Rotational Properties of Cometary Nuclei

We review several techniques used to retrieve rotational parameters from observations. The spin period of a dozen of comets retrieved with these techniques are summarized. We describe how the spin period of comet Hale-Bopp (C/1995 O1) has been calculated with a high accuracy (11.30–11.34 h). Although several authors converged to a spin axis orientation at (α,δ) = (275 ± 15°, -55 ± 5°), detailed studies indicate that the dust jets morphology in 1996–1997 may be incompatible with this orientation. Comet 19P/Borrelly has been recently observed by the Deep Space 1 spacecraft. At the same time, its spin axis orientation and period have been determined by several authors to be respectively (α,δ) = (225 ± 15°, -10 ± 10°)and 26h. These two comets are likely to be in (or close to) a principal axis spin state. We discuss new modeling of the spin state of comet 46P/Wirtanen, the target of the Rosetta mission. The model involves a three-dimensional shape and thermal model, from which the torque of the non gravitational force is calculated at each time step. The moments of inertia are computed for each irregular shape. The results from numerical integrations show that this comet can remain in a principal axis spin state during more than 10 orbits if the spin period does not get above～6 h. If the spin period increases, its nucleus gets rapidly into excited spin states. It shows that even small and very active short-period comets are not necessarily in non principal axis spin states. In the last section, the consequences of recent observations and modeling of the rotational parameters of comet nuclei are discussed, and unsolved problems are presented.     

Dust Morphology Of Comet Hale-Bopp (C/1995 O1): I. Pre-Perihelion Coma Structures In

In 1996 comet Hale-Bopp exhibited a porcupine-like coma with straight jets of dust emission from several active regions on the nucleus. The multi-jet coma geometry developed during the first half of 1996. While the jet orientation remained almost constant over months, the relative intensity of the jets changed with time. By using the embedded fan model of Sekanina and Boehnhardt (1997a) the jet pattern of comet Hale-Bopp in 1996 can be interpreted as boundaries of dust emission cones (fans) from four — possibly five — active regions on the nucleus (for a numerical modelling see part II of the paper by Sekanina and Boehnhardt, 1997b). This revised version was published online in July 2006 with corrections to the Cover Date.     

Aperture Polarimetry And Photometry Of Comet Hale-Bopp

We present results of polarimetric and photometric observations of bright comet C/1995 O1 (Hale-Bopp) obtained at the 0.7 m telescope of Kharkov University Observatory from June 18, 1996 to April 24, 1997. The IHW and HB comet filters were used. The C₂ and C₃ production rates for Hale-Bopp are more than one order of magnitude larger and the dust production rates are more than two orders of magnitude larger than the Halley ones at comparable distances. Hence, Hale-Bopp was one of the most dusty comets. The average UC-BC and BC-RC colours of the dust were −0.02 and 0.13 mag, respectively. The polarization of comet Hale-Bopp at small phase angles of 4.8–13.0° was in good agreement with the date for comet P1/Halley at the same phase angles in spite of the fact that the heliocentric distances of comments differed nearly twice. However, at intermediate phase angles of 34–49° the polarization of comet Hale-Bopp was significantly larger than the polarization of the other dusty comets. It is the first case of such a large difference found in the continuum polarization of comets. The wavelength dependence of polarization for Hale-Bopp was steeper than for other dusty comets. The observed degree of polarization for the anti-sunward side of the coma was permanently higher than that for the sunward shell side. The polarization phase dependence of Hale-Bopp is discussed and compared with the polarization curves for other dusty comets. The peculiar polarimetric properties of comet Hale-Bopp are most likely caused by an over-abundance of small or/and absorbing dust particles in the coma. This revised version was published online in July 2006 with corrections to the Cover Date.     

