titan's surface and troposphere, investigated with ground...

ICARUS 93, 362-378 (1991)

Titan's Surface and Troposphere, Investigated with Ground-Based, Near-Infrared Observations

C A I T L I N A . G R I F F I T H

Physics Department, State University of New York, Stony Brook, New York 11794

TOBIAS OWEN

Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, Hawaii 96822

AND

R I C H A R D W A G E N E R *

Space Astrophysics Laboratory, Institute for Space and Terrestrial Science, 2700 Steeles Avenue West, Concord, Ontario, Canada L4K3C8

Received October 11, 1990; revised June 24, 1991

New observations of Titan's near-infrared spectrum (4000-5000 cm l ) combined with points taken from Fink and Larson's (1979) spectrum (4000-12500 cm- t) provide information on Titan's haze, possible clouds, surface albedo, and atmospheric abundance of H 2 .

In the near-infrared, the main features in Titan's spectrum result from absorption of solar radiation by CH 4. The strength of this absorption varies considerably with wavelength, allowing us to probe various atmospheric levels down to the surface itself by choosing specific wavelengths for analysis.

At 4715 cm -t , the pressure-induced S(1) fundamental band of H E lies in the wings o f C H 4 bands. Based on current values for the CH 4 line parameters, Titan's spectrum can be best interpreted with a volume mixing ratio of H E between 0.5 and 1.0%.

Our observations suggest the existence of an optically thin CH 4 cloud layer. The optical depths that we derive for Titan's haze and clouds are small enough to allow us to sense the surface of Titan at 4900, 6250, and 7700 cm-t. The most plausible interpretation of the albedos determined at these wavenumbers suggests a surface dominated by "dirty" water ice. A global ethane ocean is not compatible with these albedos. ~ 1991 Academic Press, Inc.

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

Titan, the only satellite in the outer Solar System with a substantial a tmosphere , offers a unique opportuni ty to study the volatile components of the Saturn-orbit ing plan- etesimals and heliocentric comets that accreted to form

* Now at Brookhaven National Laboratory, Evironmental Chemistry Division, Bldg. 426, Upton, NY 11973.

0019-1035/91 $3.00 Copyright © 1991 by Academic Press, Inc. All rights of reproduction in any form reserved.

Saturn ' s satellites. When Voyager I flew by Titan in 1980, an orange blanket of aerosols obscured the lower a tmosphere and the surface f rom our view. Despi te these hazy conditions, our knowledge of the satell i te 's a tmosphere expanded enormously . A combinat ion of UV spectroscopy and radio occultat ion measuremen t s establ ished that the major consti tuent of the a tmosphere is N : , and the total surface pressure is 1.5 bars (Broadfoot et al. 1981, Lindal et al. 1983). Studies of Voyage r ' s IR spectra of Titan have greatly increased our understanding of the identities and distributions of trace organic compounds in the a tmosphere (e.g., Hanel et al. 1981, Coustenis et al.

1989). The analysis of T i tan ' s UV and visible spectra elucidated the characteris t ics of the particles in the satel- li te 's upper a tmosphere (e.g., Rages and Pollack 1983, M c K a y et al. 1989, Courtin et al. 1990). Research on cloud physics coupled with IR data led to constraints on the sizes of particles in possible C H 4 clouds as a function of optical depth (Toon et al. 1988). However , many questions concerning the composi t ion of the a tmosphere and surface that bear on the formation, evolution, and complex organic chemis t ry of the satellite remain unanswered. The volume mixing ratios of the two main const i tuents in Ti tan ' s a tmosphere are only loosely constrained (N2: 65-99%, CH4: 0 .5-3.4%, Hunten et al. 1984, Lel louch et

al. 1989). Clouds of condensed C H 4 have not yet been observed and the surface composi t ion remains unknown.

Recent advances in the study of the haze particles as well as new laboratory measurements of spect roscopic constants for methane (both gas and solid) now make it

362

TITAN'S NEAR-IR ALBEDO 363

possible to address these questions with detailed studies 00~5 of Titan's near-infrared spectrum. In the 4000-7000 cm-l spectral region, Titan's albedo results largely from ab- ~0~ sorption of solar radiation by CH 4 and scattering of radiation from particles in the atmosphere. The optical depth ~ 0026 of Titan's haze is smaller here than at visible or ultraviolet

0.02 wavelengths. Consequently, the depth penetrated by the .~ radiation depends primarily on the strength of CH 4 ab- ~ 00~5 sorption. This absorption varies considerably with wave- ! length in the near-infrared, allowing one to sample Titan's ~ 00~ atmosphere at different altitudes from the surface. There are three wavelength regions where methane absorption is o.oo5 so weak and Titan's atmosphere is sufficiently transparent that one might hope to sense the satellite's surface. These 0 are at 4900, 6250, and 7700 cm -1.

In this paper, new observations of Titan's 4000-5000 0,2 cm-~ spectrum at two resolutions (3.8 and 38 cm-~) are analyzed to determine the haze optical depth at 4620 cm- ~ 0.~ and the atmospheric abundance of H2, and to search below the tropopause for evidence of methane condensation ~ 005 clouds. To constrain Titan's surface albedo at 4900, 6250, _~ and 7700 cm-1, we also include points from a 4000-12500 ~ 90~ cm- t spectrum of Titan reproduced at a resolution of 46 cm -1 by Fink and Larson (1979). ¢o 0.04

II . O B S E R V A T I O N S

High and low resolution spectra of Titan (with a FWHM of 3.8 and 38 cm-~, respectively) were recorded at the Infrared Telescope Facility on Mauna Kea in the summer of 1989 using the Cooled-Grating Array Spectrometer (Tokunaga et al. 1987). Each spectrum is the average of several observations divided by a B2 star observed at a similar airmass to eliminate telluric absorption (Fig. 1). The airmasses and signal-to-noise ratios of the spectra are presented in Table I.

Titan's albedo was calculated by dividing the observed spectrum by a solar spectrum (Arvesen et al. 1969), convolved to the same resolution. This albedo was then normalized to match that measured by Fink and Larson (1979). In addition, the albedo was corrected by using a new radius for Titan (Toon et al. 1991), since Fink and Larson's albedo was derived before Voyager 1 measured Titan's radius. To determine the area of Titan's disk that reflects solar radiation, Titan's atmosphere was considered since it is a significant fraction of the satellite's radius. Following the analysis of Toon et al. (1991), the radius used to determine Titan's albedo, the optical radius, was measured at an atmospheric optical depth of r = 0.051. The optical radius therefore varies with wavelength, since it depends on the opacity of the atmosphere. In Appendix I, values of the optical radius are shown at a few wavelengths. The "corrected albedo" was calculated by assuming this optical radius (Appendix I). In this

I ' ' ' i ' ~ ' [ ' E I ' ' T I ~-- o Titan: 3.6 cm-' resolution J

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FIG. 1. Observations of Titan with resolutions of 38 and 3.8 c m - I made at the Infrared Telescope Facility, using the Cooled-Grating Array Spectrometer. The high resolution observation points are connected by straight lines to aid visual interpretation. The ± ltr error bars resulting from instrumental noise are shown at several wavenumbers.

analysis, the albedo determined by Fink and Larson (1979) is referred to as Titan's albedo; the albedo derived assuming the optical radius described above, the corrected albedo, is also discussed.

I I I . R A D I A T I V E T R A N S F E R C A L C U L A T I O N

Titan's near-infrared flux results mainly from sunlight reflected off haze in a CH4-rich atmosphere; both scattering and the effect of the large methane column abundance in Titan's atmosphere must be rigorously treated. To include the effect of scattering in our calculations, synthetic spectra of Titan are derived using the doubling and adding algorithm. The atmosphere is divided into 16 homoge- neous layers (Griffith 1991) and the reflection and transmission functions are calculated for each layer. (See Han- sen and Travis (1974) and Danielsen et al. (1977) for more

364 GRIFFITH, OWEN, AND WAGENER

TABLE I Observations

Wavenumber Resolution Date interval (cm I) (cm i) Signal/noise" A i r m a s s Sampling

July/4 + 13/89 4540-4662 3.8 15 1.47-1.50 Nyquist July/13/89 3909-4956 38 40 1.70-2.00 Nyquist

" S/N is calculated as the standard deviation of eight observations.

information on the doubling and adding algorithm.) These functions are then " a d d e d " to derive the reflection and transmission functions for the entire inhomogeneous atmosphere. Finally, the geometric albedo is calculated by using six Gaussian quadrature points to integrate over the solar zenith angle.

