Inverse radiation modeling of Titan's atmosphere to assimilate solar aureole imager data of the Huygens probe

During the descent of the Huygens probe through Titan's atmosphere in January 2005, the Descent Imager/Spectral Radiometer (DISR) will perform upward and downward looking measurements at various spectral ranges and spatial resolutions. This internal radiation density could be estimated by radiative transfer calculations for Titan's atmosphere. However, to do this, the optical properties—i.e. volume extinction coefficient, single scattering albedo and scattering phase function—have to be prescribed at every altitude, and these are apriori not known. Herein, an inverse approach is investigated, which retrieves the single scattering albedo and the phase function of the aerosols from DISR observations. The method uses data from a DISR subinstrument, the Solar Aureole imager (SA), to estimate the optical properties of the atmospheric layer between two successive observation altitudes. A unique solution for one layer can in principle be calculated directly from a linear system of equations, but due to the sparseness of the data and the unavoidable noise in the measurements, the inverse problem is ill-posed. The problem is stabilized by the regularization method requiring smoothness of the resultant solution. A consistent set of solutions for all layers is obtained by iterating several times downward and upward through the layers. The method is tested in a simulated radiation density scenario for Titan, which is based on a microphysical aerosol model for the haze layer. Within this scenario, the expected coverage of SA data allows a reconstruction of the angular dependence of the scattering phase function with an explained variance better than 90%.     

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.     

Stochastic Models of Hot Planetary and Satellite Coronas: Suprathermal Nitrogen in Titan's Upper Atmosphere

The processes of dissociation and dissociative ionization of molecular nitrogen by solar UV radiation and by the accompanying flux of photoelectrons, as well as sputtering of the atmosphere by fluxes of magnetospheric ions and pick-up ions, are the main sources of translationally excited (hot, or suprathermal) nitrogen atoms and molecules in Titan's upper atmosphere. Since Titan does not possess an intrinsic magnetic field, ions from Saturn's magnetosphere can penetrate into the outer layers of Titan's atmosphere and sputter atoms and molecules from the atmosphere in momentum-transfer and charge exchange collisions. Atmospheric sputtering by corotating nitrogen ions and carbon-containing pick-up ions, as well as photodissociation-related losses, was considered previously by Lammer and Bauer (1993) and Shematovich et al. (2001, 2003). In this paper we investigate the processes of the formation and evolution of the fraction of suprathermal nitrogen atoms and molecules in the transition region of Titan's upper atmosphere using the previously developed Monte Carlo model for hot satellite and planetary coronas (Shematovich, 1999, 2004). It is established that the suprathermal nitrogen fraction in the transition region of Titan's upper atmosphere includes nitrogen atoms and molecules but the suprathermal nitrogen concentration is relatively small owing to high rates of escape from the atmosphere and to the efficient thermalization of suprathermal nitrogen at the altitudes of the relatively dense lower thermosphere. However, the scale height for suprathermal nitrogen in the transition region is much higher than that for the ambient atmospheric gas. Therefore, suprathermal nitrogen becomes one of the dominant components in the outer exosphere.     

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.     

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.     

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.     

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.     

Insolation in Titan’s troposphere

Seasonality in Titan’s troposphere is driven by latitudinally varying insolation. We show that the latitudinal distributions of insolation in the troposphere and at the surface, based on Huygens DISR measurements, can be approximated analytically with nonzero extinction optical depths τ, and are not equivalent to that at the top of the atmosphere (τ = 0), as has been assumed previously. This has implications for the temperature distribution and the circulation, which we explore with a simple box model. The surface temperature maximum and the upwelling arm of thermally-direct meridional circulation reach the midlatitudes, not the poles, during summertime.     

