV cases. Gray lines show the IR and UV rates under the original settings for comparison. IR rates without H2O, with an exospheric temperature of 860 K, and these combined cases are shown by triangles, pluses, and squares, respectively.

High exospheric temperature augments the non-LTE effect at high altitudes, which is largely reflected in the low electron energy case. The effects of including H2O on IR emissions from low energy electrons are understood as follows. H2O reacts with H+ to produce þ Hþ 2 and then H3 . In addition to this production process, a reduction of H+ as well as background electrons decreases the ion recombination rate of Hþ 3 with the electrons. Water ions decrease the amount of Hþ 3 at low altitudes as seen in Fig. 8a. Increases and decreases of Hþ 3 at high and low altitudes, respectively, by H2O results in relatively larger IR emission for the low auroral electron energy case. For Jupiter, the sensitivity of UV and IR emission rates on the atmospheric temperature and the precipitating electron energy is much smaller than that for Saturn. Jovian UV and IR aurora are expected to show a high correlation when these parameters change. While the different time constants of these emissions need to be taken into consideration, these characteristics would explain why jovian polar emissions are observed in both UV and IR wavelengths while IR dominates in the polar region at Saturn. 4.2. Saturn’s IR-only emission in the polar region Here we estimate the conditions for an IR enhancement observed in the polar region at Saturn using our model. The polar IR aurora events detected by Cassini VIMS covered most of the polar region and were separated from the main oval by a narrow dark region (Stallard et al., 2008). The polar IR emission intensity was comparable to that of the main oval. On the other hand, UV aurora in Saturn’s polar regions seems to be more localized as a bright dawn emission (Clarke et al., 2005) and does not extend over to the dusk side like the IR events. Preceding the discussion about Saturn’s polar IR emission, let us firstly confirm that our model is capable of reproducing the

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observed emission intensities of Saturn’s main oval. The auroral electrons which generate Saturn’s main oval are estimated to have energies of 10–18 keV from Cassini/UVIS FUV and FUSE FUV/EUV spectra and 4.4–342 keV from Cassini/UVIS and EUV spectra (Gustin et al., 2009). Estimates of electron flux in magnetosphere– ionosphere coupling models (e.g., Cowley et al., 2004) are 0.15 lA m2. Our model predicts that auroral electrons with 10 keV and 0.15 lA m2 generate 37.3 kR emission in the 117– 174 nm UV wavelength range and 0.530 lW m2 str1 emission in the IR fundamental line emission Q(0, 1), as shown in Section 3.2. IR emission in the R(3, 3) line becomes 0.340 lW m2 str1 and 16 the Hþ m2. These are well within 3 column density is 5.62  10 the observed ranges, namely, 1–100 kR from HST/STIS observations (e.g., Clarke et al., 2005), and 0.05–0.5 lW m2 str1 in the IR R(3, 3) 16 line emission, and Hþ m2 from 3 column density of (1.9–7.3)  10 ground observations (Melin et al., 2007). Now we move onto the polar emission. In the IR, the emission ratio between the main oval and the polar emissions shown by Stallard et al. (2008) is 1:1. Since the observed UV intensity of the main oval varies from a few to several 10s kR and the HST observation threshold is 1 kR, we may say that the emission ratio between the main oval and the polar region in UV is 10:1 or larger. We investigate whether and how these emission ratios can be reproduced using our model. Fig. 12a and b shows contour maps of UV and IR intensities, respectively, as a function of electron energy and electron flux. Emission intensities are normalized to the case with electron energy of 10 keV and the flux corresponding to the FAC density of 0.15 lA m2. The energy and flux dependences along the dotted lines correspond to those shown in Fig. 9a and b. The temperature increase or decrease required to obtain the same IR emission intensity as at the main oval is shown in Fig. 12c. For example, for auroral electrons with 1 keV precipitating at the flux corresponding to 0.01 lA m2, an exospheric temperature enhancement of 120 K provides IR emission comparable with the main oval. The thick dashed line shows the cases which would produce UV emission with 10% of the intensity of the main oval. In other words, the combination of the electron energy, flux, and exospheric temperature situated on this dashed curve provides emissions of 100% IR and 10% UV relative to the main oval intensities. That is, the polar IR emission can be explained if a parameter set that is situated below this dashed curve is realized in the polar region of Saturn. Now we check if any of the three candidates raised in Section 1 can deliver the above possible solution to the saturnian polar emission problem provided by our model. The idea ‘‘(i) low energy electrons producing Hþ 3 at high altitude with a high temperature to enhance IR emission’’ indeed applies if the electron energy is a few keV. ‘‘(ii) High energy electrons depositing their energy at low altitude where hydrocarbon absorption of the UV increases the IR/UV ratio’’, does not work well, because Hþ 3 that emits IR at low altitude is also effectively reduced by reactions with hydrocarbons and H2O and low temperature. The process ‘‘(iii) enhancement of the background temperature increases the IR emission selectively and efficiently’’ indeed has a large effect. We note that in order to validate the possible solution obtained by our model, it is desirable to investigate the electron data obtained by CAPS/ELS during Cassini’s polar orbit when the IR emission is seen. In situ data from Cassini which could be used to validate our results for the event reported by Stallard et al. (2008), however, were not available, due to unfavorable positioning of the spacecraft (private communication with C. Arridge). Since Saturn’s main auroral oval is considered to be located at the open-closed field line boundary, the field lines in the polar region are supposed to be open and thus we would not expect the electron flux to be high. For the case of the Earth, moderate

