A multilayer model for thermal infrared emission of Saturn’s rings II: Albedo, spins, and vertical mixing of ring particles inferred from Cassini CIRS

Since the Saturn orbit insertion of the Cassini spacecraft in mid-2004, the Cassini composite infrared spectrometer (CIRS) measured temperatures of Saturn’s main rings at various observational geometries. In the present study, we apply our new thermal model (Morishima, R., Salo, H., Ohtsuki, K. [2009]. Icarus 201, 634-654) for fitting to the early phase Cassini data (Spilker, L.J., and 11 colleagues [2006]. Planet. Space Sci. 54, 1167-1176). Our model is based on classical radiative transfer and takes into account the heat transport due to particle motion in the azimuthal and vertical directions. The model assumes a bimodal size distribution consisting of small fast rotators and large slow rotators. We estimated the bolometric Bond albedo, A_V, the fraction of fast rotators in cross section, f_fast, and the thermal inertia, Γ, by the data fitting at every radius from the inner C ring to the outer A ring. The albedo A_V is 0.1-0.4, 0.5-0.7, 0.4, 0.5 for the C ring, the B ring, the Cassini division, and the A ring, respectively. The fraction f_fast depends on the ratio of scale height of fast rotators to that of slow rotators, h_r. When h_r = 1, f_fast is roughly half for the entire rings, except for the A ring, where f_fast increases from 0.5 to 0.9 with increasing saturnocentric radius. When h_r increases from 1 to 3, f_fast decreases by 0.2-0.4 for the B and A rings while no change in f_fast is seen for the optically thin C ring and Cassini division. The large f_fast seen in the outer A ring probably indicates that a large number of small particles detach from large particles in high velocity collisions due to satellite perturbations or self-gravity wakes. The thermal inertia, Γ, is constrained from the efficiency of the vertical heat transport due to particle motion between the lit and unlit faces, and is coupled with the type of vertical motion. We found that in most regions, except for the mid B ring, sinusoidal vertical motion without bouncing is more reasonable than cycloidal motion assuming bouncing at the midplane, because the latter motion gives too large Γ as compared with previous estimations. For the mid B ring, where the optical depth is highest in Saturn’s rings, cycloidal vertical motion is more reasonable than sinusoidal vertical motion which gives too small Γ.     

A multilayer model for thermal infrared emission of Saturn’s rings. III: Thermal inertia inferred from Cassini CIRS

The thermal inertia values of Saturn’s main rings (the A, B, and C rings and the Cassini division) are derived by applying our thermal model to azimuthally scanned spectra taken by the Cassini Composite Infrared Spectrometer (CIRS). Model fits show the thermal inertia of ring particles to be 16, 13, 20, and 11 J m⁻² K⁻¹ s^−1/2 for the A, B, and C rings, and the Cassini division, respectively. However, there are systematic deviations between modeled and observed temperatures in Saturn’s shadow depending on solar phase angle, and these deviations indicate that the apparent thermal inertia increases with solar phase angle. This dependence is likely to be explained if large slowly spinning particles have lower thermal inertia values than those for small fast spinning particles because the thermal emission of slow rotators is relatively stronger than that of fast rotators at low phase and vise versa. Additional parameter fits, which assume that slow and fast rotators have different thermal inertia values, show the derived thermal inertia values of slow (fast) rotators to be 8 (77), 8 (27), 9 (34), 5 (55) J m⁻² K⁻¹ s^−1/2 for the A, B, and C rings, and the Cassini division, respectively. The values for fast rotators are still much smaller than those for solid ice with no porosity. Thus, fast rotators are likely to have surface regolith layers, but these may not be as fluffy as those for slow rotators, probably because the capability of holding regolith particles is limited for fast rotators due to the strong centrifugal force on surfaces of fast rotators. Other additional parameter fits, in which radii of fast rotators are varied, indicate that particles less than ∼1 cm should not occupy more than roughly a half of the cross section for the A, B, and C rings.     