Heat balance in Titan's atmosphere

The recent measurements of the vertical distribution and optical properties of haze aerosols as well as of the absorption coefficients for methane at long paths and cold temperatures by the Huygens entry probe of Titan permit the computation of the solar heating rate on Titan with greater certainty than heretofore. We use the haze model derived from the Descent Imager/Spectral Radiometer (DISR) instrument on the Huygens probe [Tomasko, M.G., Doose, L., Engel, S., Dafoe, L.E., West, R., Lemmon, M., Karkoschka, E., See, C., 2008a. A model of Titan's aerosols based on measurements made inside the atmosphere. Planet. Space Sci., this issue, doi:10.1016/j.pss.2007.11.019] to evaluate the variation in solar heating rate with altitude and solar zenith angle in Titan's atmosphere. We find the disk-averaged solar energy deposition profile to be in remarkably good agreement with earlier estimates using very different aerosol distributions and optical properties. We also evaluated the radiative cooling rate using measurements of the thermal emission spectrum by the Cassini Composite Infrared Spectrometer (CIRS) around the latitude of the Huygens site. The thermal flux was calculated as a function of altitude using temperature, gas, and haze profiles derived from Huygens and Cassini/CIRS data. We find that the cooling rate profile is in good agreement with the solar heating profile averaged over the planet if the haze structure is assumed the same at all latitudes. We also computed the solar energy deposition profile at the 10°S latitude of the probe-landing site averaged over one Titan day. We find that some 80% of the sunlight that strikes the top of the atmosphere at this latitude is absorbed in all, with 60% of the incident solar energy absorbed below 150 km, 40% below 80 km, and 11% at the surface at the time of the Huygens landing near the beginning of summer in the southern hemisphere. We compare the radiative cooling rate with the solar heating rate near the Huygens landing site averaging over all longitudes. At this location, we find that the solar heating rate exceeds the radiative cooling rate by a maximum of 0.5 K/Titan day near 120 km altitude and decreases strongly above and below this altitude. Since there is no evidence that the temperature structure at this latitude is changing, the general circulation must redistribute this heat to higher latitudes.     

Model-data comparisons for Titan's nightside ionosphere

Solar and X-ray radiation and energetic plasma from Saturn's magnetosphere interact with the upper atmosphere producing an ionosphere at Titan. The highly coupled ionosphere and upper atmosphere system mediates the interaction between Titan and the external environment. A model of Titan's nightside ionosphere will be described and the results compared with data from the Ion and Neutral Mass Spectrometer (INMS) and the Langmuir probe (LP) part of the Radio and Plasma Wave (RPWS) experiment for the T5 and T21 nightside encounters of the Cassini Orbiter with Titan. Electron impact ionization associated with the precipitation of magnetospheric electrons into the upper atmosphere is assumed to be the source of the nightside ionosphere, at least for altitudes above 1000 km. Magnetospheric electron fluxes measured by the Cassini electron spectrometer (CAPS ELS) are used as an input for the model. The model is used to interpret the observed composition and structure of the T5 and T21 ionospheres. The densities of many ion species (e.g., CH⁺₅ and C₂H⁺₅) measured during T5 exhibit temporal and/or spatial variations apparently associated with variations in the fluxes of energetic electrons that precipitate into the atmosphere from Saturn's magnetosphere.     

Cassini/VIMS hyperspectral observations of the HUYGENS landing site on Titan

Titan is one of the primary scientific objectives of the NASA–ESA–ASI Cassini–Huygens mission. Scattering by haze particles in Titan's atmosphere and numerous methane absorptions dramatically veil Titan's surface in the visible range, though it can be studied more easily in some narrow infrared windows. The Visual and Infrared Mapping Spectrometer (VIMS) instrument onboard the Cassini spacecraft successfully imaged its surface in the atmospheric windows, taking hyperspectral images in the range 0.4–5.2 μm. On 26 October (TA flyby) and 13 December 2004 (TB flyby), the Cassini–Huygens mission flew over Titan at an altitude lower than 1200 km at closest approach. We report here on the analysis of VIMS images of the Huygens landing site acquired at TA and TB, with a spatial resolution ranging from 16 to14.4 km/pixel. The pure atmospheric backscattering component is corrected by using both an empirical method and a first-order theoretical model. Both approaches provide consistent results. After the removal of scattering, ratio images reveal subtle surface heterogeneities. A particularly contrasted structure appears in ratio images involving the 1.59 and 2.03 μm images north of the Huygens landing site. Although pure water ice cannot be the only component exposed at Titan's surface, this area is consistent with a local enrichment in exposed water ice and seems to be consistent with DISR/Huygens images and spectra interpretations. The images show also a morphological structure that can be interpreted as a 150 km diameter impact crater with a central peak.     

