A survey of debris trails from short-period comets
aa r X i v : . [ a s t r o - ph ] A p r A survey of debris trails from short-period comets
William T. ReachSpitzer Science Center/Infrared Processing and Analysis Center, MS 220-6, CaliforniaInstitute of Technology, Pasadena, CA 91125 [email protected]
Michael S. KelleyDepartment of Astronomy, University of Minnesota, Minneapolis, MN 55455Mark V. SykesPlanetary Science Institute, 1700 E Ft. Lowell, Suite 106, Planetary Science Institute,Tucson, AZ 85719Received ; accepted April 2007Manuscript Pages: 78, Tables: 3, Figures: 13 2 –
Proposed running head:
Cometary Debris Trails
Editorial correspondence to:
Dr. William T. ReachSpitzer Science CenterMS 220-6CaltechPasadena, CA 91125Phone: 626-395-8565Fax: 626-432-7484E-mail: reachipac.caltech.edu 3 –We observed 34 comets using the 24 µ m camera on the Spitzer Space Telescope . Eachimage contains the nucleus and covers at least 10 km of each comet’s orbit. Debris trailsdue to mm-sized or larger particles were found along the orbits of 27 comets; 4 cometshad small-particle dust tails and a viewing geometry that made debris trails impossible todistinguish; and only 3 had no debris trail despite favorable observing conditions. Thereare now 30 Jupiter-family comets with known debris trails, of which 22 are reported in thispaper for the first time. The detection rate is > g, and themedian mass loss rate is 2 kg/s. The mass-loss rate in trail particles is comparable to thatinferred from OH production rates and larger than that inferred from visible-light scatteringin comae. Keywords : comets, meteors, infrared observations, interplanetary dust 4 –
1. Introduction
The composition and structure of cometary nuclei remains largely unknown. Mostinformation about comets derives from their two best-determined observable properties:their orbits and the apparent nature of the material they eject when they approach theSun. The nuclei themselves are very dark, offering few clues to their nature other thantheir size, shape, and color (Lamy et al. 2004; Weissman and Lowry 2003). Understandingcometary structure and composition is key to understanding the formation of the outerplanets and the origin of the outermost layers, especially oceans and organic material, onEarth (Chyba et al. 1990; Thomas et al. 1996). Specifically, the Earth’s outermost layersand oceans are likely to have been deposited by the late bombardment of the early Earth bycometary bodies, if we define comets as those bodies on which water was in icy form at thetime of initial planetesimal/cometesimal coagulation in the solar nebula (Delsemme 2000).The cause of the well-known 1908 Tunguska event (Turco et al. 1982) has been debated asan asteroidal or cometary disruption in the atmosphere (Chyba et al. 1993), but how welldo we really know the difference between asteroids and comets? The cometary bodies leftover from the formation of the cores of Jupiter and Saturn may have been largely scatteredto the Oort cloud, while the remaining comets that formed Uranus and Neptune, as well astheir (and some of Saturn’s) numerous moons, are likely residents of the present KuiperBelt. The Kuiper Belt is the dynamical origin of the present Jupiter-family, also called‘short-period,’ comets (Levison and Duncan 1994), whose nature we will explore in thepresent work.The most significant breakthrough in understanding the physical nature of cometswas the revolutionary work by Whipple (1950), in which he demonstrated that cometaryorbital perturbations (beyond those that could be explained by the major planets) werecaused by non-gravitational forces due to material ejected by sublimating ices heated by 5 –the Sun during perihelion passages. The model has now advanced to include anisotropicemission from hot-spots or ‘jets’ on rotating nuclei, which are required both to provide thenon-gravitational forces that change comets’ orbits from revolution to revolution as wellas the fan-shaped comae (Sekanina 1979, 1988). Whipple’s model of the comet is oftendescribed as a ‘dirty snowball,’ a nickname that suggests several prevailing beliefs aboutcometary nature. Foremost, the nickname promotes the critical role played by icy materialin powering the mass-loss that is the defining characteristic of comets. The nickname alsosuggests that solid material is a relatively minor constituent, and that it is in the form ofsmall particles scattered throughout a loosely agglomerated set of ice crystals. This belief,however, is not borne out by observational studies of comets, including in situ studies byspacecraft (Keller et al. 2004), remote infrared observations (Sykes and Walker 1992, e.g.),and the observations presented in this paper.Whipple himself frequently mentioned and wrote about the connection between cometsand meteors. In paper II (Whipple 1951) of his classic series, he describes how solidparticles are ejected from comets. An example in that paper estimates the ejection velocityof particles with 1 cm radius as 3 m s − and associates such particles with photographicmeteors. The mass fraction of rock versus ice in cometary nuclei was unknown at the timeof the development of Whipple’s comet model. In paper III of his series, he adopted a20% fraction of cometary mass in the form of solid material. However, the model does notrequire a particularly high or low ice content in order to explain the properties of cometaryorbits or mass loss.Modern views (e.g. Prialnik et al. 2004) of comets recognize the processing andevolution of cometary material both while in the outer solar system and after capture intoorbits that characterize short-period comets. The water-powered dirty snowball modelcould not explain why many comets are active at great distances (Meech and Svoren 2004), 6 –or why activity is not restricted to being very close to the Sun for older comets. With theobservation of significant activity in jets, the evolution of comets and their devolatilizationis complicated by the details of composition and the location of active regions on a comet’ssurface coupled with the orientation of the comet spin axis. Comets possessing highlyvolatile ices such as CO may be observed to be active at great heliocentric distances. Whilesome comets can decrease in their activity as they approach perihelion as jets becomeshadowed from the Sun. This makes the detailed characterization of comet activity as agroup difficult.The current conceptual model has comets devolatilizing even while in the outer SolarSystem, then more rapidly upon entering a low-perihelion orbit. Sublimating gases carryaway particles small enough that their drag forces exceed gravitational pull of the nucleus(Whipple 1951): s < f A /r / R, (1)where s is the radius of the particle (cm), f A is the fraction of the comet surface withexposed ice (taking the latent heat to be that of H O), r is the distance from the Sun (AU),the density of the cometary nucleus is taken to be 1 g cm − , and R is the nuclear radius(km). For comets with radii of order 1 km producing dust around 1 AU from the Sun usingice covering 10% of their area, the maximum particle size is of order 2 cm. As the fine dustand ice are removed, a ‘mantle’ or ‘crust’ of larger particles dominates the outer layers, andthe fraction of the surface with exposed ice decreases. One then expects that short-periodcomets, which have been resident the inner Solar System for multiple orbits, will havesurface physical properties significantly different from Trans-Neptunian Objects (TNOs) orfrom dynamically new comets from the Oort cloud. The albedos of small TNOs (includingCentaurs) are much higher than those of short-period comets (Brown et al. 2006), whichsupports the model of rapid surface evolution. 7 –New insight into the nature of comets was provided by the discovery of cometary debristrails (Sykes et al. 1986). Unlike the small-particle tails apparent at visible wavelengths,debris trails consist of large (mm-cm), dark, low-velocity particles more readily observableat thermal infrared wavelengths. A survey of trails detected serendipitously by the InfraredAstronomical Satellite concluded that cometary mass loss was primarily in the form ofthese large particles and that comets therefore had a greater refractory or rocky componentthan previously thought, with a dust/gas mass ratio of ∼ /
