The structure of the Uranian atmosphere: Constraints from the geometric albedo spectrum and H2 and CH4 line profiles

ICARUS 65, 406-441 (1986)

The Structure of the Uranian Atmosphere: Constraints from the Geometric Albedo Spectrum and H2 and CH4 Line Profiles K E V I N H. B A I N E S AND JAY T. B E R G S T R A L H Jet Propulsion Laboratory, ('alifi,'nia Institute o f "l'echmdo~,v. 4800 Oak (;rot, e Drive, Pasadena. ('al(fin'nia 91109 Received July 8. 1985: revised N o v e m b e r 22, 1985 Constraints on the atmospheric structure of Uranus are derived rrom recently acquired, highquality spectral observations [J. S. Neff, D. C. H u m m . J, T. Bergstralh, A. L. Cochran, W. D. C o c h r a n , E. S. Barker, and R. G. Tult (19841 lcaru.s 60, 221-235; J. T. Yrauger and J. q'. Bergstralh (1981) Bull. Amer. Astron. Soc. 13, 732; K. H, Baines, W. V. Schempp, and W. H. Smith (1983) Icarus 56, 534-542]. The analysis, based on delailed modeling of a broadband 17 A) geometric albedo s p e c t r u m from 3500 to 10,500 A, and high-resolution (30 and 100 m,~, respectively) observations of H: 4 - 0 quadrupole and 6818.9-A CH4 features, yields a family of models which parameterizes an upper tropospheric haze layer, a lower optically infinite cloud at a pressure level PcLa, the cloudqevel m e t h a n e molar fraction,,/~Ha, and the mean ortho/para ratio in the visible atmosphere. Limits include 2.40 < PCld < 3.2 bars, 0.020 ./tHa "" (I.046, and 0.63 <" .I~H: < 0.95, where f.H: d e n o t e s the fraction of He in the equilibrium slate. The haze optical deplh at 6435 A is found to be 0.4 < rH (6435 A) < 1.0, in reasonable agreement with 1,. M. Traflon's [(19761 Astrophys. J. 207, 1007-1024] determination but significantly less than that reported by K. H. Baines 111983) Icarus 56, 543-559]. The single-scattering albedo of atmospheric aerosols exhibits a sleep darkening b e t w e e n 5890 and 6040 A, reminiscent of UV-irradiated H_,S ice crystals. T h e s e constraints are consistent with recent infrared and submillimeter and millimeter analyses. The analysis also agrees with the theoretical He quadrupole line strengths but conflicts with a n u m b e r of reported laboratory m e a s u r e m e n t s . ~, 1986Academic P~ess, Inc

1. I N T R O D U C T I O N

The atmospheric structure of Uranus has not been well constrained. As one example, recent studies of the appearance of methane absorption in the planet's geometric albedo spectrum have led to deep-atmosphere CH4 molar fraction ranging from 3 x 10 3 (Teifel, 1983) to as much as 0.10 (Wallace, 1980). Such discrepancies can be traced largely to assumptions about crucial model parameters which are not constrained by the data under analysis. For example, the depth of the visible atmosphere, which cannot be derived uniquely from existing geometric albedo data, is assumed by Teifel (1983) to be limited by Rayleigh scattering in a semi-infinite, aerosol-free atmosphere. On the other hand, Wallace (1980) adopts a shallower optical lower boundary from complementary data sets analyzed by

other investigators. Specifically, a visible depth of 427 km-am of He is assumed on the basis of Trafton's (19761 analysis of 3-0 and 4 - 0 quadrupole equivalent width measurements. In addition to Wallace (1980) and Trafton (19761, a number of other investigators [notably Belton et al. (1971) and Danielson el a/. (1977)] have attempted a methodical, integrated analysis of complementary data sets to establish a system of mutually consistent model constraints. Other researchers have examined more limited data sets closely (e.g., Benner and Fink, 1980: Atai et al., 1981; Teifel, 19831. However, all have been forced to combine observational data acquired over intervals of a decade or more, Many of these data are characterized by poor resolution, poor signal-to-noise ratio, and uncertain calibration. Furthermore, evidence of secular changes in 4()6

0019- I (135/86 $3.00 Cop~,right 1986 by AcademicPress, lnc All righls of reproduclion in an}' form re~er~cd

URANIAN ATMOSPHERIC STRUCTURE Uranus' spectrum (Lockwood et al., 1983) suggests an additional source of uncertainty in quantitative interpretation of these data sets. In this paper, we analyze three complementary data sets acquired during the 1980 and 1981 apparitions. Not only are these data nearly coincidental in time, but they are also characterized by good resolution and signal-to-noise ratio. These observations include the well-calibrated broadband (7-,~ resolution) 0.35- to 1.05-/xm geometric albedo spectrum of Neff et al. (1984), the high-resolution (30 mA) H2 4-0 quadrupole observations of Trauger and Bergstralh (1981), and the 6818.9-A CH4 line data of Baines et al. (1983). Concurrent analyses of these data establishes significant constraints on atmospheric structure while minimizing not only the uncertainties due to secular variations but also those due to poorly understood molecular absorption parameters. For example, the depth of the visible portion of the atmosphere is constrained by the shapes of the H2 quadrupole line profiles without regard to the poorly determined line strengths. Similarly, the methane abundance is not constrained by analysis of band absorptions, for which temperature dependences are poorly understood, but rather from a relatively wellknown CH4 absorption line. We find a family of model atmospheric structures which satisfies (1) the geometric albedo from 3500 to 10,500 ,~, ranging over nearly five orders of magnitude in CH4 absorption coefficients, (2) the shapes and equivalent widths of the 4-0 S(0) and S(1) quadrupole features, and (3) the equivalent width and full width half-maximum of the 6818.9-A line. In Section II, we briefly describe the observations. Section III describes the assumed aerosol morphology and defines the parameterization employed to quantify this structure. Section IV describes our radiative transfer algorithms and modeling procedures. In Section V, we report the results of our analysis, and we summarize these results in Section VI.

407

II. THE OBSERVATIONS A. The Geometric Albedo Spectrum The geometric albedo spectrum is shown in Fig. 1. Four distinct wavelength regions are indicated, each of which is characterized by different radiative transfer processes. Consequently, each region constrains structural properties in different atmospheric domains. The blue continuum region from 3500 to approximately 5500 ,~ is sensitive to upper level haze properties and molecular Rayleigh scattering. In particular, the wavelength dependence of the haze single-scattering albedo and optical depth as well as the distribution in the stratosphere and high troposphere is constrained by these data. The weak absorptions imbedded in the blue continuum can be used to constrain the global methane mixing ratio beneath the tropospheric methane condensation level. The intermediate methane bands from about 6000 to 8000 ,~ constrain the wavelength-dependent properties of an assumed optically infinite cloud at the bottom of the visible atmosphere as well as the global methane mixing ratio. Strong absorption by stratospheric and upper-tropospheric methane above the condensation level is responsible for the low geometric albedo in the strong methane bands at 0.9 and 1.0/xm. Residual light observed in these bands arises from Rayleigh, Raman, and high-altitude haze scattering. Thus, these data constrain wavelength-dependent haze optical properties at twice the wavelength of the blue continuum data. Other features illustrated in Fig. 1 include Raman "emissions" and "ghosts" due to filling-in and scattering of strong Fraunhofer lines, and the $3(0) collision-induced H2 dipole absorption feature. The former could be used to evaluate stratospheric structure (a possibility which we do not pursue in this paper), while the latter constrain the ortho/para H2 distribution. B. The H: 4-0 Quadrupole Lines The high-resolution observations of H:

408

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FIG. 1. Uranus geometric albedo spectrum of Neff e t al. { 19841. Four discrete spectral regions arc specified, characterized by distinct differences in the dominant radiative transfer processes which govern the appearance of the observed spectrum. The H2 3-0 S(0) collision-induced dipole feature is indicated, as are the wavelengths of the 4-0 S(0) and S(1) quadrupole features. Spurious emissions and absorptions produced by Raman-scattering interactions with strong Fraunhofer lines are also shown.

4 - 0 S(0) and S(l) quadrupole features (Trauger and Bergstralh, 1981) are shown in Fig. 2. The ratio of the observed equivalent widths can be used to constrain the ortho/ para H2 distribution, while the individual equivalent widths can be used to constrain the relationship between haze optical depth and physical depth of the visible atmosphere. H o w e v e r , owing to uncertainties in the room-temperature strengths of these lines, the individual equivalent widths are not very effective in this regard. Much tighter constraints can be derived from an analysis of the lineshapes, whose symmetries are due to strong pressure shift and narrowing effects. Uranus" unique nearly pole-onward aspect produces only relatively small (although measurable) symmetrical broadening due to planetary rotation. C. The 6818.9-f~ M e t h a n e Line

The 6818.9-A, line of methane observed by Baines et al. (1983) can be used to constrain the haze optical depth and the global methane mixing ratio, if the depth of the

visible atmosphere is known. This analysis also depends on knowing both the rotational quantum number and the temperature-dependent pressure-broadening characteristics. A previous analysis of this feature by Baines (1983) relied upon a rotational quantum number J ~< 2, and C H 4 : H2 pressure broadening given by y O.065P(To/T) °.5° cm ~ atm L. Recent laboratory measurements of this line at temperatures in the range from 82 to 295 K (Keffer et al., 1986) are consistent with a ,I 3 rotational assignment and indicate that pressure broadening is substantially larger than previously thought, i.e., ",/ O.0883P(To/T) °:~. Thus, a reanalysis of the observed feature is warranted and is reported here. In particular, we show that this feature is consistent with the atmospheric structure derived from other data sets. 111. PARAM ETERIZATION

We adopt a two-cloud model atmospheric structure as shown in Fig, 3. An

URANIAN ATMOSPHERIC STRUCTURE

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is•tropically scattering haze layer is located between two aerosol-free Rayleigh-scattering gas layers. Such a stratospheric/tropospheric haze layer was postulated previously by Trafton (1976), Wallace (1980), and Baines (1983). As noted above, each of our three data sets can be used to constrain haze layer characteristics. In our analysis, we assume identical scale heights for particles and gas in this region which extends d o w n w a r d from P~-T, the haze top pressure, to PH-~, the pressure at the bottom of the layer. Here, we assume that Pa-B corresponds to the methane condensation level. This eliminates a free parameter but implies

that at least a portion of the haze layer consists of methane ice. The wavelength-dependent nature of the single scattering and optical depth is characterized with four parameters using the analytical expressions 3500 ~,~ I and r~ = ~ ( 6 4 3 5 .~)(6435/X):'T. Here X = 1/[o?n(3500 A)] - ! is the ratio of scattered-to-absorbed c o m p o n e n t s of extinction at 3500 A. The extinction exponent, y~, has an upper limit of 4 for Rayleigh scattering and a lower limit of 0 for spheres

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F1G. 3. The adopted structure of the Uranian atmosphere. Basic aerosol morphology consists of an extended region of particulates ( " h a z e " ) located between two aerosol-free regions with an optically infinite cloud defining the bottom of the visible atmosphere. Aerosol properties constrained by this study include haze and cloud top pressures. P~.~ and PCLd.the wavelength-dependent single-scattering albedos of haze and cloud, ~bu(,k~ and (o,~,~(;~J, and the wavelength-dependent haze optical depth, ~'tdk). Constrained molecular distributions include the methane molar fraction at the bottom of the visible atmosphere, .f~ H4, and the mean ortho/para H2 ratio, here parameterized as.l~H,, the fraction of H~ distributed in an equilibrmm slate. Appleby's (1986) model c thermal profile is assumed.

much larger than the sensing wavelength. These formulas are generalizations of the expressions for haze single-scattering albedo and optical depth adopted by Trafton (1976) and Wallace (1980). Specifically, Wallace parameterized Trafton's results with X -- 0.02, y,,, 4, rl~ (6435 A) - 0.3, and yT = 4. The bottom of the visible atmosphere is defined as a sharp optical boundary at Pc~d beneath which lies an optically infinite, isotropically scattering "'cloud." This cloud has a wavelength-dependent single-scattering albedo, OSOd()~),which is constrained by the " r e d " end of the blue continuum and by continuum points in the region of the intermediate methane absorptions. Gas absorption is assumed to be negligible within the cloud.

