A spherical model for computing polarized radiation in Titan's atmosphere

The Huygens descent through Titan's atmosphere in January 2005 will provide invaluable information about Titan's atmospheric composition and aerosol properties. The Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking radiation observations at various spectral ranges and spatial resolutions. To prepare the DISR data interpretation we have developed a new model for radiation transfer in Titan's atmosphere. The model solves for the full three-dimensional polarized radiation field in spherical geometry. However, the atmosphere itself is assumed to be spherically symmetric. The model is initialized with a fast-to-compute plane–parallel solution based on the doubling and adding algorithm that incorporates a spherical correction for the incoming direct solar beam. The full three-dimensional problem is then solved using the characteristics method combined with the Picard iterative approximation as described in Rozanov et al. (J. Quant. Spectrosc. Radiat. Transfer 69 (2001) 491). Aerosol scattering properties are calculated with a new microphysical model. In this formulation, aerosols are assumed to be fractal aggregates and include methane gas absorption embedded into the extinction coefficient. The resulting radiance of the model atmosphere's internal field is presented for two prescribed DISR wavelengths.     

A model of Titan's aerosols based on measurements made inside the atmosphere

The descent imager/spectral radiometer (DISR) instrument aboard the Huygens probe into the atmosphere of Titan measured the brightness of sunlight using a complement of spectrometers, photometers, and cameras that covered the spectral range from 350 to 1600 nm, looked both upward and downward, and made measurements at altitudes from 150 km to the surface. Measurements from the upward-looking visible and infrared spectrometers are described in Tomasko et al. [2008a. Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan's atmosphere. Planet. Space Sci., this volume]. Here, we very briefly review the measurements by the violet photometers, the downward-looking visible and infrared spectrometers, and the upward-looking solar aureole (SA) camera. Taken together, the DISR measurements constrain the vertical distribution and wavelength dependence of opacity, single-scattering albedo, and phase function of the aerosols in Titan's atmosphere.Comparison of the inferred aerosol properties with computations of scattering from fractal aggregate particles indicates the size and shape of the aerosols. We find that the aggregates require monomers of radius 0.05 μm or smaller and that the number of monomers in the loose aggregates is roughly 3000 above 60 km. The single-scattering albedo of the aerosols above 140 km altitude is similar to that predicted for some tholins measured in laboratory experiments, although we find that the single-scattering albedo of the aerosols increases with depth into the atmosphere between 140 and 80 km altitude, possibly due to condensation of other gases on the haze particles. The number density of aerosols is about 5/cm³ at 80 km altitude, and decreases with a scale height of 65 km to higher altitudes. The aerosol opacity above 80 km varies as the wavelength to the −2.34 power between 350 and 1600 nm.Between 80 and 30 km the cumulative aerosol opacity increases linearly with increasing depth in the atmosphere. The total aerosol opacity in this altitude range varies as the wavelength to the −1.41 power. The single-scattering phase function of the aerosols in this region is also consistent with the fractal particles found above 60 km.In the lower 30 km of the atmosphere, the wavelength dependence of the aerosol opacity varies as the wavelength to the −0.97 power, much less than at higher altitudes. This suggests that the aerosols here grow to still larger sizes, possibly by incorporation of methane into the aerosols. Here the cumulative opacity also increases linearly with depth, but at some wavelengths the rate is slightly different than above 30 km altitude.For purely fractal particles in the lowest few km, the intensity looking upward opposite to the azimuth of the sun decreases with increasing zenith angle faster than the observations in red light if the single-scattering albedo is assumed constant with altitude at these low altitudes. This discrepancy can be decreased if the single-scattering albedo decreases with altitude in this region. A possible explanation is that the brightest aerosols near 30 km altitude contain significant amounts of methane, and that the decreasing albedo at lower altitudes may reflect the evaporation of some of the methane as the aerosols fall into dryer layers of the atmosphere. An alternative explanation is that there may be spherical particles in the bottom few kilometers of the atmosphere.     