Transmission functions in narrow band models for planetary spectra do not have the simple exponential dependence on the optical depth that is assumed in the doubling and adding algorithm. Therefore , narrow band models cannot be used in this analysis, and line-by-line techniques are needed to derive the methane absorption coefficients. Both the line-by-line and the radiative transfer calculations are computed over a wavenumber grid size of 0.1 cm- t . The width of this grid was determined to be fine enough by testing it against a variable grid size that is narrowly spaced (0.0001 cm-~) around the methane line positions and widely spaced (0.1 cm- l ) in between lines.

IV. ATMOSPHERIC MODEL

Titan 's spectrum between 4000 and 5000 cm- ~ contains signatures of the three most abundant gases previously detected in the satellite's atmosphere: N 2, H 2 , and C H 4 .

Eight trace gases (ethane, acetylene, ethylene, propane, carbon monoxide, carbon dioxide, and hydrogen cyanide) also have absorptions in the 4000-4500 cm- i region (Pier- son et al. 1956). However , only the line parameters for CO 2 and CO exist and are included in our models. At the higher wavenumbers 4500-5000 cm ~, CO2, C2H 4, and C2H2 are the strongest absorbers among the known trace gases. The effect of CO 2 on Titan 's 38 cm t resolution spectrum is found to be insignificant as the mixing ratio is extremely low. Measurements of C 2 H 4 and C2H 2 spectra at different path lengths (Cruikshank 1967) indicate that C2H4 and C2H2 absorptions are too weak to be significant. Therefore , only the effects of N 2 , H 2 , CO, and C H 4 a r e

considered in this analysis. The spectroscopic parameters of these gases are described in Appendix II. Observations in wavenumbers smaller than 4500 cm ~ are interpreted with the understanding that, in our models, we did not include absorption by hydrocarbons such as C2H 6 , which may be significant at these smaller wavenumbers.

The free parameters in our models are the gas abundances, the haze distribution, and, in spectral regions that probe below the tropopause, the surface albedo and the cloud distribution (Table II). Partial pressures of the gases, N 2 , H2, CH4, and CO, are derived from the temper- a ture-pressure profile of Lel louch et al. (1989). Hydro- gen, nitrogen, and carbon monoxide have constant mixing ratios in our models. The depletion of CO in the stratosphere, found from millimeter-wave observations (Marten et al. 1988), occurs above the altitude region that is sampled with near-infrared radiation. Since methane under- goes a phase transition in Titan 's a tmosphere, its abundance is assumed to vary with altitude. The methane distribution is determined by two variables in our models, the humidity at the surface, which we vary from 20 to 70%, and the mixing ratio above the tropopause. Above the surface, the mixing ratio is assumed constant until saturation is reached. The CH4 partial pressure then follows the vapor pressure up to the cold trap ( - 3 0 km). The CH4 abundance is assumed constant above 30 km altitude, and equal to the saturation mixing ratio at the cold trap. This value is 0.017, assuming the nominal temperature-pressure profile of Lellouch et al. 1989.

An isotropic scattering phase function is used in our radiative transfer code to increase the speed of the calculations. An equivalent isotropic scattering optical depth (%) is computed from an anisotropic Mie scattering optical depth (~'m) using the equivalence principle,

TABLE II Atmospheric Model Parameters

Model 1

N 2 column abundance 86 km-am H 2 mixing ratio 0.4% CO mixing ratio 150 x 10 CH 4 surface humidity 70% CH 4 mixing ratio above tropopause 1.7%, Haze distribution Distribution I Cloud optical depth (7"i~) 0.05 Cloud altitude range 24-30 km Surface albedo at 2 ~m 0.09

T I T A N ' S N E A R - I R A L B E D O 365

(1 -- g ) w m Wis - -

1 - g w m

"/'is = (1 - g W m ) T m ,

(i)

(2)

where w m and Wis are the single scattering albedo for Mie and isotropic scattering and g is the asymmetry factor of the scattering phase function (Chamberlain and Hunten 1987). Methane clouds and ethane mist are modeled with the optical constants of c n 4 and C2H 6 as measured by Khare et al. (1990a,b). In addition, the haze optical constants are adopted from the laboratory analog of Titan's haze called "tholins" (Khare et al. 1984). The real (n) and imaginary (k) optical constants of tholin in the near-IR are 4 × 10 -4 ~ k -> 9.0 × 10 - 9 and n = 1.63. Even allowing for a significant margin of error in the optical constants, submicron-sized tholin particles are bright in the near- infrared. We note that C2H2, C4H2, C3H4, HCN, and c3n 8 also condense in Titan's atmosphere. Their presence, however, probably does not interfere with our assumptions since they are probably bright scatterers similar to tholins and CH4 ice; the spectra of their vapors do not have strong absorptions in any of the spectral windows that we consider (Cruikshank 1967).

In the discussion that follows, we use a reference atmospheric model, Model I, defined by the parameters given in Table II. In this model, the column abundance of N 2 , 86 km-am, corresponds to an atmosphere of 99% N 2.

V. A N A L Y S I S O F T I T A N ' S S P E C T R U M B E T W E E N 4000

A N D 5000 C M - 1

Titan's flux between 4000 and 5000 cm-) results from solar radiation scattered off atmospheric particles. The depth in Titan's atmosphere penetrated by the sunlight depends primarily on the strength of methane absorption. Titan's geometrical albedo is low between 4000 and 4600 cm -~ because in this spectral region methane absorbs strongly and solar radiation is absorbed before reaching Titan's tropopause. Titan's albedo is higher at 4600-5000 cm- ', since methane absorption is weaker. Here, incident solar radiation penetrates deeper in the atmosphere where it is scattered from atmospheric particles and the surface. The altitude region sampled by radiation of a particular wavelength can be estimated from the attenuation of radiation by CH4 absorption. For this purpose, methane trans- missivities are calculated as a function of altitude at several different wavenumbers for the two spectral resolutions, 3.8 and 38.0 cm -~ (Figs. 2 and 3). These calculations indicate that Titan's spectrum between 4000 and 5000 cm-1 reflects primarily the atmospheric conditions below I00 km altitude.

Three spectral regions between 4000 and 5000 cm-] were considered separately to study independently char-

1.0

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60 80 t00 120 140 160 180

AltiLude (kin)

FIG. 2. CH 4 t ransmlss iv i ty (e - ' ) as a funct ion of altitude for four w a v e n u m b e r points. The t ransmiss iv i ty is convolved with a Gauss ian filter with a F W H M of 3.8 cm -~.

acteristics of the atmospheric gases, possible CH 4 clouds, and the surface albedo. These spectral regions each have different methane optical depths and sample the atmosphere at different altitudes (Fig. 4). Titan's albedo at 4362 cm- ] and the spectral region, 4550-4620 cm l, were analyzed first to determine the opacity of Titan's haze in the lower stratosphere. Titan's flux in this spectral region samples the atmosphere primarily between 30 and 100 km altitude. With constraints on the upper atmosphere, lower altitudes were then studied by examining Titan's 4620-4660 cm-~ spectrum. Titan's flux in this small region samples the atmosphere below the tropopause, but remains insensitive to the surface brightness. Assuming that

0,9

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Alt i tude (krn)

FIG. 3. CH 4 t ransmiss iv i ty (e -7) as a funct ion of altitude for five w a v e n u m b e r points. The t ransmiss iv i ty is convolved with a Gauss ian filter with a F W H M of 38.0 cm -I.


4900 4644 4595 4603 4362 <- Wavenumber (crn ')

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~ I 99

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• q 25 27

17

3 6 0

I L _ J , I , , , 1 , , , I , , , _ _ L , 4 6 0 80 100 120 140 160 100

T e m p e r a L u r e (K)

FIG. 4. Titan's temperature-pressure profile (Lindal et al. 1983) with a description of the processes that influence the composition and sizes of the particles in Titan's atmosphere. We have superimposed a wavelength scale showing the altitude region where solar radiation is most attenuated (solid line) for each wavelength• Only gas absorption was considered; the presence of Titan's haze and CH 4 clouds causes the altitude region probed by each wavelength to be slightly higher.

haze and clouds can be characterized by the optical constants of tholins and methane ice, the final spectrum considered (4660-5000 cm ~) is sensitive to the surface albedo.

The Haze Opacity: Titan's 4000-4620 cm-~ Spectrum

The size, shape, and distribution of haze particles in the lower stratosphere remain uncertain. The haze may be composed of large particles (of radius between 0.2 and 0.5/~m for optical depths between 0.1 and 1 at 0.64/~m wavelength) as implied by the Voyager high-phase-angle images of Titan (Rages et al. 1983), of the smaller particles indicated by the Pioneer 11 photopolarimetry experiment (Tomasko and Smith 1982), IUE observations (Courtin et al. 1990), and recent studies of Titan's spectrum from the UV to the near-infrared (Toon et al. 1991), or of irregularly shaped particles with more than one effective size (West and Smith 1991).

