Appearance of layered structures in numerical simulations of polydisperse bodies accretion: Application to cometary nuclei

A model for the aggregation of size distribution of cometesimals (Gaussian or power law) into cometary nuclei is developed. Upon disruption induced by collisions, sticking and evolution of the tensile strength and density of the cometesimals by sintering processes are taken into account. The resulting cometary nuclei present specific internal structures that have been quantified to allow the comparison with observational constraints and future in situ observations and cometary nucleus sounding with the CONSERT radar on-board the Rosetta mission. A parameter called the homogeneity exponent, μ, determines different aggregation regimes. Fractal aggregates are formed for μ < 0.4. Radial variations in tensile strength appear for 0.4 < μ < 0.6 and vanish for larger values of μ. The initial size distribution (following a Gaussian or power law) of aggregating cometesimals does not influence strongly these values but can change the extent of corresponding layers. If the layering observed on the surface of some cometary nuclei occurs often and originates from primordial structures, this constrains the velocity distribution of aggregating bodies to follow v∝m^-0.25, while a differential size distribution following a power law with exponent between −2 and −3 should result for large bodies, in agreement with current estimations of the size distributions. Such a layered structure would lead to more cohesive, dense and less porous material located near the center of mass of the nucleus predicting an increase of bulk density of comet nuclei with their erosion state.     

Micrometer-sized ice particles for planetary-science experiments - I. Preparation, critical rolling friction force, and specific surface energy

Coagulation models assume a higher sticking threshold for micrometer-sized ice particles than for micrometer-sized silicate particles. However, in contrast to silicates, laboratory investigations of the collision properties of micrometer-sized ice particles (in particular, of the most abundant H₂O-ice) have not been conducted yet. Thus, we used two different experimental methods to produce micrometer-sized H₂O-ice particles, i.e. by spraying H₂O droplets into liquid nitrogen and by spraying H₂O droplets into a cold nitrogen atmosphere. The mean particle radii of the ice particles produced with these experimental methods are (1.49 ± 0.79) μm and (1.45 ± 0.65) μm. Ice aggregates composed of the micrometer-sized ice particles are highly porous (volume filling factor: ? = 0.11 ± 0.01) or rather compact (volume filling factor: ? = 0.72 ± 0.04), depending on the method of production. Furthermore, the critical rolling friction force of F_Roll,ice = (114.8 ± 23.8) × 10⁻¹⁰ N was measured for micrometer-sized ice particles, which exceeds the critical rolling friction force of micrometer-sized SiO₂ particles . This result implies that the adhesive bonding between micrometer-sized ice particles is stronger than the bonding strength between SiO₂ particles. An estimation of the specific surface energy of micrometer-sized ice particles, derived from the measured critical rolling friction forces and the surface energy of micrometer-sized SiO₂ particles, results in γ_ice = 0.190 J m⁻².     

Explosion of Comet 17P/Holmes as revealed by the Spitzer Space Telescope

An explosion on Comet 17P/Holmes occurred on 2007 October 23, projecting particulate debris of a wide range of sizes into the interplanetary medium. We observed the comet using the mid-Infrared Spectrograph (5-40 μm), on 2007 November 10 and 2008 February 27, and the imaging photometer (24 and 70 μm), on 2008 March 13, on board the Spitzer Space Telescope. The 2007 November 10 spectral mapping revealed spatially diffuse emission with detailed mineralogical features, primarily from small crystalline olivine grains. The 2008 February 27 spectra, and the central core of the 2007 November 10 spectral map, reveal nearly featureless spectra, due to much larger grains that were ejected from the nucleus more slowly. Optical images were obtained on multiple dates spanning 2007 October 27-2008 March 10 at the Holloway Comet Observatory and 1.5-m telescope at Palomar Observatory. The images and spectra can be segmented into three components: (1) a hemispherical shell fully 28′ on the sky in 2008 March, due to the fastest (262 m s⁻¹), smallest (2 μm) debris, with a mass ; (2) a ‘blob’ or ‘pseudonucleus’ offset from the true nucleus and subtending some 10′ on the sky, due to intermediate speed (93 m s⁻¹) and size (8 μm) particles, with a total mass ; and (3) a ‘core’ centered on the nucleus due to slower (9 m s⁻¹), larger (200 μm) ejecta, with a total mass . This decomposition of the mid-infrared observations can also explain the temporal evolution of the millimeter-wave flux. The orientation of the leading edge of the ejecta shell and the ejecta ‘blob,’ relative to the nucleus, do not change as the orientation of the Sun changes; instead, the configuration was imprinted by the orientation of the initial explosion. The distribution and speed of ejecta implies an explosion in a conical pattern directed approximately in the solar direction on the date of explosion. The kinetic energy of the ejecta >10²¹ erg is greater than the gravitational binding energy of the nucleus. We model the explosion as being due to crystallization and release of volatiles from interior amorphous ice within a subsurface cavity; once the pressure in the cavity exceeded the surface strength, the material above the cavity was propelled from the comet. The size of the cavity and the tensile strength of the upper layer of the nucleus are constrained by the observed properties of the ejecta; tensile strengths on >10 m scale must be greater than 10 kPa (or else the ejecta energy exceeds the binding energy of the nucleus) and they are plausibly 200 kPa. The appearance of the 2007 outburst is similar to that witnessed in 1892, but the 1892 explosion was less energetic by a factor of about 20.     