The helium molar fi-action is assumed to be 0.09. Two quantities associated with the distributions of the two other predominant gas species, hydrogen and methane, are constrained by our analysis. The ortho-topara hydrogen ratio is expressed as the fraction of hydrogen in the equilibrium state, feud, the remainder being in the normal state. This parameter is related to the para and ortho hydrogen fraction, Jp and f , , respectively, at a temperature T (°K) by ,fp = J e H ~ [ 1 / ( 1

+ ~(T))] + ,~(1 --.f~H~)

.f~, = feH.~[¢(T)/(I

+ ¢(T))] + !~(1 -,f~'u~)

where /~(T) = Zoad(T)/Zeven(T). Here, Zo~d(T) and Zeve,~(T) are the rotational partition functions for ortho and para states, respectively, assuming no interconversion

URANIAN ATMOSPHERIC STRUCTURE between these states. Specifically, Zodd(T) and Zeve.(T) are sums over qS(J)(2J + 1) e x p [ - ( h c / k T ) B J ( J + 1)] summed over rotational quantum numbers J = l, 3, 5 . . . . and J = 0, 2, 4 . . . . . respectively, where th(J) is the nuclear spin degeneracy of the initial state (a for ortho, ~ for para), and B is the rotational constant for the ground state of H2 (Smith, 1978; Massie and Hunten, 1982). The methane mixing ratio, fCH,, is taken as the molar fraction in the deepest part of the visible atmosphere (i.e., at the top of the optically infinite cloud). We assume that the [CH4]/[H2] mixing ratio adopted for the deep mixed atmosphere prevails up to the altitude at which the methane partial pressure and the saturation vapor pressure coincide. Above this point (which, as noted above, is defined as the haze bottom pressure, PH+), the methane partial pressure follows the saturation vapor pressure, as determined from the Clausius-Clapeyron relation. Above the temperature minimum near 100 mbar, the methane mixing ratio is that found at the temperature minimum itself. Such a CH4 depletion in the stratosphere and upper troposphere is in agreement with a number of visible, near-IR, and center-to-limb CHa band observations (e.g., Belton and Price, 1973; Price and Franz, 1978; Fink and Larson, 1979; Pilcher et al., 1979). We adopt a nominal thermal structure from Appleby (1986, model c) throughout the stratosphere and upper troposphere. This profile gives a reasonably good match to well-calibrated, narrow-band infrared (15-500 /xm) observations acquired contemporaneously with the visible data under analysis in this paper (Tokunaga et al., 1983; Moseley et al., 1985; Hildebrand et al., 1985; Orton et al., 1986). In addition, this profile assumesfcH, = 0.02 and a significant distribution of aerosols above the radiative-convective boundary, in reasonable agreement with results derived in this work. Below the upper troposphere, an adia-

411

batic pressure gradient, properly accounting for methane condensation effects, is assumed. Following Trafton (1967), Wallace (1980), Orton and Appleby (1984), and Appleby (1986), we adopt "intermediate" H2 in calculations of the adiabatic lapse rate. As noted by Orton and Appleby (1984) and Orton et al. (1986), this Cp/R for H2 yields the best agreement between contemporary submillimeter-millimeter observations and synthetic spectra. The acceleration due to gravity is derived from the weighted mean gravitational acceleration at the l-bar level for the sensible planetary disk, assuming a pole-onward aspect and a planetary phase angle of 0°. The weights here include a cosine factor to approximate the effect of limb darkening. Assuming equatorial and polar gravitational accelerations of 8.8 and 9.2 m sec -2 as derived from a Uranus-to-Earth mass ratio of 14.51 and polar and equatorial radii of 25,662 and 25,046 km, respectively (Hubbard, 1984), we find the effective 1-bar gravitational acceleration to be 8.9 m sec 2 assuming a 16-hr planetary rotation rate. The method used to constrain the atmospheric structure parameters is summarized in Table I. The blue continuum spectrum is first applied to constrain the five haze parameters. It is found that the spectrum from 3500 to 5000 A can be modeled by fitting synthetic spectra to three well-spaced spectral points. Thus the number of free haze parameters is reduced to two, specifically, ~-~(6435 ,~) and y~. The strong methane absorption region is then used to constrain ~'H(6435 A) vs PH-T and y~. Hydrogen quadrupole line profiles are next employed to constrain few and ~-n(6435 ,~) vs Pcld. The 6818-,~ line is then utilized to constrain TH(6435 /~) VS Pcld and.fcH,. The weak methane bands are used to verify the CH4 line profile results. Constraints from the intermediate methane band region are then derived, principally establishing limits on the cloud single-scattering albedo from 6000 to 6300 A. Finally, the 3-0 S(0) collision-induced dipole feature near 8250 A, is ana-

412

BAINES AND BERGSTRALH FABLE 1 ~UMMARY

Observation

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ANAI.YSIS PROCF.DUR!

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lyzed to verify the quadrupole profile results for.l;n,. We note that our analysis involves a number of poorly known molecular characteristics. Several of the most consequential yet unreliable parameters are listed in Table II. We avoid using them, where possible. Instead, we find that several of these parameters, such as the room-temperature strengths of the quadrupole lines, are constrained significantly by our analysis.

leigh-scattering and gas-absorbing regions. The numbers of scattering layers used for each of the morphologically distinct regions are 9, 5, 3, and 1 for the upper aerosol-free, haze, lower aerosol-free, and cloud regions, respectively. The broadband calculations account for gaseous methane absorption, collision-induced absorption by molecular hydrogen, and Rayleigh scattering. We adopt Giver's (1978) room-temperature laboratory measurements for the methane absorption coef-

IV. RADIATIVE TRANSFER CAI.CULATIONS T h e g e o m e t r i c a l b e d o a n d line profile calc u l a t i o n s are m a d e u s i n g the m a t r i x operat o t d o u b l i n g - a d d i n g m e t h o d d e v e l o p e d by G r a n t a n d H u n t (1969). W e a s s u m e isotropic s c a t t e r i n g for a e r o s o l s a n d the Rayleigh p h a s e f u n c t i o n for m o l e c u l a r scattering. T h e a t m o s p h e r e is stratified a c c o r d i n g to the s a n d w i c h i n g s c h e m e o f B a i n e s (1983): a e r o s o l - f r e e l a y e r s are s e p a r a t e d alt e r n a t e l y into l a y e r s a c c o u n t i n g for m o l e c u lar R a y l e i g h s c a t t e r i n g a n d m o l e c u l a r gas a b s o r p t i o n , while the haze and gas layers

TABLE I1 UNCERTAIN MOLECULAR PARAMETERS

Observation

Parameter

Strong CH4 bands

CH4 absorption coefficients al relevant temperatures.

H: lines

Room-temperature line strengths, & Rotational quantum number, J

~:~LU (A, "1)

CH4 line Weak CH4 bands K(H 4 (X,T) Intermediate bands KCm (k,T) H2 3-0 S(0) dipole K~H4 (k,T): collisional time parameters, 71, r2

are segregated similarly into aerosol/Ray ............................................................................................

URANIAN ATMOSPHERIC STRUCTURE

ficients, KCH,(h). Since the temperature dependence of these coefficients is unknown, no adjustments are made for the much colder temperatures prevalent on Uranus. Similarly, absorptions due to methane ice are not explicitly evaluated. As detailed in Section V.G, a curve-of-growth analysis of the intermediate methane bands suggests that absorption by gaseous and/or solid methane is inadequately accounted for in many regions of the spectrum. Thus, relatively large uncertainties arise in deriving the methane mixing ratio from these data. The collision-induced H2 dipole spectrum is calculated following the procedure outlined by McKellar and Welsh (1971), using the semiempirical lineshapes of Birnbaum and Cohen (1976), the quadrupole moment matrix elements of Birnbaum and Poll (1969), and the polarizability matrix elements of Poll (1971). Molecular Rayleigh scattering accounts for the various components due to H2, He, and CH4. The Rayleigh phase function is used, but scattering effects are evaluated only in the total intensity Stokes component, I. Calculations by Pollack et al. (1986) show that for a pure Rayleigh-scanering atmosphere with optical depth >0.5, a detailed evaluation using all three of the linear polarization components (I, Q, and U) of the Stokes vector increases the calculated geometric albedo by about 0.04. This effect may be important in the blue continuum where Rayleigh optical depths encountered in aerosol-free layers typically exceed unity. The procedure described by Wallace (1972) is used to approximate Raman-scattering effects. Rotational Raman extinction is treated as conservative scattering without a wavelength shift, while vibrational Raman scattering is treated as pure absorption. These approximations afford accurate geometric albedo calculations throughout the spectral region 3500 ,~ to 1.05/xm without the large computer resources required to keep track of wavelength-shifted source terms. We estimate that the largest systematic errors (besides those due to Fraunhofer

413

line effects) occur in the strong methane bands near 1.05 /zm where the calculated geometric albedo is some 10% or 0.001 less than a more accurate calculation which accounts properly for wavelength-shifted Raman source terms. This difference is smaller than the precision of the Neff et al. (1984) measurements. Absorption line profiles are modeled with the Galatry (1961) lineshape for hydrogen quadrupole lines and the Voigt lineshape for methane. For the quadrupole features, we adopt the pressure shift coefficients of McKellar (1974), the collisional-narrowing parameters of James (1969), and the roomtemperature pressure-broadening coefficients of Bragg (1981). For the 6818.9-A CH4 line, the recent pressure-broadening measurements of Keffer et al. (1986) are applied. The room-temperature strength adopted for this line is 0.0262 cm -l (kinam) -1 (Baines, 1983). Spectra are calculated in increments of 5 mA for the quadrupole features and 25 mA for the CH4 line. Broadening of line profiles by planetary rotation is computed from a weighted average of Doppler-shifted line profiles for several locations on the Uranian disk, the weights accounting for limb darkening and the fractional area represented by each profile. The final line profile is calculated as the discrete convolution of the rotationally broadened profile with the measured instrumental response function. A phase angle of zero degrees is assumed for all calculations. V. RESULTS

A. Blue Continuum

The blue continuum from 3500 to 5500 is primarily influenced by Rayleigh/Raman molecular scattering and nonconservative aerosols high in the stratosphere and upper troposphere. The geometric albedo in this region is significantly suppressed below the level expected for a semi-infinite, conservative Rayleigh-scattering atmosphere, and consequently, nonconservative aerosols must be present at high altitudes (Wallace, 1972; Cochran and Trafton, 1978). Quanti-

414

BAINES AND BERGSTRALH l.O

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FIG. 4. The UV geometric albedo of Uranus, 1900-4000 A. Averaged IUE data (triangles) of Catdwell et al. (1981) and ground-based geometric albedo observations of Neff et al. (19841 are shown together with model curves for reflecting layer models. Solid curves indicate the effect of variations in the pressure level of a completely absorbing optical boundary (o)CLd -- 0). Models brighter than the observations imply that absorbing aerosols exist above the indicated pressure level (numbers, in bars). Dashed curves show the effect of variations in the single-scattering albedo (numbers) if the cloud boundary pressure is set at 2.0 bars. The 1UE data suggest a substantial abundance of aerosols in the stratosphere, while the Neff et al. observations indicate that significant aerosols reside above 1.5 bars. However, IUE observations may be subject to a systematic uncertainty which would allow agreement with aerosol-free models (Ca[dwell, 1981).