In this section, we discuss Titan's 4000-4620 cm t spectrum, analyzed to constrain the optical depth of Ti- tan's haze as a function of altitude in the lower stratosphere. Our results, combined with the haze optical depth derived at visible wavelengths (McKay et al. 1989), suggest that Titan's haze particles are smaller than the values obtained from Voyager high-phase-angle images.

The haze distribution in the lower stratosphere (30-100 km) almost exclusively determines Titan's albedo between 4000 and 4620 cm-1. Solar radiation scatters off haze particles; this effect balances the strong absorption by methane to give rise to Titan's small, but nonzero, albedo between 4000 and 4620 cm -1. Since methane ab-

sorption lines are saturated, varying the stratospheric methane abundance by a factor of 2 produces only a 10% change in the haze optical depth. Methane clouds also do not affect our interpretation of this spectral region because we are sampling altitudes above the region where they are likely to exist (Toon et al. 1988).

The stratospheric haze distribution derived for altitudes above 70 km is based on a model designed by Toon et al. (1980) and further developed by McKay et al. (1989), in which particulates are created in the upper atmosphere by coagulation and sedimentation of the products of methane photolysis. The haze distribution is characterized by two parameters: the charge radius (R c) describes the inhibition of coagulation due to electrostatic forces (and therefore controls the particle size), and the haze production rate at 300 km altitude (C) controls the number density at the top of the atmosphere. This model is used as a guide to estimate the dependence of the optical depth on the altitude. We do not uniquely solve for both the particle size and the number density of the haze, that is Rc and C, since we are working in a small wavelength region. Below 70 km altitude, condensation of organic compounds might occur (Sagan and Thompson 1984). Therefore, the haze distribution below 70 km is allowed to deviate from that described by the coagulation and sedimentation model. The differential haze optical depth OLs/Oz is assumed constant between 30 and 70 km altitude.

Titan's haze distribution is first constrained between 70 and 100 km altitude using Titan's 4362 and 4603 cm t albedo, then constrained between 30 and 70 km altitude using Titan's 4550-4620 cm i spectrum. At the wavenumbers 4362 and 4603 cm ~, solar radiation penetrates Ti- tan's atmosphere to approximately 70 and 50 km altitude, respectively (Figs. 2 and 3). A lower limit for the haze optical depth above 70 km is obtained (assuming the coagulation and sedimentation model) by fitting Titan's 4362 cm ' albedo. This spectral region might also be affected b y C2H 6 absorption; therefore, an upper limit to the haze optical depth above 70 km has to be derived from another spectral region. This upper limit is obtained by fitting the 4603 c m ' albedo with a low haze optical depth (ri~ = 0.01) at altitudes below 70 km. Titan's 4550-4620 cm -~ spectrum samples primarily the atmosphere between 30 and 70 km altitude (Fig. 2); by fitting these observations we extend the haze distributions derived for the 70-100 km region down to the tropopause.

Our final distributions correspond to a lower and upper limit on the integrated haze optical depth above 30 km (Distributions I and II, respectively), and are shown in Fig. 5. Synthetic spectra of Titan's 4550-4660 cm- i spectrum (3.8 cm- ' resolution) and 4300-5000 cm l spectrum (38 cm-~ resolution) are calculated with the two haze distributions as shown in Figs. 6 and 7. A good agreement can be seen between the observed and calculated spectra


<

15 0 l/x, '

i ' , \

I00

50

, S - . ~ , ~ , , i , , , i , , T I

Haze Distr ibut ion I - Haze Distr ibut ion II

\, 0.02 0 04 006

O p t i c a l D e p t h

I

""'"'" 1 0.08 O1

FIG. 5. H a z e op t i ca l d e p t h (for i s o t r o p i c sca t t e r ing) a t 4620 c m - 1 as a func t ion of a l t i t ude for D i s t r i b u t i o n s I and II .

except at 4750 and 4440 cm-1 (Fig. 7). The 4750 cm-1 albedo samples the atmosphere below the tropopause; the haze distribution above 30 km altitude does not strongly affect this albedo. As discussed later in this section, this spectral region is more strongly affected by H2 absorption. The mismatch at 4440 cm-t may be caused by C2H 6 absorption, not included in this analysis, which sets in at 4500 cm-1 and increases at shorter wavelengths (Cruik- shank 1967). As discussed further in Appendix I, Titan's corrected albedo is probably between 18 and 22% greater than the one shown in these figures. We find that a 19% change in the haze optical depth causes the albedo at 4620 cm- 1 to vary by 18%.

As shown in Figs. 6 and 7, the haze opacity described by Distribution I is most consistent with our data. The spectral features in Titan's high resolution spectrum (Fig. 6) are all caused by methane absorption, however, the depths of these features are in part controlled by the distribution of haze in the atmosphere. Distribution II lacks enough scattering particles in the upper atmosphere to reproduce Titan's albedo in the spectral regions that sample the higher altitudes--the troughs of the methane features at 4550, 4568, 4580, 4590, and 4603 cm -1. Titan's low resolution spectrum between 4600 and 5000 cm- i can be interpreted equally well with both haze models (Fig. 7), yet at 4300 cm -I Distribution I reproduces Titan's albedo better than does Distribution II.

The haze opacities that we derive above 70 km altitude at 4620 cm -1 can be combined with those derived by McKay et al. (1989) at 9090 cm-~ to understand how the scattering properties of the haze particles change with wavelength. The equivalent Mie scattering optical depth for our distribution above 70 km altitude 0"m = 8 × 10 -2) is half that of the McKay et al. standard model (R c = 0.09 and C = 0.35) at 4620 cm- 1. This is probably because the

7700, 6250, and 4900 cm-1 albedo points that are used in their analysis are regions of very weak methane absorption and, therefore, are mostly sensitive to the lower atmosphere and surface, and not to the upper atmospheric haze. At 9090 cm-1, however, mainly the atmosphere above 70 km is sampled. That the stratospheric haze opacity decreases quickly with decreasing wavenumber from 9090 (McKay et al. 1989) to 4620 cm-1 (this study) suggests that the haze may consist predominantly of small particles consistent with the work of Tomasko and Smith (1982), Courtin et al. (1990), and Toon et al. (1991).

We further note that Distribution I requires a mecha- nism that will deplete the haze below roughly 70 km altitude, such as diffusion or condensation and subsequent precipitation. The organic molecules C2H6, C2H2, C4H2, C3H4, HCN, and C3H8 condense at roughly 70 km altitude. As discussed in Appendix III, a coating of brightly re- flecting organic compounds will not lower the optical depth of the particles. We add that models of Titan's haze that include atmospheric dynamics and the processes of diffusion and condensation are treated in depth in the work of Toon et al. (1991).

Methane Clouds: Titan's 4620-4660 cm-1 Spectrum

At wavenumbers larger than 4620 cm-1, CH 4 lines are weaker and Titan's spectrum samples the atmosphere below 30 km altitude (Figs. 2 and 3). Of particular interest is a small spectral region, 4620-4660 cm-1, where solar radiation penetrates below the tropopause, without reaching the surface (Fig. 2). At lower wavenumbers only the atmosphere above the tropopause is sampled; at higher wavenumbers the surface albedo influences the spectrum.

The temperature lapse rate, measured by the Radio Occultation Experiment on board Voyager 1 (Lindal et

al. 1983), allows for the possibility that a global cloud cover of condensed CH 4 exists between 17 and 30 km altitude; patchy clouds can exist below 17 km altitude. By analyzing Titan's 4620-4660 cm-1 albedo, we can therefore sample Titan's atmosphere in the altitude region where CH 4 clouds may exist.

The effects of a global cloud cover are incorporated in our calculations by adding scattering particles distributed uniformly in the 17-30 km altitude region. The optical constants used for these particles are based on the recent measurements of the scattering properties of methane ice (Khare et al. 1990a), which indicate that this ice is bright (n = 1.30, k -< 10-6), with no absorption features in the 4620-5000 cm- 1 region. Synthetic spectra of Titan's 4620-4660 cm-1 albedo are calculated with the two haze distributions. The cloud opacity needed to best fit the observations is found to depend on the haze distribution.

If the upper atmospheric haze is characterized by Distri- bution I, the 4620-4660 cm-~ region cannot be modeled


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FIG. 6. Synthetic spectra reproduced with Haze Distribution 1 (with and without clouds) and Distribution II (without clouds). The cloud optical depth and altitude range as well as the gas distributions are those of Model I specified in Table II. Circles: Titan's observed albedo at 3.8 cm -1 resolution. The _+1o- error bars are shown at a couple of wavenumbers.

