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1.
Diffuse reflection and transmission coefficients in a plane parallel medium are calculated for a Rayleigh phase-function averaged over polarization and Rayleigh polarized phase-function. This is calculated by imbedding the finite medium into a semi-infinite scattering and absorbing medium. Numerical calculations for semi-infinite albedo are compared with Pomraning results. The albedos for finite medium are calculated via the imbedding equations which converge for large τ to the value of semi-infinite medium.  相似文献   

2.
Cassini 2.2-cm radar and radiometric observations of seven of Saturn's icy satellites yield properties that apparently are dominated by subsurface volume scattering and are similar to those of the icy Galilean satellites. Average radar albedos decrease in the order Enceladus/Tethys, Hyperion, Rhea, Dione, Iapetus, and Phoebe. This sequence most likely corresponds to increasing contamination of near-surface water ice, which is intrinsically very transparent at radio wavelengths. Plausible candidates for contaminants include ammonia, silicates, metallic oxides, and polar organics (ranging from nitriles like HCN to complex tholins). There is correlation of our targets' radar and optical albedos, probably due to variations in the concentration of optically dark contaminants in near-surface water ice and the resulting variable attenuation of the high-order multiple scattering responsible for high radar albedos. Our highest radar albedos, for Enceladus and Tethys, probably require that at least the uppermost one to several decimeters of the surface be extremely clean water ice regolith that is structurally complex (i.e., mature) enough for there to be high-order multiple scattering within it. At the other extreme, Phoebe has an asteroidal radar reflectivity that may be due to a combination of single and volume scattering. Iapetus' 2.2-cm radar albedo is dramatically higher on the optically bright trailing side than the optically dark leading side, whereas 13-cm results reported by Black et al. [Black, G.J., Campbell, D.B., Carter, L.M., Ostro, S.J., 2004. Science 304, 553] show hardly any hemispheric asymmetry and give a mean radar reflectivity several times lower than the reflectivity measured at 2.2 cm. These Iapetus results are understandable if ammonia is much less abundant on both sides within the upper one to several decimeters than at greater depths, and if the leading side's optically dark contaminant is present to depths of at least one to several decimeters. As argued by Lanzerotti et al. [Lanzerotti, L.J., Brown, W.L., Marcantonio, K.J., Johnson, R.E., 1984. Nature 312, 139-140], a combination of ion erosion and micrometeoroid gardening may have depleted ammonia from the surfaces of Saturn's icy satellites. Given the hypersensitivity of water ice's absorption length to ammonia concentration, an increase in ammonia with depth could allow efficient 2.2-cm scattering from within the top one to several decimeters while attenuating 13-cm echoes, which would require a six-fold thicker scattering layer. If so, we would expect each of the icy satellites' average radar albedos to be higher at 2.2 cm than at 13 cm, as is the case so far with Rhea [Black, G., Campbell, D., 2004. Bull. Am. Astron. Soc. 36, 1123] as well as Iapetus.  相似文献   

3.
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.  相似文献   

4.
The slowing-down Boltzmann equation for generalized boundary conditions is considered and transformed to one-speed equation in Laplace space. Exact relations between energy reflection and transmission coefficients for a problem with diffuse reflecting boundary conditions and the albedos for the problem with isotropic boundary conditions are obtained. The Galerkin method is used to calculate the energy reflection coefficient for a finite slab for different thicknesses at different mass ratiosA, target to projectile mass, at different synthetic-scattering kernels. The results for partial heat fluxes for isotropic and anisotropic-scattering dispersive medium are given. The results obtained for isotropic boundary conditions are compared well with the exact results.  相似文献   

5.
Exact relations for radiation heat flux at the boundaries of a slab with diffusely reflecting boundary conditions and internal source are obtained in terms of the reflection and transmission coefficients of a source free slab with isotropic boundary conditions. The integral equation defining the radiation heat flux contains explicitly the internal source. So, the particular solution for radiative transfer equation is not required. Available exact values for albedos give exact values of radiation heat flux. Padé approximant technique is used to obtain numerical values for homogenous media.  相似文献   