Titan's aerosols: Comparison between our model and DISR findings

Our model [Dimitrov, V., Bar-Nun, A., 1999. A model of energy dependent agglomeration of hydrocarbon aerosol particles and implication to Titan's aerosol. J. Aerosol. Sci. 30(1), 35-49] describes the experimentally found polymerization of C₂H₂ and HCN to form aerosol embryos, their growth and adherence to form various aerosols objects [Bar-Nun, A., Kleinfeld, I., Ganor, E., 1988. Shape and optical properties of aerosols formed by photolysis of C₂H₂, C₂H₄ and HCN. J. Geophys. Res. 93, 8383-8387]. These loose fractal objects describe well the findings of DISR on the Huygens probe [Tomasko, M.G., Bézard, B., Doose, L., Engel, S., Karkoschka, E., 2008. Measurements of methane absorption by the descent imager/spectral radiometer (DISR) during its descent through Titan's atmosphere. Planet. Space Sci., this issue, doi:10.1016/j.pss.2007]. These include (1) various regular objects of R=(0.035-0.064)×10⁻⁶ m, as compared with DISR's 0.05×10⁻⁶ m; (2) diverse low and high fractal structures composed of random combinations of various regular and irregular objects; (3) the number density of fractal particles is 6.9×10⁶ m⁻³ at Z=100 km, as compared with DISR's finding of 5.0×10⁶ m⁻³ at Z=80 km; (4) the number of structural units per higher fractals in the atmosphere at Z∼100 km is (2400-2700), as compared with DISR's 3000, and their size being of R=(5.4-6.4)×10⁻⁶ m will satisfy this value and (5) condensation of CH₄ on the highly fractal structures could begin at the altitude where thin methane clouds were observed, filling somewhat the new open fractal structures.     

Photochemical modeling of Titan's atmosphere

We have developed a new photochemical model of Titan's atmosphere which includes all the important compounds and reactions in spherical geometry from the surface to 1240 km. Compared to the previous model of Yung et al. (1984, Astrophys. J. Suppl. 55, 465-506), the most significant recent change in the reactions used is the updated methane photodissociation scheme (Mordaunt et al. 1993, J. Chem. Phys. 98(3), 2054-2065). Moreover, the transfer of the solar radiation in the atmosphere and the photolysis rates have been calculated by using a Monte Carlo code. Finally, the eddy diffusion coefficient profile is adjusted in order to fit the mean vertical distribution of HCN retrieved from millimeter groundbased observations of Tanguy et al. (1990, Icarus, 85, 43-57) using new values for the boundary flux of atomic nitrogen (Strobel et al. 1992, Icarus 100, 512-526). We have run the model in both steady-state and diurnal modes, with 62 speices involved in 249 reactions. There is little difference between diurnal and steady-state results. Overall our results are in a closer agreement with the abundances inferred from the Voyager infrared measurements at the equator than the Yung et al. results. We find that the catalytic scheme for H recombination invoked by Yung et al. only slightly improves the model results and we conclude that this scheme is not essential to fit observations.     

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.     

Polarization of continuum radiation in magnetic atmospheres

A numerical solution is presented for the problem of continuum radiative transfer in a magnetoactive medium. The continuum opacities are calculated in the presence of a strong magnetic field (H=10⁷ G) typical of magnetic white dwarfs. The L.T.E. pure absorption model is assumed for calculating the polarized radiation field emitted by a realistic model atmosphere in the plane parallel approximation. The wavelength dependence of the linear and circular polarizations are calculated for both uniform and dipole field configurations.     

