Secular light curve of Comet 9P/Tempel 1

In support of the Deep Impact Mission, we have updated the secular light curve of 9P/Tempel 1 presented in Paper I [Ferrín, I., 2005. Icarus 178, 493-516], with new data sets. The secular light curves (SLC) of the comet are presented in the log and time plots (Figs. 1 and 2) and provide a clear profile of the overall shape of the envelope. We arrive at the following conclusions: (1) Improved values of 18 photometric parameters are derived including the turn on and turn off points, RON=−3.47±0.05 AU, ROFF=+4.20±0.05 AU, and TON=−410±25 d, TOFF=+555±25 d. (2) The improved SLC shows a most interesting and peculiar shape, with a linear power law of slope n=7.7±0.1 from RON=−3.47 AU to RBP=−2.08±0.05 AU, and then converts to a law with curvature. The break point of the power law at RBP=−2.08 AU, mV(1,R)=14.0±0.1 mag, is interpreted as a change in sublimating something more volatile than water ice (most probably CO₂), to water ice sublimation. In other words, the comet's sublimation is controlled by two different substances. (3) The photometric-age (defined in Paper I) and the time-age of the comet [Ferrín, I., 2006. Icarus. In press] are recomputed, and results in a value P-AGE=21±2 and T-AGE=11±2 comet years. Thus 9P is a young comet. (4) The comet is active almost up to aphelion since the turn off point has been determined at ROFF=+4.20±0.05 AU while aphelion takes place at Q=+4.74 AU. (5) The comet exhibits activity post-aphelion which is not understood. Two hypothesis are advanced to explain this behavior.     

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.     

Rotation and color properties of the nucleus of Comet 2P/Encke

We present results from CCD observations of Comet 2P/Encke acquired at Steward Observatory's 2.3 m Bok Telescope on Kitt Peak. The observations were carried out in October 2002 when the comet was near aphelion. Rotational lightcurves in B-, V-, and R-filters were acquired over two nights of observations, and analysed to study the physical and color properties of the nucleus. The average apparent R-filter magnitude across both nights corresponds to a mean effective radius of 3.95±0.06 km, and this value is similar to that found for the V- and B-filters. Taking the observed brightness range, we obtain a/b?1.44±0.06 for the semi-axial ratio of Encke's nucleus. Applying the axial ratio to the R-filter photometry gives nucleus semi-axes of [3.60±0.09]×[5.20±0.13] km, using the empirically-derived albedo and phase coefficient. No coma or tail was seen despite deep imaging of the comet, and flux limits from potential unresolved coma do not exceed a few percent of the total measured flux, for standard coma models. This is consistent with many other published data sets taken when the comet was near aphelion. Our data includes the first detailed time series multi-color measurements of a cometary nucleus, and significant color variations were seen on October 3, though not repeated on October 4. The average color indices across both nights are: (V−R)=0.39±0.06 and (B−V)=0.73±0.06 (). We analysed the R-filter time-series photometry using the method of Harris et al. [Harris, A.W., Young, J.W., Bowell, E., Martin, L.J., Millis, R.L., Poutanen, M., Scaltriti, F., Zappala, V., Schober, H.J., Debehogne, H., Zeigler, K.W., 1989. Icarus 77, 171-186] to constrain the rotation period of the comet's nucleus, and find that a period of ∼11.45 h will satisfy the data, however the errors bars are large. We have successfully linked our data with the September 2002 data from Fernández et al. [Fernández, Y.R., Lowry, S.C., Weissman, P.R., Mueller, B.E.A., Samarasinha, N.H., Belton, M.J.S., Meech, K.J., 2005. Icarus 175, 194-214]—taken just 2-3 weeks before the current data set—and we show that a rotation period of just over 11 h works extremely well for the combined data set. The resulting best-fit period is 11.083±0.003 h, consistent with the Fernández et al. value.     

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.     