Characteristics of the radiation emerging from the top of a Rayleigh atmosphere—II Total upward flux and albedo

The solution of the equation of radiative transfer in a medium exhibiting Rayleigh scattering, as developed by S. Chandrasekhar, has been used for an extensive series of computations(³) of the characteristics of the scattered and diffusely reflected radiation emerging from the top of an atmospheric model which corresponds in many respects to the sunlit portion of the earth's atmosphere. The first part of this two-part discussion dealt with the intensity, degree of polarization, plane of polarization and the neutral points of the emergent light as functions of sun elevation, direction in the downward hemisphere, optical thickness of the model atmosphere and reflectivity of the underlying surface. This second part is concerned with the upward flux obtained by an integration of the intensity over the entire hemisphere, for the incident radiation (a) being independent of wavelength or (b) having the spectral distribution of the extra-terrestrial solar radiation. Integration with respect to wavelength in the latter case, together with an approximation for the sphericity of the atmosphere, yields a value of 7.6 per cent for the earth's planetary albedo due to scattering by the clear atmosphere. An approximation for ozone absorption decreases the computed albedo to 6.9 per cent.     

Speckle imaging of Titan at 2 microns: surface albedo, haze optical depth, and tropospheric clouds 1996-1998

We present results from 14 nights of observations of Titan in 1996-1998 using near-infrared (centered at 2.1 microns) speckle imaging at the 10-meter W.M. Keck Telescope. The observations have a spatial resolution of 0.06 arcseconds. We detect bright clouds on three days in October 1998, with a brightness about 0.5% of the brightness of Titan. Using a 16-stream radiative transfer model (DISORT) to model the central equatorial longitude of each image, we construct a suite of surface albedo models parameterized by the optical depth of Titan's hydrocarbon haze layer. From this we conclude that Titan's equatorial surface albedo has plausible values in the range of 0-0.20. Titan's minimum haze optical depth cannot be constrained from this modeling, but an upper limit of 0.3 at this wavelength range is found. More accurate determination of Titan's surface albedo and haze optical depth, especially at higher latitudes, will require a model that fully considers the 3-dimensional nature of Titan's atmosphere.     

