The size-frequency distribution of dormant Jupiter family comets

We estimate the total number and the slope of the size-frequency distribution (SFD) of dormant Jupiter family comets (JFCs) by fitting a one-parameter model to the known population. We first select 61 near-Earth objects (NEOs) that are likely to be dormant JFCs because their orbits are dynamically coupled to Jupiter [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J., Levison, H.F., Michel, P., Metcalfe, T.S., 2002a. Icarus 156, 399-433]. Then, from the numerical simulations of Levison and Duncan [1997. Icarus 127, 13-32], we construct an orbit distribution model for JFCs in the NEO orbital element space. We assume an orbit-independent SFD for all JFCs, the slope of which is our unique free parameter. Finally, we compute observational biases for dormant JFCs using a calibrated NEO survey simulator [Jedicke, R., Morbidelli, A., Spahr, T., Petit, J., Bottke, W.F., 2003. Icarus 161, 17-33]. By fitting the biased model to the data, we estimate that there are ∼75 dormant JFCs with H<18 in the NEO region and that the slope of their cumulative SFD is −1.5±0.3. Our slope for the SFD of dormant JFCs is very close to that of active JFCs as determined by Weissman and Lowry [2003. Lunar Planet. Sci. 34. Abstract 2003]. Thus, we argue that when JFCs fade they are likely to become dormant rather than to disrupt and that the fate of faded comets is size-independent. Our results imply that the size distribution of the JFC progenitors—the scattered disk trans-neptunian population—either (i) has a similar and shallow SFD or (i^′) is slightly steeper and physical processes acting on the comets in a size-dependent manner creates the shallower active comet SFD. Our measured slope, typical of collisionally evolved populations with a size-dependent impact strength [Benz, W., Asphaug, E., 1999. Icarus 142, 5-20], suggests that scattered disk bodies reached collisional equilibrium inside the protoplanetary disk prior to their removal from the planetary region.     

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].     

Debiased Orbital and Absolute Magnitude Distribution of the Near-Earth Objects

The orbital and absolute magnitude distribution of the near-Earth objects (NEOs) is difficult to compute, partly because only a modest fraction of the entire NEO population has been discovered so far, but also because the known NEOs are biased by complicated observational selection effects. To circumvent these problems, we created a model NEO population which was fit to known NEOs discovered or accidentally rediscovered by Spacewatch. Our method was to numerically integrate thousands of test particles from five source regions that we believe provide most NEOs to the inner Solar System. Four of these source regions are in or adjacent to the main asteroid belt, while the fifth one is associated with the transneptunian disk. The nearly isotropic comets, which include the Halley-type comets and the long-period comets, were not included in our model. Test bodies from our source regions that passed into the NEO region (perihelia q<1.3 AU and aphelia Q≥0.983 AU) were tracked until they were eliminated by striking the Sun or a planet or were ejected out of the inner Solar System. These integrations were used to create five residence time probability distributions in semimajor axis, eccentricity, and inclination space (one for each source). These distributions show where NEOs from a given source are statistically most likely to be located. Combining these five residence time probability distributions with an NEO absolute magnitude distribution computed from previous work and a probability function representing the observational biases associated with the Spacewatch NEO survey, we produced an NEO model population that could be fit to 138 NEOs discovered or accidentally rediscovered by Spacewatch. By testing a range of possible source combinations, a best-fit NEO model was computed which (i) provided the debiased orbital and absolute magnitude distributions for the NEO population and (ii) indicated the relative importance of each NEO source region.Our best-fit model is consistent with 960±120 NEOs having H<18 and a<7.4 AU. Approximately 44% (as of December 2000) have been found so far. The limits on this estimate are conditional, since our model does not include nearly isotropic comets. Nearly isotropic comets are generally restricted to a Tisserand parameter (with respect to Jupiter) of T<2, such that few are believed to have a<7.4 AU. Our computed NEO orbital distribution, which is valid for bodies as faint as H<22, indicates that the Amor, Apollo, and Aten populations contain 32±1%, 62±1%, and 6±1% of the NEO population, respectively. We estimate that the population of objects completely inside Earth's orbit (IEOs) arising from our source regions is 2% the size of the NEO population. This value does not include the putative Vulcanoid population located inside Mercury's orbit. Overall, our model predicts that ∼61% of the NEO population comes from the inner main belt (a<2.5 AU), ∼24% comes from the central main belt (2.5<a<2.8 AU), ∼8% comes from the outer main belt (a>2.8 AU), and ∼6% comes from the Jupiter-family comet region (2<T?3). The steady-state population in each NEO source region, as well as the influx rates needed to replenish each region, were calculated as a by-product of our method. The population of extinct comets in the Jupiter-family comet region was also computed.     