Secular light curve of Comet 28P/Neujmin 1 and of spacecraft target Comets 1P/Halley, 9P/Tempel 1, 19P/Borrelly, 21P/Giacobinni-Zinner, 26P/Grigg-Skjellerup, 67P/Churyumov-Gerasimenko, and 81P/Wild 2

We present the secular light curves of eight comets listed in the title. Two plots per comet are needed to study these objects: a reduced magnitude (to Δ=1 AU = geocentric distance) vs time, and a reduced magnitude vs LogR (R=heliocentric distance). A total of over 16 new parameters, are measured from both plots, and give an unprecedented amount of information to characterize these objects: the onset of sublimation (RON), the offset of sublimation (ROFF), the time lag at perihelion (LAG), the absolute magnitude (m(1,1)), the maximum magnitude at perihelion (mMAX(1,LAG)), the nuclear magnitudes (VN), the amplitude of the secular light curve (ASEC), plus several others, and the photometric functions needed to describe the envelope. The most significant findings of this investigation are: (a) The envelope of the observations is the best representation of the secular light curve. (b) The H10 photometric system is unable to explain the curves and a new set of photometric rules and functions is used. (c) Only four comets exhibit power laws in their secular light curves, and only partially: 1P, 19P, 21P, and 81P. All others have to be described by more complex functions. Of the four, three exhibit a break of the power law, requiring two laws pre-perihelion and one post-perihelion. The reason for this behavior is not understood. (d) We predict the existence of a photometric anomaly in the secular light curve of 67P/Churyumov-Gerasimenko, evidenced by a region of diminished activity from −119 to −6 days before perihelion, that might be interpreted as a topographic effect or the turn off of an active region. (e) We define a photometric parameter (P-AGE) that attempts to measure the relative age of a comet through the activity exhibited in the secular light curve. 81P/Wild 2 (a comet that has recently entered the inner Solar System) is confirmed as a young object, while 28P/Neujmin 1 is confirmed as a very old comet. (f) Arranging the comets by P-AGE also classifies them by shape. A preliminary classification is achieved. (g) The old controversy of what is a nuclear magnitude is clearly resolved.     

The dust trail of Comet 67P/Churyumov-Gerasimenko between 2004 and 2006

We report on observations of the dust trail of Comet 67P/Churyumov-Gerasimenko (CG) in visible light with the Wide Field Imager at the ESO/MPG 2.2 m telescope at 4.7 AU before aphelion, and at with the MIPS instrument on board the Spitzer Space Telescope at 5.7 AU both before and after aphelion. The comet did not appear to be active during our observations. Our images probe large dust grains emitted from the comet that have a radiation pressure parameter β<0.01. We compare our observations with simulated images generated with a dynamical model of the cometary dust environment and constrain the emission speeds, size distribution, production rate and geometric albedo of the dust. We achieve the best fit to our data with a differential size distribution exponent of −4.1, and emission speeds for a β=0.01 particle of 25 m/s at perihelion and 2 m/s at 3 AU. The dust production rate in our model is on the order of 1000 kg/s at perihelion and 1 kg/s at 3 AU, and we require a dust geometric albedo between 0.022 and 0.044. The production rates of large (>) particles required to reproduce the brightness of the trail are sufficient to also account for the coma brightness observed while the comet was inside 3 AU, and we infer that the cross-section in the coma of CG may be dominated by grains of the order of .     

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.     

New near-aphelion light curves of Comet 2P/Encke

We present new, near-aphelion, time series of photometry of Comet 2P/Encke in Cousins-R band. With these light curves we find that the dominant, synodic rotational periodicity is either P₀=11.079±0.009 h or 2P₀=22.158±0.012 h. This is in contrast to data from the 1980s published by others that are consistent with 15.08- and 22.6-h periods. Those periods do not satisfy our phased light curves, and also the 1980s data are not easily reconciled with our periods. This could be due to P/Encke having non-principal axis rotation or due to a drift in the rotation period caused by outgassing torques. We observed the comet at five epochs: July, August, September, and October 2001, and September 2002, and the comet was at times intrinsically brighter than expected for a bare nucleus, due to an apparent contribution from an unresolved coma. Three-quarters of the data were obtained in the second and fifth epochs, and we analyzed these two time series using both the phase-dispersion minimization and “WindowCLEAN” techniques. At both epochs and with both techniques strong periodicities were found near frequencies and . By then using visual inspection of the phased light curves to corroborate these frequencies, and by using the data from the other three epochs to properly align light curve features, we were able to derive P₀ and 2P₀ as the only solutions that satisfy all our observations. The periodicity due to f₁ is clearly seen in our data, but we cannot tell from our data alone whether it is a manifestation of the nucleus's shape, non-principal axis rotation, or both.     