Radiative transfer analyses of Titan’s tropical atmosphere

Titan’s optical and near-IR spectra result primarily from the scattering of sunlight by haze and its absorption by methane. With a column abundance of 92 km amagat (11 times that of Earth), Titan’s atmosphere is optically thick and only ～10% of the incident solar radiation reaches the surface, compared to 57% on Earth. Such a formidable atmosphere obstructs investigations of the moon’s lower troposphere and surface, which are highly sensitive to the radiative transfer treatment of methane absorption and haze scattering. The absorption and scattering characteristics of Titan’s atmosphere have been constrained by the Huygens Probe Descent Imager/Spectral Radiometer (DISR) experiment for conditions at the probe landing site (Tomasko, M.G., Bézard, B., Doose, L., Engel, S., Karkoschka, E. [2008a]. Planet. Space Sci. 56, 624–247; Tomasko, M.G. et al. [2008b]. Planet. Space Sci. 56, 669–707). Cassini’s Visual and Infrared Mapping Spectrometer (VIMS) data indicate that the rest of the atmosphere (except for the polar regions) can be understood with small perturbations in the high haze structure determined at the landing site (Penteado, P.F., Griffith, C.A., Tomasko, M.G., Engel, S., See, C., Doose, L., Baines, K.H., Brown, R.H., Buratti, B.J., Clark, R., Nicholson, P., Sotin, C. [2010]. Icarus 206, 352–365). However the in situ measurements were analyzed with a doubling and adding radiative transfer calculation that differs considerably from the discrete ordinates codes used to interpret remote data from Cassini and ground-based measurements. In addition, the calibration of the VIMS data with respect to the DISR data has not yet been tested. Here, VIMS data of the probe landing site are analyzed with the DISR radiative transfer method and the faster discrete ordinates radiative transfer calculation; both models are consistent (to within 0.3%) and reproduce the scattering and absorption characteristics derived from in situ measurements. Constraints on the atmospheric opacity at wavelengths outside those measured by DISR, that is from 1.6 to 5.0 μm, are derived using clouds as diffuse reflectors in order to derive Titan’s surface albedo to within a few percent error and cloud altitudes to within 5 km error. VIMS spectra of Titan at 2.6–3.2 μm indicate not only spectral features due to CH₄ and CH₃D (Rannou, P., Cours, T., Le Mouélic, S., Rodriguez, S., Sotin, C., Drossart, P., Brown, R. [2010]. Icarus 208, 850–867), but also a fairly uniform absorption of unknown source, equivalent to the effects of a darkening of the haze to a single scattering albedo of 0.63 ± 0.05. Titan’s 4.8 μm spectrum point to a haze optical depth of 0.2 at that wavelength. Cloud spectra at 2 μm indicate that the far wings of the Voigt profile extend 460 cm^?1 from methane line centers. This paper releases the doubling and adding radiative transfer code developed by the DISR team, so that future studies of Titan’s atmosphere and surface are consistent with the findings by the Huygens Probe. We derive the surface albedo at eight spectral regions of the 8 × 12 km² area surrounding the Huygens landing site. Within the 0.4–1.6 μm spectral region our surface albedos match DISR measurements, indicating that DISR and VIMS measurements are consistently calibrated. These values together with albedos at longer 1.9–5.0 μm wavelengths, not sampled by DISR, resemble a dark version of the spectrum of Ganymede’s icy leading hemisphere. The eight surface albedos of the landing site are consistent with, but not deterministic of, exposed water ice with dark impurities.     

Emergent radiation from the atmosphere bounded by the two halves of the Lambert surface with different albedos

For the evaluation of the effect of the nonuniform surface albedo to the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two-halves of the Lambert surface with different albedos is computed. The principal plane is assumed to be perpendicular to the boundary of surfaces. The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are 0.25, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is approximated by the contributions due to the multiple scattering in the atmosphere, directly attenuated radiation, and radiation due to single scattering in the atmosphere which is reflected by the Lambert surface (up to 4 interactive radiative modes between atmosphere and surface). For quantitative analysis, results are compared with those of the atmosphere-uniform surface model, where the multiple scattering is considered. The numerical simulation exhibits the extraordinary effect near the surface boundary of different albedos. The effect decreases exponentially with the distance from the boundary. It is a function of the observational position, difference of surface albedos, optical thickness and aerosol type.The upward radiance would simply be evaluated using the present scattering approximation method if the atmosphere is in clear condition. Whereas in hazy condition, the effect of multiple scattering in the atmosphere should be considered more precisely, since the upward radiance exhibit a strong dependence on observational nadir angles due to multiple scattering in the atmosphere. Furthermore, it depends on the optical characteristics of aerosols.     

Emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo,II

For the evaluation of the effect of the non-uniform surface albedo on the emergent radiation from the atmosphere, the emergent radiation from the atmosphere bounded by the two half Lambert surfaces composed of different albedo is computed. This paper is the improved version of the previous paper (Takashima and Masuda, 1991). The atmosphere is assumed to be homogeneous, which is composed of aerosol, molecules, and absorbent gases. Their optical thicknesses are (1) 0.25, 0.23, and 0.02, and (2) 0.75, 0.23, and 0.02, respectively. The model aerosol is of the oceanic and water soluble types.In the computational procedure, the emergent radiation is calculated approximately by the contributions due to the multiple scattering in the atmosphere, and due to the diffusely or directly transmitted radiation through the atmosphere which is reflected by the surfaces once (4 interactive radiative modes between atmosphere and surface). Furthermore, to perform the hemispherical integration processing the radiative interaction, the transmission function based on the single scattering in the atmosphere is introduced and then the transmission function is averaged over the hemisphere with weighting function. The numerical simulation exhibits the extraordinary effect near the two half surface boundary of different albedoes. The effect decreases exponentially with the distance from the boundary. The effect depends on the atmospheric aerosol type, optical thickness, and surface albedo. The present version enables us to quantitatively discuss the radiative transfer trend near the boundary of two half surfaces. The upward radiance would simply be evaluated using the present scattering approximation method if the surface albedo is less than 0.3. The present method is thought of as a first step extending the one-dimensional radiative transfer model to two-dimensional using the doubling-adding method.     