Y

k

+5

]'1 [ [lil i [1 I'(~501ll11011 l ) )SI FI DH [ lOl l

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FIG. 7. Synthetic spectra reproduced with Haze Distributions I and II. (Only the calculation using Distribution I includes a cloud optical depth of 0.05 in the 24-30 km altitude range.) Model I gas distributions (Table II) are used. C2H 6 absorption, which is not included in this analysis, may explain the disagreement between the observed and calculated albedo at 4440 cm-~. Circles: Titan's observed albedo at 38 cm-1 resolution. The -+ ltr error bar pertains to the observation points between 4460 and 4200 c m - I

unless a significant optical depth of scattering particles (0.05 -< ris -< 0.10) is added between 17 and 30 km altitude (Figs. 6 and 8). This additional opacity increases the differential optical depth of scattering particles by a factor of 10 at 30 km, suggesting that we are seeing condensed CH 4 as opposed to the extension of haze down below the tropopause. An upper limit of % -< 0.10 is derived for the cloud optical depth by fitting Titan's albedo, adjusted to take into account the uncertainty in Titan's radius, as discussed in Appendix I.

Distribution II has a small optical depth above 70 km, which requires a haze opacity in the 30-70 km altitude region that is larger than that of Distribution I in order to be consistent with Titan's 4550 cm -~ albedo. This haze distribution has a large enough optical depth above 30 km altitude that we can fit Titan's 4620-4660 cm ' spectrum without clouds (Fig. 6). The error in the albedo caused by the uncertainty in Titan's radius (Appendix I) gives us a range of 0.0 -< Tis ~ 0.02 for the cloud optical depth derived with Distribution II.

If optically thick clouds exist in the 17-30 km altitude region, they must be patchy. Spectra calculated with optically thick clouds, covering a fraction of the field of view, indicate that no more than 4% of the area of Titan's disk was covered by optically thick clouds above 17 km altitude at the time of our observations. If clouds reside at the tropopause, they are either optically thin (% -< 0. l0 at 4620 cm -~) or cover a very small fraction of Titan's disk.

Obtaining a lower limit to the cloud opacity necessitates first untangling the effects of clouds from that of the

h a z e - - a complicated task. Our observations are most consistent with haze Distribution I, and therefore suggest the existence of an optically thin layer of clouds at the tropopause. Additional observations are necessary to better constrain the cloud properties. If clouds exist they are very likely patchy and the fraction of Titan's disk that they cover varies with time. Observations of the satellite spaced in time might display a time variability of Titan's albedo at 4640 cm ~ relative to the 4580 c m - ' albedo.

o 04 i

9 c • I

<; T i L a n :38 ( r n ~ r e s o l u l i o n , /

C l o u d O p t i c a l Depth : O0 , y / / ' ~ ( l o u d O p t i c a l D e p t h 0 . 0 6 , /

( l o L l d O p t i c a l D e p t h 0 10

' ( /

/

7 ' o o 2 ' i

• u '

o ~ - x . L ~ . ~ [ : : i . z L L ~ . ] , t x J _ ~ z J A

4300 4400 4500 4600 4700 48O0 4900 5000

W a v e n u m b c r ( ( m 1)

FIG. 8. Synthetic spectra reproduced with a Model I atmosphere (Table II) and varying cloud optical depths in the 17-30 km region. Circles: Titan's observed albedo at 38 cm-J resolution. The -+ I~ error bar is shown at 4700 cm I.


4

o T.

E

C3

Q1

0 0 8

0.06

0,04

0 0 2

. . . . r

o T i t a n : 3 -1 .

. . . . . 02 % He , /Af t \

-- o s ~ H; , , ' / / / \ 7 - 1 .0 % He , / / e '

/ / / / / / o

, /o/ , / /

' / /

4300 4400 4500 4600 4700 4800 4900 50(]0 W a v e n u r n b e r ( c m - t )

FIG. 9. Synthetic spectra derived with a Model I atmosphere (Table II) for four H2 mixing ratios. Circles: Titan's observed albedo at 38 cm-1 resolution. The -+ 1o- error bars are shown at 4730 and 4780 cm-t .

Lower Atmosphere: Titan's 4660-4960 cm-~ Spectrum

Titan's 4660-5000 cm- l spectrum is affected by absorptions due to the three major gases N z, H2, and CH4 as well as the surface albedo (based on our assumptions for the optical constants of the particles in Titan's atmosphere). However, as indicated in Figs. 9, and I0, N 2 and H2 influence a different part of the spectrum than does CH4. In addition, these gases absorb only very weakly in the 4900 cm-J spectral region, where scattering particulates and the surface determine Titan's albedo. Therefore, the effects of N 2 and H2, CH4, and the surface albedo on Titan's spectrum are considered separately in this analysis.

.~ 0 0 8

"~ 0 0 6 o

o 04

0 02

.o-Q o. o " ,

T i t a n : 3 8 e m ~ r e s o l u t i o n / o', ,6 Vary Methane Abundance /

/

/

/ o /

J ] o J

; ' o

/o , b

0"

o / /

_--o 0 o<~o~o o_~o-o o o

4300 4400 4500 4800 4700 4800 4900 W a v e n u m b e r ( e m -1)

5000

FIG. 10. Synthetic spectra derived with a Model I atmosphere (Table II) for two CH4 distributions: a constant mixing ratio of 0.017 down to the surface (dashed line) and a Model I CH4 distribution (dotted line). Circles: Titan's observed albedo at 38 cm -~ resolution.

Unfortunately, the effect of the hydrogen fundamental band dominates Titan's spectrum in the 4780 cm-~ region where the N 2 overtone band occurs, and the column abundance of nitrogen cannot be constrained in this analysis. As indicated in McKellar and Welsh (1971) and Hunt and Welsh (1964), the pressure-induced fundamental S(1) band of H2 is similar in shape and strength for H2-Ar and H2-N2 mixtures. The shape of Titan's spectrum at 4780 cm-l is therefore independent of the abundances of N2 and Ar, and depends primarily on the abundance of H2 in Titan's atmosphere. As shown in Fig. 9, a calculated spectrum with 0.5-1.0% H2 agrees best with the observations. The same constraints for the H2 abundance are also derived assuming a larger albedo for Titan, using the optical radii discussed in Appendix I. We note, however, that the lower limit that we derive for the H2 abundance (0.5%) is subject to an uncertainty; very weak CH4 lines that have not been detected with current laboratory exper- iments may exist and affect the continuum. Our upper limit for the abundance of H a in Titan's atmosphere is consistent with the H2 mixing ratio determined by Samuelson et al. (1981), 0.002 --+ 0.001, and by Toon et

al. (1988), 0.004 + 0.002. The methane mixing ratio, although constrained to

-0.017 at the tropopause by condensation, may be as high as 0.21 at the surface (Lellouch et al. 1989). Assuming current C H 4 parameters, this uncertainty does not significantly affect our study of Titan's 4660-4900 cm-l spectrum (Fig. 10). However, the methane abundance in the lower atmosphere could be well constrained with high resolution observations of the weak methane lines at 5000 cm- ' in Titan's spectrum (Fig. 10).

If a cloud cover exists below 17 km altitude, it must be patchy to be consistent with the thermal lapse rate measured by Voyager (Lindal et al. 1983). The possibility that cloud opacity exists below 17 km is examined by including a global cloud cover in our model to simulate a layered patchy cloud system. This cloud cover is placed 3 km above a black surface. Atmospheric models generate albedos at 4900 cm- ' that are then compared to the observed albedo. Since solid methane is very bright and Titan's albedo at 4900 cm-1 is low, the largest possible global cloud cover consistent with Titan's 0.11 albedo has an optical depth of 7is = 0.22 (Table III). This value is similar to the equivalent optical depth for Mie scattering if the particles are small (0.1 /zm). For clouds consisting of 100-/zm-sized particles, the equivalent optical depth is 1.9 (Table III). We note that since 100-p.m-sized particles scatter 4900 cm-~ radiation largely in the forward direc- tion, 60% of solar radiation is transmitted below a cloud deck of 2.0 optical depth. As discussed in Appendix I, Titan's corrected albedo may be as high as 0.14 at 4900 cm-~; the most opaque cloud cover consistent with this albedo has an optical depth of 0.37. In addition, optically

370 GR1FFITH, OWEN, AND WAGENER

T A B L E I I I

Cloud Characteristics

r " (r = 100

ri~ 7" (r = 0.1 /~m) /xm)

Clouds above 0.10 0.10 0.88 17 km altitude b

Clouds above 0.22 0.22 1.90 3 km altitude c

a Mie scattering optical depth, calculated from isotropic scattering optical depths, ~'is, using the equivalence principal (Section IV of text) and optical constants of solid CH 4 (Khare et al. 1990a).

b Maximum optical depth at 4620 cm- 1 for a global cloud cover above 17 km altitude. The optical depth, "/is, calculated for Titan's corrected albedo is 0.12.