1, consistent with a formationlocation similar to Pluto and Triton (Sykes and Walker 1992). One of the best-observedcomets of all time, C/Hale-Bopp, yielded a wealth of new observational data, includingsubmillimeter photometry suggesting large particles dominate the mass of the coma ofC/Hale-Bopp, with dust/gas > storms (analogous to the well-known Leonids)if they intersected the Earth’s orbit: the width of debris trails matches the duration ofmeteor storms (less than an hour) but is less than that of showers (days), and the particledensity within debris trails better matches the extremely high zenith hourly rate of meteorstorms rather than the order-of-magnitude-lower meteor rate in meteor streams. Meteorstorms also appear to be associated with relatively recent cometary events, and theirorbits match the current orbits of associated comets. Meteor streams, on the other hand,significantly deviate in mean orbit from that of their associated comet, as well as havinga wide dispersion. The Taurid meteor complex is widely associated with emissions from 8 –comet 2P/Encke, not in its present orbit, but rather that of 10 − yr ago (Steel et al. 1991;Jones 1986).Spacecraft with cameras and dust sensors have now encountered five comets: Giotto passed 600 km and
Vega passed 8000 km from 1P/Halley in 1986 (McDonnell et al. 1987;Mazets et al. 1987);
Giotto subsequently passed within 100-200 km of Grigg-Skjellerup in1992 (McDonnell et al. 1993);
Deep Space 1 passed 2100 km from 19P/Borelly in 2001(Soderblom et al. 2002);
Stardust passed 236 km from 81P/Wild 2 in 2004 (Brownlee et al.2004); and then
Deep Impact met 9P/Tempel 1 in 2005 (A’Hearn et al. 2005). The sizedistribution of detected particles indicates most of the mass of cometary dust is in thelargest particles. Thus, nearly all estimates of cometary dust mass loss based on groundobservations at visible wavelengths are lower limits to the actual dust mass loss. Particularlyimportant, then, is the size of the largest particles. A particle of order 5 mg struck thefront bumper of
Giotto as it approached comet Halley; the particle perturbed the spacecraftattitude, generated an ion cloud detected by the spacecraft, and damaged the spacecraft’sstar tracker (Goldstein et al. 1991). During the flyby of Grigg-Skjellerup, the Radio ScienceExperiment detected a particle of at least 30 mg (Patzold et al. 1993). During the recent
Stardust encounter with 81P/Wild 2, there is evidence of a 14 mg particle on the dustshields (Anderson et al. 2004). The dust flux monitor yielded a large-particle-dominatedsize distribution with cumulative mass index 0.75; these results also led to the predictionthat the dust collector may contain a mm-size particle, which will dominate the totalcollected mass (Green et al. 2004). As the Deep Impact impactor spacecraft approached9P/Tempel 1, large particles caused dramatic attitude jogs (A’Hearn et al. 2005). Suchparticles would all be bright meteors if they were to enter the Earth’s atmosphere. Largeenough to be only slightly affected by radiation pressure, they follow orbits similar to theirparent nucleus and only gradually drift away. The estimated dust/gas mass loss ratio is > IRAS , suggesting that comets are mostly composed of rocky material.Furthermore, the dust-to-gas mass ratio of ejected material underestimates that of thenucleus, since it does not include objects too large to be lifted off the nucleus (unless thereare simply no particles larger than 1 g within the nucleus).Debris trails provide a unique record of comet emission history in addition to providinginsights into their composition. Over the eight trails detected by IRAS associated withknown short-period comets, Sykes and Walker (1992) determined the ages of the oldestdetected particles to be from years to centuries. They inferred that all short-period cometsshould have trails, and while the median dust to gas mass ratio for the comets studied was3, individual values ranged from 1.2 to 4.6 - indicating perhaps a significant variation incomposition from comet to comet. In this paper we report on the first survey of short-periodcomets since
IRAS made its observations more than 20 years ago, focusing on the largeparticle emissions of these objects. Taking advantage of the greater sensitivity, spatialresolution and pointing capability of the new
Spitzer Space Telescope , we have quadrupledthe detections of short-period comets and have been able to probe the similarity of the largeparticle emissions of short-period comets in more detail than has been possible previously.
2. Observations2.1. Methods of observation and data reduction
All observations presented here were performed with the Multiband ImagingPhotometer for Spitzer (MIPS; Rieke et al. 2004) at 24 µ m. The dates and viewinggeometries are summarized in Table 1. The observed comets were selected to be all thoseshort-period (Jupiter-Family) comets in the inner Solar System ( r < . Spitzer during the time period from 2004 Jan to 2005 May, corresponding to the initial 10 –guaranteed-time and first general-observation cycles on the observatory; 34 comets metthese criteria.All comets were observed using the small-field photometry mode of MIPS, whereineach 6 ′ × ′ field is observed using a set of 2 telescope positions with 7 scan-mirror dithersat each. The first set of observations (PID 210; up to 9/21/2004, excluding 141P), executedduring guaranteed time, covered only 3 fields per comet, with offsets in telescope coordinates(roughly, ecliptic longitude) centered on the nucleus, leading and trailing the nucleus byone field of view. For the remaining observations executed during general observing time(PID 20039), maps were built using 6 ′ tiles designed to follow each comet’s orbit to at least10 km following the nucleus and 10 ′ leading the nucleus. Thus a wider field on the sky,following the nucleus, was observed for the nearby comets.The basic calibrated data (individual 128 ×
128 pixel calibrated array images) wereimproved as follows. We noted a significant gradient across the individual images; thegradient is strongest at the beginning of a scan-mirror-driven dither pattern and graduallydecreases. To reduce the effect, we median-combined all images from our project at eachof the 7 scan-mirror positions (and for each exposure time), and subtracted these biascorrections from each original image. This correction is imperfect due to the prevalence ofbright cometary emission (even after excluding the brightest comets), but improved theimage quality significantly. To ensure that the bias subtraction did not remove some of thetrail brightness, we inspected each bias image to determine the amplitude of structure, on < ′ scales, is < .
05 MJy sr − . (A large-scale gradient is present, but it has no bearing onour results as we will subtract a large-scale gradient from the final mosaics.) The mosaicswere composed of 14 independent combinations of bias-subtracted images, so the amplitudeof bias-image structure that survives into the mosaics < .
01 MJy sr − . Further, therewas no evidence of ‘trail’ like structure (by which we mean the structures presented in the 11 –images in this paper) in the bias images.The basic calibrated data were then shifted to each comet’s rest frame by shifting eachimage to counter the motion of the comet between the time an image was taken and thefirst image of the sequence. The images were mosaiced using the SSC tool mopex , whichmatches the backgrounds in overlapping portions of images and combines the images intoa single celestial grid with outlier rejection to remove cosmic rays and galactic protons(Makovoz and Khan 2005).
3. Dynamics of large particles
Particles of different size can be distinguished in the images due to the size-sensitiveeffects of radiation pressure. As a first-order approximation—which is relatively accuratefor large particles far from the comet but becomes inaccurate for particles that are small,recently ejected, or close to the comet—we neglect the ejection velocity and assume theparticles come into existence with the same orbit as the nucleus. They immediatelyexperience radiation pressure from sunlight, with a r − dependence identical to solar gravityand force ratio β ≡ F rad F grav = κ Q pr ρs , (2)where Q pr is the effective efficiency of sunlight absorption and scattering for radial-directedmomentum transfer (assumed to be unity for large particles), ρ is the particle density ing cm − , and s is the particle radius (in µ m), and κ = 0 .