Realistic survey simulations for kilometer class near Earth objects

We present a new Near Earth Object (NEO) survey simulator which incorporates the four-dimensional population model of 4668 NEOs [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] and the observing strategies of most asteroid search programs. With the recent expansion of survey capabilities, previous simulators focused on a specific survey facility are no longer useful in predicting the future detection rates. Our simulation is a superposition of simplified search patterns adopted by all major wide-field surveys in operation in both hemispheres. We defined five different simulation periods to follow the evolution of survey efficiencies reflecting changes in either search volume as a result of upgrades of telescopes and instruments or in observing schedules. The simulator makes remarkably good reproductions of actual survey results as of December 2005, not only the total number of detections but also (a,e,i,H) (‘H’ means absolute magnitude of an asteroid) distributions. An extended experiment provides excellent predictions for discovery statistics of NEOs (H<18) reported to the Minor Planet Center in 2006. These support that our simulator is a plausible approximation of real surveys. We further confirm that, with the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] population model and present survey capability, the 90% completeness level of kilometer-sized NEOs will be achieved by 2010 or 2011. However, about 8% of the kilometer-sized or larger NEOs would remain undetected even after 10-year operation (2007-2016) of all current NEO survey facilities. They are apparently faint, with orbits characterized by large semimajor axis and higher eccentricity; these “hardest-to-find” objects tend to elude the search volume of existing NEO survey facilities. Our simulation suggests that 15% of undetectable objects are Atens and Inner Earth Objects. Because of their orbital characteristics, they will remain within ±45° from the Sun, thus cannot be discovered in the forthcoming decade if our effort is limited to current ground-based telescopes.     

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.     

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.     

The orbit and size distribution of small Solar System objects orbiting the Sun interior to the Earth's orbit

We present the first observational measurement of the orbit and size distribution of small Solar System objects whose orbits are wholly interior to the Earth's (Inner Earth Objects, IEOs, with aphelion <0.983 AU). We show that we are able to model the detections of near-Earth objects (NEO) by the Catalina Sky Survey (CSS) using a detailed parameterization of the CSS survey cadence and detection efficiencies as implemented within the Jedicke et al. [Jedicke, R., Morbidelli, A., Spahr, T., Petit, J.M., Bottke, W.F., 2003. Icarus 161, 17-33] survey simulator and utilizing the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] model of the NEO population's size and orbit distribution. We then show that the CSS detections of 4 IEOs are consistent with the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] IEO model. Observational selection effects for the IEOs discovered by the CSS were then determined using the survey simulator in order to calculate the corrected number and H distribution of the IEOs. The actual number of IEOs with H<18 (21) is 36±26 (530±240) and the slope of the H magnitude distribution (∝¹⁰αH) for the IEOs is . The slope is consistent with previous measurements for the NEO population of αNEO=0.35±0.02 [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] and αNEO=0.39±0.013 [Stuart, J.S., Binzel, R.P., 2004. Icarus 170, 295-311]. Based on the agreement between the predicted and observed IEO orbit and absolute magnitude distributions there is no indication of any non-gravitational effects (e.g. Yarkovsky, tidal disruption) affecting the known IEO population.     