Coma Morphology And Constraints On The Rotation Of Comet Hale–Bopp (C/1995 O1)

We present constraints on the spin state of comet Hale-Bopp based on coma morphology. Three cases of rotational states are compatible with near perihelion observations: (1) principal-axis rotation, (2) complex rotational state with a small precessional angle, or (3) complex rotational state with a large ratio between the component periods. For principal axis rotators, images from 1996 (pre-perihelion) are consistent with a rotational angular momentum vector, M, directed at ecliptic longitude and latitude (250°, -5°) while images from late 1997 (post-perihelion) indicate (310°, -40°). This may suggest a change in M. A complex rotational state with small precessional angle requires only a small or no change in M over the active orbital arc. In this case, M is directed near ecliptic longitude and latitude (270°, -20°). A rotationally excited nucleus with a large ratio between component periods requires the nucleus to be nearly spherical. The transformation of dust coma morphology from near-radial jets to bright arcs and then again to near-radial jets is interpreted as a heliocentric and geocentric distance dependent evolutionary sequence. The spiral structures seen in CN filters near perihelion (in contrast to sunward side arcs seen in continuum) can be explained if the precursor of CN molecules (likely sub-micron grains) are emitted from the nucleus at low levels (≈ 10% of the peak daytime emission) during the nighttime. This may be indicative of a nucleus with a CO-rich active area(s). This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling Dust Jets And Shells From Comet Hale-Bopp

Persistent jet and shell structures from comet Hale-Bopp showing gradual changes in the shapes and orientations with aspect angle and solar illumination geometry indicate long lived active sources. A model to simulate the dust features has been applied to the series of observations from September 1996 to May 1997. Most of the structures can be explained as arising due to ejections from persistent active regions at comet-o-centric latitudes near +65°, +55°, −5° to −15°, −35° and −65°. The best fitting pole positions vary between 255° ±10° and 275° ± 10° in right ascension and −45° ± 10° to −75° ± 10° in declination. Lower limits on the dust and gas production rates at various epochs are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dust Morphology Of The Inner Coma Of C/1995 O1 (Hale-Bopp)

Dust continuum imaging of comet C/1995 O1 (Hale-Bopp) was carried out with the Swedish Vacuum Solar Telescope (SVST)on La Palma in April, 1997. Images were reduced according to standard procedure, aligned, averaged, navigated and enhanced with azimuthal renormalization, rotational derivative, temporal derivative and unsharp masking processing. The rotational period of the nucleus was determined to 11.5 h and the mean projected dust outflow velocity to 0.41 km s⁻¹. Shell envelopes in the sunward side of the coma were separated by a projected distance of ∼15 000–20 000 km and spiralling inwards towards smaller radii in the direction of local evening. Small scale inhomogeneities of size 1 000–2 000 km, interpreted as correlated with variations in dust emission activity, were seen at radii ≤20 000 km. Two overlapping shell systems with a relative lag angle of ∼55° were evident at the time. The north pole of the nucleus was directed towards the Earth. The dust emission pattern is very complex and may be due to several active areas. The shape of the incomplete spiral shell pattern indicates that the angle between the line-of-sight and the rotational axis of the nucleus was not large. This revised version was published online in July 2006 with corrections to the Cover Date.     

Infrared Observations Of Dust Emission From Comet Hale-Bopp

We present infrared imaging and photometry of the bright, giant comet C/1995 O1 (Hale-Bopp). The comet was observed in an extended infrared and optical observing campaign in 1996–1997. The infrared morphology of the comet was observed to change from the 6 to 8 jet “porcupine” structure in 1996 to the “pinwheel” structure seen in 1997; this has implications for the position of the rotational angular momentum vector. Long term light curves taken at 11.3 μm indicate a dust production rate that varies with heliocentric distance as ∶ r^−1.4. Short term light curves taken at perihelion indicate a rotational periodicity of 11.3 hours and a projected dust outflow speed of ∶ 0.4 km s⁻¹. The spectral energy distribution of the dust on October 31, 1996 is well modeled by a mixture of 70% silicaceous and 30% carbonaceous non-porous grains, with a small particle dominated size distribution like that seen for comet P/Halley (McDonnell et al., 1991), an overall dust production rate of 2 × 10⁵ kg s⁻¹, a dust-to-gas ratio of ∶5, and an albedo of 39%. This revised version was published online in July 2006 with corrections to the Cover Date.     