57 (Burns et al. 1979). Very largeparticles, with β →
0, will follow nearly the same orbit as the nucleus, feeling negligibleradiation pressure. (In detail, they will still deviate, because of the ejection velocity ofthe particle and non-gravitational forces due to asymmetric outgassing acting on thenucleus.) As discussed above, the largest particles that can be lifted from the nucleus dueto sublimation are of order cm size, so β > × − for ρ ≤ − . The orbits of 12 –particles with such small β cannot be easily distinguished from the nucleus orbit withoutobservations over long periods. As the particles separate from the nucleus, the effect ofplanetary perturbations increases and can ultimately result in dispersal of the trail. To firstorder, the largest particles in the trail lie along the orbit of the nucleus, and we considerthe particles that have been dispersed due to perturbations as part of the more diffusezodiacal cloud. Equivalently, in the terminology of meteor science, the largest particleslie within the same storm or shower, and the particles that have been dispersed due toperturbations are sporadic meteors. Nuclear fragments will follow approximately the sameorbit, with modification due to the initial velocity of splitting, non-gravitational forces dueto asymmetric outgassing, and planetary perturbations over time. In general the largedebris from recent orbits will be splayed along the comet’s orbit.To track the locations of particles with finite β , we predict their trajectories as follows.Over the two year period preceding observation, we calculate the detailed motion of 10 particles produced at even intervals (one particle every 2 hr), for each of β = 10 , 10 − ,10 − , 10 − , and 10 − . We assume each test particle’s initial velocity and position is thesame as the nucleus, including non-gravitational effects, if known. The x, y, z locations ofall particles are then projected onto the sky for the geometry of the Spitzer observation.Particles of a given size generally lie along a simple arc on the sky. This arc of particleswith common β is the zero-velocity syndyne . The syndynes were generated and overlaidon each comet image. They trace the locations and shapes of both the comet tails andtrails. They do not match the inner cometary comae, which are due to recently-ejected,small particles with non-negligible ejection velocity and some memory of their origin onthe rotating nucleus in asymmetrically located jets. Figure 1 illustrates the zero-velocitysyndynes and their projection on the sky for one of our survey comets.To supplement the zero-velocity syndynes, we also generated Monte-Carlo simulations 13 –of particles produced over the 1-year period prior to observation. The computationaltechniques are described by Kelley et al. (2007). For the Monte-Carlo simulations, 10 particles were emitted over the 1-year period, with a power-law size distribution from10 − < β < − with mass index α = −
1, which distributes mass evenly among particlesizes but favors smaller particles for surface area. The velocity distribution is directedtoward the Sun, falling of as the cosine of the zenith angle and with peak velocity v ej = 1 . p β/r km s − , where r is the distance from the Sun at the time of particle ejection.For typical trail particles produced at r = 1 AU and with β = 10 − , the ejection velocity is10 m s − . These Monte Carlo simulations are not adeqaute to trace the debris trails overtheir entire ages, but rather they provide a somewhat improved guide to the beginning ofthe trail, near the nucleus. Longer-term simulations can follow the evolution of the debrisbut are computationally expensive (e.g. Vaubaillon et al. 2005).
4. Measured debris trail properties
For each debris trail, we measured the brightness and width in one-dimensional slicesperpendicular to the orbit (coadding along the orbit by 30-90 pixels [2.5 ′′ /pixel] dependingon signal-to-noise). Table 2 shows the slice locations in apparent angular distance fromthe nucleus, φ , and physical distance φ ∆, along the orbit projected on the sky, where ∆is the distance to the observatory at the time of observation. For each profile, a Gaussianfit was made, and Table 2 lists the peak surface brightness I ν (median 0.12 MJy sr − ,range 0.02-0.9 MJy sr − ) and full-width-at-half-maximum in angular units W (median 27 ′′ ,range 7-78 ′′ ) and physical units W δ (median 5 × km, range 0.9-15 × km), in theviewing plane perpendicular to the line of sight. When fitting the Gaussians to the slices,a polynomial was simultaneously fitted to portions of the slice on either side of the trail.The optical depth, τ , was derived by assuming the grains are blackbody emitters with 14 –temperature T = 300 r − / K, as was measured for trails with multi-band IRAS detections(Sykes et al. 2005). Note this temperature is significantly warmer than that obtained bydust (grey, isothermal particles), for which the temperature at 1 AU T <
278 K. Asdiscussed by Sykes et al. (2005), trail particles are more consistent with rapidly rotating,randomly oriented, zero-albedo particles maintaining a latitudinal temperature variationacross their surfaces. Table 2 lists the resulting τ (median 2 × − , range 0.3-16 × − ).The 1-dimensional flux of the trail, F D = I ν W , measures the flux per unit length along thetrail; Table 2 lists F D (median 4.6 mJy/arcmin, range 0.4-62 mJy/arcmin). First, we estimate the particle ages analytically, to determine how the trajectoriesof debris evolve as a function of the ratio of radiation pressure to gravity, β , the ejectionvelocity, v ej , and the comet’s orbit’s perihelion distance and eccentricity, q and e . Forparticles ejected at perihelion, in the direction of the comet’s motion, with velocity v ej , therate of separation in mean anomaly of a particle from the nucleus is dθdt = r GMa e − e β + 3 v ej a (cid:18) e − (cid:19) , (3)where the first term is due to radiation pressure and the second one is due to the ejectionvelocity (eq. 1 and 2 of Sykes and Walker 1992). If the ejection velocity scales as v ej = v β / q ( AU ) − / (4)(cf. Whipple 1951) where for example Reach et al. (2000) used v = 1 km s − for 2P/Encke,then dθdt = r GMa e − e β " v (cid:18) GM (cid:19) − / β − / √ e e . (5)For the comets in our sample, particles with β = 10 − β separate from the nucleus at a rate dθdt = 0 . (cid:20) . v km s − β − / (cid:21) β deg yr − , (6) 15 –where β ≡ β/ − , indicating that the radiation pressure and ejection velocity terms arecomparable. The median dθ/dt = 0 . ′ /yr.We can then approximately convert the change in mean anomaly to the separation, φ ,on the sky using (geometrically) dφdθ = r ∆ dfdθ , (7)and the derivative of true anomaly per unit mean anomaly dfdθ = 1 + e − e tan E cos E cos f tan f ra . (8)The median value for our observations is dφ/dθ = 1 . dφ/dt = 0 . ′ /yr.We now estimate the ages of the oldest observed particles from numerical orbitintegration, which should be more accurate, because fewer approximations are required.The orbits of particles with β = 10 − were integrated to the present beginning on anejection date ranging from 1 day to 2 years into the past. For these calculations an ejectionvelocity of zero and a comet mass of zero are assumed, i.e. the particles simply separatefrom the nucleus according to gravity from the Sun and planets, and radiation pressurefrom the Sun. Their coordinates on the date of the Spitzer observation were then comparedto those of the nucleus, yielding the separation (on the projected sky-plane) from thenucleus as a function of the particle age. This separation of any given particle increaseswith time, but particles produced at perihelion separate from the nucleus more quicklyand overtake those produced just earlier. Figure 9 shows the separation versus age for129P/Shoemaker-Levy 3. For comets observed pre-perihelion, such as 129P, the separationversus age is roughly linear for young particles. The separation is noticeably nonlinear forparticles produced near perihelion, which makes the trail expansion rate especially nonlinearfor comets observed post-perihelion. With the notable exception of 2P/Encke, the rate ofseparation is monotonic over the region covered by the