From Magnitudes to Diameters: The Albedo Distribution of Near Earth Objects and the Earth Collision Hazard

A recently published model of the Near Earth Object (NEO) orbital-magnitude distribution (Bottke et al., 2002, Icarus156, 399-433.) relies on five intermediate sources for the NEO population: the ν₆ resonance, the 3:1 resonance, the outer portion of the main belt (i.e., 2.8-3.5 AU), the Mars-crossing population adjacent to the main belt, and the Jupiter family comet population. The model establishes the relative contribution of these sources to the NEO population. By computing the albedo distribution of the bodies in and/or near each of the five sources, we can deduce the albedo distribution of the NEO population as a function of semimajor axis, eccentricity, and inclination. A problem with this strategy, however, is that we do not know a priori the albedo distribution of main belt asteroids over the same size range as observed NEOs (diameter D<10 km). To overcome this problem, we determined the albedo distribution of large asteroids in and/or near each NEO source region and used these results to deduce the albedo distribution of smaller asteroids in the same regions. This method requires that we make some assumptions about the absolute magnitude distributions of both asteroid families and background asteroids. Our solution was to extrapolate the observed absolute magnitude distributions of the families up to some threshold value H_thr, beyond which we assumed that the families' absolute magnitude distributions were background-like.We found that H_thr=14.5 provides the best match to the color vs heliocentric distance distribution observed by the Sloan Digital Sky Survey. With this value of H_thr our model predicts that the debiased ratio between dark and bright (albedo smaller or larger than 0.089) objects in any absolute-magnitude-limited sample of the NEO population is 0.25±0.02. Once the observational biases are properly taken into account, this agrees very well with the observed C/S ratio (0.165 for H<20). The dark/bright ratio of NEOs increases to 0.87±0.05 if a size-limited sample is considered. We estimate that the total number of NEOs larger than a kilometer is 855±110, which, compared to the total number of NEOs with H<18 (963±120), shows that the usually assumed conversion H=18?D=1 km slightly overestimates the number of kilometer-size objects.Combining our orbital distribution model with the new albedo distribution model, and assuming that the density of bright and dark bodies is 2.7 and 1.3 g/cm³, respectively, we estimate that the Earth should undergo a 1000 megaton collision every 63,000±8000 years. On average, the bodies capable of producing 1000 megaton of impact energy are those with H<20.6. The NEOs discovered so far carry only 18±2% of this collision probability.     

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.     

Sunskirting comets discovered with the LASCO coronagraphs over the decade 1996–2008

In addition to an unprecedented number of Kreutz sungrazing comets, the LASCO coronagraphs have discovered some 238 unrelated “sunskirting” comets over the 12 years from 1996 to 2008. This new class is organized in several groups, and at least two comets have further been found periodic. This article presents the photometry and the heliocentric light curves of these 238 sunskirting comets. The bulk of them exhibit a continuous increase of the brightness as the comet approaches the Sun, reach a peak before perihelion and then progressively fade with a large variety of brightness gradients. However some of them have peak brightness either at or post-perihelion, whereas a quite large number are approximately flat. Likewise for the sungrazers, we find a color effect prominent between 8 and 40R_⊙ (solar radii) which we interpret as resulting from the emission lines of the Na I doublet (D lines). We finally characterize the different groups of sunskirters on the basis of their cumulative distribution function of the peak brightness and of their fragmentation history.     

Nuclear spin temperature of ammonia in Comet 9P/Tempel 1 before and after the Deep Impact event

The Deep Impact mission succeeded in excavating inner materials from the nucleus of Comet 9P/Tempel 1 on 2005 July 04 (at 05:52 UT). Comet 9P/Tempel 1 is one of Jupiter family short period comets, which might originate in the Kuiper belt region in the solar nebula. In order to characterize the comet and to support the mission from the ground-based observatory, optical high-dispersion spectroscopic observations were carried out with the echelle spectrograph (UVES) mounted on the 8-m telescope VLT (UT2) before and after the Deep Impact event. Ortho-to-para abundance ratios (OPRs) of cometary ammonia were determined from the NH₂ emission spectra. The OPRs of ammonia on July 3.996 UT and 4.997 UT were derived to be 1.28±0.07 (nuclear spin temperature: Tspin=24±2 K) and 1.26±0.08 (Tspin=25±2 K), respectively. There is no significant change between before and after the impact. Actually, most materials ejected from the impact site could have moved away from the nucleus on July 4.997 UT, about 17 h after the impact. However, a small fraction of the ejected materials might remain in the slit of UVES instrument at that time because an excess of about 20% in the NH₂ emission flux is observed above the normal activity level was found [Manfroid, J., Hutsemékers, D., Jehin, E., Cochran, A.L., Arpigny, C., Jackson, W.M., Meech, K.J., Schulz, R., Zucconi, J.-M., 2007. Icarus. This issue]. If the excess of NH₂ on July 04.997 UT was produced from icy materials excavated by the Deep Impact, then an upper-limit of the ammonia OPR would be 1.75 (Tspin>17 K) for those materials. On the other hand, the OPR of ammonia produced from the quiescent sources was similar to that of the Oort cloud comets observed so far. This fact may imply that physical conditions where cometary ices formed were similar between Comet 9P/Tempel 1 and the Oort cloud comets.     