Chemical sources of haze formation in Titan's atmosphere

A prominent feature of Titan's atmosphere is a thick haze region that acts as the end product of hydrocarbon and nitrile chemistry. Using a one-dimensional photochemical model, an investigation into the chemical mechanisms responsible for the formation of this haze region is conducted. The model derives profiles for Titan's atmospheric constituents that are consistent with observations. Included is an updated benzene profile that matches more closely with—recent ISO observations (Icarus 161 (2003) 383), replacing the profile given in the benzene study of Wilson et al. (J. Geophys. Res. 108 (2003) 5014). Using these profiles, pathways from polyynes, aromatics, and nitriles are considered, as well as possible copolymerization among the pathways. The model demonstrates that the growth of polycyclic aromatic hydrocarbons throughout the lower stratosphere plays an important role in furnishing the main haze layer, with nitriles playing a secondary role. The peak chemical production of haze layer ranges from 140 to 300 km peaking at an altitude of 220 km, with a production rate of 3.2×10⁻¹⁴ gcm⁻² s⁻¹. Possible mechanisms for polymerization and copolymerization and suggestions for further kinetic study are discussed, along with the implications for the distribution of haze in Titan's atmosphere.     

An investigation of Titan's aerosols using microwave analog measurements and radiative transfer modeling

A combination of laboratory experiments, theoretical modeling, and spacecraft observations is employed to characterize the aerosols in the atmosphere of Titan. The scattering properties of model aerosols were measured using the Microwave Analog Light Scattering Facility at the University of Florida and complemented with theoretical modeling of single scattering characteristics and radiative transfer in Titan's atmosphere. This study compares these modeling results with photopolarimetric observations made over a range of phase angles by the Pioneer 11 and Voyagers 1 and 2 spacecraft. Important results of this work include a survey of the scattering properties of different particle morphologies and compositions necessary to accurately interpret these observations without introducing non-physical assumptions about the particles or requiring additional free parameters to the radiative transfer models. Previous studies use calculation methods which, due to computing memory and processing time requirements, a priori exclude much of the parameter space that the microwave analog laboratory is ideal for exploring. The goal of the present work, to directly constrain aerosol physical characteristics, is addressed by studying in a consistent manner how a variety of particle morphologies and refractive indices affect the polarization and intensity reflected by Titan's atmosphere. Based on comparisons of model results to spacecraft observations, many model morphologies are excluded from further consideration. The most plausible physical particle models suggest that a combination of Rayleigh-like single particles and aggregates that are larger than those previously suggested and investigated [West, R.A., Smith, P.H., 1991. Evidence for aggregate particles in the atmospheres of Titan and Jupiter. Icarus 90, 330-333; Rannou, P., Cabane, M., Botet, R., Chassefière, E., 1997. A new interpretation of scattered light measurements at Titan's limb. J. Geophys. Res. 102, 10997-11013] provide the best fit to the existing data. Additional laboratory experiments and more refined modeling awaits the results of the new rich observational dataset from the Cassini/Huygens encounter with Titan.     

Large-scale electric fields in post-flare loops

As the electrical conductivity along the magnetic field in solar atmosphere is large, parallel electric fields have been neglected in most investigations. We will first demonstrate their importance for post-flare loops, and then introduce a model for them which takes into account the effect of parallel electric fields. The electric field calculated from the model is consistent with the electric field observed by Foukal et al. (1983).     

Atmospheres and spectra of strongly magnetized neutron stars

We construct atmosphere models for strongly magnetized neutron stars with surface fields     and effective temperatures     . The atmospheres directly determine the characteristics of thermal emission from isolated neutron stars, including radio pulsars, soft gamma-ray repeaters, and anomalous X-ray pulsars. In our models, the atmosphere is composed of pure hydrogen or helium and is assumed to be fully ionized. The radiative opacities include free–free absorption and scattering by both electrons and ions computed for the two photon polarization modes in the magnetized electron–ion plasma. Since the radiation emerges from deep layers in the atmosphere with     , plasma effects can significantly modify the photon opacities by changing the properties of the polarization modes. In the case where the magnetic field and the surface normal are parallel, we solve the full, angle-dependent, coupled radiative transfer equations for both polarization modes. We also construct atmosphere models for general field orientations based on the diffusion approximation of the transport equations and compare the results with models based on full radiative transport. In general, the emergent thermal radiation exhibits significant deviation from blackbody, with harder spectra at high energies. The spectra also show a broad feature     around the ion cyclotron resonance     , where Z and A are the atomic charge and atomic mass of the ion, respectively; this feature is particularly pronounced when     . Detection of the resonance feature would provide a direct measurement of the surface magnetic fields on magnetars.