Rotational modeling of Hyperion

Saturn’s moon, Hyperion, is subject to strongly-varying solid body torques from its primary and lacks a stable spin state resonant with its orbital frequency. In fact, its rotation is chaotic, with a Lyapunov timescale on the order of 100 days. In 2005, Cassini made three close passes of Hyperion at intervals of 40 and 67 days, when the moon was imaged extensively and the spin state could be measured. Curiously, the spin axis was observed at the same location within the body, within errors, during all three fly-bys—~ 30° from the long axis of the moon and rotating between 4.2 and 4.5 times faster than the synchronous rate. Our dynamical modeling predicts that the rotation axis should be precessing within the body, with a period of ~ 16 days. If the spin axis retains its orientation during all three fly-bys, then this puts a strong constraint on the in-body precessional period, and thus the moments of inertia. However, the location of the principal axes in our model are derived from the shape model of Hyperion, assuming a uniform composition. This may not be a valid assumption, as Hyperion has significant void space, as shown by its density of 544± 50  kg m⁻³ (Thomas et al. in Nature 448:50, 2007). This paper will examine both a rotation model with principal axes fixed by the shape model, and one with offsets from the shape model. We favor the latter interpretation, which produces a best-fit with principal axes offset of ~ 30° from the shape model, placing the A axis at the spin axis in 2005, but returns a lower reduced χ ² than the best-fit fixed-axes model.     

Near-Infrared Imaging Spectrophotometry Of Comet C/1995 O1 (Hale-Bopp) Near Perihelion

We present 1- to 5-μm broadband and CVF images of comet Hale-Bopp taken 1997 February 10.5 UT, 50 days before perihelion. All the images exhibit a nonspherical coma with a bright “ridge” in the direction of the dust tail approximately 10″ from the coma. Synthetic aperture spectrophotometry implies that the optically important grains are of a radius ≤0.4 μm; smallest radius for any comet seen to date. The variation of the integrated surface brightness with radial distance from the coma (ρ) in all the images closely follows the “steady state” ρ⁻¹ model for comet dust ablation (Gehrz and Ney, 1992). The near-infrared colors taken along the dust tail are not constant implying the dust grain properties vary with coma distance. This revised version was published online in July 2006 with corrections to the Cover Date.     

Spin Axis Direction of Comet 19p/Borrelly Based on Observations from 2000 and 2001

We calculate the direction of the rotational angular momentum vector,M, of comet 19P/Borrelly based on rotational lightcurve data from 2000, groundbased imaging of the coma during the Deep Space 1encounter, and the basic near-nucleus coma morphology as revealed by the Deep Space 1 spacecraft. For the most likely direction, we derivea family of solutions (with center at RA = 221°, Dec = -7°) if the direction of M is towards the sunward hemisphere during the Deep Space 1 encounter, whereas if the rotation is of opposite sense, the diametrically opposite family of solutions (with center at RA = 41°, Dec = 7°) would result. We argue that the coma morphology in September 2001 is consistent with the nucleus being a principal axis rotator or one observationally indistinguishable from it. Therefore, for all practical purposes, the direction of the rotational angular momentum vector coincides with the spin axis. We also discuss why the determination of the spin axis direction based on observations from the last apparition is in disagreement with the current result.     

An idealized short-period comet model: Surface insolation,H2O flux,dust flux,and mantle evolution