6.
Albedos for 57 asteroids were determined using diameters obtained from stellar occultations. For 18 objects, the occultation albedos were determined to accuracies better than 5%. The effect on the occultation albedo due to errors in the asteroid absolute magnitude is discussed and correlations between the occultation albedos and IRAS and polarimetric albedos are presented. The higher-quality occultation albedos presented here are suitable for calibrating albedos obtained by indirect methods.  相似文献   

7.
Some earlier statistical investigations of the reflection effect are repeated using a more precise theory. The conclusions of earlier workers are reversed: it is found that the albedos of earlytype binaries are broadly in agreement with the theory, but that those of cooler systems are substantially less than unity.Various hypotheses to account for this phenomenon are investigated. It is concluded that the observations verify a prediction by Rucinski: cool secondary components possess deep convective envelopes whose structure is altered by the incident radiation in such a way as to depress the radiation from the far interior of the reflecting star.  相似文献   

8.
J. Veverka 《Icarus》1973,20(3):304-310
Using the white light measurements of Knowles Middleton and Mungall (1952), the Minnaert constants k and B0 are derived for six types of snow surfaces for phase angles up to 80°. The conclusion is that snow is in general a quasi-Lambert scatterer (k = 1.04?1.35). Even in an extreme case of specular reflection (a “glazed rain crust”), k is less than 2 at these phase angles. The range in k and B0 suggested by these data are then used to estimate some fundamental photometric parameters of smooth snow-covered planets: geometric albedos, phase integrals, Bond albedos, and phase coefficients.  相似文献   

9.
G.J. Black  D.B. Campbell 《Icarus》2007,191(2):702-711
We have measured the bulk radar reflectance properties of the mid-size saturnian satellites Rhea, Dione, Tethys, and Enceladus with the Arecibo Observatory's 13 cm wavelength radar system during the 2004 through 2007 oppositions of the Saturn system. Comparing to the better studied icy Galilean satellites, we find that the total reflectivities of Rhea and Tethys are most similar to Ganymede while Dione is most similar to Callisto. Enceladus' reflectivity falls between those of Ganymede and Europa. The mean circular polarization ratios of the saturnian satellites range from ∼0.8 to 1.2, and are on average lower than those of the icy Galilean satellites at this wavelength although still larger than expected for single reflections off the surface. The ratio for the trailing hemisphere of Enceladus may be the exception with a value ?0.56. The 13 cm wavelength radar albedos and polarization ratios may be systematically lower than similar results from the Cassini orbiter's RADAR instrument at 2.2 cm wavelength [Ostro, S.J., and 19 colleagues, 2006. Icarus 183, 479-490]. Overall, these reflectivities and polarization properties, together with the shapes of the echo spectra, suggest subsurface multiple scattering to be the dominant reflection mechanism although operating less efficiently than on the large icy moons of Jupiter. All these saturnian moons and icy jovian moons are atmosphere-less, low temperature water ice surfaces, and any differences in radar properties may be indicative of differences in composition or the effects of various processes that modify the regolith structure. The degree of variation in radar properties with wavelength on each satellite may constrain the thickness and efficiency of the scattering layer.  相似文献   

10.
We review the current state of models for the optical and near‐infrared reflection spectra of exoplanetary atmospheres, with particular reference to the close‐orbiting giant planets that offer the best prospects for high‐resolution spectroscopic detection.We describe the main steps in the tomographic procedures that have been used in recent attempts to separate these faint signals from the direct spectra of the parent stars.We compare recent, deep upper limits on planetary albedos with model predictions, and discuss prospects for future attempts to detect and characterise the reflection, transmission and thermal emission spectra of these planets at optical and infrared wavelengths. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