Saturn's rings: 3-mm low-inclination observations and derived properties

Recent 3-mm observations of Saturn at low ring inclinations are combined with previous observations of E. E. Epstein, M. A. Janssen, J. N. Cuzzi, W. G. Fogarty, and J. Mottmann (Icarus41, 103–118) to determine a much more precise brightness temperature for Saturn's rings. Allowing for uncertainties in the optical depth and uniformity of the A and B rings and for ambiguities due to the C ring, but assuming the ring brightness to remain approximately constant with inclination, a mean brightness temperature for the A and B rings of 17 ± 4°K was determined. The portion of this brightness attributed to ring particle thermal emission is 11 ± 5°K. The disk temperature of Saturn without the rings would be 156 ± 6°K, relative to B. L. Ulich, J. H. Davis, P. J. Rhodes, and J. M. Hollis' (1980, IEEE Trans. Antennas Propag.AP-28, 367–376) absolutely calibrated disk temperature for Jupiter. Assuming that the ring particles are pure water ice, a simple slab emission model leads to an estimate of typical particle sizes of ≈0.3 m. A multiple-scattering model gives a ring particle effective isotropic single-scattering albedo of 0.85 ± 0.05. This albedo has been compared with theoretical Mie calculations of average albedo for various combinations of particle size distribution and refractive indices. If the maximum particle radius (≈5 m) deduced from Voyager bistatic radar observations (E. A. Marouf, G. L. Tyler, H. A. Zebker, V. R. Eshleman, 1983, Icarus54, 189–211) is correct, our results indicate either (a) a particle distribution between 1 cm and several meters radius of the form r^?s with 3.3 ? s ? 3.6, or (b) a material absorption coefficient between 3 and 10 times lower than that of pure water ice Ih at 85°K, or both. Merely decreasing the density of the ice Ih particles by increasing their porosity will not produce the observed particle albedo. The low ring brightness temperature allows an upper limit on the ring particle silicate content of ≈10% by mass if the rocky material is uniformly distributed; however, there could be considerably more silicate material if it is segregated from the icy material.     

Radar imaging of Saturn's rings

We present delay-Doppler images of Saturn's rings based on radar observations made at Arecibo Observatory between 1999 and 2003, at a wavelength of 12.6 cm and at ring opening angles of 20.1°?|B|?26.7°. The average radar cross-section of the A ring is ∼77% relative to that of the B ring, while a stringent upper limit of 3% is placed on the cross-section of the C ring and 9% on that of the Cassini Division. These results are consistent with those obtained by Ostro et al. [1982, Icarus 49, 367-381] from radar observations at |B|=21.4°, but provide higher resolution maps of the rings' reflectivity profile. The average cross-section of the A and B rings, normalized by their projected unblocked area, is found to have decreased from 1.25±0.31 to 0.74±0.19 as the rings have opened up, while the circular polarization ratio has increased from 0.64±0.06 to 0.77±0.06. The steep decrease in cross-section is at variance with previous radar measurements [Ostro et al., 1980, Icarus 41, 381-388], and neither this nor the polarization variations are easily understood within the framework of either classical, many-particle-thick or monolayer ring models. One possible explanation involves vertical size segregation in the rings, whereby observations at larger elevation angles which see deeper into the rings preferentially see the larger particles concentrated near the rings' mid-plane. These larger particles may be less reflective and/or rougher and thus more depolarizing than the smaller ones. Images from all four years show a strong m=2 azimuthal asymmetry in the reflectivity of the A ring, with an amplitude of ±20% and minima at longitudes of 67±4° and 247±4° from the sub-Earth point. We attribute the asymmetry to the presence of gravitational wakes in the A ring as invoked by Colombo et al. [1976, Nature 264, 344-345] to explain the similar asymmetry long seen at optical wavelengths. A simple radiative transfer model suggests that the enhancement of the azimuthal asymmetry in the radar images compared with that seen at optical wavelengths is due to the forward-scattering behavior of icy ring particles at decimeter wavelengths. A much weaker azimuthal asymmetry with a similar orientation may be present in the B ring.     