Energy balance of the Deep Impact experiment

We present results on the energy balance of the Deep Impact experiment based on analysis of 180 infrared spectra of the ejecta obtained by the Deep Impact spacecraft. We derive an output energy of 16.5 (+9.1/−4.1) GJ. With an input energy of 19.7 GJ, the error bars are large enough so that there may or may not be a balance between the kinetic energy of the impact and that of outflowing materials. Although possible, no other source of energy other than the impactor or the Sun is needed to explain the observations. Most of the energy (85%) goes into the hot plume in the first few seconds, which only represents a very small fraction (<0.01%) of the total ejected mass. The hot plume contains 190 (+263/−71) kg of H₂O, 1.6 ± 0.5 kg of CO₂, 8.2 (+11.3/3.1) kg of CO (assuming a CO/H₂O ratio of 4.3%), 27.9 (+25.0/−8.9) kg of organic material and 255 ± 128 kg of dust, while the ejecta contains ∼10⁷ kg of materials. About 12% of the energy goes into the ejecta (mostly water) and 3% to destroy the impactor. Volatiles species other than H₂O (CO₂, CO or organic molecules) contribute to <7% of the energy balance. In terms of physical processes, 68% of the energy is used to accelerate grains (kinetic energy), 16% to heat them, 6% to sublimate or melt them and 10% (upper limit) to break and compress dust and/or water ice aggregates into small micron size particles. For the hot plume, we derive a dust/H₂O ratio of 1.3 (+1.9/−1.0), a CO₂/H₂O ratio of 0.008 (+0.009/−0.006), an organics/H₂O ratio of 0.15 (+0.29/−0.11) and an organics/dust ratio of 0.11 (+0.30/−0.07). This composition refers to the impact site and is different from that of the bulk nucleus, consistent with the idea of layers of different composition in the nucleus sub-surface. Our results emphasize the importance of laboratory impact experiments to understand the physical processes involved at such a large scale.     

Comets in the near-Earth object population

Because the lifespan of near-Earth objects (NEOs) is shorter than the age of the Solar System, these objects originate elsewhere. Their most likely sources are the main asteroid belt and comets. Through physical observations we seek to identify potential dormant or extinct comets among “asteroids” catalogued as NEOs and thereby determine the fraction of “comet candidates” within the total NEO population. Both discovery statistics and dynamical models indicate that candidate cometary objects in near-Earth space are predominantly found among those having a jovian Tisserand parameter Tj<3. Therefore, we seek to identify comet candidates among asteroid-like NEOs using three criteria: Tj<3, spectral parameters (C, D, T, or P taxonomic types), and/or low (<0.075) albedos. We present new observations for 20 NEOs having Tj<3, consisting of visible spectra, near-infrared spectra, and/or albedo measurements obtained using the NASA Infrared Telescope Facility, the Kitt Peak National Observatory 4 m, and the Magellan Observatory 6.5-m. Four of our “asteroid” targets have been subsequently confirmed as low activity comets. Thus our sample includes spectra of the nuclei of Comets 2002 EX12 = 169P (NEAT), 2001 WF2 = 182P (LONEOS), 2003 WY25 = D/1891 W1 (Blanplain), and Halley Family Comet 2006 HR30 = P/2006 HR30 (Siding Spring). From the available literature, we tabulate physical properties for 55 NEOs having Tj<3, and after accounting for possible bias effects, we estimate that 54±10% of NEOs in Tj<3 orbits have “comet-like” spectra or albedos. Bias corrected discovery statistics [Stuart, J.S., Binzel, R.P., 2004. Icarus 170, 295-311] estimate 30±5% of the entire NEO population resides in orbits having Tj<3. Combining these two factors suggests that 16±5% of the total discovered “asteroid-like” NEO population has “comet-like” dynamical and physical properties. Outer main-belt asteroids typically have similar taxonomic and albedo properties as our “comet candidates.” Using the model of Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.M., Levison, H., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] to evaluate source region probabilities, we conclude that 8±5% of the total asteroid-like NEO population have the requisite orbital properties, physical properties, and dynamical likelihood to have originated as comets from the outer Solar System.     