tative e s t i m a t e s of the vertical l o c a t i o n of t h e s e a e r o s o l s are i l l u s t r a t e d in Fig. 4 w h e r e we c o m b i n e the I U E data of C a l d w e l l e t al. (1981 ) with the p o r t i o n of the N e f f e t al. (1984) g e o m e t r i c a l b e d o spect r u m b e l o w 400 ,~. H e r e we a s s u m e a simple " r e f l e c t i n g l a y e r " m o d e l (i.e., an optically infinite c l o u d b e l o w a Rayleigh/ R a m a n - s c a t t e r i n g layer). T h e solid c u r v c s i n d i c a t e r e s u l t s for m o d e l s i n c o r p o r a t i n g a c o m p l e t e l y a b s o r b i n g (o5 = 0) c l o u d layer at v a r i o u s p r e s s u r e levels. T h e c a l c u l a t e d geom e t r i c a l b e d o is t h u s e n t i r e l y a t t r i b u t a b l e to R a y l e i g h s c a t t e r i n g a b o v e the cloud. T h e

i n t e r s e c t i o n of the m o d e l e d s p e c t r u m with the o b s e r v e d g e o m e t r i c a i b e d o i n d i c a t e s the m a x i m u m p r e s s u r e , as a f u n c t i o n of w a v e length, above which an aerosol-tree atmos p h e r e c a n be s u s t a i n e d . T h u s the I U E data b e l o w 2200 A suggest that a e r o s o l s exist a b o v e 100 m b a r , while the shortest w a v e length N e f f e t al. d a t a i n d i c a t e the p r e s e n c e o f a e r o s o l s a b o v e i.5 bars. H o w e v e r , it should be n o t e d that the I U E o b s e r v a t i o n s are s u b j e c t to a s y s t e m a t i c c a l i b r a t i o n error, the c o r r e c t i o n of which w o u l d i n c r e a s e the g e o m e t r i c a l b e d o s significantly at all obs e r v e d w a v e l e n g t h s (Caldwell e t a l . , 1981).

URANIAN ATMOSPHERIC STRUCTURE

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I I

5OOO

FIG. 5. The blue spectrum of Neff et al. (1984). This spectral region is characterized by continuum aerosol and molecular scattering effects together with artifacts of Raman scattering, Major Fraunhofer "emissions" and "ghosts" generated from Raman-scattering interactions are designated. Geometric albedos at 3500, 4100. and 4700 • constrain three of the haze parameters. Various values of the geometric albedos at these wavelengths (symbols) denote target values for "nominal," "dark," and "polarization correction" models as explained in the text.

Thus, these data are also consistent with an aerosol-free region extending significantly below the stratosphere. The dashed curves in Fig. 4 illustrate the effect o f changing the single-scattering albedo in the models, assuming a fixed cloud pressure o f 2.0 bars. L o n g w a r d of 3800 ~ , the s p e c t r u m can be m a t c h e d by a wavelength-dependent single-scattering albedo. The bright cloud model, with OSCld= 0,9985, is required to m a t c h the peak geometric albedo at 5150 A. T h e r e is thus considerable evidence that an aerosol region exists a b o v e a pressure level of a few bars. H o w e v e r , while this region m a y be quite absorbing in the UV, it must be relatively nonabsorbing in the region 4500-5000 ,X, to allow for the amount o f m e t h a n e absorption o b s e r v e d in the w e a k m e t h a n e bands. Indeed, as discussed

in Section V . F below, the depths of these bands indicate that photons penetrate to at least the 2.4-bar level. Thus, we are compelled to a d o p t a two-cloud model, one being an " u p p e r l e v e l " haze which primarily characterizes the U V blue continuum observations, and the second being an underlying, optically infinite cloud which limits p h o t o n penetration longward of about 4500 ~ . T h e r e are no observational constraints on the haze b o t t o m altitude (i.e., the haze m a y merge with the underlying cloud). H o w e v e r , m e t h a n e condensation occurs in this portion of the a t m o s p h e r e , at a level b e t w e e n 1.8 and 3.2 bars depending on global m e t h a n e mixing ratio in the range 0.020 to 0.046 (i.e., the range of mixing ratios derived in Sections V.E and V.F). F o r simplicity, we a s s u m e that the UV-absorbing and m e t h a n e ice aerosols are uniformly

416

BAINES AND BERGSTRALH 0.70

I

[

1

NOMINAL MODE L

0.65

[CH4

';

TH (6435'L')

PH-T

PCId

c~CIcI

003

]

04605

0 67

2.66

0.9985

0,60

P~ 055

050

":

-....

....'-'""

".

_ • -":.:.."

I

3500

.

"-,'"" :-.

0.45

0.40

"

L

4000

J 450O

"1 5000

F[o. 6. Nominal model: 3500-5000 A. Data of Neff et al. ll984) are displayed together with a nominal model fit for a methane deep-atmosphere molar fraction of 0.03. Open circles indicate points specifically used to constrain haze parameters. mixed throughout the haze region, and thal the depth of this composite aerosol region is bounded by the level at which methane condenses. We use the geometric albedo spectrum from 3500 to 5150 ,& to constrain the haze parameters, PH:I, TH(6435 A), YT, X, and y,,,, defined in Section III above. The blue continuum spectrum is detailed in Fig. 5. High spectral frequency components shortward of 4300 .& are due to Raman-scattering effects associated with strong Fraunhofer lines. Absorption by weak methane bands produces departures from the continuum longward of about 4400 A. Three equally spaced wavelengths, reasonably well separated from high spectral frequency effects, are chosen to constrain the DC level, slope, and curvature of the continuum level. These points, located at 3500, 4100, and 4700 .&, are depicted for three model types in Fig. 5. " N o m i n a l m o d e l " points (open

circles) correspond to a best-guess estimate of the true continuum level from inspection. A model fitted to these points yields the typical synthetic spectrum shown in Fig. 6. The " d a r k " points (filled circles) are a conservative estimate of the true continuum geometric albedo. Model points representing a correction for polarization effects are shown as diamonds. These points are offset from the nominal points by 0.04 unit of geometric albedo, the amount by which calculations of pure Rayleigh-scattering models which include detailed accounting for linear polarization exceed intensitybased calculations which account only for the intensity component of the Stokes vector (Pollack e t a l . , 1986). We suppose, then, that matching these points with our algorithm would coincide to matching the nominal model points with a more sophisticated polarization procedure. Results of fitting the nominal data points

URANIAN ATMOSPHERIC STRUCTURE

11, T A

'.ot 0.9

,

::;

. . . . .

----:;

iif

2

/ ......_..

....."":

-"

!ct

417

."

,!

• I

0.00o

,o

PH T {BARS)

20

X

30

,o

~ ~ ~ 7~

i

'\ ~ i"

FIG. 7. Haze aerosol characteristics derived from the observed blue geometric albedo spectrum. Nominal reflectances at 3500, 4100, and 4700 ~ as indicated in Fig. 5 constrain PH-T, X, and y~ as functions of rn(6435 ~,) and y,. The haze bottom pressure is assumed to coincide with the condensation level associated with a deep-atmosphere methane molar fraction of 3% (i.e., Pn s = 2.14 bars).

are shown in Fig. 7, where the haze bottom at 3500 -~ is invariant with respect to haze is assumed to lie at 2.14 bars, correspond- position. The flux impinging on the haze top ing to the methane condensation level for a can be approximated by I0(l-K PH-T) where 3% global methane composition. The three I0 is the solar flux and K is a constant acdata points constrain three of the five pa- counting for average air mass, the Rayleigh rameters. We chose the two free parame- optical depth per bar in the clear region ters to be ~'n(6435 A) and TT. Panel A of Fig. above the haze, and the Rayleigh-scattering 7 indicates a maximum haze top pressure of efficiency. The flux absorbed in the haze at 700 mbar. As the haze optical depth de- 3500 A may be approximated for optical creases, the haze top pressure also de- depths less than unity as 10(l-K PH-T)'rH-Abscreases in order to preserve the effective- (3500 ,~). Setting the absorbed flux to a conness of haze absorption, particularly at the stant, ~XH,yields shortest wavelengths. This behavior is PIt-T = (I/K)[I - ~n/(10 ~'n-abs(3500 ~,))]. more clearly exhibited in Fig. 8, where haze top pressure is plotted against the absorp- We let K = 0.92 (which is just the Rayleigh tion component of haze optical depth at optical depth per bar at 3500 ,~), and thus 3500/~, TH.Ab s (3500 A), defined as assume that the air mass factor and Rayleigh-scattering efficiency cancel. Using the TH_Abs(3500 A ) = [l - o) H(3500)] 7 H ( 3 5 0 0 ) observed data point, "rH-Abs(3500 -~) = 0.2 at = [X/( 1 + X)] rn(6435 A) PH-T = 0.4 bar, yields Curve A in the figure, i.e., (6435/)~)~r. An analytical approximation is shown in Curve A of the figure, derived from the assumption that the flux absorbed by the haze

PH-T = 1.0811 -- 0.13/rn_Ab~(3500 ,~)]. We note that the derived value of O~n/lo (i.e., 0.13) indicates that a significant frac-

418

BAINES AND BERGSTRALH 0.7

T

1

I

I

T

T

"rT

4 - - - - 3 .

.

.

.

A4D N4P 2

0.6

40

............... 0

3.0 0.5

Ii --

2.0 o~

0.4

y

i 10

'

I

0.3 050

025

02

0

L

I

1

0.2

03

04

I 05 OH • (BARS)

J

I

06

0.7

08

FIo. 8. Haze top pressure vs the absorption component of haze optical depth at 3500 A. Plotted against ~-u ~,b,(3500 ,~), the well-separated curves in Fig. 7A collapse together. An analytical approximation (curve A) is also s h o w n . Dark (triangles) and polarization correction (squares) models, s h o w n for R a y l e i g h - s c a n e r i n g type aerosols (i.e., yT = 4), indicate significantly higher altitude haze tops.

tion of the solar flux is absorbed by aerosols. As expected, this approximation holds quite well until zn(3500), i.e., the total optical depth, exceeds unity, corresponding to a pressure of 700 mbar for the haze top. Figure 8 also illustrates results for the " d a r k " and "polarization correction" data points. Owing to the reduced geometric albedo of these points at 3500 ,~, the haze top is required to be at much higher altitudes. Specifically, the "polarization correction" model allows a maximum haze top pressure of about 250 mbar, while the " d a r k " model requires the haze top to be above the 180mbar level. A similar analysis for models incorporating a haze bottom at 1.3 bars (i.e., at the methane condensation level for a 1.5% methane global composition) is shown in Fig. 9. The haze top pressures for these models are approximately 250 mbar greater than for the 3% methane composition

models. This behavior can be readily understood: Compression of the absorbing aerosol layer from the bottom increases its effectiveness because there is less conservative Rayleigh scattering within the physically thinner aerosol structure. To compensate, more Rayleigh scattering is required above the absorbing haze layer; i.e., the haze top altitude must be lowered to levels of greater pressures. Panel B of Fig. 7 shows results for X, defined as the ratio of absorption to scattering at 3500 ~,. The family of curves collapses together in Fig. 10, where the absorption component of haze extinction at 3500 A is plotted against the single-scattering albedo at 3500 A. Again, the " d a r k " and "polarization '" model results have a character distinctly different from those of the nominal model. On the other hand, 1.5% methane composition models agree well with 3% models, as shown in Fig. 11.