Photometric study of the major satellites of Uranus

In this paper, we analyze the results of ground-based and space-born photometric observations of the major satellites of Uranus—Miranda, Ariel, Umbriel, Titania, and Oberon. All sets of photometric observations of the satellites available in the literature were examined for uniformity and systematic differences and summarized to a unified set by wavelength ranging from 0.25 to 2.4 μm. This set covers the interval of phase angles from 0.034° to 35°. The compound phase curves of brightness of the satellites in the spectral bands at 0.25, 0.41, 0.48, 0.56, 0.75, 0.91, 1.4, and 1.8 μm, which include a pronounced opposition surge and linear part, were constructed. For each satellite, the geometric albedo was found in different spectral bands taking into account the brightness opposition effect, and its spectral dependence was studied. It has been shown that the reflectance of the satellites linearly depends on the wavelength at different phase angles, but has different spectral gradients. The parameters of the phase functions of brightness, including the amplitude and the angular width of the brightness opposition surge, the phase coefficient, and the phase angle at which the nonlinear increase in brightness starts, were determined and their dependences on wavelength and geometric albedo were analyzed. Our investigations show that, in their optical properties, the satellites Miranda and Ariel, Titania and Oberon, and Umbriel present three types of surfaces. The observed parameters of the brightness opposition effect for the Uranian satellites, some ice satellites of Jupiter and Saturn, and the E-and S-type asteroids are analyzed and compared within the framework of the coherent backscattering and mutual shadowing mechanisms.     

Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan's atmosphere

New low-temperature methane absorption coefficients pertinent to the Titan environment are presented as derived from the Huygens DISR spectral measurements combined with the in-situ measurements of the methane gas abundance profile measured by the Huygens Gas Chromatograph/Mass Spectrometer (GCMS). The visible and near-infrared spectrometers of the descent imager/spectral radiometer (DISR) instrument on the Huygens probe looked upward and downward covering wavelengths from 480 to 1620 nm at altitudes from 150 km to the surface during the descent to Titan's surface. The measurements at continuum wavelengths were used to determine the vertical distribution, single-scattering albedos, and phase functions of the aerosols. The gas chromatograph/mass spectrometer (GCMS) instrument on the probe measured the methane mixing ratio throughout the descent. The DISR measurements are the first direct measurements of the absorbing properties of methane gas made in the atmosphere of Titan at the pathlengths, pressures, and temperatures that occur there. Here we use the DISR spectral measurements to determine the relative methane absorptions at different wavelengths along the path from the probe to the sun throughout the descent. These transmissions as functions of methane path length are fit by exponential sums and used in a haze radiative transfer model to compare the results to the spectra measured by DISR. We also compare the recent laboratory measurements of methane absorption at low temperatures [Irwin et al., 2006. Improved near-infrared methane band models and k-distribution parameters from 2000 to 9500 cm⁻¹ and implications for interpretation of outer planet spectra. Icarus 181, 309-319] with the DISR measurements. We find that the strong bands formed at low pressures on Titan act as if they have roughly half the absorption predicted by the laboratory measurements, while the weak absorption regions absorb considerably more than suggested by some extrapolations of warm measurements to the cold Titan temperatures. We give factors as a function of wavelength that can be used with the published methane coefficients between 830 and 1620 nm to give agreement with the DISR measurements. We also give exponential sum coefficients for methane absorptions that fit the DISR observations. We find the DISR observations of the weaker methane bands shortward of 830 nm agree with the methane coefficients given by Karkoschka [1994. Spectrophotometry of the jovian planets and Titan at 300- to 1000-nm wavelength: the methane spectrum. Icarus 111, 174-192]. Finally, we discuss the implications of our results for computations of methane absorption in the atmospheres of the outer planets.     