Deep Impact, Stardust-NExT and the behavior of Comet 9P/Tempel 1 from 1997 to 2010

We present observational data for Comet 9P/Tempel 1 taken from 1997 through 2010 in an international collaboration in support of the Deep Impact and Stardust-NExT missions. The data were obtained to characterize the nucleus prior to the Deep Impact 2005 encounter, and to enable us to understand the rotation state in order to make a time of arrival adjustment in February 2010 that would allow us to image at least 25% of the nucleus seen by the Deep Impact spacecraft to better than 80 m/pixel, and to image the crater made during the encounter, if possible. In total, ∼500 whole or partial nights were allocated to this project at 14 observatories worldwide, utilizing 25 telescopes. Seventy percent of these nights yielded useful data. The data were used to determine the linear phase coefficient for the comet in the R-band to be 0.045 ± 0.001 mag deg⁻¹ from 1° to 16°. Cometary activity was observed to begin inbound near r ∼ 4.0 AU and the activity ended near r ∼ 4.6 AU as seen from the heliocentric secular light curves, water-sublimation models and from dust dynamical modeling. The light curve exhibits a significant pre- and post-perihelion brightness and activity asymmetry. There was a secular decrease in activity between the 2000 and 2005 perihelion passages of ∼20%. The post-perihelion light curve cannot be easily explained by a simple decrease in solar insolation or observing geometry. CN emission was detected in the comet at 2.43 AU pre-perihelion, and by r = 2.24 AU emission from C₂ and C₃ were evident. In December 2004 the production rate of CN increased from 1.8 × 10²³ mol s⁻¹ to Q_CN = 2.75 × 10²³ mol s⁻¹ in early January 2005 and 9.3 × 10²⁴ mol s⁻¹ on June 6, 2005 at r = 1.53 AU.     

The Umov effect for single irregularly shaped particles with sizes comparable with wavelength

The Umov effect manifests itself as an inverse correlation between the linear polarization maximum of an object’s scattered light P_max and its geometric albedo A. This effect is observed for the Moon, Mercury and Mars, and there are data suggesting this effect is valid for asteroids. The Umov effect is due to the contribution of interparticle multiple scattering that increases albedo and decreases polarization. We here study if the Umov effect can be extended to the case of single irregularly shaped particles with sizes comparable with the wavelength. This, in particular, is important for cometary dust polarimetry. We show the Umov effect being valid for weakly absorbing irregular particles (Im(m) ? 0.02) almost through the entire range of size parameters x considered. Highly absorbing particles (Im(m) > 0.02) follow the Umov effect only if x exceeds 14. In the case of weakly absorbing particles, the inverse correlation is essentially non-linear, which is caused by the contribution of particles with small x. However, averaging over many different types of irregularly shaped particles could make it significantly more linear. The size averaging does not change qualitatively the diagram log(P_max)-log(A) for weakly absorbing particles. For single irregular particles whose sizes are comparable with wavelength, there is no reliable correlation between the slope of the polarization curve h near the inversion phase angle and geometric albedo A. Using the extended Umov Law, we estimate the geometric albedo of dust particles forming cometary circumnuclear haloes A = 0.1 − 0.2, which is a few times larger than the average geometric albedo over the entire comae. Note that, using the obtained values for A of cometary particles, one can derive their number density in circumnuclear haloes from photometric observations.     

Investigations of the pre-Deep Impact morphology of the dust coma of Comet Tempel-1

The pre-Deep Impact images of Comet Tempel-1 obtained at the Indian Astronomical Observatory are used to investigate the morphology of the dust coma of the comet. We show that the trajectory of a cometary grain under the influence of solar radiation pressure is a reliable diagnostic to estimate its initial velocity. Four main active regions at mean latitudes +45° ± 5°(D), 0° ± 5° (E),−30° ± 5°(A) and−60° ± 5°(F) are found to explain the morphology of the dust coma in the ground-based and published images obtained by the High Resolution Instrument(HRI) cameras aboard the Deep Impact flyby spacecraft. From a χ² fit of the intensity distribution in the observed and the simulated images, we derive the fraction of the productivity of the active vents to the total dust emission of the comet to be 27%. Of this the southern source alone accounts for 19.8%. The grains are found to be ejected with a velocity distribution with an upper limit of 70 ± 7 m s⁻¹. However, the broad region ‘A’ appears to eject slower grains with an upper limit of 24 ± 2.5 m s⁻¹. This source, that is active throughout the cycle is likely to be driven by CO₂ sublimation. We compute the dependence of the percentage contribution of the southern source on the heliocentric distance and show that this ratio varies over the apparition and reaches a maximum at around 260 days before perihelion. The published images of the nucleus of Comet Tempel-1 show significant departure from sphericity. Therefore, the torque exerted by the enhanced activity of the southern region may be significant enough to produce changes in the rotational state of the nucleus before each perihelion passage.     