" Maximum optical depth at 4900 em i for a global cloud cover above 3 km altitude. The optical depth, zis, calculated for Titan's corrected albedo is 0.37.

thick clouds are found to cover less than 21% of the area of Titan's disk if Titan's albedo at 4900 cm I is 0.11; clouds cover less than 28% of the area if the albedo is the corrected value (0.14). Assuming that the particles in Titan's troposphere are highly reflective (like tholins, or ices of ethane or methane), we find that clouds do not completely obscure Titan's surface at 4900 cm 1.

Titan's Albedo in the Methane Windows

There are three regions in Titan's near-infrared spectrum at 1.3, 1.6, and 2.0 ~m (7700, 6250, and 4900 cm 1 wavenumbers) where methane does not adsorb strongly and the atmosphere is therefore relatively transparent. As observed by Fink and Larson (1979), Titan's albedo at these three "methane windows" increases with decreasing wavelength (Table IV). The satellite's albedo has also been measured at the IRTF telescope with a circular variable filter at a resolution of 100 cm-~ (Neff et al. 1985). These observations agree roughly with those of Fink and Larson (1979), with differences due primarily to the lower

TABLE IV Near-IR Reflectivity of Titan and the Icy Jovian Satellites

2.0 ~m 1.6 /~m 1.3 /zm

Europa ~ 0.09 0.25 0.45 Ganymede" 0.15 0.22 0.35 Callisto a 0.15 0.16 0.18 Titan's observed albedo b 0.11 0.14 0.22 Titan's corrected albedo C 0.14 0.18 0.27

a Clark and McCord (1980). b Fink and Larson (1979). c Discussed in Appendix 1.

resolution (Neff et al. 1985). What causes the change in albedo at these three wavelengths? Is it a result of absorption by gases or a variation in the haze or cloud opacity? Or is it characteristic of the surface albedo?

In the center of the methane window at 2.04/xm, N2, Hz, and C H 4 absorptions do not significantly limit the transmissivity of the atmosphere (Fig. 3). Eliminating all the gaseous opacity from a calculation of Titan's 2/zm albedo (at 38 cm-1 resolution) increases the resultant albedo by only 2%. CH 4 absorption may be stronger in the other two windows, yet this would cause Titan's albedo to decrease at 1.3 and 1.6 p,m relative to Titan's 2.0/xm albedo, just the opposite of the observations. An indica- tion that these two windows indeed allow sunlight to reach the lower levels of Titan's atmosphere was already provided in the measurements of CH 4 bands at !.27 and 1.56 /xm by Fink and Larson (1979). The methane column abundances derived from these bands in Titan's spectrum are approximately four times greater than abundances determined from bands of comparable strength in the visible. On Jupiter and Saturn, the abundances from the near- infrared and the visible bands are the same. As discussed in Section IV, none of the trace gases detected by Voyager were found to have significant absorption at 2.04/xm. That Titan's albedo is lower at 2.04/xm than at 1.3 or 1.6/zm cannot be explained by gas absorption.

Simple hydrocarbons are expected to condense in the lower stratosphere (Sagan and Thompson 1984) and form a coating on the haze nuclei. The most abundant hydrocarbon, C 2 H 6 , forms highly reflective micron-sized particles (Khare et al. 1990b). In the gas phase, the other hydrocarbons detected by Voyager do not have strong absorption features at 2 /zm that would suggest a similarly strong absorption in the solid phase. We therefore assume that a coating of these hydrocarbons does not change the optical qualities of the already bright haze and only increases the radius of the haze particles.

Titan's albedo may be higher at 1.3/zm than at 2.0 p~m as a result of the scattering of radiation by particles in the atmosphere or the brightness of Titan's surface. To distinguish between these two effects, Titan's spectrum in the methane windows is analyzed with a two-layer radiative transfer model consisting of a layer of scattering particles above a surface; gas absorption is ignored. In this exercise, the size of the scattering particles is used to determine the total optical depth of the clouds and haze at 1.3 and 1.6/zm from the optical depth established at 2.0 /xm. Titan's observed albedos at 1.3, 1.6, and 2.0/xm are then modeled for these haze and cloud optical depths by adjusting the surface albedo. These calculated surface albedos depend on the assumptions made for the scattering particles--their total optical depth at 2.0/zm and the particle size distribution. First, we simply assume that haze is the only source of particles in the atmosphere. We


T A B L E V

T i t a n ' s S u r f a c e Albedo , C a l c u l a t e d a t T h r e e W a v e l e n g t h s

Albedo" at: 2 / ~ m 1.6 /zm 1.3 /zm

Haze Distr ibution I, 0.09 0.11 ± 0.01 0.18 -+ 0.01 large particles b

Haze Distribution I, 0.09 0.10 ± 0.01 0.16 -+ 0.01 small particles r

Haze Distr ibution II, 0.08 0.09 ± 0.01 0.17 ± 0.02 large particles b

Haze Distr ibution II, 0.08 0.07 ± 0.01 0.12 ± 0.02 small part icles '

~ Phoebe + ~ 0.09 0.11 0.16 Ganymede

sized particles. To simulate the effect of an ethane mist, scattering due to particles of radii r = 0.18/~m are added to the atmospheric model defined by the smallest particle size distribution and the Distribution II haze. These particles are modeled with the optical constants, n = 1.32 and k = 10 -5, independent of wavelength, based on the measurements of the C2H 6 scattering properties by Khare et al. (1990b). As shown in Fig. 1 lb, adding an ethane mist lowers the computed surface albedo at 1.6/zm relative to that at 1.3 and 2.0 /zm. This occurs as a result of two competing effects: submicron-sized particles scatter more strongly at smaller wavelengths and the large optical depth

" Surface albedo errors were calculated a s suming 5% relative error in the satell i te 's observed albedo. The surface albedos calculated for Ti- t an ' s corrected albedos (Appendix I) are qualitatively similar to these values.

The particle size distribution of M c K a y et al. (1989), with particles of radii r < 0 .5/~m.

The same size distr ibution as above, scaled down to smaller particles o f radii r < 0 .18/zm.

then explore the effect of adding C H 4 clouds and/or an ethane mist.

In this analysis, four different haze distributions are considered; these are formed from two optical depths, those of Distributions I and II, and two particle size distributions, that of McKay et al. (1989) with particles of radii r < 0.5/zm and the same size distribution scaled down to smaller particles of radii r < 0.18 /zm. Two sources of error are considered: the uncertainty in Titan's optical radius and an error in the relative albedo of 5%. The results from calculations of Titan's albedo are shown in Table V. Models of both Titan's albedo and corrected albedo produce similar surface albedos for each haze distribution; the satellite's observed albedo can be reproduced with a surface albedo that is roughly the same at 2.0 and 1.6/zm (maybe a little higher at 1.6/zm) and much higher, by 50-100%, at 1.3/zm.

A similar result is derived when CH 4 clouds are added to the analysis. Since haze particles provide only few condensation nuclei, cloud particles are expected to grow rapidly to sizes larger than 1.0/xm (Toon 1988). These cloud particles scatter radiation uniformly from 1.3 to 2.0 /zm. Therefore, although the presence of C H 4 clouds in the lower atmosphere implies a lower surface albedo for Titan, the qualitative nature of the surface albedo calculated at 1.3, 1.6, and 2.0/zm--increasing with decreasing wavelength--remains unchanged from the no-cloud case (Fig. 1 la).

Although as yet undetected, an ethane mist (with dis- solved methane, propane, and nitrogen) might exist near the surface (Lunine et al. 1983) and consist of submicron-

0)

-¢

bq

0 2 a

t

o , \ - - - - \

\

\ \ \

\ \

0 . 0 5 "x \

0

L 3 1.4 1.5 1.6 1.7 1.8 1.9 0 .2

k i ~ . . . . . . . . . . . I . . . . I ~ r ~ ' I . . . . J ' ' ' ' J u

0 , 5 " -

0.1 .