11.
In this paper the Stardust disk-integrated phase curve at phase 47.2-134.6° of the Asteroid 5535 Annefrank, combined with groundbased observations (at phase 2.3-18.3°), are fit with Hapke’s photometric model. We confirm Newburn et al.’s (Newburn, R.L. et al. [2003]. J. Geophys. Res. 108 (E11), 5117. doi:10.1029/2003JE002106) observation that Annefrank exhibits a steep phase curve. This manifests itself in an unusually high fit surface roughness parameter of 49°. The single particle scattering albedo is 0.62, also high for an S-asteroid, while the fit phase function is more forward scattering than the typical S-asteroid being nearly isotropic with an asymmetry parameter of −0.09. The fit opposition surge width (h = 0.015) is typical of S-asteroids. However these fits assume a spherical shape to the asteroid. Li et al. (Li, J., A’Hearn, M.F., McFadden, L.A. [2004]. Icarus, 415-431) have shown that this assumption may lead to significant errors particularly at high phase angles leading to higher modeled single particle scattering albedos, macroscopic roughnesses and more forward scattering phase functions than actually exhibited. Our results confirm this finding—fitting only the data below 90° phase yields lower particle albedos (0.41) and roughnesses (20°) and more backscattering particles (−0.19) than the fit including the high phase angle data. Overall Annefrank appears to be on the bright side but otherwise is typical for an S-type asteroid suggesting that it may be a recent collisional fragment with a relatively immature surface which has had relatively little time to be weathered.  相似文献   

12.
Bruce Hapke 《Icarus》2002,157(2):523-534
A model published previously by the author that describes light scattering from particulate media is modified to include several improvements: (1) a better approximation to the Ambartsumian-Chandrasekhar H-functions that is especially important for particles with single scattering albedos close to 1.00, (2) increased accuracy for anisotropically scattering particles, and (3) incorporation of coherent backscattering. The goal of the original model of being analytic and mathematically tractable is preserved. No new parameters are introduced by the first and second modifications; however, the third unavoidably adds two new parameters: the amplitude and width of the coherent backscatter opposition effect. Several examples are given in which the results of calculations using the original and new models are compared with exact numerical computations.It is shown that a medium composed of complex particles that are large compared to the wavelength can have a coherent backscatter opposition effect (CBOE) that is broad enough to be readily observable. The CBOE multiplies the entire reflectance and not just the multiply scattered component, so that a low-albedo medium, such as lunar regolith, can have a strong CBOE.  相似文献   

13.
J.B. Murray 《Icarus》1975,25(3):397-404
Visual and photographic observations of the Galilean satellites of Jupiter made in September 1973 with the 108 cm reflector at Pic-du-Midi Observatory are presented. A method of estimating the contrasts and albedos of surface markings on the satellites during transit by comparing them with the adjacent surface of Jupiter is described. Results for Io, Europa, and Ganymede give albedo ranges of 0.28 to 0.67, 0.45 to 0.67, and 0.22 to 0.47, respectively. These are geometric albedos for a phase angle of 5°. The percentages of the disks covered by high albedos are consistent with the conclusions of previous workers regarding the fraction of exposed water ice on the surface.  相似文献   

14.
A time-sequential set of bolometric albedo maps for Mars has been constructed from Viking Infrared Thermal Mapper data. The maps provide global coverage in longitude for latitudes -60° to +60° at 1° by 1° spatial resolution. Individual maps are constructed under strict geometric constraints for a narrow range of Ls. The set of albedo maps spans a Martian year and includes maps before, during, and after the global dust storms of 1977. Transient brightenings associated with local dust storms or condensate clouds are apparent in some of the maps. During dust-free periods, bolometric albedo maps are generally similar to classical, visual albedo map of Mars. The distribution of bolometric surface albedos is bimodal with typical, clear-sky, Lambert albedos of 0.27 and 0.16 for bright and dark areas, respectively. Atmospheric effects strongly influence apparent surface albedos, especially for dark areas. Neither bright nor dark regions show measurable, long-term variations of bolometric albedos during clear periods.  相似文献   