Determination of a precise rotation period for the Deep Space 1 target, Comet 19P/Borrelly

The rotation period derived by Mueller and Samarasinha (Mueller, B.E.A., Samarasinha, N.H. [2002]. Earth Moon Planets 90, 463-471) of the Deep Space 1 (DS1) mission target, Comet 19P/Borrelly, using ground-based data from July 28 to August 1, 2000, is improved by two orders of magnitude. This precision is reached in a multistep process.Combining all available ground-based data in 2000 decreases the error by an order of magnitude. Next, assuming that the rotation period did not change between 2000 and 2001, constraints from the HST 2001 data (Weaver, H.A., Stern, S.A., Parker, J.Wm. [2003]. Astron. J. 126, 444-451) yield three possible rotation periods: P = 1.088 ± 0.003 days, P = 1.108 ± 0.002 days, and P = 1.135 ± 0.003 days, which are consistent with our initial derivation of P = 1.08 ± 0.04 days (Mueller, B.E.A., Samarasinha, N.H. [2002]. Earth Moon Planets 90, 463-471).These three periods are further refined and the error bars further improved by another order of magnitude by linking the combined ground-based data from 2000 to the nuclear orientation of Borrelly at the DS1 encounter in 2001 (see Table 2). Due to aliasing, there are seven possible rotation periods around P = 1.088 days, five possible periods around P = 1.108 days, and six possible periods around P = 1.135 days, with precisions of the order of 0.0002 days (≈17 s).     

Secular light curve of 2P/Encke, a comet active at aphelion

We present the secular light curve of Comet 2P/Encke in two phase spaces, the log plot, and the time plot. The main conclusions of this work are: (a) The comet shows activity at perihelion and aphelion, caused by two different active areas: Source 1, close to the south pole, active at perihelion, and Source 2, at the north pole, centered at aphelion. (b) More than 18 physical parameters are measured from the secular light curves, many of them new, and are listed in the individual plots of the comet. Specifically we find for Source 1 the location of the turn on and turn off points of activity, RON=−1.63±0.03 AU, ROFF=+1.49±0.20 AU, TON=−87±5 d, TOFF=+94±15 d, the time lag, LAG(q)=6±1 d, the total active time, TACTIVITY=181±16 d, and the amplitude of the secular light curve, ASEC(1,1)=4.8±0.1 mag. (c) From this information the photometric age and the time-age defined in Ferrín [2005a. Icarus 178, 493-516; 2006. Icarus 185, 523-543], can be calculated, and we find P-AGE = 97 ± 8 comet years and T-AGE = 103 ± 9 comet years (cy). Thus Comet 2P/Encke is an old comet entering the methuselah stage (100 cy < age). (d) The activity at aphelion (Source 2), extends for TACTIVITY=815±30 d and the amplitude of the secular light curve is ASEC(1,Q)=3.0±0.2 mag. (e) From a new phase diagram an absolute magnitude and phase coefficient for the nucleus are determined, and we find RNUC(1,1,0)=15.05±0.14, and β=0.066±0.003. From this data we find a nucleus effective diameter DEFFE=5.12(+2.5;−1.7) km. These values are not much different from previous determinations but exhibit smaller errors. (f) The activity of Source 1 is due to H₂O sublimation because it shows curvature. The activity of Source 2 might also be due to H₂O due to the circumstantial situation that the poles point to the Sun at perihelion and aphelion. (g) We found a photometric anomaly at aphelion, with minimum brightness between +393 and +413 days after perihelion that may be an indication of topography. (h) We have re-reduced the 1858 secular light curve of Kamel [1991. Icarus 93, 226-245]. There are secular changes in 7 physical parameters, and we achieve for the first time, an absolute age calibration. We find that the comet entered the inner Solar System and began sublimating in 1645±40 AD. (i) It is concluded that the secular light curve can place constraints on the pole orientation of the nucleus of some comets, and we measure the ecliptic longitude of the south pole of 2P/Encke equal to 213.2±4.5°, in excellent agreement with other determinations of this parameter, but with smaller error. (j) Using the observed absolute magnitude of 1858 and 2003 and a suitable theoretical model, the extinction date of the comet is determined. We obtain ED=2056±3 AD, implying that the comet's lifetime is 125±12 revolutions about the Sun after entering the inner Solar System.     