Spin rate distribution of small asteroids

The spin rate distribution of main belt/Mars crossing (MB/MC) asteroids with diameters 3-15 km is uniform in the range from f=1 to 9.5 d⁻¹, and there is an excess of slow rotators with f<1 d⁻¹. The observed distribution appears to be controlled by the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. The magnitude of the excess of slow rotators is related to the residence time of slowed down asteroids in the excess and the rate of spin rate change outside the excess. We estimated a median YORP spin rate change of ≈0.022 d⁻¹/Myr for asteroids in our sample (i.e., a median time in which the spin rate changes by 1 d⁻¹ is ≈45 Myr), thus the residence time of slowed down asteroids in the excess is ≈110 Myr. The spin rate distribution of near-Earth asteroids (NEAs) with sizes in the range 0.2-3 km (∼5 times smaller in median diameter than the MB/MC asteroids sample) shows a similar excess of slow rotators, but there is also a concentration of NEAs at fast spin rates with f=9-10 d⁻¹. The concentration at fast spin rates is correlated with a narrower distribution of spin rates of primaries of binary systems among NEAs; the difference may be due to the apparently more evolved population of binaries among MB/MC asteroids.     

Simulations of dense planetary rings: IV. Spinning self-gravitating particles with size distribution

Previous self-gravitating simulations of dense planetary rings are extended to include particle spins. Both identical particles as well as systems with a modest range of particle sizes are examined. For a ring of identical particles, we find that mutual impact velocity is always close to the escape velocity of the particles, even if the total rms velocity dispersion of the system is much larger, due to collective motions associated to wakes induced by near-gravitational instability or by viscous overstability. As a result, the spin velocity (i.e., the product of the particle radius and the spin frequency) maintained by mutual impacts is also of the order of the escape velocity, provided that friction is significant. For the size distribution case, smaller particles have larger impact velocities and thus larger spin velocities, particularly in optically thick rings, since small particles move rather freely between wakes. Nevertheless, the maximum ratio of spin velocities between the smallest and largest particles, as well as the ratio for translational velocities, stays below about 5 regardless of the width of the size distribution. Particle spin state is one of the important factors affecting the temperature difference between the lit and unlit face of Saturn's rings. Our results suggest that, to good accuracy, the spin frequency is inversely proportional to the particle size. Therefore, the mixing ratio of fast rotators to slow rotators on the scale of the thermal relaxation time increases with the width of the particle size distribution. This will offer means to constrain the particle size distribution with the systematic thermal infrared observations carried by the Cassini probe.     

Infrared radiometry of the rings of Saturn

Broad-band radiometry with a spatial resolution of 5 arc sec is presented of Saturn and its rings. The brightness temperature of the B ring is 96 ± 3°K at 20 μm and 91 ± 3°K at 11 μm. These values constrain the bolometric Bond albedo of the ring particles to be less than 0.6, thus requiring a phase integral of less than unity. From differences in the thermal emission of the ansae, I suggest that the leading side of the particles has higher albedo than the trailing side. A measured drop in temperature of the B ring following eclipse of 2.0 ± 0.5°K is consistent with radii for the ring particles of 2 cm or larger.     

Infrared brightness temperature of Saturn's rings based on the inhomogeneous multilayer assumption

Models of Saturn's rings based on the classical multilayer assumption have been studied in the infrared. Thermal energy balance of Saturn's rings is treated rigorously by solving the infrared radiative transfer equations. It was found that a homogeneous multilayer model is incompatible with the observed infrared brightness variation of the A and B rings, although it can fit that of the C ring. The alternative inhomogeneous multilayer model with dark particles within a bright haze of small icy particles is presented in order to satisfy the available infrared data of the A, B, and C rings. The results based on the inhomogeneous multilayer model may be summarized as follows: The observed infrared brightness data of the three rings are explained in terms of the different optical thickness without having significant differences in the ring-particle properties, such as albedo, spin rate, and sizes. But each ring contains a different amount of bright haze particles and their concentration within the rings depends on whether or not dark particles emit radiation mostly from one hemisphere (slow rotator and/or low thermal inertia). If a dark particle is an isothermal radiator, the possible ranges of A₁ and A₂ for all three rings are given by 0.9 ? A₁ ? 0.95 and 0.0 ? A₂ ? 0.15, where A₁ and A₂ are the bolometric bond albedos of a bright haze and a dark particle, respectively. The possible ranges of the optical thickness ratio X of the dark particle layer to the total ring layer for the rings A, B, and C are given by 0.65 ? X ? 0.75, 0.8 ? X ? 0.9, and 0.8 ? X ? 1.0, respectively. If a dark particle is a slow rotator, we obtain 0.9 ? A₁ ? 0.95 and 0.0 ? A₂ ? 0.4 for all three rings. The ranges of X for the rings A, B, and C are given by 0.35 ? X ? 0.7, 0.65 ? X ? 0.9, and 0.35 ? X ? 1.0, respectively. In this paper, for the first time, a consistent model is presented which is applicable to all three rings from the multilayer point of view.     