URANIAN

0.6

ATMOSPHERIC

i

0.5

1

................

STRUCTURE

419

i

[

0

I

I

--

!

.~

'"..

0.4

I ~

,

0.3

....~:J"

.......... ::.:¢"~

,o,.°"

,....°,° 0.2

..........

. .......

fell 4 = 0 0 3

.......... """

fCH 4 = 0 0 1 5

PH B = 2.14 BARS

0.3

....~...~"Y

PH B = 1.3 BARS

[

I

I

I

I

0.4

0.5

0.6 PH T (BARS)

0.7

0.8

0.9

FIG. 9. Effect of haze bottom pressure on derived haze top pressure. A decrease in the haze bottom pressure from 2.14 to 1.3 bars, as warranted by modifying the CH4 molar fraction from 0.03 to 0.015, requires an increase in haze top pressure of some 0.2 bars. Thus the haze layer for a 3% CH4 concentration has a vertical extension some three times that required for a 1.5% CH4 mixing ratio.

0.6

I

I

i

i

I

/

0.5

;~- 0.4

8

z

0.3

0.2

0.3

I

I

I

]

I

0.4

0.5

0.6

0.7

0.8

0.9

~ H (3500'6')

FIG. 10. Single-scattering albedo vs the absorption component of haze optical depth at 3500 ,~. Results shown are for fcH4 = 0.03. Lines represent results for nominal models. Dark (triangles) and polarization correction (squares) models are depicted for Rayleigh-scattering-type aerosols.

420

BAINES AND BERGSTRALH 0.6

I

I

I

I

]

4

0.5

u

./ ~_I 0 3

--

--

02

\• ~

\

~ICH 4

03

0015

L

L

I

,

i

04

05

06

07

08

09

/ H (3500A)

FIG. 11. Effect of deep-atmosphere methane molar fraction on 3500-A haze single-scatteringalbedo. Slightly darker aerosol particles are indicated for.f~,m = 0.03 than forf~ m 0.015. Panel C of Fig. 7 shows results for y,o, the exponent of the single-scattering albedo's wavelength dependence. This family of curves also collapses together when plotted as ~u(3500) vs y~ + TT, as illustrated in Fig. 12. Furthermore, y~ + T, is nearly a constant, varying by only 15% over an octave in ~'R(3500). This "spectral invariant'" is a consequence of matching the shape of the blue continuum with the wavelength-dependent aerosol absorption. For optical depths much less than unity, haze absorption is proportional to

~- [O ,--~-I(3500]"°~"X , /T ,'1/I +

(3500) '''1~

,

where D = X ~u(6435 A) (6435/3500F,. For wavelengths much larger than 3500 A the denominator is nearly unity because 7,, > 4 and X < 4 in these models. Thus, to first order, the wavelength dependence of haze absorption depends on one parameter, i.e., yT + 7,0. If haze absorption is to be preserved as a function of wavelength regard-

less of choice of TT, then T, ~- y,,, must be nearly constant. The spectral invariant, -/,~ + 7¢, is distinctly different for the dark and polarization correction models, being about one unit less than for the nominal model. As with X, changing the global methane mixing ratio from 0.03 to 0.015 appears to have very little effect. Thus, the haze single-scattering albedo is not sensitive to the choice ofZcH~. B. S t r o n g M e t h a n e B a n d s

The low geometric albedo observed in these bands is primarily due to methane absorption above the condensation level. For typical absorption coefficients greater than 10 ( k m - a m ) ' , unity opacity is reached above the 750-mbar level. Virtually all photons which penetrate this level are lost owing to the rapidly increasing concentration of methane in this region of the atmosphere. Therefore, the nonzero geometric albedo measured in these bands is indicative of scattering processes above this

URANIAN ATMOSPHERIC STRUCTURE 5.0

I

I

r

I

421 i

7r -

4

-

3

-

2

fCH 4

0.03 fCH 4 = 0.015

4.0 '

.................

3.0

0

•

4-D

•

4-P

2.0

1.0

0.0

I 7

L 8

9

10

8

9

10

"r~ + "rr

FIG. 12. Haze power-law invariant. Less than 15% variation is indicated over an octave in haze optical depth. The deep-atmosphere methane mixing ratio has only a small effect on y~ + y~. On the other hand, both dark (triangles) and polarization correction (squares) models yield significantly smaller y~ + % values.

level. Thus, these data help discriminate among the haze solutions derived in the previous section. These bands do not discriminate among viable single-scattering albedos because all blue continuum solutions exhibit o~r~(X) > 0.98 in the red, indicating that there is little variation in microphysical scattering characteristics there. Furthermore, the effect of single-scattering albedo on total absorption is undetectable because opacity is dominated by methane gas extinction. The remaining three haze parameters, r~(6435 .~), y~, and PH-T, however, are constrained by the observations since they directly influence the scattering efficiency of the atmosphere above 750 mbar. Figure 13 shows three synthetic spectra for a range of solutions which satisfy the nominal blue continuum points. As the haze top is raised to higher altitudes, the residual light increases almost uniformly for all wavelengths in the band. We explore in depth two wavelengths which occur in

neither the peak nor the continuum region of these bands. Specifically, we examine the model behavior at 9960 and 10,150 A, wavelengths characterized by KCH4 -- 12 (km-am) -~. The observed geometric albedo varies between these points by some 20% (i.e., 0.012 vs 0.010 for 9960 and 10,150 A). Our models, however, indicate nearly identical geometric albedos. The difference may be attributable to diverse temperature effects on absorption coefficients, with some small influence from vibrational Ramanscattering variations. Due to such uncertainties, we chose as a discrimination threshold a geometric albedo greater than that observed (i.e., 0.013). We then reject from further consideration models which exceed this limit at both wavelengths. Figure 14 shows the results of such an analysis, together with the blue continuum determinations. Solutions which lie to the left of the strong methane band constraints (solid curves) are rejected. Thus a portion of y~ = 1 and all of the y~ = 0 blue contin-

422

BAINES AND BERGSTRALH 005

I

I

l

004 rH(6435A)

PH T

X

0.46

0,67

06

016

0.41

2.00

0.12

0.20

4.00

. . . . ....

0.03

P~

0.02

\ / j ' k .~

.

.

.

.

.

0.01

9600

I

9800

I

10000

l

10200

10400

A

FIG. 13. Residual light models. Nonzero reflectivity in the strong CH4 bands near I ~ m is indicative of aerosol scattering in the stratosphere and upper troposphere. This portion of the observed geometric albedo spectrum can be used effectively to constrain the family of haze solutions shown in Fig. 7. Filled circles show specific points used to discriminate among the blue continuum solutions.

uum solutions are eliminated• Viable solutions which satisfy both the strong methane band and blue continuum constraints require haze top pressures greater than 350 mbar for haze optical depths, 7n (6435 A), greater than 0.1.

C. 112 Line Profiles: f~14, Constraints The observed shapes of the 4-0 S(0) and S(1) quadrupole lines effectively constrain the cloud pressure, PCld, and the mean ortho/para ratio above it. Other parameters which significantly affect H2 lineshapes are the haze optical depth, rH(6435 A), and the thermal profile. All of these parameters influence line absorption through their effect either on mean absorption path length or on

line strength. Other parameters such as X, 7a,fcu,, and ~c~dinfluence the continuum in the neighborhood of line absorption, but not, to first order, the lineshape. Nevertheless, all of our models are constrained to fit the observed broadband geometric albedo at these wavelengths by adjustments to O3CLd. Figure 15 illustrates the sensitivity of these data to fell2, the fractional H2 population in the equilibrium ortho/para state. Theoretical line strengths are assumed. Other parameters include PC~d = 2.25 bar, ~'H(6435 A) = 0.5, and an Appleby (1986) thermal profile. The best fit, as listed under O'rms(%), the root-mean-square difference between model and observation points, oc-

URANIAN ATMOSPHERIC STRUCTURE t

1.0

423

O'rms(f~H2,Si) = [(m - n)/rO2r/O2fen 2] i/2

t

STRONG CH 4 ~

BLUE

CONTINUUM 0.9-

0.8

-

0.6

o.s

0.4

It' /

0.7

I

t

Ii I /

I

/ / /

jr I

where r is the residual, and Si refers to the 4-0 S(i) quadrupole line. The number of degrees of freedom, m - n, is conservatively assumed to be I. The combined uncertainty is 0.013, as estimated from [~/ Orfeu2 =

1-1/2 (O-rms(feH2,Si)) -2] .

The nominal value of f~n, as derived from the weighted mean of the individual quadrupole measurements fen2 = E

i

2 [feH2,Si/O'rms(feH2,Si)]/[l/O'~eH2]

2

is fen2 = 0.76. These results are represented by the error bar in Fig. 16. ¢ 4 2 The effect on fen,. of variations in Pcld, rH(6435 .A), and thermal structure are illus0.2 ~ Y trated in Figs. 17 and 18. Results are plotted /\ against best-fit line strengths [i.e., room/ \ 0.1 ~ temperature line strengths which yield a t j I minimum O'~ms(%) for a particular model]. I Line strength uncertainties are evaluated 0 ------J'~ 0 0.2 with a procedure similar to that described 0.4 0.6 0.8 1.0 PH-T (BARS) for uncertainties inf~n2. We find typical unFIG. 14. Combined haze constraints from residual certainties of 0.44 and 1.6 [10 -5 cm-=(km light and blue continuum spectra. Modeled geometric am)-q for the S(0) and S(1) lines, respecalbedos at 9960 and 10,150 A discriminate among blue tively, as depicted by the dashed error bars. continuum solutions. Specifically, regions to the left of solid curves yield geometric albedos greater than 0.013 Models of quadrupole lines on Uranus are at both wavelengths and are thus deemed inconsistent consistent with the theoretical line with the observations. Numbers refer to y, values. strengths but are inconsistent with aspects Strong CH4 band constraints eliminate 3,, = 0 and a of many previous laboratory measurements portion of YT= 1 as indicated by shading. (i.e., Bragg et al., 1982; Bergstralh et al., 1978; Mickelson et al., 1977). These models curs for thef~i~2 = 0.75 model for both quad- agree with the most recent S(1) line rupole features. Here and throughout our strength determinations of B r a g g e t al. modeling, line center position is left as a (1982) and Brault and Smith (1980). Howfree parameter which is varied to yield the ever, they are inconsistent with the Bragg minimum o-~s(%). These minimum root- et al. (1982) S(0) determination, the only mean-square residuals are more clearly il- published measurement. lustrated in Fig. 16. The uncertainty in f~H2 Smith (1978) showed that for unsaturated can be estimated from the curvature of the lines in a relatively clear atmosphere, the root-mean-square residual vs f~H2. Specifi- ratio of observed S(0) and S(1) equivalent cally, the uncertainty associated with each widths depends only on the assumed line quadrupole line's determination of f~H~ is strength ratio, the effective temperature, (following Orton and Ingersoll, 1976) and the ortho/para ratio. In Fig. 19, we 0.3

I

424

BAINES AND BERGSTRALH

H240S(1)

&\ 0.8

.~

-

,~:~/,~

-

........

o.gs

1+8

~:6555

12"~30


L .30

[ .35

I ,40

I 6369+45

t +50

L 55

I 60

H 2 4 0 S(O) 1.0

""

°

" "'°

,/rn7s ( ~'{~) kk ,~,/f ~[k~.~/~.tjZtZ

0.8

. . . . . . . . .

.

.

.

.