Spitzer images, allowing an accurate 16 –numerical derivative. For all comets, we estimate dφ/dt using the geometric mean of theseparation/age for particles that are 1 ′ and 10 ′ from the nucleus. The resulting values havemedian dφ/dt = 15 ′ /yr, with a range 5.7–40 ′ /yr. The numerical results need to be increasedto take into account the effect of nonzero ejection velocity. Based on the equations above,the increase in separation for v = 1 km s − , β = 10 − , and sunward-hemisphere ejection, isa factor of 2.6.The numerical determinations of the rate of separation are consistently higher thanthe analytic estimate. Further, the numerical determinations of the separation rate for β = 10 − and β = 10 − do not scale with β as the analytic relations predict (being insteadmuch more shallow). In order to reach the analytic estimate, some approximations weremade, which apparently led to the difference. We will use the numerical results from theorbit integrations in this paper. The trail profiles in Table 2 cover φ ∼ ′ from the nuclei.Thus the observed debris trail particles are ∼ . − /β ) yr old. Taking into account thesizes of the Spitzer images for the various comets, the range of ages is 0.3–2 yr. This doesnot mean that all (or even most) of the particles were emitted 0.6 yr ago, but only thata particle with β ∼ − emitted 0.6 yr ago would be at the observed location; particlesa factor of 2 smaller or larger in size than β = 10 − (or ejected with velocities smaller orlarger) would be correspondingly further behind or closer to the nucleus.In many cases, the debris trails continue to the edges of the Spitzer image, so olderparticles are certainly present, as clearly demonstrated by the
IRAS trails that extend frommore than 1 ◦ up to 90 ◦ of the comet orbit in mean anomaly, corresponding to minimumtrail ages of 2.6–140 yr (Sykes and Walker 1992). The trail ages exceed the orbital periodfor many comets, so a given trail contains debris from many revolutions.Further evidence of the longevity of debris trail particles is that trails are present evenfor comets observed far before perihelion. Figure 10 shows that there is no significant 17 –asymmetry in the trail optical depth with respect to perihelion. While comets show awide range of behaviors pre- and post-perihelion, none of them are active only at aphelion.Thus, the material observed in a trail on the present revolution was largely producedon previous revolutions. This is in contrast to the dust tails and comae, which areephemeral and only due to the present revolution. The near-nuclear observations we presenthere contain β = 10 − particles from the present and previous revolution, for cometsobserved post-perihelion, and particles from the previous revolution, for comets observedpre-perihelion. They also contain β ≤ − particles from previous revolutions.An upper limit on the debris trail age is set by gravitational perturbations. If debristrails were due only to very large particles, e.g. with β < − , then trails arise frommany revolutions of the comet. In this case, the trail particles would diffuse from thepresent comets’ orbits due to differential gravitational perturbations. Indeed even minorperturbations and orbital shifts due to non gravitational and Yarkovsky forces (which willbe different for meteoroids and the nucleus) make it very unlikely to have more than a fewrevolutions contributing to the debris trails, which follow the current orbit of the nucleusvery closely. Instead, the trail would be distorted by minor perturbations and truncatedby significant perturbations. Table 1 shows the date, T pert , of the last passage of eachcomet within Jupiter’s Laplacian gravitational sphere of influence (0.32 AU) as calculatedby K. Kinoshita . We see that the date of the last significant perturbation by Jupiter wasbefore 1950 for all but 7 comets. (62P, 65P, 67P, 103P, 111P, 116P, and 120P), and thesecomets present a range of trail properties similar to the rest of the sample, including onecomet with a very bright leading+following trail (65P) and one nondetection (103P). Minorperturbations, within 1 AU of Jupiter, are much more common; the median time since sucha perturbation for our sample comets is 35 yr. β , by requiring particles ejected at perihelion have enough time to reach both thefurthest leading and following extents of the observed trails. They found ages of 11–660 yrwith a median of 74 yr. These ages are often greater than the time since the last minorperturbation (within 1 AU of Jupiter), suggesting such minor perturbations are not effectiveat dispersing trails. The masses of the debris trails are estimated as follows. A straightforward estimate ofthe mass per unit projected angle on the sky, φ , assuming a tapered cylindrical shape forthe trail, yields dMdφ = π κW ∆ τ β − = 1 . × W (arcsec)∆(AU) (cid:16) τ − (cid:17) (cid:18) − β (cid:19) g / deg . (9)Since the brightness profiles are only taken in the debris trail, only the values of β = 10 − (3 − that are consistent with the centroid, width, and length of the trail apply.We list the mass per unit apparent separation in Table 2 as dM /dφ , for an assumedparticles size β = 10 − . For many of the images, this is an upper limit to β , and therefore dM /dφ is a lower limit to the mass. The values of dM /dφ are independent of the particledynamics. For all the trail profiles in Table 2, the median value dM /dφ = 21 × g/deg,and the range is 0.6–430 × g/deg.We can now use the particle separation rates (from the numerical integrations discussedin the previous section), dφ/dt , together with the observed mass per unit separation, dM /dφ , to estimate the mass-loss rates, dM/dt , required to produce the debris trails. Themedian dM/dt = 4 kg s − , and the range for all the comet profiles is 0.2–36 kg s − . Notethat dM/dφ ∝ β − while the analytic estimate dφ/dt ∝ β , so the mass loss rate dM/dt
19 –should be independent of the assumed particle size. However the numerical estimates of dφ/dt show much less dependence on β , with the data in Figure 9 yielding dφ/dt ∝ β . andsuggesting the mass-loss rates scale as ( β/ − ) − . .For comparison, using his ”inverse tail method” to compare dynamical models tosurface brightness images, Fulle (1996) measured as meteoroid mass production rate of100 kg s − near perihelion for 10P/Tempel 2, and Fulle (1990) measured meteoroid massproduction rates of 30–50 kg s − for 2P/Encke and 6P/D’Arrest; those results are in generalagreement with ours, being somewhat higher because they refer to dust production closerto perihelion. Sykes and Walker (1992), using the IRAS observations of entire debris trailsfor 8 comets, measured meteoroid mass production rates of 4–250 kg s − . For the 5 cometsin common between the IRAS and
Spitzer surveys (2P, 9P, 10P, 65P, and 67P), the dM/dt inferred in this paper are comparable (this paper/SW92 = 0.1, 1.8, 2.3, 0.6, 8, respectively).The comet for which the mass-loss rates are most discrepant is 2P/Encke. Reach et al. (2000) used ISOCAM observations and Monte Carlo simulations of 2P/Encke to obtain200-600 kg s − for the 1997 apparition, in agreement with Sykes and Walker (1992)’s valueof 260 kg s − . The low value for 2P/Encke in the present paper is likely due to observingonly a small portion of the trail, hence sampling a very restricted range of emission history.The high value for 67P is likely due to a line-of-sight enhancement or ‘neck-line’ as discussedbelow. The overall agreement between the different observations and calculations in thispaper and Sykes and Walker (1992) is encouraging.Total trail masses are discussed for individual comets in §
5. Since our
Spitzer imagesgenerally cover only limited portions of the orbits, and many trails clearly extend to theedges of the images, we can estimate in general only lower limits to the trail mass. (Thiseffect goes in the same direction [underestimating the mass] as our conservative assumptionof β = 10 − .) For the 6 comets with reasonable total mass estimates, the range is 4 ×
20 –g to 9 × g. Lower limits for the others range from > × g to > × g.The trail lengths found in the IRAS survey were of order degrees (in mean anomaly), sothe total trail masses from the present survey are of order dM/dθ (with θ in degrees), i.e.typically 10 − g. These masses extend to about 1 order of magnitude lower than thoseof the IRAS -detected trails (Sykes and Walker 1992), due to the greater sensitivity of thepresent survey. The masses remain lower limits, because even larger (cm-sized) particlesmay be present, and there could be a fainter component of the debris trails extending overa large fraction of the orbit, which our observations do not cover. The existence of meteorshowers over large fractions of comets’ orbits testifies to the existence of such an extendedpopulation of debris.