0 . 0 5 , 1 ~

i - - - ...- o

-i i - i - i i i i I L J I I 1 3 t .4 , . 5 1.6 , . 7 , 8 1.9

W a v e l e n g t h ( u r n )

FIG. 11. (a) T i tan ' s surface albedo calculated using Haze Distribu- tion I with large particles (Table IV). Clouds with particles o f radii ->3 /zm are included by adding bright particles with a cons tan t opacity throughout the near-infrared. Boxes: no clouds; circles: cloud optical depth ris = 0.05; triangles: cloud optical depth ris = 0.22. (b) Ti tan ' s surface albedo calculated using Haze Distribution I with small particles (Table IV). To simulate the possible presence of a C2H 6 mist above the surface the opacity of small particles was increased until the surface albedo at 1.6 /zm was black. Boxes: Distribution I (optical depth of particles at 2.0 p.m, % = 0.07). Circles: Distribution II (T i s = 0.11). Triangles: ris = 0.16. Pentagons: % = 0.21.


of the stratospheric haze at 1.3/zm lessens the effect of particles in the lower atmosphere.

If the particle size of the C 2 H 6 mist is changed from the case discussed above, the surface albedos that we obtain are qualitatively similar to those derived above except for one particular case. Calculations including mist particle sizes different from 0.18/xm (Griffith 1991) indicate that only with a mist with an optical depth of 0.02 and particles of sizes in the range 0.04 > r > 0.012/zm can we model Titan's albedo with a surface of uniform albedo at 1.3, 1.6, and 2.0/xm. The surface albedo of this solution is 0.08. Models of Titan's corrected albedo do not yield uniform surface albedos, regardless of the haze, cloud, and mist particle sizes and optical depths.

VI. D I S C U S S I O N

A. The Haze and Cloud Opacity

The constraints that we derive for Titan's haze optical depth are consistent with those obtained from Titan's 1.16-1.75/zm spectrum (Tomasko et al. 1989). In addition, using a haze optical depth at 2.16/zm that is consistent with that determined in this study, Titan's spectrum can be fit from the UV to near-infrared (Toon et al. 1991).

The upper limit for the cloud optical depth that we derive as a function of particle size (Table III) agrees with the cloud constraints found from an analysis of Titan's 500-600 cm-1 spectrum (Toon et al. 1988). Clouds of small particles (r -< 0.1/zm) may exist globally only as a very thin covering of low optical depth 0" -< 0.37) at 2/xm. Clouds composed of large particles (r >-- 50/zm) may be present with optical depths no greater than 3.4. Patchy, optically thick clouds can cover no more than 28% of Titan's disk.

B. Interpretation o f Titan's Near-Infrared Albedo at 1.3, 1.6, and 2.0 Ixm

1. Existing views on the possible composit ion o f Titan's surface. The constraints on the reflective properties of Titan's surface, developed in Section V, are useful for addressing questions on the coupled evolution of Titan's atmosphere and surface. The composition of sediments and liquids on Titan's surface is a consequence of the evolution of the carbon monoxide and methane abundances in the atmosphere. The areal extent of these mate- rials is a manifestation of geological processes at Titan's surface. The composition of Titan's lithosphere reflects the composition and kinetics of the nebula in which Titan accreted, and the processes of differentiation and possible mantle convection that have taken place since the satellite formed.

Some of the main constituents of Titan's surface are expected to be the by-products of CH4 photolysis. Com-

TABLE VI Reflectance of a few Solids"

2.0 p.m 1.6 /~m 1.3 /~m

H20 (Clarke 1981)~' 0.07 0.14 0.46 CH 4 (Brown et al. 1985) 0.20 0.20 0.20 Tholins (Sagan et al. 1984)' 2.30 2.60 2.65 CO z (Smythe et al. 1979) 0.70 0.75 0.78

" Note that ice absorption features (e.g., at 1.6 and 2.0/xm for H20 and at 2.0/zm for CO,,) become deeper the larger the grain size.

h Coarse grained (400-2000 ~m) H20 frost. ' Normalized to 1.0 at 0.56/zm.

plex hydrocarbons, such as Titan's haze, and simple organic compounds such as C2H6, C2H2, C4H2, C3H4, HCN, and C3H 8, must precipitate to the surface. The depth of this sediment depends on the rate at which C H 4 has been supplied to Titan's atmosphere over the course of its his- tory. Only the present atmospheric abundances of these hydrocarbons are known (Hanel et al. 1981, Coustenis et al. 1989), from which the present production rates can be inferred (Yung et al. 1984).

Lunine et al. (1983) recognized that the main by-product of methane photolysis, C2H6, is a liquid at Titan's surface temperature and proposed a C2H6-CH a ocean as a surface reservoir of C H 4 . Based on the photochemical rates computed by Yung et al. (1984) and a methane loss rate of 1.2 × 10 l° c m -2 s e c - ~, the C 2 H 6 production rate is 5.8 × 109 cm -2 sec I (Lunine et al. 1989). Propane, which also condenses on Titan's surface, is produced at roughly 2% of the C2H 6 production rate in this photochemical model. Depending on the CH 4 mixing ratio in the tropopause, C H 4 rain may also exist (Toon et al. 1988). CH 4 would be expected to condense into a mixture with C 2 H 6 and S 2,

and would therefore most likely be a liquid at the temperatures in Titan's tropopause. Complex and simple hydrocarbons that are solid, as opposed to liquid, are also produced by methane photolysis; however, their production rate is much smaller according to the photochemical models. The most abundant solid hydrocarbon, C2H 2 , is produced at ] the rate of C2H 6 . Titan's haze is produced at a rate of roughly 1.2 × 10-14 g cm 2 sec-I ~ the mass production rate of C 2 H 6 (Toon et al. 1991, McKay et al. 1989). The ratio of liquid to solid raining on the surface may be large enough to cleanse the satellite's higher topographic surfaces, thereby exposing bedrock, and concen- trating sediments in the low topographic basins.

If Titan's bedrock is exposed by either rain or recent resurfacing, a number of other surface constituents may be observed. Based on models of Titan's accretion and measurements of the densities of the satellites in the outer Solar System, the solid that is expected to be most abundant on the surface is H20. That is, the most likely bed-


rock is water ice. Depending on the composition of the nebula in which Titan formed, ammonia hydrate or CO2 might also exist. Ammonia hydrate might be present if the N2 in Titan's atmosphere formed from photolysis and shock heating of NH3. Carbon dioxide should be present, having formed from reactions of CO with OH, if CO was one of Titan's original sources of carbon. The present atmospheric CO content is very small (6 to 15 × 10 -5, Lutz et al. 1983). A primordial CO mixing ratio of 0.1 could have produced a large enough pressure of CO 2 for a meter of CO2 to precipitate onto the surface (Samuelson et al. 1983).

The proceeding discussion has focused primarily on the results of atmospheric photochemistry. In fact, other processes such as electron precipitation from Saturn's magnetosphere and cosmic ray bombardment may play major roles in Titan's atmospheric chemistry (Strobel 1982, Campone et al. 1983, Thompson et al. 1990). As a result, it is entirely possible at this stage of our understanding to consider models in which something other than ethane is the dominant end product. Similarly, if CO was originally present in the atmosphere in the propor- tions found in interstellar clouds, tens of meters of CO2 may have accumulated on Titan's surface (Owen and Gautier 1989). In any case, however, we would still expect ponds or lakes of liquid hydrocarbons, but the landscape might also include deep drifts of precipitated aerosols, with exposed, elevated, and windswept terrains composed of H20 and/or CO 2 ice (see Table VI).

2. Results o f this analysis regarding the composition o f Titan's surface. Recent measurements of the optical constants of solid and liquid ethane (Khare et al. 1990b) indicate that although this ice forms highly reflective micron-sized particles, ethane oceans with depths greater than a few centimeters would have very low albedos. This is similar to the difference between the visible reflectivity of a snow flake (>80%) and that of the terrestrial ocean (-5%). Assuming that the imaginary index of refraction for C2H 6 liquid is 10 -5, 4900 cm- 1 radiation is attenuated to 1% of its initial value when it passes through a 3-cm column of C2H 6 liquid. Real refractive indices for liquid ethane (Khare et al. 1990b), at 1.3, 1.6, and 2.0 /zm, indicate that only 2% of light incident normally on a fiat C2H 6 sea would be reflected back from the surface at these wavelengths. We note that solid matter would not be expected to be suspended near the surface of Titan's oceans, since the most abundant solid constituent produced, C2H2, is denser than the proposed C2H6-CH 4 ocean, and would therefore sink. Carbon dioxide is also denser than C 2 H 6 and C H 4 . The geometric albedo of Ti- tan's ocean, even with the presence of waves, would be expected to be lower than 0.02 as seen from the Earth at opposition. Therefore, for Titan's surface to be covered uniformly with an ethane ocean, the surface albedo must

be both wavelength independent and lower than 0.02 at 1.3, 1.6, and 2.0 t~m. As discussed in Section V, Titan's albedo (and corrected albedo) cannot be modeled with a uniform surface albedo that is -<0.02. Our results therefore suggest that a global ocean does not exist at Titan's surface; however, it does not rule out the presence of C2H6-CH 4 lakes or isolated seas.