Rain and dewdrops on titan based on in situ imaging

The Descent Imager/Spectral Radiometer (DISR) of the Huygens probe was in an excellent position to view aspects of rain as it descended through Titan's atmosphere. Rain may play an important part of the methane cycle on Titan, similar to the water cycle on Earth, but rain has only been indirectly inferred in previous studies. DISR detected two dark atmospheric layers at 11 and 21 km altitude, which can be explained by a local increase in aerosol size by about 5-10%. These size variations are far smaller than those in rain clouds, where droplets grow some 1000-fold. No image revealed a rainbow, which implies that the optical depth of raindrops was less than ∼0.0002/km. This upper limit excludes rain and constrains drizzle to extremely small rates of less than 0.0001 mm/h. However, a constant drizzle of that rate over several years would clear the troposphere of aerosols faster than it can be replenished by stratospheric aerosols. Hence, either the average yearly drizzle rate near the equator was even less (<0.1 mm/yr), or the observed aerosols came from somewhere else. The implied dry environment is consistent with ground-based imaging showing a lack of low-latitude clouds during the years before the Huygens descent. Features imaged on Titan's surface after landing, which might be interpreted as raindrop splashes, were not real, except for one case. This feature was a dewdrop falling from the outermost baffle of the DISR instrument. It can be explained by warm, methane-moist air rising along the bottom of the probe and condensing onto the cold baffle.     

Simulations of Titan's brightness by a two-dimensional haze model

We have used a 2-D microphysics model to study the effects of atmospheric motions on the albedo of Titan's thick haze layer. We compare our results to the observed variations of Titan's brightness with season and latitude. We use two wind fields; the first is a simple pole-to-pole Hadley cell that reverses twice a year. The second is based on the results of a preliminary Titan GCM. Seasonally varying wind fields, with horizontal velocities of about 1 cm sec-1 at optical depth unity, are capable of producing the observed change in geometric albedo of about 10% over the Titan year. Neither of the two wind fields can adequately reproduce the latitudinal distribution of reflectivity seen by Voyager. At visible wavelengths, where only haze opacity is important, upwelling produces darkening by increasing the particle size at optical depth unity. This is due to the suspension of larger particles as well as the lateral removal of smaller particles from the top of the atmosphere. At UV wavelengths and at 0.89 micrometers the albedo is determined by the competing effects of the gas the haze material. Gas is bright in the UV and dark at 0.89 micrometers. Haze transport at high altitudes controls the UV albedo and transport at low altitude controls the 0.89 micrometers albedo. Comparisons between the hemispheric contrast at UV, visible, and IR wavelengths can be diagnostic of the vertical structure of the wind field on Titan.     

International conference on planetary satellites

Further analysis of visual (V) wavelength photometric function data for Saturn's ring is presented. Evidence indicating both that primary scattering dominates, and that mutual shadowing is an irrelevant concept, is reviewed. Simple anisotropic scattering radiative transfer models are used to define the probable ranges in the single scattering albedo, and in the general shape of the scattering phase function of the individual particles. Limitations on the mean perpendicular optical thickness of the ring are also obtained. Results indicate that the ring particles are highly efficient back-scatterers of visual radiation. Macroscopic particles account for the basic shape of the scattering phase function. Based on an infinite optical thickness for the ring, a minimum single scattering albedo ≈0.75 is found. Use of conservative scattering leads to a minimum optical thickness ≈0.7. The analysis is consistent with the ring particles being centimeter-size pieces of ice.     