Saturn's rings: 3-mm observations and derived properties

We have used 3-mm Saturn observations, obtained from 1965 through 1977 and with Jupiter as a reference, to derive a ring brightness temperature of 18 ± 8°K. Thebrightness temperature of the disk of Saturn is 156 ± 9° K. Part of the ring brightness (≈62K) may be accounted for as disk emission which is scattered from the rings; the remainder (12 ± 8° K we attributed to ring particle thermal emission. Because this thermal component brightness temperatures is so much less than the particle physical temperature, limits are placed on the mean size and composition of the ring particles. In particular, as found by others, the particles cannot be rocky, but must be either metallic or composed of extremely low-loss dielectric material such as water ice. If the particles are pure water ice, for example, then a simple slab model and a multiple-scattering model both give upper limits to the particle sizes of ≈ 1 m, a value three times smaller than previously available. The multiple-scattering model gives a particle single-scattering albedo at 3 mm of 0.83±0.13.     

Saturn's rings: Infrared brightness variation with solar elevation

The variation in infrared equilibrium brightness temperature of Saturn's A, B, and C rings is modeled as a function of solar elevation B′ with respect to the ring plane. The basic model includes estimates of minimum and maximum interparticle shadowing in a monolayer approximation. Simple laboratory observations of random particle distributions at various illumination angles provide more realistic shadowing functions. Radiation balance calculations yield the physical (kinetic) temperature of particles in equilibrium with radiation from the Sun, Saturn, and neighboring particles. Infrared brightness temperatures as a function of B′ are then computed and compared to the available 20-μm data (Pioneer results are also briefly discussed). The A and B rings are well modeled by an optically thick monolayer, or equivalently, a flat sheet, radiating from one side only. This points to a temperature contrast between the two sides, possibly due to particles with low thermal inertia. Other existing models for the B ring are discussed. The good fit for the monolayer model does not rule out the possibility that the A and B rings are many particles thick. It could well be that a multilayer ring produces an infrared behavior (as a function of tilt angle) similar to that of a monolayer. The C ring brightness increases as B′ decreases. This contrast in behavior can be understood simply in terms of the low C ring optical depth and small amount of interparticle shadowing. High-albedo particles (A?0.5) can fit the C ring infrared data if they radiate mostly from one hemisphere due to slow rotation or low thermal inertia (or both). Alternatively, particles isothermal over their surface (owing to a rapid spin, high inertia, or small size), and significantly darker (A?0.3) than the A and B ring particles, can produce a similar brightness variation with ring inclination. In any case, the C ring particles have significantly hotter physical temperatures than the particles in the A and B rings, whether or not the rings form a monolayer.     

Brightness of Saturn's rings with decreasing solar elevation

Early ground-based and spacecraft observations suggested that the temperature of Saturn's main rings (A, B and C) varied with the solar elevation angle, B^′. Data from the composite infrared spectrometer (CIRS) on board Cassini, which has been in orbit around Saturn for more than five years, confirm this variation and have been used to derive the temperature of the main rings from a wide variety of geometries while B^′ varied from near −24^° to 0^° (Saturn's equinox).Still, an unresolved issue in fully explaining this variation relates to how the ring particles are organized and whether even a simple mono-layer or multi-layer approximation describes this best. We present a set of temperature data of the main rings of Saturn that cover the ∼23^°—range of B^′ angles obtained with CIRS at low (α∼30^°) and high (α≥120^°) phase angles. We focus on particular regions of each ring with a radial extent on their lit and unlit sides. In this broad range of B^′, the data show that the A, B and C rings’ temperatures vary as much as 29-38, 22-34 and 18-23 K, respectively. Interestingly the unlit sides of the rings show important temperature variations with the decrease of B^′ as well. We introduce a simple analytical model based on the well known Froidevaux monolayer approximation and use the ring particles’ albedo as the only free parameter in order to fit and analyze this data and estimate the ring particle's albedo. The model considers that every particle of the ring behaves as a black body and warms up due to the direct energy coming from the Sun as well as the solar energy reflected from the atmosphere of Saturn and on its neighboring particles. Two types of shadowing functions are used. One analytical that is used in the latter model in the case of the three rings and another, numerical, that is applied in the case of the C ring alone. The model lit side albedo values at low phase are 0.59, 0.50 and 0.35-0.38 for the A, B and C rings, respectively.     