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(a)

(a)

(b)

(b)

(c)

(c)

Fig. 12. (a) UV and (b) IR emission intensities normalized to the case with electron energy of 10 keV and flux of 0.15 lA m2, and (c) required temperature increase (positive value) or decrease (minus value) to compensate the IR reduction/ enhancement for the Saturn case, as a function of electron energy and FAC. The thick dashed line in (c) shows the 10% UV line as in (a).

charged particle precipitation in the polar cap region is available by ‘‘polar rain’’ or by ‘‘Sun-aligned arcs’’. Since the former precipitation covers much of the polar cap and has similar characteristics to the IR emission event reported by Stallard et al. (2008), we consider polar rain for comparison here. Polar rain originates from the high energy and field-aligned component of solar wind called ‘‘strahl.’’ The strahl component can sometimes have high enough energy and flux to create auroral emission in the polar cap (Zhang et al., 2007). The terrestrial polar rain observed on September 13, 2004 reached an energy flux of 0.2–0.9 erg cm2 s1 and a mean energy of 0.6–1.6 keV, which produced auroral emission of a few kR. Assuming the solar wind density decreases with orbital distance squared, the corresponding polar rain flux at Saturn (at 9.6 AU) becomes 0.002–0.01 erg cm2 s1 = 0.002–0.01 lA m2. Assuming 1 keV electron energy, Fig. 12c indicates that an atmospheric temperature increase of 100 K above that in the main oval would produce an IR emission intensity comparable with that in the main oval. In addition, field-aligned acceleration above Saturn’s polar cap could operate to increase the energy flux of precipitating electrons, which reduces the required temperature increase. 4.3. Jupiter’s UV/IR variation Fig. 13a and b shows the energy and flux dependence of UV and IR emissions for Jupiter. The variation of the UV emission is similar

Fig. 13. As Fig. 12, except for Jupiter. The color contours in (c) are shaded on the same scale as Fig. 12c, with line contours drawn at levels of different levels at 1000, 400, 200, 0, 200, 400, 1000, and 10,000 K.

to Saturn’s case shown in Fig. 12a. For the IR emissions, the decrease of the ratio of 1–0.3 over the few keV range is steeper than that obtained for Saturn. The temperature enhancement required to obtain the same IR emission as the case of 10 keV and 0.15 lA m2 increases as shown in Fig. 13c. A small temperature variation does not change the IR emission, indicating that this emission thus becomes an effective diagnostic of incident electron energy and flux, i.e., magnetospheric activity. 5. Conclusions We have developed a new emission model which provides UV and IR auroral emission rates from Jupiter and Saturn. Using this model, we obtain the following results. 1. The UV emission rate increases with incident electron energy, while the IR emission rate increases more slowly with energy and decreases in the high electron energy range of >10 keV. The increase of IR emissions over the range 0.5–5 keV at Jupiter is larger than that at Saturn, which is attributed to the different exospheric temperatures and the existence of H2O at Saturn. 2. The UV intensity is proportional to incident electron flux, while the IR intensity is directly related to the square root of the flux. The latter relation is explained by ion chemistry. 3. The general sensitivity of IR emission to the atmospheric temperature is greater at Saturn than at Jupiter following Eq. (3).

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4. We estimate the parameter sets that would explain a polar IR enhanced event at Saturn. Assuming the emission intensity ratio of the main oval to that in the polar region to be 1:1 in the IR and 10:1 in the UV, we have obtained the required ranges of electron energy, electron flux, and atmospheric temperature to achieve this event. 5. Points 1 and 3 above indicate that the difference between IR and UV emissions depending on electron energy and temperature are smaller for Jupiter than for Saturn. This fact may explain the different appearances of polar UV and IR emissions at Jupiter and Saturn, i.e., polar IR emission is reported at Saturn while both polar UV and polar IR emission exist at Jupiter. The limitations of our current model are as follows. The exospheric temperature and excited H2 in our current model are assumed to have no relationship to the auroral electron precipitation. In addition, we consider emission intensity in steady state conditions while the observed UV and IR emissions vary greatly with time, especially for polar emissions (e.g., Clarke et al., 2004; Stallard et al., 2008). Including the relationships between auroral electron and atmospheric heating and H2 vibrational states, as well as the time dependence of these emissions are targets of our future modeling work. While we have used the emission intensity integrated over the UV wavelength ranges and the IR fundamental line to characterize the auroral emission, utilizing more information available from other spectroscopic emission lines should also be done as the next step.

Acknowledgments C. Tao thanks Dr. S. Kasahara and Dr. C. Arridge for useful discussions. We thank the referees for their productive and valuable comments.

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