The range of validity of the Eddington approximation

The Eddington approximation is often assumed to be useful only for optically thick media having a single-scattering albedo near unity. We present detailed evidence in this paper that, for homogeneous layers illuminated by a beam of radiation, the Eddington approximation predicts albedo and absorptivity reasonably well for all values of optical depth and single-scattering albedo, for several scattering phase functions (Rayleigh, Henyey-Greenstein, and Mie) having asymmetry factors less than or equal to $\text{1}\text{2}$. The worst errors are in the neighborhood of optical depth unity and single-scattering albedo 0.5. The Eddington approximation is further found to maintain good accuracy over almost the full range of incident beam directions and surface albedos. It is least accurate for the Mie phase function example, where one can obtain a dramatic improvement in accuracy by going over to the δ-Eddington approximation; this shows that the forward peak of the Mie phase function, and not its detailed shape, is the primary cause of diminished accuracy in the Eddington approximation.     

Shading under Titan's sky

During the descent of the Huygens probe in January 2005, its Descent Imager/Spectral Radiometer (DISR) will take the first close up images of Titan's surface. The shading imposed by the illumination of a planetary surface contains information on its topography. For planetary bodies without an optically thick atmosphere, the light can be assumed to stem from a point source. In this case, methods are available in order to estimate the shape of surface features from shading. The situation is quite different for Titan, as its atmosphere is optically thick at optical wavelengths. The sun is visible from the surface, but the illumination is dominated by diffuse radiance. In order to investigate the characteristics of shading under Titan's sky and to assess methods to retrieve the shape, different digital terrain models (DTMs) are used to simulate images according to different types of illumination. For an idealized DTM, the shape is retrieved from the shading in the simulated images. Deriving the shape from shading under Titan's sky using existing methods is only possible if the topography is relatively flat, i.e. in the absence of steep slopes.     

Impact cratering on Titan II. Global melt, escaping ejecta, and aqueous alteration of surface organics

New three-dimensional hydrodynamic simulations of hypervelocity impacts into the crust of Titan were undertaken to determine the fraction of liquid water generated on the surface of Saturn's largest moon over its history and, hence, the potential for surface—modification of hydrocarbons and nitriles by exposure to liquid water. We model in detail an individual impact event in terms of ejecta produced and melt generated, and use this to estimate melt production over Titan's history, taking into account the total flux of the impactors and its decay over time. Our estimates show that a global melt layer at any time after the very beginning of Titan's history is improbable; but transient melting local to newly formed craters has occurred over large parts of the surface. Local maxima of the melt are connected with the largest impact events. We also calculate the amount of volatiles delivered at the impact with various impact velocities (from 3 km/s for possible Hyperion fragments to 11 km/s for Jupiter family comets) and their retention as a possible source of Titan's atmosphere. We find the probability of impact ejecta escaping Titan with its modern dense and thick atmosphere is rather low, and dispersal of Titan organics throughout the rest of the Solar System requires impactors tens of kilometers in diameter. Water ice melting and exposure of organics to liquid water has been widespread because of impacts, but burial or obscuration of craters by organic deposits or cryovolcanism is aided by viscous relaxation. The largest impactors may breach an ammonia-water mantle layer, creating a circular albedo contrast rather than a crater.     