0 65 075

130 1.14

o++

1 +o

0.7

--

~

o.6

1 .55

.60

L 65

I 643670

1

I

I

75

80

85

.90

FIG. 15. Modeled H2 line profiles for various ortho/para ratios. Calculated profiles are depicted for a range off~Hz, the fraction of H2 in local thermodynamic equilibrium. Best-fit models indicatef,H== 0.75 for each line. O'rm,(%) refer to the root-mean-square difference between models and observations, expressed in percentage units. In these fits, the absolute wavelength of peak model absorption is that which yields the minimum o-,,1, for the model. Other adopted parameter values are Pc~a 2.25 and those for the "standard model": ,JlH+ -- 0.03, PH-I -- 0.66 bars. rH = 0.5, % I, X - 0.6, y,o 7.24, a planetary rotation rate of 16 hr, and a thermal structure following model c of Appleby (1986). Theoretical room-temperature line strengths are assumed (i.e., 3.7 and 16.2 [10 5cm ~(kin-am) q for S(0) and S( 1), respectively).

s h o w r e s u l t s u s i n g S m i t h ' s f o r m u l a t i o n s for b o t h the t h e o r e t i c a l a n d the Bragg et al. (1982) m e a s u r e d line s t r e n g t h ratios. T h e t h e o r e t i c a l v a l u e is c o n s i s t e n t with J'~H: = 0.75 if the effective t e m p e r a t u r e of line form a t i o n is a b o u t 72°K, c o r r e s p o n d i n g r o u g h l y to the 9 0 0 - m b a r level in U r a n u s . O n the o t h e r h a n d , the Bragg et al. v a l u e is i n c o n s i s t e n t with t e m p e r a t u r e s g r e a t e r t h a n 69°K (i.e., b e l o w the 800 m b a r level). Since the effective level o f line f o r m a t i o n is r o u g h l y h a l f the d e p t h of the a t m o s p h e r e , the Bragg et al. line s t r e n g t h ratio does not

agree with a n o p t i c a l l y infinite c l o u d residing significantly b e l o w 1.6 bars. As exp l a i n e d in S e c t i o n V. E, the l o w e r b o u n d a r y o f the visible a t m o s p h e r e m u s t be at least 2.4 bars d e e p to satisfy the s h a p e s of the q u a d r u p o l e a n d m e t h a n e lines as well as weak methane band absorptions. W e find that o u r detailed c a l c u l a t i o n s inc o r p o r a t i n g a e r o s o l effects in an i n h o m o g e n e o u s a t m o s p h e r e , as well as t e m p e r a t u r e d e p e n d e n t p r e s s u r e shift a n d p r e s s u r e b r o a d e n i n g effects, are r e m a r k a b l y c o n s i s t e n t with S m i t h ' s r e l a t i v e l y simple f o r m u l a -

URANIAN ATMOSPHERIC STRUCTURE 1.7

1.6

1.5

1.4 Orms (%)

/ /J I

I

I

I

\\

/

\\\

\

/11

\\

s~I /I

_

1.3

/ / /

_

1.2

1.1

I

I

I

-

fell2 = 0.76_+0.13 1.0 0.50

I

I

1

I

0.60

0.70

0.80

0.90

1.00

fell 2

FIG. 16. Uncertainty determination for f~n2- Residuals, in percentages, vSf~H2are shown for modeled H2 4-0 S(0) and S(I) line profiles wherein peak absorption wavelength is a free parameter. The nominal value of f~H2 is the weighted mean of the individual nominal values defined by the minimum o'.~s. The one standard deviation uncertainty is derived from the curvature of o'rm~ vs f~H2, as explained in the text.

tions. In particular, fen, appears to depend principally on line strength ratio. Thus, for theoretical line strengths, fell2 = 0.75 for a range of cloud pressures and haze optical depths. We note that aerosol characteristics vary by less than 4% in the 70-,~ interval between quadrupole lines. This implies that both features are influenced by nearly identical line formation mechanisms. Moreover, pressure shift effects serve to reduce saturation greatly for wavelengths which probe tropospheric H2. These features, then, are relatively unsaturated, and their equivalent width ratios are independent of rH(6435 ,~). Consequently, they satisfy the conditions upon which Smith's expressions are based and are adequate for reliable modeling of the Uranian ortho/para ratio.

425

The sensitivity offeH~ to the thermal profile is illustrated in Fig. 18, where we show results for Appleby's (1986) nominal thermal profile and a profile in which the temperature has been reduced by 5°K at all levels. A change in f~H2 from 0.75 to 0.68 results. Since the Uranus effective temperature has an uncertainty of 2°K (Hildebrand et al., 1985), the uncertainty in f~H., due to temperature is roughly 0.03 (i.e., significantly less than the uncertainty associated with o-~s described previously).

D. H2 Line Profiles: PCld Constraints Pressure broadening is quite small for H2 quadrupole lines, being about 10% of the effect for typical methane features. Furthermore, for pressures less than a few bars, the intrinsic broadening is further diminished by pressure narrowing. However, in a hydrostatic atmosphere, hydrogen line profiles are susceptible to another effect which broadens the observed lineshape. Because the central frequency of line absorption increases monotonically with pressure, the observed profile is characterized by a relatively broad wing on its long wavelength side owing to the net effect of various amounts of pressure shifts throughout the accessible atmosphere. On the other hand, the blue wing can be quite sharp, its width being determined principally by the Doppler broadening from planetary rotation. Figure 20 depicts the effects of pressure on line formation for a nonscattering Uranian atmosphere. Populations for both S(0) and S(1) as a function of Uranian pressure, normalized to the J = 0 population near the temperature minimum, Tmi,, show how line strengths vary within the atmosphere. Using the pressure shift coefficients of McKellar (1974), a wavelength scale is associated with the pressure scale, as shown. The FWHM due to pressure broadening and pressure narrowing is also plotted for a few representative pressures. Dividing the relative populations by the FWHM as a function of pressure yields the solid curves,

I

I 0.50 ,~/

20

I T

*~``

0 ~5,,~,

--

J

``~

o.75 ~ \ ,

F- ____

--

16

--

14

--

12

--

qL. _ _ _ _ ~

"',,

//~, % " " 18

I

(6435~)0' 75/~k~,

rH

_

I

",,

1

E

%

x

I I

o.7~"/~

.

.

.

.

~--

i0

Pcld

eH 2

'H(6435A)

2.00 2.25 2.50

0.75 0.76 080

005 0.50 0.85

I

2.0

°rms(%)

"~.

"~ ~

[

30

",'~ 0 75

050

--

I

35

-

~025

138 1.17 113

I

25

~..~

[

4.0

4.5

SO I× 105crn 1!
FIG. 17. ortho/para distribution vs line strengths, haze optical depth, and cloudtop pressure. For each cloudtop pressure, families of isopleths in.f~H2 and TH(6435 ,~) are shown vs room-temperature line strengths which yield the minimum o-,m~. Typical uncertainties in the derived line strengths are represented by the dashed cross. The table shows the J~H: and TH(6435 ,~) which are consistent with theoretical room4emperature line strengths (diamond), together with the corresponding average residuals of the two quadrupole features. Uncertainty inJeHz for theoretical line strengths is shown by solid error bar. Model results do not agree with the measured room-temperature line strengths of Bragg et al. (1982), shown as a triangle with a cross depicting their published uncertainties. I

22

0.75 I

TH

(6435,&)

21

/~\ / \

0.50 /

-

I

\

I ~,T(K) - -

\

I

feB2 ~'H(6435A) I)rms (%)

0 5

0.75 068

m

F- .

0.50 0.67

.

T

.

.

-4

.j_

.75 16

117 1.18

/

-

0,7

~\'~.

~2 2.0

"',Z"

~0~o

I

I

I

I

I

2.5

3.0

8.5

4.0

4.5

SO (x 105cm'l/(km am))

FIG. 18. Effect of thermal structure. Constraint diagrams similar to Fig. 17 are shown for two thermal structures. Calculations for a model (dashed) employing a thermal profile 5 K colder than the model c of Appleby (1986) (solid) suggest an~H2 0.07 less than that for the latter structure. Uncertainty in the thermal structure, estimated to be -+2 K (Hildebrand et aL, 1985), yields an uncertainty of -+0.03

inLH2.

U R A N I A N ATMOSPHERIC STRUCTURE

01

URANUS PRESSURE

05

(BARS)

20

1O I

I

i

04 S1/S o 0S

THEORETICAL

--

BRAGG ET

AL

O6

427

l i n e s h a p e a p p r o x i m a t i o n is o b t a i n e d by acc o u n t i n g for the n o n l i n e a r i t y b e t w e e n pressure and w a v e l e n g t h in the p r e s s u r e shift e f f e c t d u e to t e m p e r a t u r e . S p e c i f i c a l l y , div i d i n g the solid c u r v e s b y (Tmin/T) effect i v e l y a c c o u n t s for the variation o f h y d r o -

1.8

fell 2

/ 1.4

O7

/ \

08

1.0

09

0.6

/

/

//

/

/

/

/

H2 4-0 S(1)

PJ=l

/ ~

~

INSTR

100

5O TMI N

60

7O

80

0.2 FWHM I • I [ i L 0 0.02

TIK)

FIG. 19. Estimate of the ortho/para distribution in the Uranus atmosphere vs effective temperature, f~H2 VS T (K) consistent with the observed S(0) and S(1) equivalent widths for Uranus are shown for theoretical (solid) and Bragg et al. (1982; dashed) room-temperature line strength ratios. Estimate assumes unsaturated line profiles and negligible aerosol scattering effects. Uranus temperature minimum of 51 K implies f~r~: > 0.40. Assuming that the effective pressure level of line formation lies below 750 mbar, more than twothirds of the H2 population is characterized by an equilibrium distribution of states.

1.0

I I

/ --

jl 0.04

iI

I I

• I 0.06

I

0.06

I

A.~

H2 4-0 S(0)

~.~. 0.8

%%%%.

--

0.6

~ ' ~

0.4--

0.2

which become measures of peak line opacity v s p r e s s u r e . G i v e n the narrow w a v e l e n g t h i n t e r v a l (as i n d i c a t e d b y the F W H M ) o v e r w h i c h v a r i o u s p r e s s u r e l e v e l s absorb, t h e s e c u r v e s t h e n m i m i c the actual l i n e s h a p e s . O w i n g to e n h a n c e d p o p u l a t i o n s at the c o l d e r t e m p e r a t u r e s a s s o c i a t e d w i t h s t r a t o s p h e r i c p r e s s u r e l e v e l s , the S(0) line is s i g n i f i c a n t l y n a r r o w e r than the S(1) feature. T h u s this line is superior for m e a s u r ing D o p p l e r rotation e f f e c t s in the blue wing. O n the o t h e r hand, the S(1) line is s u p e r i o r for m e a s u r i n g t r o p o s p h e r i c c l o u d l e v e l s s i n c e p e a k a b s o r p t i o n r e m a i n s relat i v e l y high for p r e s s u r e s greater than a bar d u e to e n h a n c e d line strengths at t h e s e w a r m e r t e m p e r a t u r e s . [A m o r e a c c u r a t e

0

I 00J

I

I

I

I

I

I

I

O.2

O.4

0.8

1.2

~.6

2.0

BARS

FIG. 20. Effect of pressure on H2 4-0 quadrupole

line formation in the Uranus atmosphere. Fractional populations for the S(0) and S(I) lines as a function of pressure are shown (dashed) normalized to the fractional population at the temperature minimum. Dividing these curves by FWHM (shown as bars for a selection of pressures) yields a measure of peak line opacity vs pressure (solid, also normalized). Due to the pressure-shift effect, these curves may be associated with a wavelength scale, as shown. Given the narrow width, as indicated by the FWHM, over which a given pressure level absorbs, the solid curves mimic the (inverted) shapes of actual line profiles under unsaturated conditions. Estimates of Uranus' rotational and instrumental broadening components are also depicted (horizontal bars).