Small-scale dust structures in Halley's coma: II. Disintegration of large dust bodies

Small-scale dust structures, SDSs, altogether ∼35 events with extent ∼30-220 km, have been recognized owing to electric field records, mostly near the closest approach of Vega-2 to Halley's nucleus. Several (8-9) morphological forms of SDS have been identified, and all they make one family. Among the family members, the key form (with respect to which, all other forms can be regarded as degenerate) is a sequence of 3-5 dust clouds. The morphological forms represent various Vega-2 passes through SDSs at different stages of development. SDSs observable as the key form consisted of several fairly regularly spaced dust subpopulations, whose plane of symmetry was parallel to the comet orbit plane. That regularity together with specific features of morphological forms strongly constrain disintegration scenarios and dynamics of fragments, and allow to draw a number of conclusions, the main of which are: SDS parent bodies were ice-free dust aggregates lifted from the nucleus near the comet perihelion, whose masses were in the range ∼0.1-1 of the biggest emitted mass (mass of a body accelerated to the escape velocity, i.e., ∼300-1500 kg); the disintegration scenario comprised a few steps, and the first-step disintegration consisted mainly in consecutive detachments of biggest first-step fragments (BF-SFs) from the parent body; a SDS observable as the key form included the dust minitail of parent body and a few BF-SF minitails, the former one being longer than the latter ones; SDS parent bodies had a fractal-like internal structure, and the BF-SF mass was a few percent of the parent body mass; the thermal conductivity of SDS parent body was less than ∼0.4 W m⁻¹ K⁻¹ or so, while the latent heat of gluing organics was roughly 80 kJ mol⁻¹; the disintegration mechanism was a combination of sintering and sublimation of organics. The multistep disintegration of SDS parent bodies can be reconciled with the basically one-step disintegration of aggregates responsible for the dust boundary (Oberc, P., Icarus 1996, 124, 195-208). The fractal-like structure and the relation between BF-SF mass and parent body mass are in agreement with predictions from the Weidenschilling model of comet formation. Large ice-free dust bodies, in particular SDS parent bodies, can be identified with refractory boulders postulated by some comet nucleus models.     

Thermal conductivity measurements of porous dust aggregates: I. Technique, model and first results

We present a non-invasive technique for measuring the thermal conductivity of fragile and sensitive materials. In the context of planet-formation research, the investigation of the thermal conductivity of porous dust aggregates provide important knowledge about the influence of heating processes, like internal heating by radioactive decay of short-lived nuclei, e.g. ²⁶Al, on the evolution and growth of planetesimals. The determination of the thermal conductivity was performed by a combination of laboratory experiments and numerical simulations. An IR camera measured the temperature distribution of the sample surface heated by a well-characterized laser beam. The thermal conductivity as free parameter in the model calculations, exactly emulating the experiment, was varied until the experimental and numerical temperature distributions showed best agreement. Thus, we determined for three types of porous dust samples, consisting of spherical, 1.5 μm-sized SiO₂ particles, with volume filling factors in the range of 15-54%, the thermal conductivity to be 0.002-0.02 W m⁻¹ K⁻¹, respectively. From our results, we can conclude that the thermal conductivity mainly depends on the volume filling factor. Further investigations, which are planned for different materials and varied contact area sizes (produced by sintering), will prove the appropriate dependencies in more detail.     

The aftermath of the July 2009 impact on Jupiter: Ammonia, temperatures and particulates from Gemini thermal infrared spectroscopy

We obtained longitudinally resolved thermal infrared spectra (8-13 μm and 17-25 μm) of Jupiter’s impact debris at the Gemini South Telescope on July 24, 2009; five days after the July 19th collision. These were used to study the mechanisms responsible for the redistribution of thermal energy and material (ammonia and stratospheric particulates) following the impact. Upwelling of (8.5 ± 4.1) × 10¹⁴ g of tropospheric air was sufficient to deposit (6.7 ± 4.1) × 10¹² g of NH₃ over a 6° longitude range above the impact core. The NH₃ was distributed over the 20-80 mbar region with a peak abundance of 1.0 ± 0.6 ppm at 45 mbar. Only a 10th of this abundance was observed over the western ejecta, and it is unlikely that these observations were sensitive to NH₃ entrained in the ballistic plume itself. The pattern of excess thermal energy was markedly different from that of Shoemaker-Levy 9 (SL9), with a localized tropospheric perturbation of 2.0 ± 1.0 K at 200-300 mbar and a broader stratospheric warming of up to 3.5 ± 2.0 K at 10-30 mbar. We find no evidence of residual warmth at p < 1 mbar five days after the impact. The excess thermal energy places lower limits on the total energy of the impact (1.8-15.7 × 10²⁶ ergs), which limits the impactor diameter to 70-510 m (depending on the bulk density chosen for the material).The models of the Gemini spectra required three distinct aerosol features, indicative of the mineralogy of the dark particulate debris, centred at 9.1, 10.0 and 18.5 μm. The retrieved opacities for each of these features were distributed over a larger area (9-10° longitude) and at higher altitudes (above the 10-mbar level) than the stratospheric NH₃, and they are more spatially inhomogeneous. This implies the particulates were either entrained with the rising hot plume or created upon plume re-entry and are subsequently redistributed by stratospheric winds. The three particulate features were consistent with a mixture of amorphous iron and magnesium-rich silicates and silicas in the debris field. A broad 10-μm signature was coincident with peaks expected from material rich in amorphous olivines (but poor in pyroxenes), and similar to silicate features observed during SL9. A narrow 9.1-μm signature was interpreted as a combination of amorphous and crystalline silica. Finally, a broad 18.5-μm emitter was not adequately reproduced by a mixture of simple olivines and pyroxenes and remains to be identified.     