Cassini thermal observations of Saturn's main rings: Implications for particle rotation and vertical mixing

In late 2004 and 2005 the Cassini composite infrared spectrometer (CIRS) obtained spatially resolved thermal infrared radial scans of Saturn's main rings (A, B and C, and Cassini Division) that show ring temperatures decreasing with increasing solar phase angle, α, on both the lit and unlit faces of the ring plane. These temperature differences suggest that Saturn's main rings include a population of ring particles that spin slowly, with a spin period greater than 3.6 h, given their low thermal inertia. The A ring shows the smallest temperature variation with α, and this variation decreases with distance from the planet. This suggests an increasing number of smaller, and/or more rapidly rotating ring particles with more uniform temperatures, resulting perhaps from stirring by the density waves in the outer A ring and/or self-gravity wakes.The temperatures of the A and B rings are correlated with their optical depth, τ, when viewed from the lit face, and anti-correlated when viewed from the unlit face. On the unlit face of the B ring, not only do the lowest temperatures correlate with the largest τ, these temperatures are also the same at both low and high α, suggesting that little sunlight is penetrating these regions.The temperature differential from the lit to the unlit side of the rings is a strong, nearly linear, function of optical depth. This is consistent with the expectation that little sunlight penetrates to the dark side of the densest rings, but also suggests that little vertical mixing of ring particles is taking place in the A and B rings.     

Five-color photometry of Saturn and its rings

Analysis of 206 high-quality plates from three recent apparitions taken in five colors has yielded several photometric parameters for Saturn and its A and B rings. Phase curves and geometric albedos are derived for two regions of Saturn and for each ring. The phase coefficients of the rings are found to be independent of the ring-plane inclination angle. A comparison of the phase curves shows that the particles of ring A exhibit a larger phase coefficient than do those of ring B. When examined with a multiple-scattering model using Henyey-Greenstein phase functions, the observations of the ring tilt effect indicate that the particles of ring A may also have lower single-scattering and geometric albedos. The color dependence of the geometric albedo of the particles in ring B is shown to be very similar to that of Europa (J II). We find for ring A an optical thickness of 0.50 (0.45 ≤ τ_A ≤ 0.57) and for the Cassini division, 0.018 ± 0.004.     

Saturn's F Ring: Kinematics and Particle Sizes from Stellar Occultation Studies

The occultation of GSC5249-01240 by Saturn's rings was observed in a spectrally resolved mode using the Faint Object Spectrograph on the Hubble Space Telescope. By combining these data with other occultation data, we have determined the inclination of the F ring to be 0.0065±0.0014 deg. Our inclined F ring orbit model explains an abrupt decrease in flux at the west ansa of the ring that was observed during the November 1995 ring-plane crossing as well as the nondetection of 1995 S5 during one set of observations in November 1995. The F ring's equivalent depth is found to have no significant dependence on wavelength between 0.27 and 0.74 μm, indicating the presence of a population of ring particles larger in size than ∼10 μm. This contrasts with the results from a previous analysis of Voyager images at various phase angles, in which the particles were determined to be predominantly submicron in size. The difference may be due to temporal or longitudinal variability within the ring.     