428

BAINES AND BERGSTRALH

e'- oi°e~

142 4 0 S(1)

-

1.0

0.9

~

0.8

0.7

.30

t 35

l .40

.~,//"

I 6369.45

--- ..... I 50

185 236 287 I .55

1.86 1.20 1.48 i 60

H 2 4 0 S(0) 1.0

• .e° ee ~°

°

e

• *..

' Se

*f

• "co

0.9

i /

0.8

Pcld

,/t

-- -- .....

J ,,,~ o

1.85 2.36 787

O~ms(%) 139 1.14 1.37

0.7

0.6 .55

I

I

l

I

I

I

.60

.65

6436.70

.75

.80

.85

90

FIG. 21. Cloudtop pressure effect on lineshapes. Modeled line profiles are depicted for a nominal model (solid), as defined by a minimum value in ~r...... and for models which deviate from the nominal by one standard deviation in pressure (dashed). Uncertainty of individual data points, as determined by photon statistics, is 1.1% (error bars), close to the nominal model residuals. Residual values shown are the minimum values derived by letting line strengths and peak absorption wavelengths be free parameters. Other model parameters are those for the -slandard model" specified in Fig. 15.

gen column abundance per angstrom. This s e r v e s to f u r t h e r b r o a d e n the red w i n g in particular.] Results from a model/observation residual a n a l y s i s y i e l d Pcla = 2.36 -+ 0.51 b a r for p a r a m e t e r s w h i c h c o m p l y w i t h the n o m i n a l fit to t h e o r e t i c a l line s t r e n g t h s as d e p i c t e d in Fig. 17 [i.e., 3¢~u, - 0.75, ~H(6435 A) = 0.5] a n d A p p l e b y ' s (1985) t h e r m a l s t r u c ture. A r o t a t i o n a l p e r i o d o f 16 hr a n d a U r a nian o b l i q u i t y o f 70 ° a r e a l s o a s s u m e d to m a t c h t h e b l u e wing. I n this a n a l y s i s , h o w e v e r , line s t r e n g t h is a f r e e p a r a m e t e r w h i c h is v a r i e d to y i e l d t h e m i n i m u m O-rms(%). Figure 21 s h o w s m o d e l line profiles for the

n o m i n a l Pcla a n d t h o s e w h i c h d e v i a t e f r o m this v a l u e b y o n e s t a n d a r d d e v i a t i o n . F i g u r e 22 s h o w s the n o m i n a l a n d stand a r d d e v i a t i o n v a l u e s for Pcld as a f u n c t i o n o f h a z e o p t i c a l d e p t h . A n i n c r e a s e in h a z e o p t i c a l d e p t h c a n b e c o m p e n s a t e d b y an inc r e a s e in t h e c l o u d p r e s s u r e . H o w e v e r , m o d e l / o b s e r v a t i o n r e s i d u a l s for the best-fit line s t r e n g t h i n c r e a s e d r a m a t i c a l l y as rH(6435 ,~) b e c o m e s l a r g e r t h a n 1. T h u s , upp e r b o u n d s o f Polo = 3.2 b a r s , ~'H(6435 ,~) = 1.0 r e s u l t f r o m o u r line profile a n a l y s i s , irr e s p e c t i v e o f the c h o i c e o f r o o m - t e m p e r a ture line s t r e n g t h s . C o n s t r a i n t s o n r o t a t i o n a l p e r i o d , To,, are

URANIAN 20

ATMOSPHERIC STRUCTURE

I

I,L

I

J

J

429

f

J

S(~)I

1

1.6

14

1,2 o~

10 v

E 0.8

0.6

04

0.2

0 20

24

28

3 2

3.6

4.0

PCId(BARS)

FIG. 22. Cloudtop pressure vs haze optical depth. Nominal cloudtop pressures for each of the quadrupole lines is shown (solid). Representative values of the residuals, O'rm~(%), are depicted by tic marks. Also shown are the I-o- standard deviations in Pcla, rH(0435 ,~)-space for each of the quadrupole lines (dashed). Shaded area indicates region within which models satisfy the 1-o- standard deviation criterion for both lines simultaneously. Constraint implies rH(0435 ,3,) < 1.7, Pc'Ja < 4.0 bars, without regard to minimum residual values. Rapidly rising minimum model residuals effectively constrain rH(0435 .~) < 1.0, Pc'la < 3.2 bars. 1.5

I

I

I

I

I

I

I

1.4--

(0)

1.3 Urrns (%) 1.2

1.1--

I -6 HRS T U = 16+14

1.0

I

I

[

[

I

]

I

10

12

14

16

18

20

22

T U (H RS)

FIG. 23. Rotational period determination. Residuals, in percentage root-mean-square deviations, are shown for modeled H2 4-0 S(0) and S(I) line profiles wherein both line strength and peak absorption wavelength are parameters constrained to minimize o'rm~(%). Other parameters are defined for the standard model described in Fig. 15, with Pc~o = 2.25 bars. The standard deviation in rotational period is derived as in Fig. 16 and described in the text.

430

BAINES AND BERGSTRALH 1.1

I

1.0

......

1

I

T

T

1

T

--.

H2 4 0S(0)

• °,o

%,

0.9

0.8

07

0.6 .55

I

I

1

1

I

I

.60

.65

6436.70

75

.80

.85

.90

FIG. 24. Profiles for nominal and one-standard-deviation rotational periods. Line strengths, profile positions, and other parameters are as defined for the "standard model" in Fig. 15.

depicted in Figs. 23 and 24. Relatively shallow curvature is illustrated for the model/ observation residuals vs Tu, so that the derived uncertainties are large. Nevertheless, these observations rule out rotational periods less than 10 and more than 30 hr. The nominal fit of 16 hr is in remarkable agreement with other determinations. In particular, G o o d y (1982) finds Tu = 16.31 -+ 0.27 hr from measurements of several hundred line tilts. He also reports a theoretical determination of 16.7 -+ 0.5 hr based on the Elliot et al. (1981) J2 determination and the Franklin et al. (1980) oblateness from Stratoscope II observations. We believe our result is n o t e w o r t h y as a confirmation of the quality of our high-resolution data sets and modeling techniques. E. CH4 6818.9-/t Line Profile The equivalent width and F W H M of the 6818.9-A line can be used to determine ~-H(6435 ,~) and fcH, for a specific value of Pcld, as is demonstrated by Baines (1983). We note, however, that constraints from such an analysis depend strongly on the assumed line strength and pressure-broadening characteristics. For example, ~-n(6435

A), which restricts the number of photons reaching the CH4-rich portion of the atmosphere, influences the modeled equivalent width and is thus sensitive to the assumed rotational quantum number. For example, i f J - 0, as adopted by Baines (1983), then ~-H(6435 A) -- 2-3. However, J = 3 restricts TH(6435 A) to 0.4-1.0. Similarly, fcH, influences not only the equivalent width, but the F W H M , and is thus sensitive to the assumed pressure-broadening characteristics. N e w laboratory measurements (Keffer et al., 1986) suggest that the molecular parameters used by Baines (1983) are incorrect. Specifically, the measured room-temperature CH4:H2 pressure-broadening coefficient for this line is some 35% larger than the value of 0.065 cm J/arm Baines estimated from the broadening characteristics of typical low-J near-IR features. Moreover, low-temperature measurements by Keffer strongly suggest 2 < J < 5, although a specific quantum number assignment cannot yet be deduced (Smith, 1985, personal communication). The low-pressure (5 Torr) measurements of Keffer et al. (1986) imply that the feature is a singlet and not a manifold under Ura-

URANIAN ATMOSPHERIC

I

I

I

::$ :::

STRUCTURE

431

I

tive study of this line at room temperature. Examination of the low-pressure lineshape PCId = 275 BARS i i J=2 o5 with the photoacoustic technique discussed o~ 200 o.os in Conner et al. (1984) reveals, within the less than 1 mA uncertainty of the measureo.5 ment, no increase in the measured width of 0015 ::i:ii....... : ~0 7~ i z~ ~so I the 6818.9-A feature above that expected i ~ i i i::::i::::~:~...... from Doppler, pressure, and instrumental broadening (Smith, 1985, personal com100 360 380 400 420 440 460 480 munication). It seems, then, that there is FWHM (rnA) little doubt that this is a singlet line. We FIG. 25.fcH, VS rH(6435 ,~) constraints from 6818.9- adopt this result in our synthetic spectrum •~, CH4 line observations, assuming PcJa = 2.75. Curves calculations. of constantfcH4 are shown for 1.5, 3.0, and 4.0% cloudAs shown in Fig. 25, we find that a rotatop methane mixing ratios (solid). Curves of constant tional quantum assignment J = 3 and the haze optical thickness (dashed) are depicted for new pressure-broadening characteristics rH(6435 ,4.) = 0.5, 0.75, and 1.0, assuming % = 1. Region constrained by the observations (shaded) sug- satisfy the observed equivalent width and gests 0.028 < fcH~ < 0.042, 0.5 < ru(6435 A) < 0.85, FWHM for models incorporating 0.03 < and a rotational quantum assignment J = 3. fCH4 < 0.045 and 0.5 < ~'H(6435 A) < 0.85, assuming PcJd = 2.75 bars. The effect of Pcld onfcu, is shown by the shaded region in nian conditions. Specifically, the linewidth Fig. 26. A lower boundary to the visible behaves as expected, collapsing monotoni- atmosphere at 2.4 bars is established by cally to essentially the thermal-broadened these data. Recalling the hydrogen quadruwidth as pressure is decreased, with no ad- pole constraints, we find that the cloudtop ditional features becoming evident. Further pressure is restricted to 2.4 < Pcld < 3.2 evidence comes from a detailed quantita- bars, as depicted by the thickly shaded rel

o3

0.06

I

I

I

0.o4

o ~. ~ ! ~ i " .9 0.os

o

.

9

2

~

/

~ 4860 [."1 ~'H = 0.5 /

542oj

%-B

~

0.91

9.1 I

I 32

H 2 4-0 0 L 1.0

0.5

I 1.5

[ 2.0

I 2.5

I 3.0

3.5

Pcld (BARS) FIG. 26. fcu~ vs ecId constraints from 6818.9-A CH4 line, H2 4-0 quadrupole profiles, and weak CH4 band observations. Minimum cloudtop pressure allowed for fcm is the associated condensation level, PH-B (solid). Constraints satisfying CH4 line are depicted by shaded region. Thick shaded region also satisfies Pad constraints from the H2 quadrupole line shapes. Numbers within shaded region denote r~(6435 A) values. Two solutions for 4860- and 5430-A peak absorption models are also shown (thin solid), as are curves for o~aa(6500 ~,). Standard solution, fcu4 = 0.03, Pc'ld : 2.66 bars, is also depicted (diamond).

432

BAINES AND BERGSTRALH

~

~i~

~

~0028

as illustrated by the shaded and "horizontal" striped region in Fig. 27. In short, our integrated analysis determines the haze optical depth, rH(6435 A), to be limited to 0.4 < Tn(6435 ,&) < 1.0, i.e., slightly above that deduced by Trafton (1976) and adopted by Wallace (1980).

~

0 023

F. Weak CH4 Bands

ICH4 (max.) 0 033

14

[

0041

....

0 04

10~ ~ 08

y

0 047

06

0035

t"

..

04

~ :: :::::;~i

:

/

02

f~' •

:.