15.
We present observations of thermal emission from fifteen transneptunian objects (TNOs) made using the Spitzer Space Telescope. Thirteen of the targets are members of the Classical population: six dynamically hot Classicals, five dynamically cold Classicals, and two dynamically cold inner Classical Kuiper belt objects (KBOs). We fit our observations using thermal models to determine the sizes and albedos of our targets finding that the cold Classical KBOs have distinctly higher visual albedos than the hot Classicals and other TNO dynamical classes. The cold Classicals are known to be distinct from other TNOs in terms of their color distribution, size distribution, and binarity fraction. The Classical objects in our sample all have red colors yet they show a diversity of albedos which suggests that there is not a simple relationship between albedo and color. As a consequence of high albedos, the mass estimate of the cold Classical Kuiper belt is reduced from approximately 0.01 M⊕ to approximately 0.001 M⊕. Our results also increase significantly the sample of small Classical KBOs with known albedos and sizes from 21 to 32 such objects.  相似文献   

16.
Cassini radar tracks on Saturn’s icy satellites through the end of the Prime Mission in 2008 have increased the number of radar albedo estimates from 10 (Ostro et al., 2006) to 73. The measurements sample diverse subradar locations (and for Dione, Rhea, and Iapetus almost always use beamwidths less than half the target angular diameters), thereby constraining the satellites’ global radar albedo distributions. The echoes result predominantly from volume scattering, and their strength is thus strongly sensitive to ice purity and regolith maturity. The combination of the Cassini data set and Arecibo 13-cm observations of Enceladus, Tethys, Dione, Rhea (Black et al., 2007), and Iapetus (Black et al., 2004) discloses an unexpectedly complex pattern of 13-to-2-cm wavelength dependence. The 13-cm albedos are generally smaller than 2-cm albedos and lack the correlation seen between 2-cm and optical geometric albedos. Enceladus and Iapetus are the most interesting cases. We infer from hemispheric albedo variations that the E-ring has a prominent effect on the 13-cm radar “lightcurve”. The uppermost trailing-side regolith is too fresh for meteoroid bombardment to have developed larger-scale heterogeneities that would be necessary to elevate the 13-cm radar albedo, whereas all of Enceladus is clean and mature enough for the 2-cm albedo to be uniformly high. For, Iapetus, the 2-cm albedo is strongly correlated with optical albedo: low for the optically dark, leading-side material and high for the optically bright, trailing-side material. However, Iapetus’ 13-cm albedo values show no significant albedo dichotomy and are several times lower than 2-cm values, being indistinguishable from the weighted mean of 13-cm albedos for main-belt asteroids, 0.15 ± 0.10. The leading side’s optically dark contaminant must be present to depths of at least one to several decimeters, so 2-cm albedos can mimic the optical dichotomy; however, it does not have to extend any deeper than that. The fact that both hemispheres of Iapetus look Asteroid-like at 13 cm means that coherent backscattering itself is not nearly as effective as it is at 2 cm. Since Iapetus’ entire surface is mature regolith, the wavelength dependence must involve composition, not structure. Either the composition is a function of depth everywhere (with electrical loss much greater at depths greater than a decimeter or two), or the intrinsic electrical loss of some pervasive constituent is much higher at 13 cm than at 2 cm. Ammonia is a candidate for such a contaminant. If ammonia’s electrical properties do not depend on frequency, and if ammonia is globally much less abundant within the upper one or two decimeters than at greater depths, then coherent backscattering would effectively be shut down at 13 cm, explaining the Asteroid-like 13-cm albedo.  相似文献   