The mass-loss rate in large particles can be compared to that due to ice sublimation asfollows. If the H O production rate is Q H O , then the mass loss rate of sublimating ice is dM ice dt = 2 . × h Q H O i molecule s − kg s − , (10)where h Q H O i is the mass production rate averaged over the orbit. For the Jupiter-familycomets studied by A’Hearn et al. (1995), the peak H O production rate (obtained byextrapolating observed production rates to perihelion using the estimated dependenceof Q on r ) has a median of Q H O (peak) ∼ . × and a range from (0.02–5) × molecule s − . To estimate the average H O production rate over the orbit, we assume theproduction rate scales as Q ∝ r − α , with α taken from Table V of A’Hearn et al. (1995)or set to the nominal value of 2.7; we also set the ice production to zero when r > α are highly uncertain, because comets generally exhibit temporalvariations that are very different from power-laws. Further, the values of Q H O are rather 21 –uncertain and may be statistically biased toward higher values by selection effects. Themedian dM ice /dt = 9 . − with a range from 1.2–390 kg s − .For comparison, Kres´ak and Kres´akov´a (1987) calculated dM/dt by averaging overorbits in a similar manner. Instead of using the ice production rate Q H O , they use a roughcalibration of cometary total visual magnitudes, using 1P/Halley as a calibration sourceand assuming a production rate ∝ r − . Each revolution is calculated with its appropriateosculating orbital elements, over the 100 yr period from 1885–1985. The visible magnitudesare a measure of the total scattering by dust, and Kres´ak and Kres´akov´a (1987) convertthem to mass loss rates assuming a gas-to-dust mass ratio of 3:1. Their ice mass loss ratesare included for the relevant comets in Table 3. The mass-loss rates inferred from the visualmagnitudes and the H O production rates do not agree very well. Only a small part ofthe difference is due to assumptions about α ; we found less than a factor of 2 variationin dM/dt for a wide range of α , with the median changing from 9.1 to 7.2 kg s − if we set α = 4 for all comets.Given the wide range of dM ice /dt estimates, debris-to-ice ratios for individual cometscannot be considered accurate. But there are enough comets in the sample that outlierscan be identified and a statistical result can be obtained. Taking the ratio of the median dM/dt and dM ice /dt , the debris-to-ice mass ratio is 0.5. But this ratio of medians may notbe particularly meaningful, due to the wide range of actual mass-loss rates for comets andthe discrepancies between methods for estimating the ice mass loss rates. There may be awide diversity of meteoroid:ice fractions among comets, and detailed studies of individualcomets are needed to make reliable measurements. The infrared survey results presented inthis paper demonstrate that meteoroids are at least comparable to ice mass production in alarge sample of Jupiter-family comets. 22 – Brightness enhancements near a comet’s projected orbit plane are not necessarily olddebris trails. The particles’ orbits are only slightly different from that of the nucleus: theradiation pressure and the in-orbit-plane components of the ejection velocity will tend tospread particles only within the orbit plane, and only the out-of-plane component of theejection velocity (and gravitational perturbations by the planets) will cause perpendicularspread. Particles released with a non-zero velocity perpendicular to the comet orbit willstill cross the orbital plane every 180 ◦ of true anomaly. If the nucleus is observed at a trueanomaly of f then particles emitted at true anomaly f − ◦ will form a thin ridge ofhigh column density when viewed at a low orbital plane angle. The thin ridge has beennamed a ‘neck-line structure’ (Kimura and Liu 1975; Pansecchi et al. 1987; Fulle 1987). Aneck-line requires particles produced at true anomaly f − ◦ , and a low angle of the lineof sight with respect to the orbit plane.The infrared emission in some of our comet images occupies narrow, linear structuresthat are not precisely aligned with the projected orbital plane at the time of observation.These were prime candidates for neck-line structures. In each case, a Monte Carlosimulation was performed and the particles produced near a true anomaly 180 ◦ from thenucleus (at the time of observation) were isolated. Separate sky-plane images were made forthe neck-line particles and the remainder (debris trail particles). The debris trails follow theorbit of the comet precisely, but the neck-lines are often at a nonzero position angle withrespect to the orbit. Experiment showed that the neck-line position angle was usually veryclose to that of the β = 10 − syndyne. For 67P, Kelley et al. (2007) have cleanly separatedneck-line and debris trail using infrared images, while the optical image was dominated bythe neck-line. For comets whose infrared emission follows the nucleus but is closer to the β = 10 − syndyne than the trail, we found the simulations are consistent with a neck-line 23 –structure rather than strictly a debris trail. There will inevitably be a mixture of both thenodally enhanced neck-line and the debris trail, from particles produced over the remainderof the orbit not close to f − ◦ . A neck-line structure is essentially a portion of the debristrail with brightness enhanced due to projection effects. The neck-lines observed in oursurvey have ages that range from 1.1 to 3.3 yr, and are observed within a few arcmin of thenucleus. Therefore, these structures are necessarily comprised of large ( β < − ) particles.Both neck-lines and debris trails require large particles, and the mass estimates perunit path length dM/dφ and total mass taking into account the extent on the sky arecalculated in precisely the same manner as in the previous section. The neck-lines weobserve are old ( >
400 days, but < β . But in practice the ejection velocities andsubsequent trajectories must be modeled relatively accurately to allow such an inversion tothe particle size distribution. Such work is beyond the scope of this paper. (Note also thatthe mass-loss rate, dM/dt , from the previous section does not strictly apply to neck-lines.)The presence of neck-lines for individual comets is discussed below.
5. Descriptions of individual comets (Fig. 2) shows a debris trail that spans the image, as well as a highly-elongated pseudo-coma. The
Spitzer
MIPS and IRAC images are discussed in detail inReach et al. (2007); earlier results from
ISO are discussed in Reach et al. (2000); and thefirst detection from
IRAS is discussed in Sykes and Walker (1992). The brightness andinferred mass per unit mean anomaly are relatively flat across the image. The
Spitzer image 24 –measures only a small fraction of the total mass of the trail, which was seen to extendover 93 ◦ of mean anomaly in the IRAS data. The total trail mass, estimated using the
IRAS -observed mean anomaly range and 1/2 the
Spitzer -observed dM /dθ (to account fora falloff of trail brightness with distance behind the nucleus), is 7 × g. (Fig. 8) shows a distinct debris trail leading the nucleus. Following thenucleus, there are both a bright tail and a distinct trail, as can be seen from the projectedsyndynes. The trail of this comet was the first to be detected optically, extending over 10 ◦ with 2 ′ width in 1991 Spacewatch images (Rabinowitz and Scotti 1991). Figure 8shows thetrail both leading the and following comet, as was seen for 2P and 10P, both of which hadlong trails in the IRAS data, supporting a common origin for the Spacewatch and
Spitzer trails. (Fig. 2) shows a faint debris trail due to its relatively large heliocentricdistance ( r = 3 .