20

24

v

/

f I

_

28 PCId {BARS/

~

32

.

36

Fro. 27. ru(6435 A) vs Pc~aconstraints from Hz 4-0 quadrupole profiles, 6818.9-A, CH4 line, and weak CH4 band observations. Shaded region shows quadrupole constraints. Models which satisfy theoretical line strengths are indicated by Curve A. Methane line constraints which also satisfy the quadrupole lines are depicted by "horizontal" stripes. Numbers indicate constrained methane molar fractions. Curve B indicates solutions which satisfy the nominal observed values of the 6818.9-A CH4 equivalent width and lull width halt'maximum. Also shown are constraints from weak methane bands (dashed), with "vertical" stripes depicting the region which also satisfies the quadrupole lines. Shaded, cross-hatched region satisfies all three data sets simultaneously. "Standard" model, with rH (6435 A,) = 0.5, Pcld = 2.66 bars, and fH~ = (/.(13, is represented by the diamond.

gion in the figure. This, in turn, implies that the methane molar fraction which simultaneously satisfies both data sets is limited to 0.020 < fCH, < 0.046. Thus, our integrated analysis agrees with the range of C H 4 molar fractions derived by Baines (1983). The range of haze optical depths constrained by the CH4 line, however, is significantly less than that previously derived by Baines. Specifically, we find for c[oudtop pressures near those assumed by him (i.e., Pc'~d < 2.5 bars) that 0.4 < ~-u(6435 A) < 0.5 compared with 2.2 < rH(6435 A) < 2.7. We note, however, that our constraints on rH(6435 A.) vs Pcla are in striking agreement with that derived from the He quadrupole lines,

Methane bands imbedded within the blue continuum constrain the same model parameters as the CH4 line profile. As with the previous analysis, weak band calculations are hampered by uncertainties in the temperature dependence of absorption parameters. Furthermore, disagreements exist among measurements of room-temperature absorption parameters which complicate the analysis. Figure 28 shows the correlation between the observed geometric albedo and the room-temperature absorption coefficients of Giver (1978) and Fink et al. (1977). The Fink et al. data exhibit significantly more scatter, particularly for the 5100- and 5430-A bands. To minimize the uncertainty associated with absorption coefficients, we chose only those portions of the 4850- and 5430-,~ bands where the two laboratory measurements agree within 10% (correcting for a spurious 10-A red shift of Fink's 4850-A band data). Figure 29 shows model spectra for typical fits to the data of both Giver (1978) and Fink et al. (1977). For an assumed 3% methane molar fraction, derived parameters are rH(6435 A) - 0.46, Pcld -- 2.66 bars. This solution, depicted as a diamond in Figs. 26 and 27, agrees well with the Hz a n d C H 4 line constraints. Constraints derived from an analysis of peak absorptions at 4860 and 5420 A are depicted explicitly in these figures. G. Intermediate CH4 Bands

In principle, these bands constrain the same parameters as the weak bands. In addition, the pseudocontinuum between bands constrains O)cla(X). In practice, however, we again find significant scatter in

URANIAN ATMOSPHERIC STRUCTURE '

'

'

'

'

'

'

I

433

'

'

'

'

'

'

'

'

I

t

i

,

,

,

,

,,I

0.60

0.5C

0.40

PX 0.30

0.20 BAND GIVER FINK 0.10

0 0.~I

4850

•

©

5100

•

,~

5430

©

0

I

I

I

I

I

I i l I 0.01

0. I0

KCH 4

FIG. 28. Observed geometric albedos vs room-temperature absorption coefficients for the weak C H 4 bands. Large variations between the Fink et al. (1977) and Giver (1978) measurements are apparent, particularly near KCH4= 0.02 (km-am)-L Standard model as defined in Fig. 15 with Pc~J = 2.66 bars yields the modeled curves of growth shown. plots o f o b s e r v e d geometric albedo vs absorption coefficient which affects severely their usefulness in the red. T e m p e r a t u r e effects are s u s p e c t e d as the primary cause of the o b s e r v e d scatter, but some contribution due to u n d e t e r m i n e d m e t h a n e ice effects m a y be present as well. Figure 30 illustrates the o b s e r v e d curve of growth as well as a curve of growth calculated for a " s t a n d a r d m o d e l " which satisfies the preceding analyses [i.e., ~-H(6435 ,&) = 0.46, y~ = 1, X = 0.6, y~ = 7.24, PH-T = 0.66 bar, PCld = 2.66 bars, f c n , = 0.03, and fell2 = 0.75]. The cloud single-scattering albedo, constrained to m a t c h the o b s e r v e d geometric albedo at 6500 A, is oScmd= 0.96. H e r e , the data h a v e been split into several wavelength ranges in order to reduce the contribution to the scatter f r o m low-frequency variations in Rayleigh and aerosol extinction. Significant scatter exists a m o n g points within any specific wavelength

range, indicating that high-frequency variations in CH4 absorption coefficients have not been evaluated adequately. In particular, several p s e u d o c o n t i n u u m regions, labeled A through D in the figure, are considerably brighter than other nearby points exhibiting similar r o o m - t e m p e r a t u r e coefficients, suggesting that for m a n y wavelengths absorption coefficients are substantially less under Uranian conditions than in the laboratory. Figure 31 shows these regions of the o b s e r v e d spectrum, together with the modeled spectrum. N o t only are the modeled spectral points too dark in the p s e u d o c o n t i n u u m regions, but points near absorption p e a k s are too bright as well. This b e h a v i o r is that which would be expected for absorption in a cold planetary a t m o s p h e r e w h e r e predominantly high-J lines in the wings are diminished and low-J lines in the p e a k s are enhanced. Such p s e u d o c o n t i n u u m points can be

0.65

I

•

..-.

0.60

0.55

0.50 PX 045

040

,,,..

I

0-35 1

CoCId - 0.99851 ----0.99291

G,VER

....

FFNK

09985 ] 4500

0.30 ~ 4000

KCH4 ! ] 5000

~,6 I 5500

6000

FIG. 29. Standard model: Weak CH4 band spectra. Models for bright (solid) and darker (dashed) cloud reflectivities are shown, where the dark cloud OSc=jis chosen to fit the continuum geometric albedo at 5890 A. (circled). A bright cloud model incorporating the Fink et al. (1977) absorption coefficients is also depicted, showing best agreement with the Giver (1978) absorption coefficients near the peaks of the 4850- and 5430-,~ bands.

0.60 I

3.0

250 I

r' 0,50

*f~PH p~: BHCH4~ 0045

o 40

~.,...~..-,.~,,%

2.00

BARS

r~

I

003

1.00

0.75

i

I

0015 OBSERVED

o,o

-....'~.,

/~

:j,

A

o10

O o~

I 0.03

I

k

1 0.10

0.20

0.30

~Cld 0.9786 0.9598 0,9598

7200 - 7700 . . . . . . . . . . . . . . 8600 - 8800 -

0.9598 0.9598

6230 6290 6730 - 6790 7110 7160 7400 7160

" " " " . . . ~ ' ~ -!....m

I 0.02

MODEL

6000 - 6390 ~ 6400 - 6790 - --6800 7190 . . . . . .

........... .,,..=.==

~

t J ~lJ 1.00

I J I 3.00 4.00 B.O0

I ZOO

~

~:CH 4

FIG. 30. Observed geometric albedos vs room-temperature absorption coefficients for the intermediate CHa bands. Giver's (1978) absorption coefficients are used. T w o - w a y optical depth of unity for CH4 absorption vs Kcn4 is depicted by the pressure scale, where the methane partial pressure follows the saturated vapor pressure and a mean air mass of 3 is assumed for the visible disk. Condensation levels for various CH4 molar fractions are indicated by PH a. Methane absorption coefficients less than 1.0, typical of these bands, are sensitive to CH4 molar fractions greater than 1.5%. Regions A to D indicate relatively large departures from the nominal curve of growth, suggesting large temperature effects. Curves of growth for the standard model, as defined in Fig. 15, are shown as curves. 434

URANIAN ATMOSPHERIC STRUCTURE 0.70

f

I

I

I

. . . . . . . . .

....... . . . . . . . . . - -

0.60

S'\

0.50

435

-

-

wCld

~.(,~)

0.9985 0.9957 0.9929 0.9786 0.9716 0.9598

5000-5500 5600 5890 6040 6330 6500

a~

0.40

0,30

0.20

0.10

I 6500

I

0,0£ 5,5OO

6000

I 7000

I 7500

81300

k

FIG. 31. Standard model: Intermediate band spectra. Regions A - D d i s c u s s e d in Fig. 30 are s h o w n as s h a d e d regions. True continuum level setting KCH4 = 0 is s h o w n by straight dashed line. Fits to selected near-continuum wavelengths using Giver's absorption coefficients are s h o w n (dots) together with local

spectra and fitted a3Od values (table).

used to constrain the single-scattering albedo spectrum of the underlying (presumed optically infinite) cloud. Specifically, we use the five wavelengths indicated in Fig. 31 to constrain ~Cld(X) assuming absorption coefficients of 0 and Giver (1978) as limits to the actual absorption coefficients. The resulting limits on the cloud single-scattering albedo are illustrated in Fig. 32. A sharp drop in ~Cld(h) is indicated between 5890

and 6040 A. The cloud remains relatively dark until at least 6500 ,~, beyond which meaningful limits on oScta(k) cannot be determined owing to generally increasing room-temperature coefficients in the pseudocontinuum. There is no a prior reason to suppose that the aerosol darkening is limited to the cloud. Indeed, a potential darkening process, irradiation of ice crystals by ultravio-

1.00

~CId

KCH4

0.95

0.~ 5OOO

- -

GIVER

. . . .

0

I 55OO

I 6O0O

6 ~

FIG. 32. Standard model: Cloud spectral constraints, o~oa(k) is s h o w n b a s e d on a n a l y s i s o f the nearcontinuum points shown in Fig. 3 I. Upper limits (solid) for O~cw(k/are determined from G i v e r ' s (1978) absorption coefficients. Lower limits (dashed) are determined setting KCH4 = 0.

436

BAINES AND BERGSTRALH 1.00

1 O0

0.90

0.80

0,80

060 ~

O-H

0.70

-- -T2

/ /

- -

•

0.60 3500

340

UNIRRADITTED IRRADIATED

I

L

1

I

L

4000

4500

5000

5500

6000

3.20 6500

FIG. 33. Standard model: Haze spectral constraints. ~.(X) is shown based on an analysis of the nearcontinuum points shown in Fig. 31 and assuming o3c~d(X) 0.9985 everywhere. Upper and lower limits are derived as in Fig. 32. The reflectivity spectrum measured by Lebofsky and Fegley (1976) for 1-hr UV-irradiated H2S frost (dotted line) is a better qualitative match than the unirradiated sample (dashed).

let light [as suggested by Lebofsky and Fegley's (1976) measurements of H2S and NH4SH crystals] is most efficient in the stratosphere. Figure 33 shows the calculated haze single-scattering albedo spectrum, assuming the previously defined model above with O3c~d(X) = 0.9985 at all wavelengths. We note that the spectrum qualitatively mimics that of irradiated H2S frost.