Dark red debris from three short-period comets: 2P/Encke, 22P/Kopff, and 65P/Gunn

We present observations of the extended dust structures near the orbits of three short-period comets: 2P/Encke, 22P/Kopff, and 65P/Gunn. The dust trails were originally discovered by the Infrared Astronomical Satellite (IRAS). Our observations were made using wide-field optical CCD cameras on the University of Hawaii 2.24-m telescope, the Canada-France-Hawaii 3.6-m telescope, and the Kiso 1.05-m Schmidt telescope. We compared the observed images with models and found that the extended structures seen around 2P/Encke and 22P/Kopff before perihelion passage were most likely “dust trails,” whereas images taken after perihelion passage show a high contamination by recently released particles (i.e., particles in Neck-Line structures are visible). We could not confirm the existence of a dust trail from 65P/Gunn within the field of view of the camera used. The effective sizes of the particles responsible for the scattered light were estimated at 1-100 mm (2P/Encke), 1-10 mm (22P/Kopff), and 100 μm-1 mm (65P/Gunn), respectively, which is consistent with previous studies of dust trails made with infrared space telescopes and optical telescopes. We evaluated the mass loss rates of these comets, averaged over their orbits, as reaching (2P/Encke), (22P/Kopff), and (65P/Gunn). These values are consistent with previous work. Therefore, the total amount of material ejected from these three comets is , which would contribute a considerable fraction of the lost within 1 AU that needs to be replaced if the zodiacal cloud is to be maintained in a steady state. We also found that the particles in the dust structures are significantly redder than the Sun and the zodiacal light, and might be redder than the average short-period comet nuclei. Specifically, the reflectivity gradients of 2P/Encke, 22P/Kopff, and 65P/Gunn are 13±7 (% ¹⁰³ Å⁻¹), 20±5 (% ¹⁰³ Å⁻¹), and 15±4 (% ¹⁰³ Å⁻¹), respectively. We examined the change in color with distance from the nucleus. No clear correlation was detected for 2P/Encke or 22P/Kopff to an accuracy of 3-11%, while the 65P/Gunn tail did show color variation, becoming redder with increasing distance from the nucleus. This dark red material, consisting of particles of sand-cobble size, has marginally escaped from the nuclei and will evolve into finer-grained interplanetary dust particles after subsequent collisions.     

Near-nucleus photometry of comets using archived NEAT data

Though optimized to discover and track fast moving Near-Earth Objects (NEOs), the Near-Earth Asteroid Tracking (NEAT) survey dataset can be mined to obtain information on the comet population observed serendipitously during the asteroid survey. We have completed analysis of over 400 CCD images of comets obtained during the autonomous operations of two 1.2-m telescopes: the first on the summit of Haleakala on the Hawaiian island of Maui and the second on Palomar Mountain in southern California. Photometric calibrations of each frame were derived using background catalog stars and the near-nucleus comet photometry measured. We measured dust production and normalized magnitudes for the coma and nucleus in order to explore cometary activity and comet size-frequency distributions. Our data over an approximately two-year time frame (2001 August-2003 February) include 52 comets: 12 periodic, 19 numbered, and 21 non-periodic, obtained over a wide range of viewing geometries and helio/geocentric distances. Nuclear magnitudes were estimated for a subset of comets observed. We found that for low-activity comets (Afρ<100 cm) our model gave reasonable estimates for nuclear size and magnitude. The slope of the cumulative luminosity function of our sample of low-activity comets was 0.33 ± 0.04, consistent with the slope we measured for the Jupiter-family cometary nuclei collected by Fernández et al. [Fernández, J.A., Tancredi, G., Rickman, H., Licandro, J., 1999. Astron. Astrophys. 392, 327-340] of 0.38 ± 0.02. Our slopes of the cumulative size distribution α=1.50±0.08 agree well with the slopes measured by Whitman et al. [Whitman, K., Morbidelli, A., Jedicke, R., 2006. Icarus 183, 101-114], Meech et al. [Meech, K.J., Hainaut, O.R., Marsden, B.G., 2004. Icarus 170, 463-491], Lowry et al. [Lowry, S.C., Fitzsimmons, A., Collander-Brown, S., 2003. Astron. Astrophys. 397, 329-343], and Weissman and Lowry [Weissman, P.R., Lowry, S.C., 2003. Lunar Planet. Sci. 34. Abstract 34].     

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.     