Near-infrared adaptive optics imaging of the satellites and individual rings of Uranus

We present the first Earth-based images of several of the individual faint rings of Uranus, as observed with the adaptive optics system on the W.M. Keck II telescope on four consecutive days in October 2003. We derive reflectivities based on multiple measurements of 8 minor moons of Uranus as well as Ariel and Miranda in filters centered at wavelengths of 1.25(J), 1.63(H), and 2.1(Kp) μm. These observations have a phase angle of 1.84°-1.96°. We find that the small satellites are somewhat less bright than in observations made by the HST at smaller phase angles, confirming an opposition surge effect. We calculate albedoes for the ring groups and for each ring separately. We find that the ε ring particles, as well as the particles in the three other ring groups, have albedoes near 0.043 at these phase angles. The equivalent depths of some of the individual rings are different than predicted based upon ring widths from occultation measurements (assuming a constant particle ring brightness); in particular the γ ring is fainter and the η ring brighter than expected. Our results indicate that q, the ratio of ε ring intensity at apoapse vs. periapse, is close to 3.2±0.16. This agrees well with a model that has a filling factor for the ε ring of 0.06 (Karkoschka, 2001, Icarus 151, 78-83). We also determine values of the north to south brightness ratio for the individual rings and find that in most cases they are close to unity.     

Influence of the YORP effect on rotation rates of near‐Earth asteroids

The distribution of near‐Earth asteroid (NEA) rotation rates differs considerably from the similar distribution of Main Belt asteroids (MBAs) by the presence of excesses of fast and slow rotators, which are not observed or not so prominent in the distribution for MBAs. Among possible reasons for the difference, there can be influence of solar radiation on spin rate of small NEAs, the so‐called “YORP effect,” which appears due to reflection, absorption, and IR re‐emission of the sunlight by an irregularly shaped rotating asteroid. It is known that the YORP‐effect action strongly depends on the amount of solar energy obtained by the body (insolation), its size, and albedo. The analysis of observation data has shown that: (1) the mean diameter of NEAs decreases from the middle of the distribution to its ends, that is, the excesses of slow rotators (ω ≤ 2 rev day^?1) and fast rotators (ω ≥ 8 rev day^?1) are composed of smaller NEAs than in the middle of the distribution; (2) NEAs of both excesses are in the orbits where their insolation is about 8–10% larger than that of NEAs in the middle of the distribution; and (3) the objects in both excesses have a little lower albedo on average than that of objects in the middle of the distribution. All these results qualitatively agree well with the YORP‐effect action and may be considered as independent arguments in favor of it.     

A Study of Saturn's Ring Phase Curves from HST Observations

Solar phase curves between 0.3° and 6.0° and color ratios at wavelengths λ=0.336 μm and λ=0.555 μm for Saturn's rings are presented using recent Hubble Space Telescope observations. We test the hypothesis that the phase reddening of the rings is less due to collective properties of the ring particles than to the individual properties of the ring particles. We use a modified Drossart model, the Hapke model, and the Shkuratov model to model reddening by either intraparticle shadow-hiding on fractal and normal surfaces, multiple scattering, or some combination. The modified Drossart model (including only shadowing) failed to reproduce the data. The Hapke model gives fair fits, except for the color ratios. A detailed study of the opposition effect suggests that coherent backscattering is the principal cause of the opposition surge at very small phase angles. The shape of the phase curve and color ratios of each main ring regions are accurately represented by the Shkuratov model, which includes both a shadow-hiding effect and coherent backscatter enhancement. Our analysis demonstrates that in terms of particle roughness, the C ring particles are comparable to the Moon, but the Cassini division and especially the A and B ring particles are significantly rougher, suggesting lumpy particles such as often seen in models. Another conspicuous difference between ring regions is in the effective size d of regolith grains (d∼λ for the C ring particles, d∼1-10 μm for the other rings).     