Comet classification with new methods for gas and dust spectroscopy

We present the results of a program of comet long-slit spectroscopy with the Kast Dual Spectrograph on the 3-m Shane Telescope at Lick Observatory. A total of 26 comets, from a variety of dynamical families, were observed on 39 different nights from 1996 to 2007. A new statistical method extracted the twilight sky from comet frames, because traditional sky subtraction techniques were inadequate. Because previously published Haser model parent and daughter scale lengths did not fit the data well, unbiased ranges of scale lengths were searched for the best-fitting pairs. Coma gas production rates for OH, CN, C₂, C₃, NH, NH₂, and OH confirmed the widely reported carbon-chain depletion for a sub-class of comets, most notably high-perihelion Jupiter-family comets observed at r_h > 1.5 AU, with different behaviors for C₂ and C₃. Our long-slit spectroscopy data was also adapted for the A(θ)fρ dust production parameter. The assumption that A(θ)fρ is constant throughout the nucleus was not upheld. High dust-to-gas ratios for comets with large perihelia were not a selection effect, and suggest that the dust was released earlier in the formation of the coma than the gas. The dust-to-gas ratio did not exhibit any evolutionary traces between different comet dynamical families. The comet survey illuminates the diversity among comets, including the unusually carbon poor Comet 96P/Machholz.     

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.     

The key role of massive stars in Oort cloud comet dynamics

The effects of a sample of 1300 individual stellar encounters spanning a wide range of parameter values (mass, velocity and encounter distance) are investigated. Power law fits for the number of injected comets demonstrate the long range effect of massive stars, whereas light stars affect comets mainly along their tracks. Similarly, we show that the efficiency of a star to fill the phase space region of the Oort cloud where the Galactic tides are able to inject comets into the observable region - the so-called “tidally active zone” (TAZ) - is also strongly dependent on the stellar mass. Power laws similar to those for direct injection are obtained for the efficiency of stars to fill the TAZ. This filling of the tidally active zone is crucial for the long term flux of comets from the Oort cloud. Based on long-term Monte Carlo simulations using a constant Galactic tide and a constant flux of stellar encounters, but neglecting the detailed effects of planetary perturbations, we show that this flux essentially results from a two step mechanism: (i) the stellar injection of comets into the TAZ; and (ii) the tidal injection of TAZ comets into the loss cone. We find that single massive stars are able to induce “comet drizzles” - corresponding to an increase of the cometary flux of about 40% - which may last for more than 100 Myr by filling the TAZ to a higher degree than normal. It appears that the stars involved in this process are the same that cause comet showers.     

Detecting active comets in the SDSS

Using a sample of serendipitously discovered active comets in the Sloan Digital Sky Survey (SDSS), we develop well-controlled selection criteria for greatly increasing the efficiency of comet identification in the SDSS catalogs. After follow-up visual inspection of images to reject remaining false positives, the total sample of SDSS comets presented here contains 19 objects, roughly one comet per 10 million other SDSS objects. The good understanding of selection effects allows a study of the population statistics, and we estimate the apparent magnitude distribution to r∼18, the ecliptic latitude distribution, and the comet distribution in SDSS color space. The most surprising results are the extremely narrow range of colors for comets in our sample (e.g. root-mean-square scatter of only ∼0.06 mag for the g-r color), and the similarity of comet colors to those of jovian Trojans. We discuss the relevance of our results for upcoming deep multi-epoch optical surveys such as the Dark Energy Survey, Pan-STARRS, and the Large Synoptic Survey Telescope (LSST), and estimate that LSST may produce a sample of about 10,000 comets over its 10-year lifetime.     