Coupling photochemistry with haze formation in Titan's atmosphere, Part II: Results and validation with Cassini/Huygens data

The new one-dimensional radiative-convective/photochemical/microphysical model described in Part I is applied to the study of Titan's atmospheric processes that lead to haze formation. Our model generates the haze structure from the gaseous species photochemistry. Model results are presented for the species vertical concentration profiles, haze formation and its radiative properties, vertical temperature/density profiles and geometric albedo. These are validated against Cassini/Huygens observations and other ground-based and space-borne measurements. The model reproduces well most of the latest measurements from the Cassini/Huygens instruments for the chemical composition of Titan's atmosphere and the vertical profiles of the observed species. For the haze production we have included pathways that are based on pure hydrocarbons, pure nitriles and hydrocarbon/nitrile copolymers. From these, the nitrile and copolymer pathways provide the stronger contribution, in agreement with the results from the ACP instrument, which support the incorporation of nitrogen in the pyrolized haze structures. Our haze model reveals a new second major peak in the vertical profile of haze production rate between 500 and 900 km. This peak is produced by the copolymer family used and has important ramifications for the vertical atmospheric temperature profile and geometric albedo. In particular, the existence of this second peak determines the vertical profile of haze extinction. Our model results have been compared with the DISR retrieved haze extinction profiles and are found to be in very good agreement. We have also incorporated in our model heterogeneous chemistry on the haze particles that converts atomic hydrogen to molecular hydrogen. The resultant H₂ profile is closer to the INMS measurements, while the vertical profile of the diacetylene formed is found to be closer to that of the CIRS profile when this heterogenous chemistry is included.     

Laboratory experiments of Titan tholin formed in cold plasma at various pressures: implications for nitrogen-containing polycyclic aromatic compounds in Titan haze

Titan, the largest satellite of Saturn, has a thick nitrogen/methane atmosphere with a thick global organic haze. A laboratory analogue of Titan's haze, called tholin, was formed in an inductively coupled plasma from nitrogen/methane=90/10 gas mixture at various pressures ranging from 13 to 2300 Pa. Chemical and optical properties of the resulting tholin depend on the deposition pressure in cold plasma. Structural analyses by IR and UV/VIS spectroscopy, microprobe laser desorption/ionization mass spectrometry, and Raman spectroscopy suggest that larger amounts of aromatic ring structures with larger cluster size are formed at lower pressures (13 and 26 Pa) than at higher pressures (160 and 2300 Pa). Nitrogen is more likely to incorporate into carbon networks in tholins formed at lower pressures, while nitrogen is bonded as terminal groups at higher pressures. Elemental analysis reveals that the carbon/nitrogen ratio in tholins increases from 1.5-2 at lower pressures to 3 at 2300 Pa. The increase in the aromatic compounds and the decrease in C/N ratio in tholin formed at low pressures indicate the presence of the nitrogen-containing polycyclic aromatic compounds in tholin formed at low pressures. Tholin formed at high pressure (2300 Pa) consists of a polymer-like branched chain structure terminated with CH₃, NH₂, and CN with few aromatic compounds. Reddish-brown tholin films formed at low pressures (13-26 Pa) shows stronger absorptions (almost 10 times larger k-value) in the UV/VIS range than the yellowish tholin films formed at high pressures (160 and 2300 Pa). The tholins formed at low pressures may be better representations of Titan's haze than those formed at high pressures, because the optical properties of tholin formed at low pressures agree well with that of Khare et al. (1984a, Icarus 60, 127-137), which have been shown to account for Titan's observed geometric albedo. Thus, the nitrogen-containing polycyclic aromatic compounds we find in tholin formed at low pressure may be present in Titan's haze. These aromatic compounds may have a significant influence on the thermal structure and complex organic chemistry in Titan's atmosphere, because they are efficient absorbers of UV radiation and efficient charge exchange intermediaries. Our results also indicate that the haze layers at various altitudes might have different chemical and optical properties.     