75 AU). It was included in the survey despite being somewhat outsideour r < . Deep Impact mission(A’Hearn et al. 2005). The debris trail was known from
IRAS in 1997, and the opticaldepth inferred from our data is consistent with that inferred from
IRAS (Sykes and Walker1992). Multiple-epoch observations with
Spitzer are under way to monitor the evolution ofthe debris trail. The trail extends beyond the edge of the image; using the
IRAS -observedlength in mean anomaly (7 ◦ ) the total mass is 1 × g. (Fig. 2) shows a long debris trail similar to 2P/Encke, spanning theimage and with significant brightness leading the nucleus. This trail was seen by IRAS in1983, with comparable optical depth, spanning 60 ◦ mean anomaly (Sykes 1990) makingit the longest and best-detected of the IRAS debris trails (Sykes and Walker 1992). Lessmaterial is leading the nucleus than following it, and the mass profile increases somewhattoward the ‘following’ edge of the image. To calculate the mass of debris leading the 25 –nucleus, we use a constant dM /dθ = 8 × g/deg (from the Spitzer image) and a lengthof 5 . ◦ mean anomaly (from the IRAS data). To calculate the mass of debris following thenucleus, we use a constant dM /dθ = 1 . × (from the Spitzer image) and a length of60 ◦ mean anomaly (from the IRAS data). The total mass is 9 × g. (Fig. 2) presented a very large and bright coma and tail from smallparticles. The coma is fan-shaped, with the opening angle not in the anti-solar directionbut rather approximately perpendicular to the projected orbit. The dust tail is roughlybisected by the β = 10 − syndyne and bounded by the β = 10 − and 10 − . syndynes. The debris trail can be barely discerned but appears as a thin linear feature, closely followingthe comet’s projected orbit, with a gap in azimuth between the trail and tail and inradial distance between the trail and coma. This phenomenon is also seen in 2P/Encke(Reach et al. present orbit still being closeto the nucleus, while the large particles from the previous orbits are already located alongthe comet’s orbit. The total extent of the debris trail is unknown, so we estimate only thelower limit of its mass using constant dM /dθ = 3 × g/deg over a nominal 1 deg ofmean anomaly. (Fig. 2) had a small round coma centered on the nucleus and a 5 ′ longlinear feature, 15 ′′ wide, extending behind the nucleus. The linear feature does not preciselyfollow the comet’s projected orbit, as expected for very large particles. Instead, it followsthe zero-velocity syndyne for β ≃ − . , which corresponds to particle size ∼ . ∼ − ), which we will refer to as ‘intermediate-sized’ particles; suchparticles are still within the range of radar meteor studies and are apparently common incometary orbits (Brown et al. 2002). The position angle of the infrared feature matches thatof a ‘neck-line’ structure due to particles produced 3.3 yr prior to observation. The massprofile following the nucleus is fairly flat, and the total extent of the emission is unknown, 26 –so we estimate a lower limit to the mass assuming a nominal 1 ◦ length in mean anomalyand correcting to the slightly smaller particle size M > dM /dθ × . − = 3 × g. (Fig. 3) had a faint tail, 30 ′′ wide, extension following the nucleus.This is apparently a dust tail, as it does not follow the projected orbit. Enough area wascovered, and the anti-solar direction was nearly opposite the projected orbit direction, sothat an upper limit I ν < .
02 MJy sr − could be placed on the debris trail using the portionof the image away from the coma and tail. (Fig. 3) was bright and had one of the best viewing geometries, andcleanest separation between trail and tail, in the survey. The fan-shaped dust coma isroughly bounded by the β = 10 − to 10 − syndynes. The debris trail is clearly distinctfrom the coma and follows the projected orbit very precisely, so it can only be composed oflarge particles with β < − . The trail is 17 ′′ wide; such narrow trails, frequently foundin this survey, would have been highly beam diluted to IRAS so are not surprisingly notdetected. The trail is fainter, but present, leading the comet, requiring non-zero ejectionvelocity. The trail extends to at least the edge of the image; an estimated lower limit to itsmass, assuming constant mass per unit mean anomaly and a length of 1 ◦ mean anomaly, is2 × g. (Fig. 3) has a bright point-like nucleus with diffraction rings anda dust tail due to small particles, β = 10 − to 10 − . There is no debris trail, despiteexcellent viewing geometry and high-quality data. We place an upper limit on the surfacebrightness, I ν < .
03 MJy sr − corresponding to an optical depth τ < × − , which islower than that of detected trails. Because the comet was close, the trail is expected to bewider than those for most other comets ( ∼ ′ , scaling other comets trail widths by ∆), buta very wide area (30 ′ ) was mapped and should have included the debris trail. The upperlimit on the debris trail is therefore very strict, and an explanation for the lack of trail 27 –is required. As discussed below, comets with more non-asteroidal orbits (lower Tisserandparameter), like 49P, seem to have weaker trails. It is quite possible that the close approachto Jupiter in 1997 is the root cause for the lack of a detectable trail. Particles from theprevious revolution are normally the ones that would be detected in the debris trail on thisrevolution. The 1997 close approach may have perturbed the orbits of large particles fromthe previous revolution, scattering them to a different location or dispersing them widely. (Fig. 3) had a poor viewing geometry, with the tail and trailsuperposed to within 3 ◦ position angle. There was no debris leading the comet, down to anupper limit of 0.05 MJy sr − surface brightness, which corresponds to τ < × − . (Fig. 4) has one of the most clear-cut debris trails, with anexcellent viewing geometry. The debris trail is narrow, extends both leading and followingthe nucleus, precisely following the projected orbit as expected for particles with β ≪ − experiencing negligible radiation pressure. The lower limit to the trail mass, for β = 10 − particles and a length of 1 ◦ mean anomaly is 8 × g. (Fig. 4) was observed to have both a tail, roughly bounded by the β = 10 − to 10 − zero-velocity syndynes, and a debris trail. The trail is separated from thetail following the comet, thanks to a favorable viewing geometry. It is however faint, andthe trail mass can only be crudely bounded, if we assume > ◦ mean anomaly length, as M > × g. (Fig. 4) was observed with a very bright tail following the comet as wellas a prominent debris trail leading the comet. The dust tail is slightly shifted from theorbit, mostly consistent with the zero-velocity syndynes of β = 10 − to 10 − , but includingthe projected orbit ( β = 0). The debris trail leading the comet is closely aligned with theorbit. This trail had been previously detected by IRAS (Sykes and Walker 1992). The trailextends to the edge of the
Spitzer image without decreasing significantly in brightness. 28 –Using the
IRAS -observed lengths of 0 . ◦ mean anomaly leading and 5 . ◦ following thenucleus, together with the Spitzer -observed brightnesses, yields a total mass 9 × g. (Fig. 4) had previously been found to have a debristrail by IRAS (Sykes and Walker 1992). The
Spitzer observation is discussed in detail ina separate paper (Kelley et al. 2007). The portion of the debris trail leading the comet isevident, while the portion following the comet is contaminated by a neck-line structure andis therefore not solely a debris trail. The mass of the trail can be roughly estimated usingits brightness leading the nucleus and the
IRAS -observed length, yielding 1 × g. (Fig. 5) has a bright tail with a range of particle sizes, with the bulkfalling within the β = 10 − to 10 − zero-velocity syndynes. A debris trail precisely alignedwith the orbit is clearly evident leading the comet; it is confused with the tail following thecomet. Kres´ak (1993) discussed the case of 69P/Taylor, which was observed split in 1916but was subsequently perturbed by Jupiter in 1925 so that debris from the splitting shouldbe widely dispersed. He mentions that a trail should be present but below the detectionlimit of IRAS . Our new observations are more sensitive, allowing us to detect the debristrail with