2006 Fragmentation of Comet 73P/Schwassmann-Wachmann 3B observed with Subaru/Suprime-Cam

The fragmentation of the split Comet 73P/Schwassmann-Wachmann 3 B was observed with the prime-focus camera Suprime-Cam attached to the Subaru 8.2-m telescope. The fragmentation revealed dozens of miniature comets [Fuse, T., Yamamoto, N., Kinoshita, D., Furusawa, H., Watanabe, J., 2007. Publ. Astron. Soc. Jpn. 59 (2), 381-386]. We analyzed the Subaru/Suprime-Cam images, detecting no fewer than 154 mini-comets, mostly extending to the southwest. Three were close to the projected orbit of fragment B. We applied synchrone-syndyne analysis, modified for rocket effect analysis, to the mini-fragment spatial distribution. We found that most of these mini-comets were ejected from fragment B by an outburst occurring around 1 April 2006, and three fragments on the leading side of nucleus B could have been released sunward on the previous return. Several fragments might have been released by successive outbursts around 24 April and 2 May 2006. The ratio of the rocket force to solar gravity was 7-23 times larger than that exerted on fragment B. No significant color variation was found. The mean color index, V-R = 0.50 ± 0.07, was slightly redder than that of the Sun and similar to that of the largest fragment, C, which suggests that these mini-fragments were detected mainly through sunlight reflected by dust particles and materials on the nuclei. We examined the surface brightness profiles of all detected fragments and estimated the sizes of 154 fragments. We found that the radius of these mini-fragments was in the 5- to 108-m range (equivalent size of Tunguska impactor). The power-law index of the differential size distribution was q = −3.34 ± 0.05. Based on this size distribution, we found that about 1-10% of the mass of fragment B was lost in the April 2006 outbursts. Modeling the cometary fragment dynamics [Desvoivres, E., Klinger, J., Levasseur-Regourd, A.C., Lecacheux, J., Jorda, L., Enzian, A., Colas, F., Frappa, E., Laques, P., 1999. Mon. Not. Roy. Astron. Soc. 303 (4), 826-834; Desvoivres, E., Klinger, J., Levasseur-Regourd, A.C., Jones, G.H., 2000. Icarus 144, 172-181] revealed that it is likely that mini-fragments smaller than ∼10-20 m could be depleted in water ice and become inactive, implying that decameter-sized comet fragments could survive against melting and remain as near-Earth objects. We attempted to detect the dust trail, which was clearly found in infrared wavelengths by Spitzer. No brightness enhancement brighter than 30.0 mag arcsec⁻² (3σ) was detected in the orbit of fragment B.     

Non-LTE radiative transfer for sub-millimeter water lines in Comet 67P/Churyumov-Gerasimenko

The European Space Agency (ESA) Rosetta spacecraft (Schulz, R., Alexander, C., Boehnhardt, H., Glassmeier, K.H. (Eds.) [2009]. “ROSETTA - ESA”) will encounter Comet 67P/Churyumov-Gerasimenko in 2014 and spend the next 18 months in the vicinity of the comet, permitting very high spatial and spectral resolution observations of the coma and nucleus. During this time, the heliocentric distance of the comet will change from ∼3.5 AU to ∼1.3 AU, accompanied by an increasing temperature of the nucleus and the development of the coma. The Microwave Instrument for the Rosetta Orbiter (MIRO) will observe the ground-state rotational transition (1₁₀-1₀₁) of H₂¹⁶O at 556.936 GHz, the two isotopologues H₂¹⁷O and H₂¹⁸O and other molecular transitions in the coma during this time (Gulkis, S. et al., [2007]. MIRO: Microwave Instrument for Rosetta Orbiter. Space Sci. Rev. 128, 561-597).The aim of this study is to simulate the water line spectra that could be obtained with the MIRO instrument and to understand how the observed line spectra with various viewing geometries can be used to study the physical conditions of the coma and the water excitation processes throughout the coma. We applied an accelerated Monte Carlo method to compute the excitations of the seven lowest rotational levels (1₀₁, 1₁₀, 2₁₂, 2₂₁, 3₀₃, 3₁₂, and 3₂₁) of ortho-water using a comet model with spherically symmetric water outgassing, density, temperature and expansion velocity at three different heliocentric distances 1.3 AU, 2.5 AU, and 3.5 AU. Mechanisms for the water excitation include water-water collisions, water-electron collisions, and infrared pumping by solar radiation.Synthetic line spectra are calculated at various observational locations and directions using the MIRO instrument parameters. We show that observations at varying viewing distances from the nucleus and directions have the potential to give diagnostic information on the continuum temperature and water outgassing rates at the surface of the nucleus, and the gas density, expansion velocity, and temperature of the coma as a function of distance from the nucleus. The gas expansion velocity and temperature affect the spectral line width and frequency shift of the line from the rest frequency, while the gas density (which is directly related to the outgassing rate) and the line excitation temperature determine the antenna temperature of the absorption and emission signal in the line profile.     