A model of cometary activity is developed which integrates the feedback processes involving heat, gas, and dust transport, and dust mantle development. The model includes the effects of latitude, rotation, and spin axis orientation. Results are obtained for various grain size distributions, dust-to-ice ratios, and spin axis orientations. Attention is focused on the development, change of structure and distribution of dust mantles and their mutual interaction with ice surface temperature and gas and dust production. In this model the dust mantle controls the mechanism of gas transport not onlu by its effect on the temperature but, more importantly, by its own dynamic stability. Results suggest that an initially homogeneous short-period comet with a “cosmic” dust-to-water ice ratio, typical orbit, rotation rate, and grain size distribution would develop at most only a thin (<1 mm) cyclic mantle at all points on the nucleus. Such a fully developed temporary mantle would exist throughout the diurnal cycle only beyond ～4AU. Thus, cyclic behavior would be expected for such an idealized comet, at least for most of its lifetime. Long-term irreversible mantle development on comets with typical rotation rates was not found except regionally on Encke and also on objects with perihelia ?1.5 AU. Even in these cases, free silicate exists, after a few cycles, only as relatively rare large grains and agglomerates with radii ～1 cm scattered over exposed ice. Full mantle development would require hundreds to thousands of cycles. In the case of an initially homogeneous comet Encke, this slow incipient mantle development is shown to be the direct result of its peculiar axial orientation. High obliquity appears required for long-term mantle development for typical rotation rates and perihelia ?1.5 AU. Heat conduction into the nucleus for an incompletely mantled or bald comet has been found to be very important in maintaining relatively higher ice surface temperatures, and hence fluxes, during those portions of the diurnal and orbital cycles which would otherwise be cooler. It is also shown to be at least one cause of post perihelion brightness asymmetries, especially in lower obliquity comets. Maximum heliocentric distances at which 1-μm dust, sand, pebbles, cobbles, and boulders can be permanently ejected from the subsolar point by H₂O (CO₂) are (in AU): 6.9 (16.8), 5.2 (11.5), 1.8 (3.0), 0.21 (0.34) and 0.07 (0.11), respectively. A detailed anatomy of temperature, gas and dust fluxes vs latitude and longitude for a homogeneous rotating comet with fixed axis is given for comparison with future observations. Most H₂O flux histories deduced from brightness data are found to be in reasonable agreement with the model, allowing for uncertainty in radius and albedo. A clear exception is Encke. It is shown that the large discrepancy between Encke's observed and model predicted fluxes, based on radar cross section, can be used to evaluate the extent of exposed ice (<10%). The model is then used to place an active area so as to explain a reported sharp drop in flux on approach to the Sun at 0.78 AU. An active area or areas, <10% of the comet's surface, centered near 65°N latitude appears indicated. Although cyclic mantles are generally indicated for the set of parameters we used, our results show that a global mantle only 1 to 3 cm thick (depending on the orbit) consisting of a full range of grain sizes can cause irresversible evolution to a noncometary body. We investigated the long-term evolution of such a postulated initially thinly mantled cometary object. It was found that after the first few passes and until the end of its dynamic lifetime the object averaged <3 × 10^?12 g cm^?1 sec^?1 H₂O flux. Therefore, if cometary objects evolve into Apollo asteroids, ice should always be accessible within 10 m of the surface despite numerous close perihelion passages. The possible impact of factors not included in the model, such as initial inhomogeneities, coma scattering of radiation, and global redistribution of ejected silicate around the nucleus, are discussed.     

Dust tail streamers of a comet with rotating nucleus

Synthetic images of the dust tail are presented for a comet which has a rotating nucleus with one predominant dust source fixed to it. The images have been generated using a new computer model which, unlike similar models, allows for the study of dust tails caused by a rotating nucleus with an anisotropic distribution of sources.The dust tail is studied in the post-perihelion phase of a parabolic comet with a perihelion distance of 0.5 AU. One finds that in the case of a rotating nucleus with anisotropic emission characteristics streamers caused solely by the dynamics of the dust particles are forming in the dust tail even if there is no dependence between the solar irradiation angle of the source and the amount of dust emitted. If the dust emission depends on the solar irradiation angle of the dust source, then the brightest tail regions do not necessarily coincide with the synchrones for the times of maximum dust emission.As a consequence, a thorough analysis of streamer patterns in a cometary dust tail requires assumptions on the rotational state and the dust source distribution of the nucleus. Otherwise, it seems not possible to discern between streamers which are caused dynamically by nucleus rotation and others which reflect variations in the emission activity.     

Predictions for the Aurigid Outburst of 2007 September 1

The September 2007 encounter of Earth with the 1-revolution dust trail of comet C/1911 N1 (Kiess) is the most highly anticipated dust trail crossing of a known long period comet in the next 50 years. The encounter was modeled to predict the expected peak time, duration, and peak rate of the resulting outburst of Aurigid shower meteors. The Aurigids will radiate with a speed of 67 km/s from a radiant at R.A. = 92°, Decl. = +39° (J2000) in the constellation Auriga. The expected peak time is 11:36 ± 20 min UT, 2007 September 1, and the shower is expected to peak at Zenith Hourly Rate = 200/h during a 10-min interval, being above half this value during 25 min. The meteor outburst will be visible by the naked eye from locations in Mexico, the Western provinces of Canada, and the Western United States, including Hawaii and Alaska. A concerted observing campaign is being organized. Added in proof: first impression of the shower. Prepared as a contribution to the conference proceedings of “Meteoroids 2007”, to be published in the journal “Earth, Moon, and Planets”.     