Spitzer . If the comet were only discovered a few years ago, we would never knowit had split in the past; this is an example of cometary calving, which is apparently frequent(Chen and Jewitt 1994). The total extent of the trail is not known, so we only estimate arough lower limit for 1 ◦ mean anomaly of M > × g. (Fig. 5) was detected as a long debris trail, but without a bright nucleus orcoma at the predicted location (using the orbit from 1998). Using the updated orbit afterrecovery in 2005 ( ? ), a compact source at the nucleus’ position is indeed present 2 ′ ahead ofthat predicted from the 1998 orbit; this source is moving at the predicted rate based on the2006 ephemeris. The most fascinating result for this comet is that its debris trail is longand even increases in brightness following the comet, peaking 11 ′ behind it. This cannot be 29 –explained by a simple dust production history. The 10 particle Monte Carlo simulation(with r − dust production) for this comet shows only a coma and trail, so the enhancementin trail behind the comet is not due to a geometric projection effect. The mass per unitmean anomaly seems to increase with distance following the nucleus, and the trail extent isunknown. A lower-limit mass for 1 ◦ mean anomaly is 8 × g. In 2006, this comet wasobserved again at much closer distance; Figure 8 shows a clearly-detected trail leading thenucleus. The trail following the nucleus cannot be cleanly discerned from a possible tailuntil near the edge of the image, at which point we see that the narrow ridge of emissionextending across the entire image is indeed the debris trail, following closely the projectedorbit of the comet. (Fig. 4) was exceptionally bright when observed, with a bright tail dueto particles of indeterminate size (due to the unfavorable viewing geometry with the antisolar direction nearly parallel to the orbit-following direction). Leading the comet, thereis a narrow feature that lies precisely along the projected orbit, which we identify as thedebris trail. Using the mass per unit mean anomaly leading the comet, and a lower-limitlength of 1 ◦ mean anomaly, yields a mass M > × g. (Fig. 5) was observed when it was relatively closeby, with unfavorablegeometry (tail and trail overlapping), and covering a relatively small field of view. Theextremely bright tail is likely due to small particles. The only portion of the image freeof small particles is leading the comet, where there is a faint linear feature parallel to butslightly shifted (by less than its width) from the projected orbit of the comet. Based oncomparison to images of other comets (78P, 123P) viewed similarly and with clear ‘leading’debris trails despite bright tails, we tentatively identify this feature as Howell’s debris trail.The lower-limit mass, derived as for 78P, is M > × g. (Fig. 5) has a moderately bright debris trail following the nucleus, 30 –with no detectable emission leading the nucleus. The Spitzer observation was adverselyaffected by an observation of Saturn immediately preceding, but the image was adequatelyrecovered. The trail is close to the projected orbit but follows the β = 10 − syndyne better.Based on comparison to simulations, much of the infrared feature is likely to be a neck-linestructure due to particles produced 2.0 yr prior to observation. The estimated mass of thestructure > × g. (Fig. 6) had a bright tail, roughly bounded by the zero-velocitysyndynes for β = 10 − and 10 − . The separation between the tail and trail was large enoughto set an upper limit to the trail brightness relatively far behind the comet; no trail wasseen leading the comet with an upper limit I ν < . − . (Fig. 6) had extensive infrared emission following the nucleus, butthe apparent trail does not precisely follow the comet’s orbit. Instead, it is closer tothe β = 10 − syndyne and may contain significant contribution from intermediate-sizedparticles. The mass estimate M > × g is a lower limit because of the unknown totalextent, though the surface brightness does decrease significantly before the edge of theimage (suggesting most of the mass was observed). The orientation of the infrared featureis similar to that expected for a ‘neck-line’ from particles ejected 1.1 yr prior to observation,but the feature is broader than a neck-line. The feature is more likely a tail, due primarilyto intermediate-sized particles. (4015) 107P/Wilson-Harrington was not strictly part of the short-period comet surveybut was observed in the same manner. It was found to be a point source, with no extendedemission along the orbit to a limit of I ν < .
05 MJy sr − . At the observed heliocentricdistance r = 2 .
25 AU, this corresponds to an optical depth limit τ < × − . (Fig. 8) shows a narrow trail in the orbit of the comet. The bright sourceat the predicted location of the nucleus looks point-like and may actually be a celestial 31 –source coincidentally close to the ephemeris position. A smaller, somewhat resolved sourceis located following the predicted location of the nucleus and within the debris trail. Thisobject appears to be the actual nucleus, at least in terms of debris trail production, basedon the location of some debris leading and most following its location. While the syndynesin Fig. 8 are centered on the predicted location of the nucleus, the flux reported in Table 1is that of the smaller source. More detailed modeling is required to address these issues. (Fig. 6) has a thin trail extending to the edge of the imageand precisely following the comet’s orbit. The brightness does not decrease significantly atthe edge of the image, suggesting the trail may be massive; its narrow width shows it is alsodevoid of small particles. An estimate lower-limit to the mass M > × g. (Fig. 6) was observed when relatively closeby and presented a very brightdust tail that makes it impossible to separately locate a possible debris trail. (Fig. 6) has a prominent debris trail both leading and following thenucleus, closely following the orbit. Assuming a length at least 0 . ◦ leading and 1 ◦ followingthe nucleus, the trail mass M > × g. (Fig. 6) had a bright elongated coma/tail due to particlesof indeterminate size. While the anti solar and comet-following angles were not widelyseparated, a long enough field was observed to allow a debris trail in the comet’s orbitto be distinguished from a small-particle-only tail far from the nucleus. There is noclear, contiguous debris trail in the comet’s orbit, as there was for most of the othercomets in the sample. However, there were two patches of emission along the comet’sorbit. The first patch is circular, located 9 . ′ following the nucleus, and the second one iselongated along the orbit, approximately 15 . ′ following the nucleus; their brightness ∼ . − corresponds to an optical depth ∼ × − . While these patches are alignedalong the orbit, it is very likely (and cannot be determined with the present data) that 32 –these patches are small interstellar clouds. Inspecting the IRAS images as reprocessed byMiville-Deschˆenes and Lagache (2005), there is significant, structured interstellar emissionin the field. (Fig. 7) was observed relatively close by and had a very bright tailof small particles. The debris trail following the comet can be barely distinguished fromthe tail. Leading the comet, the debris trail precisely along the projected orbit, is detectedwithout confusion from smaller particles. The presence of a significant trail leading thecomet suggests the debris trail may be massive, but from the present observations only arough lower limit can be made, by assuming a length 0 . ◦ leading and 1 ◦ following thenucleus; this yields M > × g. (Fig. 7) was observed under very favorable geometric conditions,with the small-particle production being minimal at r = 2 .
74 AU and the anti solar (tail)direction 169 ◦ from the trailing direction. The brightness decreases significantly beforethe edge of the image, suggesting we have observed the bulk of the debris (though therecould always be a fainter trail of larger particles). These factors combine to allow an actualmeasurement (rather than a limit) of the mass of M ≃ × g. The extended emissionstretches approximately along the orbit, completely inconsistent with a small-particle tail.But the orientation is not precisely along the orbit, being closer to the β = 10 − syndyne.The orientation of the infrared emission matches very well that of a ‘neck-line structure’due to particles ejected 1.7 yr prior to observation. (Fig. 7) had one of the best-defined debris trails owing toits brightness and favorable viewing geometry. The trail extends to the edge of the imagewithout decreasing significantly in brightness, so only a lower limit to the mass can bemade, assuming trail length at least 0 . ◦ leading and 1 ◦ following the nucleus in meananomaly, yielding M > × g. 33 – (Fig. 7) had very faint extended emission, evident only after smoothingthe image. This faint emission is only present following the comet and would correspond toa lower limit to the trail mass assuming 1 ◦ length in mean anomaly of M > × g. has a very faint ( ∼ .
02 MJy sr − ), narrow debris trail confined veryprecisely to the comet’s orbit. This comet has an orbit similar to main belt asteroids andexemplifies the class as defined by Hsieh and Jewitt (2006). The debris trail appears similarto other narrow trails in our sample, suggesting that the main belt comet lose significantmass in the form of large meteoroids, just like the Jupiter-family comets. More detailedmodeling and image analysis are under way to better constrain mass production history. P/2003 S2 (Fig. 7) had a debris trail precisely following the comet’s orbit. Thebrightness decreases significantly by the edge of the image, allowing a mass estimate M ≃ × g, although faint trail emission extends to the edge of the image (so the totaltrail mass could be significantly higher). Part of the infrared emission may be due to aneck-line structure; it is not possible to separate them due to the viewing geometry placingthe trail and neck-line on top of one another.