Limits on the size and orbit distribution of main belt comets

The first of a new class of objects now known as main belt comets (MBCs) or “activated asteroids” was identified in 1996. The seven known members of this class have orbital characteristics of main belt asteroids yet exhibit dust ejection like comets. In order to constrain their physical and orbital properties we searched the Thousand Asteroid Light Curve Survey (TALCS; Masiero, J.R., Jedicke, R., Durech, J., Gwyn, S., Denneau, L., Larsen, J. [2009]. Icarus 204, 145-171) for additional candidates using two diagnostics: tail and coma detection. This was the most sensitive MBC survey effort to date, extending the search from MBCs with H ∼ 18 (D ∼ 1 km) to MBCs as small as H ∼ 21 (D ∼ 150 m).We fit each of the 924 objects detected by TALCS to a PSF model incorporating both a coma and nuclear component to measure the fractional contribution of the coma to the total surface brightness. We determined the significance of the coma detection using the same algorithm on a sample of null detections of comparable magnitude and rate of motion. We did not identify any MBC candidates with this technique to a sensitivity limit on the order of cometary mass loss rate of about 0.1 kg/s.Our tail detection algorithm relied on identifying statistically significant flux in a segmented annulus around the candidate object. We show that the technique can detect tail activity throughout the asteroid belt to the level of the currently known MBCs. Although we did not identify any MBC candidates with this technique, we find a statistically significant detection of faint activity in the entire ensemble of TALCS asteroids. This suggests that many main belt asteroids are active at very low levels.Our null detection of MBCs allows us to set 90% upper confidence limits on the number distribution of MBCs as a function of absolute magnitude, semi-major axis, eccentricity, and inclination. There are ?400,000 MBCs in the main belt brighter than H_V = 21 (∼150-m in diameter) and the MBC:MBA ratio is ?1:400.We further comment on the ability of observations to meaningfully constrain the snow line’s location. Under some reasonable and simple assumptions we claim 85% confidence that the contemporary snow line lies beyond 2.5 AU.     

Comet nucleus size distributions from HST and Keck telescopes

The Wide Field Camera (WFC) on the Hubble Space Telescope and the Low Resolution Imaging Spectrograph (LRIS) on the Keck II telescope have been used to image 21 distant dynamically new, long-period (LP) and short-period (SP) Jupiter-family (JF) comet nuclei (near aphelion), as part of a long-term program to search for physical differences between short-period comets and Oort cloud comets. WFC data were obtained on Comets C/1987 H1 (Shoemaker) and C/1984 K1 (Shoemaker) during Cycle 5 (1995 December) and on C/1988 B1 (Shoemaker), C/1987 F1 (Torres), and C/1983 O1 (?ernis) during Cycle 6 (1997 April, May, and June). The HST comets were at heliocentric distances 20.4 < r[AU] < 29.5. Each comet observation was allocated 7 orbits, for ≈3.6 hrs of integration. The most difficult part of the image reduction was the removal of cosmic rays. We present our scheme for cosmic ray removal. None of the HST comet nuclei was detected to the 3-σ level at m_R∼27. The inferred upper limits to the nucleus radii are . The SP comets range in radius between , with a median value of R_N∼1.61 km. The LP comets ranged in size between <4.0-56 km. Over a range of radii between 1-10 km, the nuclei can be fit with a cumulative distribution N(>R_N)∝R_N^−α with α=1.45±0.05, and for nuclei in the range 2-5 km, α=1.91±0.06. Statistical analysis and modeling shows that the slopes of the observed TNO and JF comet distributions are not compatible, suggesting that the intrinsic distribution of JF comet nuclei is a differential a^−3.5 power law truncated at small nucleus radii between 0.3 and 2.0 km.