This finding agrees with the results of recent measurements of Titan's radar reflectivity at 3.5 cm (Muhleman et al. 1990), which reveal an echo that is an order of magnitude brighter than that of a global ocean as shallow as 200 m. A global ocean less than 400 m deep or nonglobal deep oceans would have led to tidal modifica- tion of Titan's eccentric orbit around Saturn (Sagan and Dermott 1982). Taken together, the radar observations, the tidal argument, and the near-infrared albedos suggest that liquid can only exist on Titan as lakes or isolated shallow seas.

The high degree of precipitation that is likely on Titan leads to the question of whether or not the bedrock is exposed, or whether the dry land is completely covered with the organic sediments expected to precipitate with the ubiquitous haze. This is an important question since if the bedrock is exposed, observations with high spectral resolution might reveal traces of solid CO2 and NH 3 hydrate. At the low spectral resolution of our observations (38 cm 1), spectra of mixtures of COz or NH 3 with H20 ice are usually dominated by water ice features. For example, the spectrum of CO2 ice will be dominated by H20 ice features if 0.1 weight fraction of H20 is present in a coarse grained mixture (Kieffer 1970).

The solid sediments that would be expected to cover the dry ground are principally C2H z and haze particles. Tholins have a gray near-IR spectrum (Sagan et al. 1984), suggesting that Titan's haze likewise has a flat near-IR spectrum. Gaseous CzH 2 does not have strong absorption features at 2.0, 1.6, and 1.3/zm; this suggests that the CzH 2 ice spectrum also is gray at these wavelengths. The surface albedos that we calculate with models of Titan's corrected albedo vary with wavelength, indicating that Titan's surface is not globally covered with these sediments. Some other surface constituent is necessary to interpret Titan's near-infrared spectrum.

The surface albedos at 1.3, 1.6, and 2.0/.tm that are derived assuming the existence of an ethane haze do not resemble the reflectivity of any known candidate for Ti- tan's surface. However, assuming the absence of an ethane mist in the lower atmosphere, Titan's surface albedo at 1.3, 1.6, and 2.0 ~m increases with decreasing wavelength. This pattern is familiar, since we find it in the spectra of most of the icy satellites in the outer Solar System (Table IV). On these airless bodies, it is easy to

374 GRIFFITH, OWEN. AND WAGENER

see that this variation in albedo with wavelength is nicely matched by the reflection spectrum of water ice (Table VI). It therefore seems likely that we are seeing evidence of exposed H20 "bedrock" on the surface of Titan.

The possible presence of liquids on the surface as well as the high solubility of H20 in CH 4 (Lunine and Steven- son 1985) suggests that erosion may be important. Physi- cal models of the erosion of a water ice surface by a C 2 H 6 - C H 4 o c e a n (Lunine and Stevenson 1985) indicate that topographical relief on the order of 100 m would erode away on a 109-year time scale. Whether this would help create a global ocean, lakes, or large ice mass continents is an open question. The topographical relief due to cratering might be on the order of 1 km, the depth of 10 km diameter craters on Ganymede (Passey 1982); or Titan's surface might be smooth like Europa with relief on the order of 100 m.

If, indeed, we are seeing the effect of exposed water ice at the surface, dark impurities must also be present to explain Titan's overall low albedo. This dark material may consist of tholins, which, with absorption lengths M47rn = 177/~m at 2/~m, form a dark surface if the scale of the surface grains is on the order of 0.02 cm or larger. The dark material on Phoebe, with a flat geometrical albedo of 0.06 across the near-infrared (Degewij 1978, Degewij et al. 1980) is another possibility; a surface with § Phoebe material and ½ Ganymede material agrees with the albedo that we calculate for Titan in the noncloud case (Table V). Another possible source of dark material is C 2 H 6 - C H 4

lakes, which, as explained above, have a low near-infrared reflectivity. One can imagine a scenario where rain, consisting mostly of liquid hydrocarbons, cleans the ice of solid sediments and concentrates these organic compounds in low-lying seas.

VII. C O N C L U S I O N S

Titan's near-infrared spectrum provides new information on the composition of the satellite's lower atmosphere and surface. In this paper, Titan's 4000-5000 and 4550-4660 cm-1 spectra (at 38 and 3.8 cm ~ resolution, respectively) are analyzed along with the satellite's albedo at 1.3, 1.6, and 2.0 p.m to probe the composition of the lower atmosphere and the surface. The main assumption in this analysis is that Titan's haze, possible clouds, and possible mist can be characterized by the optical constants of tholins, CH4, and CzH 6 , respectively. Our results also depend on current values of C H 4 line parameters. Based on these assumptions, the observations can best be interpreted by a model atmosphere with a thin or sparse cloud cover, a maximum of 1% H 2, the haze Distribution i, described in Fig. 5, and a surface albedo of 0.09 at 2/~m. In addition, the surface albedo must vary with wavelength to fit Titan's albedos at 1.3, 1.6, and 2.0 p.m. The most straightforward match to this variation is produced by

water ice. We believe that the mos~ important outcomes of this study are the following:

(1) For current values of CH 4 line parameters, the abundance of H 2 in Titan's atmosphere is found to be between 0.5 and 1.0%.

(2) At 2/~m, the optical depth of a global cloud cover at 17-30 km altitude is smaller than a value between 0.1 and 0.88, which depends upon the particle size (Table III). The existence of clouds at the tropopause could be confirmed if new observations of Titan at 4640 cm- 1 indicate a time varying albedo.

(3) If methane clouds are optically thick, they must have been patchy and covered no more than 28% of the area of Titan's disk at the time of our observations.

(4) An estimate of the clarity of Titan's atmosphere at 2/~m, obtained by assuming a black surface and either a near global or patchy cloud covering at 3 km altitude, indicates that Titan's albedo at 2/~m is sensitive to the surface albedo (Table III). Titan's 2-/~m window is therefore a good wavelength for the Visible-Infrared Mapping Spectrometer (VIMS) on board the Cassini orbiter to image the satellite's surface. The 1.3- and 1.6-/~m windows are also good choices for exploration by Cassini.

(5) A simple study of Titan's corrected albedo in the methane windows, 1.3, 1.6, and 2.0/~m, indicates that the satellite's surface albedo is not gray at these wavelengths. Our calculated surface albedos are not consistent with a surface covered globally with an C2H6-CH 4 ocean. How- ever, they are consistent with a surface of H20 ice and a dark material. Possible candidates for this material are CzH6-CH 4 lakes and sediments of organic solids with low reflectivities such as tholins.

Additional observations of Titan and laboratory spectroscopic work will help us further understand the satellite's lower atmosphere and surface:

(1) The abundance of methane in the lower atmosphere can be constrained with high resolution observations of Titan's 5000 cm ~ spectrum.

(2) Laboratory measurements of the reflectivity of simple hydrocarbon ices that are produced from methane photolysis (such as C2H 2 and C3H 8) will be useful to further understand the surface composition of Titan (and Triton).

(3) With additional high-pathlength laboratory data on weak C H 4 lines, measurements of Titan's C H 4 column abundances at 1.1, 1.3, 1.6, and 2.0 p.m, similar to those made by Fink and Larson (1979), can be improved upon. This would help constrain the nature of the scattering particles in the lower atmosphere and their opacity in these methane windows. This would also allow for a more precise determination of the C H 4 transmission at these wavelengths.

(4) Titan's 2.9-3.0 ~m region might also be a window in the atmosphere. Observations of Titan in this spectral region have recently been made with the Cooled-Grating


TABLE VII Titan's Corrected Albedo

Resolution Wavenumber Optical radius (cm - I) (cm - i) (km) RFL/R 0 2 2

38 4362 2770 1.14 3.8 4595 2685 1.22

38 4600 2697 1.21 3.8 4603 2730 1.18 3.8 4644 2675 i.23

38 4900 2645 1.26 38 6250 2670 1.23 38 7700 2690 1.21

Array Spectrometer on the IRTF and are in the process of being analyzed.

(5) The ProtoCAM camera has recently been made available on the IRTF, and can be used to image Titan and possibly it's surface at 2 /zm. If such observations reveal brightness variations across Titan's disk, a value for Titan's rotation rate may be detectable with long-term monitoring of the satellite.