HCN and CN in Comet 2P/Encke: Models of the non-isotropic, rotation-modulated coma and CN parent life time

Axisymmetric models of the outgassing of a cometary nucleus have been constructed. Such models can be used to describe a nucleus with a single active region. The models may include a solar zenith angle dependence of the outgassing. They retrieve the outgassing flux at distances from the nucleus where collisions between molecules are unimportant, as function of the angle with respect to the outgassing axis. The observed emissions must be optically thin. Furthermore the models assume that the outflow speed at large distance from the nucleus does not depend on direction. The value of the outflow speed is retrieved. The models are applied to CN images and HCN spectra of Comet 2P/Encke, obtained nearly simultaneously in November 2003 with the 2 m optical telescope on Mount Rozhen, Bulgaria, and with the 10 m Heinrich Hertz Submillimeter Telescope on Mount Graham, Arizona, USA. According to Sekanina (1988), Astron. J. 95, 911-924, at that time a single outgassing source was active. Input parameters to the models like the rotation period of the nucleus and a small correction to Sekanina’s rotation axis are determined from a simpler jet position angle model. The rotation is prograde with a sideric period of 11.056 ± 0.024 h, in agreement with literature values. The best fit model has an outflow speed of 0.95 ± 0.04 km s⁻¹. The same value has been derived from the corkscrew appearing in the CN images. The location of the outgassing axis is at colatitude δ_a = 7.4° ± 2.9° and longitude λ_a = 235° ± 17° (a definition of zero longitude is provided). Comet Encke’s outgassing corresponds approximately to the longitudinally averaged solar input on a spherical nucleus (i.e. very likely comes from deeper layers) but with some deficiency of outgassing at mid-latitudes and non-zero outgassing from the dark polar cap. The presence of gas flow from the dark polar cap is explained as evidence of gas flow across the terminator. The models rely mostly on the CN images. The HCN spectra are more noisy. They provide information how to determine the best fit outflow velocity and the sense of rotation. The model HCN spectra are distinctly non-Gaussian. Within error limits they are consistent with the observations. Models based solely on the HCN spectra are also presented but, because of the lower quality of the data and the unfavorable observing geometry, yield inferior results. As a by-product we determine the CN parent life time from our CN observations. The solar EUV and Lyα radiation field at the time of our observations is taken into account.     

Photometric observations of 107P/Wilson-Harrington

We present lightcurve observations and multiband photometry for 107P/Wilson-Harrington using five small- and medium-sized telescopes. The lightcurve has shown a periodicity of 0.2979 day (7.15 h) and 0.0993 day (2.38 h), which has a commensurability of 3:1. The physical properties of the lightcurve indicate two models: (1) 107P/Wilson-Harrington is a tumbling object with a sidereal rotation period of 0.2979 day and a precession period of 0.0993 day. The shape has a long axis mode (LAM) of L₁:L₂:L₃ = 1.0:1.0:1.6. The direction of the total rotational angular momentum is around λ = 310°, β = −10°, or λ = 132°, β = −17°. The nutation angle is approximately constant at 65°. (2) 107P/Wilson-Harrington is not a tumbler. The sidereal rotation period is 0.2979 day. The shape is nearly spherical but slightly hexagonal with a short axis mode (SAM) of L₁:L₂:L₃ = 1.5:1.5:1.0. The pole orientation is around λ = 330°, β = −27°. In addition, the model includes the possibility of binary hosting. For both models, the sense of rotation is retrograde. Furthermore, multiband photometry indicates that the taxonomy class of 107P/Wilson-Harrington is C-type. No clear rotational color variations are confirmed on the surface.     