A Study of Non-Gravitational Effects of Comet C/1995 O1 HALE–BOPP

The role of non-gravitational forces in the evolution of orbitalmotion of C/1995 O1 (Hale–Bopp) has been investigated. Inorbital calculations the observational material covering theperiod from April 1993 up to August 2001 was used. To model thenon-gravitational acceleration, observed and theoretical profilesof the H₂O production rates were employed. A set of forcedprecession models of a rotating cometary nucleus consistent withthe observed spin axis orientation was fitted to positionalobservations. The non-gravitational models allowed us to constrainthe mass and radius of the comet. The orbitalevolution of Comet Hale–Bopp was investigated over ±400 k yusing two sets of randomly varied orbital elements wellrepresenting all positional observations in the pure gravitationalcase, as well as in the non-gravitational case. The calculationsshowed that the comet's motion is predictable only over an interval ofa few orbital periods. The statistical conclusions changesignificantly when non-gravitational effects are included in the analysis.     

Spectrocam-10 Thermal Infrared Observations Of The Dust In Comet C/1995 O1 Hale-Bopp

We describe 5 to 18 μm broadband images and R ∼ 100 spectra of comet Hale-Bopp taken with SpectroCam-10 on the 5 m Hale telescope during six runs between 1996 June and 1997 April. Our data show the gradual warming of dust grains as the comet approached perihelion. In June, the 10 μm silicate emission feature was already stronger than observed in any other comet, and it increased to about 3 times the continuum level near perihelion. Spectral structure attributed to a crystalline olivine grain component remained relatively constant, but other features associated with pyroxenes appeared to vary with heliocentric distance. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Rotational Parameters Of Hale–Bopp (C/1995 O1) From Observations Of The Dust Jets At Pic Du Midi Observatory

We observed comet Hale-Bopp (C/1995 O1) at Pic du Midi Observatory in 1997 from February 2.24 UT to March 31.89 UT with the 1.05-m telescope equipped with a CCD camera and broad- and narrow-band IHW filters. A total of 30000 images were acquired both during night- and day-time. The images were automatically reduced and all the images obtained within 10 min. were co-added to give a set of ∼1000 images used during the analysis. We can identify two jets on the images. The position angle of the brightest jet from February 2.24 UT to March 5.22 UT is measured using an automatic routine which searches for the averaged position angle of the maximum of brightness at a projected distance of 3200–6100 km from the optocenter. A preliminary model of nucleus rotation is used to fit the data and retrieve the rotational parameters of the nucleus. The best fit is found for a source located at a latitude of 64 ± 3°, a sidereal rotation period of 11.35 ± 0.04 h and a right ascension and declination of the North pole of 275 ± 10° and -57 ± 10°. This preliminary analysis shows no evidence for a precession. Grains with velocities of 450–600 m s⁻¹ and radii <;∼ 1 μm dominate the optical scattering cross section in the jets. This revised version was published online in July 2006 with corrections to the Cover Date.     

Mid-Infrared Spectro-Imaging Observations Of Comet Hale-Bopp

Comet C/1995 O1 (Hale-Bopp) was observed with camiras, the Saclay mid-infrared camera, mounted on the Nordic Optical Telescope (Roque de los Muchachos, La Palma), from April 14th to April 25th, 1997. This observing run was part of the European campaign devoted to Hale-Bopp observations from the Canary Islands (PI R. West). camiras spectro-imaging capabilities, achieved with a Circular Variable Filter (of spectral resolution R ≈ 50), were used to obtain spectra of the comet in the N atmospheric window (8–13 μm) over a large field of view (52″ × 78″), at a spatial resolution of ∼1 arcsec. Data were also collected at shorter wavelengths (in the L and M bands). The silicate dust feature around 10 μm is clearly apparent in the data. The shape of the feature varies continuously according to the position in the field. A dust model developed at Saclay in the framework of β-Pictoris dust disk studies was used to interpret the observations. The presence of both olivine and pyroxene with a high degree of crystallinity is needed to account for the observations. A change in the size distribution of the grains allows to reproduce the spatial change of the silicate feature according to the position in the field. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comet McNaught (260P/2012 K2): spin axis orientation and rotation period