A tale of two very different comets: ISO and MSX measurements of dust emission from 126P/IRAS (1996) and 2P/Encke (1997)

We present the characteristics of the dust comae of two comets, 126P/IRAS, a member of the Halley family (a near-isotropic comet), and 2P/Encke, an ecliptic comet. We have primarily used mid- and far-infrared data obtained by the ISOPHOT instrument aboard the Infrared Space Observatory (ISO) in 1996 and 1997, and mid-infrared data obtained by the SPIRIT III instrument aboard the Midcourse Space Experiment (MSX) in 1996. We find that the dust grains emitted by the two comets have markedly different thermal and physical properties. P/IRAS's dust grain size distribution appears to be similar to that of fellow family member 1P/Halley, with grains smaller than 5 microns dominating by surface area, whereas P/Encke emits a much higher fraction of big (20 μm and higher) grains, with the grain mass distribution being similar to that which is inferred for the interplanetary dust population. P/Encke's dearth of micron-scale grains accounts for its visible-wavelength classification as a “gassy” comet. These conclusions are based on analyses of both imaging and spectrophotometry of the two comets; this combination provides a powerful way to constrain cometary dust properties. Specifically, P/IRAS was observed preperihelion while 1.71 AU from the Sun, and seen to have a 15-arcmin long mid-infrared dust tail pointing in the antisolar direction. No sunward spike was seen despite the vantage point being nearly in the comet's orbital plane. The tail's total mass at the time was about 8×10⁹ kg. The spectral energy distribution (SED) is best fit by a modified greybody with temperature T=265±15 K and emissivity ε proportional to a steep power law in wavelength λ: ε∝λ^−α, where α=0.50±0.20(2σ). This temperature is elevated with respect to the expected equilibrium temperature for this heliocentric distance. The dust mass loss rate was between 150-600 kg/s (95% confidence), the dust-to-gas mass loss ratio was about 3.3, and the albedo of the dust was 0.15±0.03. Carbonaceous material is depleted in the comet's dust by a factor of 2-3, paralleling the C₂ depletion in P/IRAS's gas coma. P/Encke, on the other hand, observed while 1.17 AU from the Sun, had an SED that is best fit by a Planck function with T=270±15 K and no emissivity falloff. The dust mass loss rate was 70-280 kg/s (95% confidence), the dust-to-gas mass loss ratio was about 2.3, and the albedo of the dust was about 0.06±0.02. These conclusions are consistent with the strongly curved dust tail and bright dust trail seen by Reach et al. (2000; Icarus 148, 80) in their ISO 12-μm imaging of P/Encke. The observed differences in the P/IRAS and P/Encke dust are most likely due to the less evolved and insolated state of the P/IRAS nuclear surface. If the dust emission behavior of P/Encke is typical of other ecliptic comets, then comets are the major supplier of the interplanetary dust cloud.     

R- and J-band photometry of Comets 2P/Encke and 9P/Tempel 1

Near-simultaneous R- and J-band photometric measurements of the short-period Comets 2P/Encke and the Deep Impact mission target 9P/Tempel 1 were obtained. The resulting R-J colors are +0.82±0.08 mag and +1.46±0.13 mag for Encke and Tempel 1, respectively. Tempel 1's color is redder than the solar R-J color index of +0.76. The Tempel 1 observations directly detected the nucleus while the Encke observations likely suffered from coma contamination.     