H. H2 3-0 S(O) Dipole Constraints Collision-induced absorptions depend primarily on the ortho/para ratio and cloud pressure. Another factor which affects the appearance of these features is methane absorption, which is governed by the absorption coefficient and the methane mixing ratio. Indeed, as depicted in Fig. 34, methane absorption overwhelms the appearance of most 3 - 0 features, the only clearly discernible feature being the S(0) line at 8260 A. This feature appears in the wing of the strong 0.8-#m band where, as discussed

above, methane absorption coefficients appropriate for Uranus conditions are uncertain. The B i r n b a u m - C o h e n (1976) lineshape employed here depends on two collisional time parameters, r~ and r2. We use r~ = r2 = 5.0 (10 ~4) sec from an empirical fit to the obsevations of McKellar and Welsh (1971) as illustrated in Fig. 35. As shown in Fig. 34, the standard model described previously does not fit the observed spectrum well in the relatively weak CH4 absorption region from 8100 to 8300 A. The modeled geometric albedo in this region can be increased by decreasing J'~',4, P('kl, or Kc.4(x), or by increasing O)C~d(X). H o w e v e r , constraints from the CH4 line profile and weak bands do not afford sufficient flexibility in.l~:H~ and PCLd alone to fit the observations. For example, Panel A of Fig. 36 indicates that a cloud at just 1.9 bars is required to match the spectrum, a pressure level precluded by the previous analyses (e.g., Fig. 26). H o w e v e r , Panel B displays possible solutions found by varying

URANIAN ATMOSPHERIC STRUCTURE 070

1

0.60 --

o.5o~

I

I

62(01+QI(1'0) S1(0)+Q2(1,0) S2(1)+Q1(1'0) $1(0)+Q2(1,0)

/

I

%(O)

]

]

PX 0.3~L~] 0'~[/~/ <

Q (1) 3

s31,s3(o~ _l_J_

_L_L

_

0.20

437

I ._L_

/

~

]

0.10

I

7500

]

8000

8500

3,

9000

FIG. 34. Standard model: 7500-9200 ,~. H2 3-0 collision-induced dipole spectrum (long dashed) and true continuum level (short dashed) are shown assuming ECru(X) = 0. $3(0) feature is evident in the observations and model spectra. Modeled geometric albedo is a poor fit to the observations in the vicinity of the 3-0 S(0) feature.

the CH4 absorption coefficients, singlescattering albedo, and ortho/para ratio. These solutions are constrained to match both the peak and continuum absorption levels for the S(0) feature. The derived value of fell2 is significantly less than that

found from our previous quadrupole line analysis. However, we find that nonuniform variations in the temperature dependence of the CH4 absorption coefficients may be accountable. Specifically, the data can be fitted by f~H. = 0.75 if CH4 absorp-

11800

f 2000

12200

I

I

I

cm 1 12400

12600

I

I

I

t¢'~. "rl(X 1014)T2(X 1014).r~[~i~ 'E 3

-- 5.0

1.8

-_-m

] 2800 fell 2 = 0 T=85K

dll

II

o 2 x

1 8500

8400

8300

8200

,&

8100

8000

7900

7800

FIG. 35. Birnbaum and Cohen (1976) collisional time constants determined for the 3-0 spectrum. Three synthetic spectral profiles are shown for various 72 compared to the 85 K, normal Hz observations (solid) of McKellar and Welsh (1971).

438

BAINES AND BERGSTRALH 0 30

I

I Pcld = 19 BARS

L A

KCH4

fell 2

UJCId

GIVER GIVER

100 075

0.9708 09672

PCLd KCH4

0.25 .... - -

2 661 BARS fell 2

GIVER 1130 GIVER 046 1 '2 GrVER 030

.":.

0.20

0.9598 09992 0.957?

f

P~ 015

010

0.05

0 8000

I 8500

9000

•7

1

I ;,,,

8000

B

wCid

85OO

I A

9000

FIG. 36. Effect of Pcld, ¢CH4,f~H:, and o)c~jon calculated spectra. Satisfactory fits to the observations may be derived by decreasing the cloudtop pressure (A) or by decreasing the CH4 absorption coefficients and/or increasing the cloud single-scattering albedo (B). First procedure yields cloud pressures inconsistent with 6818-,~ line and weak CH4 band results, although resultingf, H~agrees well with H~ quadrupole line analysis, Second procedure yields a bright cloud for Giver's absorption coefficients or a dark cloud using absorption coefficients halt" as large. This approach requires J~u2 significantly less than values consistent with the observed quadrupole features. Differences in the sensitivity of K~'H~to temperature at various wavelengths may explain this discrepancy.

tion at 8260 A is some 20% more sensitive to the l a b o r a t o r y - U r a n u s temperature difference than the absorption at 8310 ,/~. VI. DISCUSSION

We have shown that three complementary, high-quality observational data sets can be employed to constrain an eight-parameter model of Uranus" atmospheric structure. Useful constraints, summarized in Figs. 7, 17, 26, 27, and 32, may be used to derive meaningful information about the deposition of sunlight in the stratosphere and upper troposphere (Appleby, 1986), the bond albedo (Pollack et al., 1986), as well as planetary formation and dynamic mechanisms. We find that Uranus is significantly enhanced in carbon over the solar value. In particular, at least 15% of the weight of Uranus is in the form of methane• Owing to our inability to probe beneath the cloudtop. the actual deep-atmosphere global-mean CH4 molar fraction may be substantially greater than the cloudtop limit of./i,tt.

0.046. The cloud itself, then, may be composed primarily of condensed CH4 extending upward from the condensation level at ,several bars to the hazetop above 700 mbar. On the other hand, our observations may indeed be sensing the deep-atmosphere CH4 concentration if the cloud lies below the CH4 condensation level (Fig. 26). In this case, the cloud itself is likely to be composed of H~S of NH4SH (Macy, 1979). We find that complete equilibration of H2 has not occurred in Uranus' atmosphere. Given a 3-year time constant for ortho/para conversion, our derived 0.63 < ./eH~ < 0.95 implies a time scale for vertical mixing of 3 l0 years. Indeed, vertical motions may be substantially more energetic if catalytic processes (e.g., Farkas, 1935; Massie and Hunten, 1982; Conrath and Gierasch, 1984) are involved. UV-absorbing aerosols are present above at least the 800-mbar level. Indeed, we have shown that the brightening effect of polarization on Rayleigh scattering discussed by

URANIAN ATMOSPHERIC STRUCTURE Pollack et al. (1986) requires haze top pressures less than 300 mbar (Fig. 8). Calculations with the Raman-scattering approximation recently developed by Pollack et al. (1986) indicate haze top pressures close to the temperature minimum near 100 mbar. Thus, aerosols are prevalent above the radiative-convective boundary (400-500 mbar; Appleby, 1986). A more physical model of the aerosol morphology then consists of two distinct aerosol layers--a stratospheric haze n o t composed of condensed C H 4 particles, and a lower, tropospheric, CH4-rich condensate aerosol which extends upward from the CH4 condensation level within the convectively mixed adiabatic region. The UV-absorbing aerosol is possibly produced in the stratosphere by photochemical processes involving CH4 (Atreya, 1984). Such an aerosol morphology does not significantly modify our derived constraints on fell_,, fCH4, o r PCid if TH(6435 ,g,) refers to the combined optical depth of the upper level haze layers. We note that recent analysis of ground-based images of Uranus (Terrile and Smith, 1984) by Baines et al. (1985) agrees with this morphology. In particular, they find that an optically thin (~- = 0.1), nonscattering " d u s t " layer above a bright (O3H --~ 0.99) tropospheric cloud yields center-to-limb profiles which match observations in the pseudocontinuum at 6310 A as well as in methane bands at 7260 and 10,000/~. We have found that Y,~ + yr is an indicator of microphysical aerosol properties which is insensitive to macrophysical conditions such as the optical and physical depths of aerosol layers. Values in the range 7-9 are determined for Uranus. Preliminary values for Neptune indicate y,~ + % - 4, and thus strongly suggest that these upper level aerosols are distinctly different in their microphysical properties from those in the Uranian atmosphere. In particular, we find that the reflection spectrum in Uranian haze is similar to that of UV-irradiated ices, while Neptune's brighter, nearly wavelength-independent blue geometric al-

439

bedo spectrum is consistent with unirradiated condensates. Finally, our derived atmospheric structure is consistent with recent results from infrared, submillimeter, and millimeter observations. In particular, Orion et al. (1986) find a deep-atmosphere methane molar fraction on the order of 2% from synthetic fits to submillimeter and millimeter observations. Their analysis is presently unable to constrain f c a , to within an order of magnitude of this value due to other parametric uncertainties. Appleby's (1986) analysis of recent infrared observations is also insensitive to the deep-atmosphere methane mixing ratio since these thermal wavelengths do not probe below the l-bar pressure level. His model c thermal profile, adopted here for the stratosphere and upper troposphere, is consistent with a range of our derived atmospheric structures permitting aerosol opacity above the level 400-500 mbar (cf. Appendix of Appleby, 1986). ACKNOWLEDGMENTS We thank G. S. Orton and J. Martonchik for providing the core computer code used to generate spectra for inhomogeneous atmospheres. We are grateful to J. Appleby, J. B. Pollack, M. G. Tomasko, and J. T. Trauger for many helpful discussions. Finally, we thank C. F. Keffer and W. H. Smith for providing important laboratory results prior to publication. The work described in this paper was carried out by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration, with primary support from the Planetary Atmospheres Discipline, NASA Office of Space Sciences and Applications. REFERENCES APPLEBY, J. F. (1986). Radiative-convective equilibrium models of Uranus and Neptune. Submitted for publication. ATAI, A. A., V. D. VDOVICHENKO, K. S. KURATOV. AND V. G. TEIFEL (1981). Spectrum of Uranus at 0.47-1.00 /zm: A comparison with the simplest models of the formation of the CH4 absorption bands. Astron. Vestn. 15, 17-24. ATREYA, S. K. (1984). Aeronomy. In Uranus and N e p t u n e (J. T. Bergstralh, Ed.), NASA CP-2330, pp. 55-88. BAINES, K. H. (1983). Interpretation of the 6818.9-A methane feature observed on Jupiter, Saturn, and Uranus. Icarus 56, 543-559.

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gan, T. Owen, and H. Smith, Eds.), pp. 384-391. Reidel, Dordecht. POLLACK, J. B., K. RAGES, K. H. BAINES, J. T. BERGSTRALH, O. WENKERT, AND G. E. DANIELSON (1986). Estimates of the bolometric albedoes and radiation balance of Uranus and Neptune. Submitted for publication. PRICE, M. J., AND O. G. FRANZ (1978). Limb brightening on Uranus. II. The visible spectrum. Icarus 34, 355-373. SMITH, W. H. (1978). On the ortho-para equilibrium of H2 in the atmospheres of the Jovian planets. Icarus 33, 210-216. SMITH, W. H. (1985). Personal communication. TEIFEL, V. G. (1983). Methane abundance in the atmosphere of Uranus. Icarus 53, 389-398. TERRILE, R. J., AND B. A. SMITH (1984). Cloud features on Uranus from CCD imaging. Bull. Amer. Astron. Soc. 16, 657. TOKUNAGA, A. T., G. S. ORTON, AND J. CALDWELL (1983). New observational constraints on the temperature inversions of Uranus and Neptune. Icarus 53, 141-146. TRAETON, L. M. (1967). Model atmospheres of the major planets. Astrophys. J. 147, 765-781. TRAFTON, L. M. (1976). The aerosol distribution in Uranus' atmosphere: Interpretation of the hydrogen spectrum. Astrophys. J. 207, 1007-1024. TRAUGER, J. T., AND J. T. BERGSTRALH(1981). Asymmetrical profiles of the H2 4-0 quadrupole lines in the spectrum of Uranus. Bull. Amer. Astron. Soc. 13, 732. WALLACE, L. (1972). Rayleigh and Raman scattering by H2 in a planetary atmosphere. Astrophys. J. 176, 249-257. WALLACE, L. (1980). The structure of the Uranus atmosphere. Icarus 43, 231-259.