Extensive observations of comet 260P/McNaught were carried out between August 2012 and January 2013. The images obtained were used to analyze the comet’s inner coma morphology at resolutions ranging from 250 to about 1000 km/pixel. A deep investigation of the dust features in the inner coma allowed us to identify only a single main active source on the comet’s nucleus, at an estimated latitude of ?50^°±15^°. A thorough analysis of the appearance and of the motion of the morphological structures, supported by graphic simulations of the geometrical conditions of the observations, allowed us to determine a pole orientation located within a circular spot of a 15^°-radius centered at RA=60^°, Dec=0^°. The rotation of the nucleus seems to occur on a single axis and is not chaotic, furthermore no precession effects could be estimated from our measurements. The comet’s spin axis never reached the plane of the sky from October 2012 to January 2013; during this period it did not change its direction significantly (less than 30^°), thus giving us the opportunity to observe mainly structures such as bow-shaped jets departing from the single active source located on the comet’s nucleus. Only during the months of August 2012 and January 2013 the polar axis was directed towards the Earth at an angle of about 45^° from the plane of the sky; this made it possible to observe the development of faint structures like fragments of shells or spirals. A possible rotation period of 0.340±0.01 days was estimated by means of differential photometric analysis.     

Ir Observations Of An Outburst In Comet Hale-Bopp (C/1995 O1)

The comet Hale-Bopp (C/1995 O1) has been observed in the infrared (1–2.5 μm) with the Nordic Optical Telescope (NOT) equipped with the Arcetri NICMOS3 camera (ARNICA). Two observational campaigns, each one lasting about one week, were made when the comet heliocentric distance was about 3 AU. The first campaign was at the end of August and the second at the end of September 1996. During both runs two major outbursts were observed, the more intense of them started the day before the beginning of the second run. In the images recorded during the first three nights (24.8–26.8 Sept.) of the second run a dust shell expanding in the northern quadrant with a projected velocity of 0.14–0.28 km/s is clearly evident. The dust production rate increased by at least a factor ≈3 at the time of the outburst. Also evident on the first night is a change in the IR color that is well correlated with the dust shell. This is an indication that the material released by the outburst has a different composition and/or size distribution than that in the “quiescent” dust coma. In this paper we present preliminary results about the evolution and the photometric characteristics of the dust shell. This revised version was published online in July 2006 with corrections to the Cover Date.     

Thermal Emission From The Dust Coma Of Comet Hale-Bopp And The Composition Of The Silicate Grains

The dust coma of comet Hale-Bopp was observed in the thermal infrared over a wide range in solar heating (R = 4.9–0.9 AU) and over the full wavelength range from 3 μm to 160 μm. Unusual early activity produced an extensive coma containing small warm refractory grains; already at 4.9 AU, the 10 μm silicate emission feature was strong and the color temperature was 30% above the equilibrium blackbody temperature. Near perihelion the high color temperature, strong silicate feature, and high albedo indicated a smaller mean grain size than in other comets. The 8–13 μm spectra revealed a silicate emission feature similar in shape to that seen in P/Halley and several new and long period comets. Detailed spectral structure in the feature was consistent over time and with different instruments; the main peaks occur at 9.3, 10.0 and 11.2 μm. These peaks can be identified with olivine and pyroxene minerals, linking the comet dust to the anhydrous chondritic aggregate interplanetary dust particles. Spectra at 16–40 μm taken with the ISO SWS displayed pronounced emission peaks due to Mg-rich crystalline olivine, consistent with the 11.2 μm peak. This revised version was published online in July 2006 with corrections to the Cover Date.