Molecular line parameters for the strong CH 4 lines in the 2 to 2.5/zm region are compiled by the 1986 Air Force Geophysical Laboratory (AFGL), available on magnetic tape. These lines include the three com- bination bands: v 1 + /J4 (4224 cm-I), u 3 + 114 (4321 cm- l ) , and u2 + v3 (4544 cm-I). Since the path lengths of CH 4 that we probe in Titan's atmosphere are from 0.27 km-am at 4300 cm -1 to roughly 4 km-am at 4900 cm- 1, the strong lines mentioned above are not sufficient to analyze Titan's spectrum and weaker lines must be considered, Positions and strengths of weak methane lines have recently been measured in both the 3700 to 4136 cm -1 and 4500 to 5000 cm -I spectral regions using the Fourier transform spectrometer at the Kitt Peak National Observatory/ National Solar Observatory (Brown 1988, L. Brown 1988, private communication). Lower energy states are needed to determine the temperature dependence of the transitions. We calculate approximate values for these states by fitting synthetic CH 4 spectra to laboratory spectra (kindly provided by Lawrence Giver) at three different temperatures and several different pressures and column abundances. In these calculations, line- by-line techniques are used, assuming a CH 4 pressure broadened half- width (due to CH4-CH4 collisions) of y = y0(273/T)% where Y0 = 0.088 cm -I atm -I and a = 0.81 (Apt et al. 1981). Examples of the results of this analysis can be seen in Figs. 12a-12c.

For Titan's atmosphere the CH 4 pressure broadening is mainly due to N2-CH 4 collisions. When modeling Titan's atmosphere the values Y0 = 0.0575 cm-E atm-J and c~ = 0.78 are assumed, based on Varanasi and Chudamani's work (1989) involving N2-CH 4 gas mixtures. The Lorentz line wings are cut off at 100 cm-J from line center. There is no significant effect if a greater wing extent is assumed.

A P P E N D I X I: TITAN'S ALBEDO

The work in this appendix is based on the analysis of Titan's albedo by Toon et al. (1991). Refer to this paper for a more detailed discussion. Titan's albedo is determined by dividing the flux observed from the satellite by the area of the disk that reflects the solar radiation. Therefore, a correct measurement of Titan's radius is necessary to determine the albedo. Fink and Larson's radius for Titan, 2964 km, is 389 km larger than the solid radius measured by Voyager 1. In addition, it is larger than the optical radius that determines the area of Titan's disk (including the atmosphere) that reflects solar infrared radiation (Toon et al. 1991). In Table VII, Titan's optical radius is computed at an atmospheric optical depth o f t = 0.051 (based on the work ofToon et al. 1991). The corrected albedo, (A), derived assuming the optical radii in Table VII, is proportional to

R~L A -- AFL" R-~o' (3)

where AFL is the albedo determined by Fink and Larson, and RFL and R o are Fink and Larson's estimated radius and the optical radius, respectively. The correction factors, R~L/R~, are given in Table VII.

A P P E N D I X III: CONDENSATION OF ORGANIC

COMPOUNDS IN THE STRATOSPHERE

Many of the organic compounds, such as C2H6, created in Titan's upper atmosphere are expected to condense above the tropopause in the lower stratosphere (Sagan and Thompson 1984). The stratospheric haze provides condensation nuclei. Assuming a mixing ratio for the condens- ing hydrocarbons of 1.4 × 10 -5 (Coustenis et al. 1989), a haze particle number density of 8 cm -3 (McKay et al. 1989) at 80 km altitude, and, in addition, that the gas condenses uniformly on each haze particle, the haze particle radius increases on the order of 3 ~m due to condensation of organic compounds above the tropopause. Scattering properties are a function of the particle size; larger particles exhibit more forward scattering. In addition, the extinction coefficient (Q) and the optical depth (~-) increase as the particle radius increases.

Condensation of hydrocarbons on the haze particles, which in turn increases the fall velocity of the particles, does not cause the optical depth of the haze to decrease. To show this, we assume that the terminal velocity (v) of the haze particle is proportional to the radius squared (the Stokes regime). The optical depth is then dependent on the particle radius only through the extinction coefficient,

A P P E N D I X II: SPECTROSCOPIC PARAMETERS

In this analysis, we use the absorption coefficients of the first overtone band of N 2 and the fundamental band of H2 (due to N2-Hz collisions) that were measured at 97.5 and 77 K, respectively (McKellar 1989). A H 2 para ratio of 0.4 is assumed in our calculations. At densities less than 100 am only bimolecular collisions need to be considered. The transmission can then be expressed as

T = e -an~, (4)

where a is the absorption coefficient (cm-l-am-2), n is the density (am), and u is the column abundance (cm-am).

"r = 7rr2nQ, (5)

and

~- ~ Q (6)

since the number density (n) is proportional to the inverse of the velocity. The extinction coefficient is a strongly increasing function of particle radius. Thus condensation of hydrocarbons on haze particles increases Titan's Mie scattering optical depth at 2/~m. Even the equivalent isotropic scattering optical depth (ris ~ Q(1 - gw), using Eq (2)) increases in magnitude, unless the newly condensed organics are less reflective


a 1.0

0 .9

0 . 8

0 .7

o ~ 0 . 6

~ 0.5

~ 0.4

0.3

0.2

0.1

0.0 4 6 3 0

4 6 3 5

. . . . I . . . . I ~ , 1 . . . . I . . . . I . . . . I . . . . i , ~ , 1 . . . . i . . . . I . . . . i , , , , l u , , i . . . . i , ,

4640 4650 4660 4670 4680 4690 4700 4645 4655 4665 4675 4685 4695

Wavenumber (era ')

b 1.0

0 . 9

0 . 8

0 .7

°~ 0 .6 r-,

m~ 0 . 5

¢, 0.4

0 . 3

0.2

O.t

0+0 4 6 3 0 4 6 4 0

4 [ 0 5 4 6 3 5 4 6 4 5

, , i . . . . i . . . .

l

,,,i .... i .. . . i,,,

~ 1 1 ' I . . . . I . . . . I . . . . [ . . . . l . . . . I . . . . + . . . . ~ . . . . I . . . . l , l l l l l ' ' ' l ' + ' d ~ U ~ ± ~

4650 4660 4670 4680 4690 4700

4655 4665 4675 4685 4695 4705

W a v e n u m b e r (etTl -I )

1.0 e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

0.9 ~ ?

0.8

0.7

o ~ 0.6

~ 0.5

..1 t-, 0 .4

0 .3

0 . 2

0 .1

0.0 I i . . . . i . . . . i . . . . i . . . . i . . . . i . . . . ~ . . . . i . . . . i . . . . i . . . . i , , , 1 1 1 1 1 1 1 ,

4630 4640 4650 4660 4670 4680 4690 4700 4635 4645 4655 4665 4675 4685 4695 4705

W a v e n u m b e r (era -t)

FIG. 12. A comparison of methane laboratory spectra (Lawrence Giver, private communication) and synthetic spectra. Solid line: In (a) and (b), CH4 spectra measured at a temperature, pressure, and path length of 295 K, 0.25 atm, and 26.6 m, respectively; in (c) the CH4 spectra were measured at a different temperature, pressure, and path length of 187 K, 0.16 atm, and 27.6 m. In (a), the dotted line is the synthetic spectrum reproduced using only the CH 4 lines compiled in the AFGL tape. In (b) and (c), the dotted lines are spectra reproduced with both the AFGL lines and the weaker CH 4 lines whose lower state energy levels we have determined.

than the haze. Recent measurements of the optical constants of solid ethane (the most abundant trace hydrocarbon observed in Titan's atmosphere), by Khare et al. (1990b), indicate that this hydrocarbon is more reflective than are tholins in the 4550-5000 cm i spectral region.

A C K N O W L E D G M E N T S

We thank B. N. Khare, L. R. Brown, L. P. Giver, and A. R. W. McKellar for helpful information about laboratory spectroscopic data and for the use of unpublished data. R. D. Cess and D. Katz helped us develop our atmospheric models. A. T. Tokunaga and T. Y. Brooke provided valuable training in the use of the Cooled-Grating Array Spec- trometer. R. F. Knacke and two referees (A. Coustenis and one anony- mous) provided editorial comments on the manuscript. We also thank M. G. Tomasko, L. Doose, C. P. McKay, and O. B. Toon for illuminating

discussions on the properties of Titan's haze. This research was sup- ported in part by NASA Grant NGR 33-015-141.

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titan's surface and troposphere, investigated with ground...

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