17.
Anthony Mallama 《Icarus》2009,204(1):11-499
The empirically derived phase curves of terrestrial planets strongly distinguish between airless Mercury, cloud-covered Venus, and the intermediate case of Mars. The function for Mercury is steeply peaked near phase angle zero due to powerful backscattering from its surface, while that for Venus has 100 times less contrast and exhibits a brightness excess near 170° due to Mie scattering from droplets in the atmosphere. The phase curve of Mars falls between those of Mercury and Venus, and there are variations in luminosity due to the planet’s rotation, seasons, and atmospheric states. The phase function and geometric albedo of the Earth are estimated from published albedos values. The curves for Mercury, Venus and Mars are compared to that of the Earth as well as theoretical phase functions for giant planets. The parameters of these different phase functions can be used to characterize exoplanets.  相似文献   

18.
Radar observations of the Galilean satellites, made in late 1976 using the 12.6-cm radar system of the Arecibo Observatory, have yielded mean geometric albedos of 0.04 ± , 0.69 ± 0.17, 0.37 ± 0.09, and 0.15 ± 0.04, for Io, Europa, Ganymede, and Callisto, respectively. The albedo for Io is about 40% smaller than that obtained approximately a year earlier, while the albedos for the outer three satellites average about 70% larger than the values previously reported for late 1975, raising the possibility of temporal variation. Very little dependence on orbital phase is noted; however, some regional scattering inhomogeneities are seen on the outer three satellites. For Europa, Ganymede, and Callisto, the ratios of the echo received in one mode of circular polarization to that received in the other were: 1.61 ± 0.20 1.48 ± 0.27, and 1.24 ± 0.19, respectively, with the dominant component having the same sence of circularity as that transmitted. This behavior has not previously been encountered in radar studies of solar system objects, whereas the corresponding observations with linear polarization are “normal.” Radii determined from the 1976 radar data for Europa and Ganymede are: 1530 ± 30 and 2670 ± 50 km, in fair agreement with the results from the 1975 radar observations and the best recent optical determinations. Doppler shifts of the radar echoes, useful for the improvement of the orbits of Jupiter and some of the Galilean satellites, are given for 12 nights in 1976 and 10 nights in 1975.  相似文献   

19.
A method of analysis is presented for solving the radiative transfer problem in an absorbing, emitting, inhomogeneous, and anisotropically scattering plane-parallel medium with specular and diffuse reflecting boundaries and internal source (problem 1). Exact relations for the radiation heat flux at the boundaries of problem 1 are obtained in terms of the radiation density and albedos of the corresponding source-free medium with specular reflecting boundaries (problem 2). Two coupled integral equations for the radiation density and the second moment of the radiation intensity for problem 2 with Rayleigh phase functions are obtained. The Galerkin method is used to solve these equations. Albedos of problem 2 are compared with theF n method. Numerical results for radiation heat fluxes at the boundaries of problem 1 are tabulated for different forms of the internal source.  相似文献   

20.
We present the results of thermal-infrared observations of 20 near-Earth asteroids (NEAs) obtained in the period March 2000-February 2002 with the 10-m Keck-I telescope on Mauna Kea, Hawaii. The measured fluxes have been fitted with thermal-model emission continua to determine sizes and albedos. This work increases the number of NEAs having measured albedos by 35%. The spread of albedos derived is very large (pv=0.02−0.55); the mean value is 0.25, which is much higher than that of observed main-belt asteroids. In most cases the albedos are in the ranges expected for the spectral types, although some exceptions are evident. Our results are consistent with a trend of increasing albedo with decreasing size for S-type asteroids with diameters below 20 km. A number of objects are found to have unexpectedly low apparent color temperatures, which may reflect unusual thermal properties. However, the results from our limited sample suggest that high thermal-inertia, regolith-free objects may be uncommon, even amongst NEAs with diameters of less than 1 km. We discuss the significance of our results in the light of information on these NEAs taken from the literature and the uncertainties inherent in applying thermal models to near-Earth asteroids.  相似文献   

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