Thermal response of Saturn's ring particles during and after eclipse

We present infrared (20 μm) observations of Saturn's rings for a solar elevation angle of 10° and phase angle of 6°. Scans across the rings yield information about the cooling of particles during eclipse and the subsequent heating along their orbits. All three rings exhibit significant cooling during eclipse, as well as a 20-μm brightness asymmetry between east and west ansae, the largest asymmetry occuring in the C ring (the brightest ring). The eclipse cooling is a simple and adequate explanation for 20-μm brightness asymmetries between the ansae of Saturn's rings. The relatively large C ring asymmetry is thought to be primarily due to the short travel time of the particles in that ring from eclipse exit to east ansa. We compare the B ring data to the theoretical models of H.H. Aumann and H.H. Kieffer (1973, Astrophys. J.186, 305–311) in order to set constraints on the average particle size and thermal inertia. The rather rapid heating after exit from eclipse points to low-conductivity-particle surfaces, similar to the water frost surfaces of Galilean satellites. If the surface conductivity is indeed low, one cannot determine an upper limit for the particle size through such infrared observations, since only the uppermost millimeters experience a thermal response during eclipse. However, based on these infrared data alone, it is clear that particles of radius equal to a few millimeters or less cannot occupy a significant fraction of the ring surface area, because-regardless of thermal inertia-their thermal response is much faster than observed.     

A survey of Karin cluster asteroids with the Spitzer Space Telescope

The Karin cluster is one of the youngest known families of main-belt asteroids, dating back to a collisional event only 5.8±0.2 Myr ago. Using the Spitzer Space Telescope we have photometrically sampled the thermal continua (3.5-22 μm) of 17 Karin cluster asteroids of different sizes, down to the smallest members discovered so far, in order to make the first direct measurements of their sizes and albedos and study the physical properties of their surfaces. Our targets are also amongst the smallest main-belt asteroids observed to date in the mid-infrared. The derived diameters range from 17.3 km for 832 Karin to 1.5 km for 75176, with typical uncertainties of 10%. The mean albedo is pv=0.215±0.015, compared to 0.20±0.07 for 832 Karin itself (for H=11.2±0.3), consistent with the view that the Karin asteroids are closely related physically as well as dynamically. The albedo distribution (0.12?pv?0.32) is consistent with the range associated with S-type asteroids but the variation from one object to another appears to be significant. Contrary to the case for near-Earth asteroids, our data show no evidence of an albedo dependence on size. However, the mean albedo is lower than expected for young, fresh “S-type” surfaces, suggesting that space weathering can darken main-belt asteroid surfaces on very short timescales. Our data are also suggestive of a connection between surface roughness and albedo, which may reflect rejuvenation of weathered surfaces by impact gardening. While the available data allow only estimates of lower limits for thermal inertia, we find no evidence for the relatively high values of thermal inertia reported for some similarly sized near-Earth asteroids. Our results constitute the first observational confirmation of the legitimacy of assumptions made in recent modeling of the formation of the Karin cluster via a single catastrophic collision 5.8±0.2 Myr ago.     

Photometric analysis and disk-resolved thermal modeling of Comet 19P/Borrelly from Deep Space 1 data

Images returned from the Deep Space 1 (DS-1) spacecraft during its encounter with Comet 19P/Borrelly are used to study its disk-integrated and disk-resolved photometry and its thermal properties. A disk-integrated phase function was constructed from a combination of DS-1 images and ground-based observations, giving a geometric albedo of 0.072±0.020 and a phase slope of 0.043 mag deg⁻¹. The shape model of Borrelly [Kirk, R.L., Howington-Kraus, E., Soderblom, L.A., Giese, B., Oberst, J., 2004a. Icarus 167, 54-69] and the ephemerides of DS-1 were used to analyze the disk-resolved photometric data with Hapke's theoretical model. It was found that the surface of Borrelly displays large photometric heterogeneities in its photometric parameters. The single-scattering albedo, w, varies by a factor of 2.5 with an average of 0.057±0.009; the asymmetry factor, g, ranges from almost isotropic (−0.1) to strongly backscattering (−0.7) with an average of −0.43±0.07; the roughness parameter, , is less than 35° for most parts of surface but ranges up to 55° in some areas. Its average is 22°±5°. The observed 1-D temperature profile is modeled well by the standard thermal model (STM) for inactive regions and is found to be consistent with a very low thermal inertia. Water sublimation in the source region of the fan jet is observed to decrease the surface temperature from the STM predictions by 20-40 K. The source areas of two collimated jets could not be determined from either photometric model or thermal model. It is evident that the fan jet activity occurring on Borrelly's surface can be correlated to areas of relatively high albedo, weak backscattering, and high roughness.