The near-IR spectrum of Titan modeled with an improved methane line list

We have obtained spatially resolved spectra of Titan in the near-infrared J, H and K bands at a resolving power of ∼5000 using the near-infrared integral field spectrometer (NIFS) on the Gemini North 8 m telescope. Using recent data from the Cassini/Huygens mission on the atmospheric composition and surface and aerosol properties, we develop a multiple-scattering radiative transfer model for the Titan atmosphere. The Titan spectrum at these wavelengths is dominated by absorption due to methane with a series of strong absorption band systems separated by window regions where the surface of Titan can be seen. We use a line-by-line approach to derive the methane absorption coefficients. The methane spectrum is only accurately represented in standard line lists down to ∼2.1 μm. However, by making use of recent laboratory data and modeling of the methane spectrum we are able to construct a new line list that can be used down to 1.3 μm. The new line list allows us to generate spectra that are a good match to the observations at all wavelengths longer than 1.3 μm and allow us to model regions, such as the 1.55 μm window that could not be studied usefully with previous line lists such as HITRAN 2008. We point out the importance of the far-wing line shape of strong methane lines in determining the shape of the methane windows. Line shapes with Lorentzian, and sub-Lorentzian regions are needed to match the shape of the windows, but different shape parameters are needed for the 1.55 μm and 2 μm windows. After the methane lines are modeled our observations are sensitive to additional absorptions, and we use the data in the 1.55 μm region to determine a D/H ratio of 1.77 ± 0.20 × 10⁻⁴, and a CO mixing ratio of 50 ± 11 ppmv. In the 2 μm window we detect absorption features that can be identified with the ν₅ + 3ν₆ and 2ν₃ + 2ν₆ bands of CH₃D.     

Photometric analysis of the nucleus of Comet 81P/Wild 2 from Stardust images

The disk-resolved flyby images of the nucleus of Comet 81P/Wild 2 collected by Stardust are used to perform a detailed study of the photometric properties of this cometary nucleus. A disk-integrated phase function from phase angle 11° to about 100° is measured and modeled. A phase slope of 0.0513 ± 0.0002 mag/deg is found, with a V-band absolute magnitude of 16.29 ± 0.02. Hapke’s photometric model yields a single-scattering albedo of 0.034, an asymmetry factor of phase function −0.53, a geometric albedo 0.059, and a V-band absolute magnitude of 16.03 ± 0.07. Disk-resolved photometric modeling from both the Hapke model and the Minnaert model results in 11% model RMS, indicating small photometric variations. The roughness parameter is modeled to be 27 ± 5° from limb-darkening profile. The modeled single-scattering albedo and asymmetry factor of the phase function are 0.038 ± 0.004 and −0.52 ± 0.04, respectively, consistent with those from disk-integrated phase function. The bulk photometric properties of the nucleus of Wild 2 are comparable with those of other cometary nuclei. The photometric variations on the surface of the nucleus of Wild 2 are at a level of or smaller than 15%, much smaller than those on the nucleus of Comet 19P/Borrelly and comparable or smaller than those on the nucleus of Comet 9P/Tempel 1. The similar photometric parameters of the nuclei of Wild 2, Tempel 1, and the non-source areas of fan jets on Borrelly may reflect the typical photometric properties of the weakly active surfaces on cometary nuclei.     

Secular light curves of comets, II: 133P/Elst-Pizarro, an asteroidal belt comet

We present the secular light curve (SLC) of 133P/Elst-Pizarro, and show ample and sufficient evidence to conclude that it is evolving into a dormant phase. The SLC provides a great deal of information to characterize the object, the most important being that it exhibits outburst-like activity without a corresponding detectable coma. 133P will return to perihelion in July of 2007 when some of our findings may be corroborated. The most significant findings of this investigation are: (1) We have compiled from 127 literature references, extensive databases of visual colors (37 comets), rotational periods and peak-to-valley amplitudes (64 comets). 2-Dimensional plots are created from these databases, which show that comets do not lie on a linear trend but in well defined areas of these phase spaces. When 133P is plotted in the above diagrams, its location is entirely compatible with those of comets. (2) A positive correlation is found between cometary rotational periods and diameters. One possible interpretation suggest the existence of rotational evolution predicted by several theoretical models. (3) A plot of the historical evolution of cometary nuclei density estimates shows no trend with time, suggesting that perhaps a consensus is being reached. We also find a mean bulk density for comets of 〈ρ〉=0.52±0.06 g/cm³. This value includes the recently determined spacecraft density of Comet 9P/Tempel 1, derived by the Deep Impact team. (4) We have derived values for over 18 physical parameters, listed in the SLC plots, Figs. 6-9. (5) The secular light curve of 133P/Elst-Pizarro exhibits a single outburst starting at +42±4 d (after perihelion), peaking at LAG=+155±10 d, duration 191±11 d, and amplitude 2.3±0.2 mag. These properties are compatible with those of other low activity comets. (6) To explain the large time delay in maximum brightness, LAG, two hypothesis are advanced: (a) the existence of a deep ice layer that the thermal wave has to reach before sublimation is possible, or (b) the existence of a sharp polar active region pointing to the Sun at time = LAG, that may take the form of a polar ice cap, a polar fissure or even a polar crater. The diameter of this zone is calculated at ∼1.8 km. (7) A new time-age is defined and it its found that T-AGE = 80 cy for 133P, a moderately old comet. (8) We propose that the object has its origin in the main belt of asteroids, thus being an asteroid-comet hybrid transition object, an asteroidal belt comet (ABC), proven by its large density. (9) Concerning the final evolutionary state of this object, to be a truly extinct comet the radius must be less than the thermal wave depth, which at 1 AU is ∼250 m (at the perihelion distance of 133P the thermal wave penetrates only ∼130 m). Comets with radius larger than this value cannot become extinct but dormant. Thus we conclude that 133P cannot evolve into a truly extinct comet because it has too large a diameter. Instead it is shown to be entering a dormant phase. (10) We predict the existence of truly extinct comets in the main belt of asteroids (MBA) beginning at absolute magnitude ∼21.5 (diameter smaller than ∼190 m). (11) The object demonstrates that a comet may have an outburst of ∼2.3 mag, and not show any detectable coma. (12) Departure from a photometric R⁺² law is a more sensitive method (by a factor of 10) to detect activity than star profile fitting or spectroscopy. (13) Sufficient evidence is presented to conclude that 133P is the first member of a new class of objects, an old asteroidal belt comet, ABC, entering a dormant phase.     