The excited spin state of Comet 2P/Encke

Ways to rationalize the different periods (e.g., 15.08 h, Luu and Jewitt, 1990, Icarus 86, 69-81; 11.01 h, Fernández et al., 2004, Icarus, in this issue; Lowry et al., 2003, Lunar Planet. Sci. XXXIV, Abstract 2056) seen in near aphelion R-band light curves of Comet 2P/Encke are explored. We show that the comet is usually active at aphelion and it's observed light curves contain signal from both the nucleus and an unresolved coma. The coma contribution to the observed brightness is generally found to dominate with the nucleus providing from 28 to 87% of the total brightness. The amplitude of the observed variations cannot be explained by the nucleus alone and are due to coma activity. We show that some seven periodicities exist in the observed light curves at various times and that this is likely the result of an active nucleus spinning in an excited spin state. The changing periodicities are probably due to changes in the relative strengths of the active areas. We work out possible excited states based on experience with model light curves and by using an analogy to light curve observations of Comet 1P/Halley for which the spin state has been separately determined from spacecraft observations. There is a possibility of a fully relaxed principal axis spin state (0.538 d⁻¹; P=44.6 h) but, because it provides a poorer fit to the observed periodicities than the best fit excited state together with the absence of a peak near 1.08 d⁻¹ (2fφ) in the frequency spectrum of the Fernández et al. (2000, Icarus 147, 145-160) thermal IR lightcurve, we consider it unlikely. Both SAM and LAM excited states are allowed by the underlying periodicities and additional information is needed to choose between these. Our choice of a low excitation SAM state, i.e., one in which the instantaneous spin axis nutates around the total angular momentum vector in a motion that is characterized by limited angular oscillations around the long axis, is based on Sekanina's (1988, Astron J. 95, 911-924, 1988, Astron. J. 96, 1455-1475) interpretation of the fan coma that this comet often displays. We argue that possible LAM states are excluded either because they are too difficult to excite or because they would be inconsistent with the formation of the observed fan morphology. Two possible SAM states emerge that provide good fits to the observed periodicities, one with a precessional frequency for the long axis about the total angular momentum vector of 1.614 d⁻¹ (P?=14.9 h) and an oscillation frequency around the long axis of 0.539 d⁻¹ (Pψ=44.5 h) and a second with a precessional frequency of 2.162 d⁻¹ (P?=11.1 h) combined with an oscillation around the long axis of 0.502 d⁻¹ (Pψ=47.8 h). While either solution is possible, the latter is, in a least squares sense, more likely to be the actual spin state. In both cases the direction of the total angular momentum vector (αM,δM[J2000]=198.6, −0.3 deg) is assumed to be defined by the evolving geometry and morphology of the coma (Sekanina, 1988, Astron J. 95, 911-924, 1988, Astron. J. 96, 1455-1475; Festou and Barale, 2000, Astron J. 119, 3119-3132). We discuss the possible locations of the primary active areas found by Sekanina (1988, Astron J. 95, 911-924, 1988, Astron. J. 96, 1455-1475) and, while they are at high cometographic latitudes, they do not have to be physically located close the region were the axis of maximum moment of inertia pierces the surface (i.e., at high cometocentric latitude). We offer a new interpretation of the 10.7 μm data by Fernández et al. (2000, Icarus 147, 145-160) which yields an axial ratio a/b=2.04. This, with the two SAM states that we have found, requires that b/c>1.18 or >1.09 implying a significant asymmetry in the shape of the elongated nucleus. For the observed fan morphology to be maintained, the true axial ratio b/c cannot be much larger than these limiting values otherwise the amplitude of the oscillation about the long axis becomes too large and the fan morphology would be destroyed. The precise phasing of the spin modes, i.e., the value of the Euler angles at a particular time, is not determinable from the current data set, but a set of well sampled thermal infrared observations of the nucleus covering many periods and a wide range of observing geometries could provide this information in the future as well as clearly distinguishing between the two excited spin states.     

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.     

Non-constant rotation period of Comet C/2001 K5 (LINEAR)

The article presents results of CCD photometry in R-band of a dynamically new Comet C/2001 K5 (LINEAR), obtained at a heliocentric distance of about 5.6 AU, after the perihelion passage. Being so distant from the Sun, this comet was extremely active (Afρ close to 2000 cm), exhibiting quite well developed dust coma and tail. During the observations, general photometric behavior of the comet with heliocentric distance r was well described by the 2.5nlog(r) function with coefficient n=5. The radial profiles of the coma were found to be undulated, with mean slope of the dependence between cometary magnitude and 2.5log of aperture radius (at comet distance) equal to . The light curve of Comet LINEAR exhibited short-term variability which we attributed to cyclic changes of dust emission, induced by nucleus rotation. Model computations by some authors have revealed that active comets can change their spin status quite substantially even during a single orbital revolution. Thus, attempting to search for a rotation frequency, we have modified the classical PDM approach by including the spin acceleration term. Such DynamicalPDM (DPDM) method revealed the most reliable solution for the frequency f₀=0.019048±0.000013 h⁻¹ and its first time-derivative (index “zero” denotes reference to the mid time of the whole observing run), indicating a rapid spin-down of the nucleus. These parameters are equivalent to the rotation period of 52.499±0.036 h and its relative increment of 0.02729±0.00013. We present the most probable evolution of the rotation frequency of Comet LINEAR, based on the results of periodicity analysis and a simple, almost parameter independent, dynamical model of nucleus rotation. It is also shown that the DPDM may be an effective tool for determination of a nucleus radius, which provided us with the value of 1.53±0.25 km for Comet LINEAR.     