A physical model of Titan's aerosols

Microphysical simulations of Titan's stratospheric haze show that aerosol microphysics is linked to organized dynamical processes. The detached haze layer may be a manifestation of 1 cm sec-1 vertical velocities at altitudes above 300 km. The hemispherical asymmetry in the visible albedo may be caused by 0.05 cm sec-1 vertical velocities at altitudes of 150 to 200 km, we predict contrast reversal beyond 0.6 micrometer. Tomasko and Smith's (1982, Icarus 51, 65-95) model, in which a layer of large particles above 220 km altitude is responsible for the high forward scattering observed by Rages and Pollack (1983, Icarus 55, 50-62), is a natural outcome of the detached haze layer being produced by rising motions if aerosol mass production occurs primarily below the detached haze layer. The aerosol's electrical charge is critical for the particle size and optical depth of the haze. The geometric albedo, particularly in the ultraviolet and near infrared, requires that the particle size be near 0.15 micrometer down to altitudes below 100 km, which is consistent with polarization observations (Tomasko and Smith 1982, West and Smith 1991, Icarus 90, 330-333). Above about 400 km and below about 150 km Yung et al.'s (1984, Astrophys. J. Suppl. Ser. 55, 465-506) diffusion coefficients are too small. Dynamical processes control the haze particles below about 150 km. The relatively large eddy diffusion coefficients in the lower stratosphere result in a vertically extensive region with nonuniform mixing ratios of condensable gases, so that most hydrocarbons may condense very near the tropopause rather than tens of kilometers above it. The optical depths of hydrocarbon clouds are probably less than one, requiring that abundant gases such as ethane condense on a subset of the haze particles to create relatively large, rapidly removed particles. The wavelength dependence of the optical radius is calculated for use in analyzing observations of the geometric albedo. The lower atmosphere and surface should be visible outside of regions of methane absorption in the near infrared. Limb scans at 2.0 micrometers wavelength should be possible down to about 75 km altitude.     

The reflectance spectrum of Titan's surface at the Huygens landing site determined by the descent imager/spectral radiometer

The descent imager/spectral radiometer aboard the Huygens probe successfully acquired images and spectra of the surface of Titan. To counter the effects of haze and atmospheric methane absorption it carried a surface science lamp to illuminate the surface just before landing. We reconstruct the reflectance spectrum of the landing site in the 500-1500 nm range from downward looking visual and infrared spectrometers data that show evidence of lamp light. Our reconstruction is a followup to the analysis by Tomasko et al. [2005. Rain, winds and haze during the Huygens probe's descent to Titan's surface. Nature 438, 765-778], who scaled their result to the ratio of the up- and down flux measured just before landing. Instead, we use the lamp flux from the calibration experiment, and find a significantly higher overall reflectance. We attribute this to a phase angle dependance, possibly representing the opposition surge commonly encountered on solar system bodies. The reconstruction in the visible wavelength range is greatly improved. Here, the reflectance spectrum features a red slope, consistent with the presence of organic material. We confirm the blue slope in the near-IR, featureless apart from a single shallow absorption feature at 1500 nm. We agree with Tomasko et al. that the evidence for water ice is inconclusive. By modeling of absorption bands we find a methane mixing ratio of 4.5±0.5% just above the surface. There is no evidence for the presence of liquid methane, but the data do not rule out a wet soil at a depth of several centimeters.     

Average photon path-length of radiation emerging from finite atmospheres

The determination of the average path-length of photons emerging from a finite planeparallel atmosphere with molecular scattering is discussed. We examine the effects of polarisation on the average path-length of the emergent radiation by comparing the results with those obtained for the atmosphere where the scattering obeys the scalar Rayleigh function. Only the axial radiation field is considered for both cases.To solve this problem we have used the integro-differential equations of Chandrasekhar for the diffuse scattering and transmission functions (or matrices). By differentiation of these equations with respect to the albedo of single scattering we obtain new equations the solution of which gives us the derivatives of the intensities of the emergent radiation at the boundaries.As in the case of scalar transfer the principles of invariance by Chandrasekhar may be used to find an adding scheme to obtain both the scattering and transmission matrices and their derivatives with respect to the albedo of single scattering. These derivatives are crucial in determining the average path length.The numerical experiments have shown that the impact of the polarisation on the average pathlength of the emergent radiation is the largest in the atmospheres with optical thickness less than, or equal to, three, reaching 6.9% in the reflected radiation.