In situ observation of penetration process in silica aerogel: Deceleration mechanism of hard spherical projectiles

A large number of cometary dust particles were captured with low-density silica aerogels by NASA’s Stardust Mission. Knowledge of the details of the capture mechanism of hypervelocity particles in silica aerogel is needed in order to correctly derive the original particle features from impact tracks. However, the mechanism has not been fully understood yet. We shot hard spherical projectiles of several different materials into silica aerogel of density 60 mg cm⁻³ and observed their penetration processes using an image converter or a high-speed video camera. In order to observe the deceleration of projectiles clearly, we carried out impact experiments at two velocity ranges; ∼4 km s⁻¹ and ∼200 m s⁻¹. From the movies we took, it was indicated that the projectiles were decelerated by hydrodynamic force which was proportional to v² (v: projectile velocity) during the faster penetration process (∼4 km s⁻¹) and they were merely overcoming the aerogel crushing strength during the slower penetration process (∼200 m s⁻¹). We applied these deceleration mechanisms for whole capture process to calculate the track length. Our model well explains the track length in the experimental data set by Burchell et al. (Burchell, M.J., Creighton, J.A., Cole, M.J., Mann, J., Kearsley, A.T. [2001]. Meteorit. Planet. Sci. 36, 209-221).     

Tidal disruptions: II. A continuum theory for solid bodies with strength, with applications to the Solar System

We present a comprehensive theory for the breakup conditions for ellipsoidal homogeneous secondary bodies subjected to the tidal forces from a nearby larger primary: for materials ranging from purely fluid ones, to granular rubble-pile gravel-like ones, and to those with either cohesive or granular strength including cohesive rocks and metals. The theory includes but greatly extends the classical analyses given by Roche in 1847, which dealt only with fluids, and also our previous analysis [Holsapple, K.A., Michel, P., 2006. Icarus 183, 331-348], which dealt only with solid but non-cohesive bodies. The results here give the distance inside of which breakup must occur, for both a steadily orbiting satellite and for a passing or impacting object. For the fluid bodies there is a single specific shape (a “Roche Ellipsoid”) that can be in equilibrium at any given distance from a primary, and especially only one shape that can exist at the overall minimum distance (d/R)(ρ/ρp)^1/3=2.455, the classical well-known “Roche limit.” In contrast, solid bodies can exist at a given distance from a primary with a range of shapes. Here we give multiple plots of the minimum distances for various important combinations of body shape, spin, mass density, and the strength parameters characterized by an angle of friction and cohesive strength. Such results can be used in different ways. They can be used to estimate limits on strengths and mass densities for orbiting bodies at a known distance and shape. They can be used to determine breakup distances for passing bodies with an assumed strength and shape. They can be used to constraint physical properties such as bulk density of bodies with a known shape that were known to breakup at a given distance. A collection of approximately 40 satellites of the Solar System is used for comparison to the theory. About half of those bodies are closer than the Roche fluid limit and must have some cohesion and/or friction angle to exist at their present orbital distance. The required solid strength for those states is determined. Finally, we apply the theory to the break up of the SL9 comet at close approach with Jupiter. Our results make clear that the literature estimates of its bulk density depend markedly on unknown parameters such as shape, orientation and spin, and most importantly, material strength characterization.