On the origin of the unusual orbit of Comet 2P/Encke

The orbit of Comet 2P/Encke is difficult to understand because it is decoupled from Jupiter—its aphelion distance is only 4.1 AU. We present a series of orbital integrations designed to determine whether the orbit of Comet 2P/Encke can simply be the result of gravitational interactions between Jupiter-family comets and the terrestrial planets. To accomplish this, we integrated the orbits of a large number of objects from the trans-neptunian region, through the realm of the giant planets, and into the inner Solar System. We find that at any one time, our model predicts that there should be roughly 12 objects in Encke-like orbits. However, it takes roughly 200 times longer to evolve onto an orbit like this than the typical cometary physical lifetime. Thus, we suggest that (i) 2P/Encke became dormant soon after it was kicked inward by Jupiter, (ii) it spent a significant amount of time inactive while rattling around the inner Solar System, and (iii) it only became active again as the ν₆ secular resonance drove down its perihelion distance.     

The nucleus of Deep Impact target Comet 9P/Tempel 1

On UT 2000 August 21 we obtained simultaneous visible and mid-infrared observations of Comet 9P/Tempel 1, the target of the upcoming NASA Discovery Program mission Deep Impact. The comet was still quite active while 2.55 AU from the Sun (post-perihelion). Two independent analyses of our data, one parameterizing the coma morphology and the other modeling infrared spectrophotometry, show that the nucleus's cross section at the time the data were taken corresponds to an effective radius of 3.0±0.2 km. Based on visible-wavelength photometry of the comet taken during this observing run and others in the summer of 2000, all of which show the rotational modulation of the nucleus's brightness, we find that the infrared data were obtained near the maximum of the light curve. If we assume that the nucleus's light curve had a peak-to-valley range of 0.6±0.2 mag, then the mean effective radius is 2.6±0.2 km. Visible-wavelength photometry of the nucleus, including data published by other groups, lets us constrain the nucleus's R-band geometric albedo: 0.072±0.016. The nucleus's flux contributed about 85% of the light in the mid-infrared images.     

Surface temperature of the nucleus of Comet 9P/Tempel 1

The Deep Impact (DI) spacecraft encountered Comet 9P/Tempel 1 on July 4th, 2005 and observed it with several instruments. In particular, we obtained infrared spectra of the nucleus with the HRI-IR spectrometer in the wavelength range of 1.0-4.9 μm. The data were taken before impact, with a maximum resolution of ∼120 m per pixel at the time of observation. From these spectra, we derived the first directly observed temperature map of a comet nucleus. The surface temperature varied from 272±7 to 336±7 K on the sunlit hemisphere, matching the surface topography and incidence angle. The derived thermal inertia is low, most probably <50 W K⁻¹ m⁻² s^1/2. Combined with other arguments, it is consistent with the idea that most of rapidly varying thermal physical processes, in particular the sublimation of volatiles around perihelion, should occur close to the surface. Thermal inertia is sufficient to explain the temperature map of the nucleus of Comet Tempel 1 to first order, but other physical processes like roughness and self-radiation are required to explain the details of the temperature map. Finally, we evaluated that the Standard Thermal Model is a good approximation to derive the effective radius of a cometary nucleus with an uncertainty lower than ∼10% if combined with a thermal infrared light curve.     

Observations of the inner coma of C/1995O1 (Hale-Bopp)—gas and dust production

Hale-Bopp (C/1995 O1) was the most productive recent comet observed in terms of gas and dust output. Since its discovery in 1995 at a distance of 7.14 AU from the Sun, the comet has been well observed, revealing the dynamics of a rare and large comet. Hale-Bopp showed strong emissions of the principle cometary gases CN, C₃, and C₂, as well as an abundance of dust. The production rates of these gases were found to be 1.45×10²⁸, 1.71×10²⁸, and , respectively, with dust production, in terms of Afρ, , as measured in the green continuum (5260 Å). The observations for this paper are presented in two groups spanning 10 days each, one group centered near 32 days prior to and the other 21 days after perihelion. The averages of dust and gas production rates show a slightly higher value for each prior to perihelion than after perihelion, consistent with a possible peak in production a few weeks prior to perihelion passage.