6. Statistical Trends of debris trail properties
We summarize properties of each comet that might influence the properties of theirdebris trails in Table 1. The orbital size and eccentricity are listed, together with theTisserand invariant for gravitational scattering by Jupiter, T J (Levison and Duncan 1997).And the date of the last passage of a comet into Jupiter’s gravitational sphere of influenceis T pert .The amount of material in a given comet’s debris trail may be correlated with thepresent shape of the comet’s orbit. Figure 11 shows the debris mass production rate versus 34 – q . Weak correlations are present between ˙ M and a or q . The correlation coefficients between˙ M and a or q are -0.64 and -0.32, respectively; while the correlation coefficients betweenlog ˙ M and a or q are -0.66 and -0.62, respectively. This apparent correlation is unlikely tobe purely a selection effect. While comets observed at large r could only be detected ifthey have relatively larger ˙ M (at fixed sensitivity limit), our survey does not appear to besensitivity limited for trail detection. Indeed the comets with no detected trails tended tobe observed at smaller r . Further, the comets with small q were not preferentially observedat small r (where they would be brighter).The correlation with orbital shape ( q or a ) can also be expressed in terms of theTisserand invariant for Jovian perturbations, T J . Comets with little interaction with Jupiter(asteroidal or Encke-type orbits, T J > .
94) have a median dM/dt = 3 . − , while thosewith T J < .
94 have a median dM/dt = 0 . − . (A clear outlier is 67P, which is theonly low- T J comet with dM/dt > − .) These trends suggest that comets spendingmore time closer to the Sun may produce more debris, and comets dynamically decoupledfrom Jupiter may retain debris longer.The general trend of more-massive trails for comets with smaller q goes somewhatcounter to what might be expected from the trend of dust-to-gas ratio being lower at smaller q as found in the visible-light survey by A’Hearn et al. (1995). However, if the grains beingdetected in the inner coma photometry, traced by the scalar Af ρ by A’Hearn et al. (1995)are predominantly small grains, perhaps from fresher surface material, then the new resulton debris trails could be explained as an evolution of the size of the material ejected fromcomets. Comets spending more time in the inner Solar System may be dynamically olderand more depleted in small particles, while they still appear capable of ejecting largerparticles, which build up in their orbits.For the observations presented in this paper, there is no clear correlation between the 35 –amount of debris in an orbit and the date of last perturbation. Such a correlation wouldbe expected if the perturbations brought comets that were previously in outer-solar-systemorbits into q < q > q was typically of order 0.1AU.) Thus the date of the last strong perturbation does not have a dramatic influence onthe amount of debris trail material close to the nucleus, as traced by our Spitzer survey. Wedo expect a significant correlation between T pert and the trail length ; however, the presentobservations do not cover enough of each comet’s orbit to show the ends of the trails.The widths of the debris trails also show some systematic trends. Figure 12 shows thetrail width versus the time since perihelion. The trails observed furthest from perihelion (i.e.larger | T − T p | or r ) are wider. If the observations were sensitive to particles emitted withinmonths of the time of observation, the observed trend would be counter to expectations:particles released further from perihelion would be moving slower and would remain closerto the midplane. However if the particles are years old, which we believe to be the case,and they are mostly produced near perihelion, then the width should increase with time 36 –since perihelion: W ∝ V ⊥ | T − T p | , (11)where V ⊥ is the component of the ejection velocity perpendicular to the comets’ orbits.Gravitational perturbations would further increase the trail width for older particles, buton timescales of multiple orbits. If we interpret the increasing width as due only to ejectionvelocity, the slope of the trend in Figure 12 yields V ⊥ ∼ − . Using equation 4, assumingparticles are mostly produced near perihelion, with angle ψ relative to the orbit plane, weestimate the particle size β ∼ (cid:18) v ⊥ cos ψv (cid:19) q ( AU ) , (12)yielding β ∼ × − for a typical perihelion q ∼ . ψ = 30 ◦ , and v = 1 km s − . This size estimate is in accord with the results presented elsewhere in thispaper, which show β ≪ − . For the trail width trend to be produced by particles with β as large as 10 − requires v = 0 .
07 km s − , a value too slow to explain the morphologyof 2P/Encke’s coma (Reach et al. IRAS (Sykes and Walker 1992).
7. Conclusions
The
Spitzer /MIPS images presented in this paper demonstrate that the productionof mm-sized debris is a common feature of Jupiter-family comets: the orbits of most (atleast 27 out of the 34 in the present survey) comets are delineated on the sky by ‘trails’ ofmid-infrared emission. The debris trails can only be due to particles with a small ratio ofradiation pressure to gravity, β < − .The extended surface brightness near Jupiter-family comets contains a mix of particlesizes, 1 < β < − ( ∼ µ m for density ∼ − ). Generally, the comae aremuch brighter in the regions traveled by large particles, bounded by the 10 − < β < −
37 –(100-1000 µ m) syndynes, than in the regions traveled by smaller particles. Examples ofobservations of large-particle-dominated comae include 2P/Encke and 48P/Johnson, forwhich the viewing geometry allowed straightforward separation of particles of different size.Dust tails , stretching roughly between the anti-solar direction and the β = 1 syndyne,were detected from some comets, indicating that small particles can also be detected inthe mid-infrared images when they are present. Tails are routinely detected for cometsobserved closest to the Sun. The strong heliocentric and comet-to-comet variety of tails,in contrast to the prevalence and similarity of trails suggests a variation in the dust sizedistributions—specifically, the ratio of surface area in large versus small particles—amongcomets. Further work is required to determine whether it is the actual surface area of grainsthat is varying or the manner in which they are produced (i.e. the velocity distribution orefficiency of fragmentation).Debris trails are massive, and the inferred mass production rate of mm-sized debris islarger than that of sublimating ice. The predominance of large particles in cometary massloss agrees with in situ spacecraft observations of cometary particles. Green et al. (2004)showed that the mass distribution detected during all three the comet encounters with dustmonitors is completely dominated by large particles. We separate the particles into threepopulations based on the shape of the mass distribution: small particles , smaller than 10 − g (size less than 50 µ m, β > − ), have a cumulative mass distribution N ( < m ) ∝ m − . ; intermediate particles above this mass and until ∼ − g (size 250 µ m, β ∼ − )have relatively constant cumulative fluence; then for large particles the cumulative massdistribution decreases again, approximately as m − . . Such a size distribution is consistentwith the in situ observations during the Giotto encounter with 1P/Halley (McDonnell et al.1987) the
Stardust encounter with 81P/Wild 2 (Green et al. 2004), and interplanetarymeteoroids detected by near-Earth spacecraft and meteor magnitudes (Gr¨un et al. m ∼ − g, size ∼ µ m, and β ∼ − .Figure 13 shows the size distribution weighted by the effective surface area. For 24 µ memission, the effective surface area is the cross-sectional area times the absorption efficiency Q = (2 πa/λ ) for a < λ/ π with λ = 24 µ m. For scattering, Q = (2 πa/λ ) for a < λ/ π with λ = 0 . µ m for visible light and 1 cm for radar. The efficiencies are all set to unity for a > λ/ π . Using the size distribution observed within the coma of 81P/Wild 2 (Green et al.2004), the effective surface area for mid-infrared emission is strongly dominated by theparticles of β ∼ − , while the effective surface area for visible-light scattering has asignificant but not dominant contribution from smaller particles. (Radar backscatter wouldbe produced only by the large particles.) The nature of the size distribution, which is not asingle power law over the range of sizes from micron to cm , explains why the debris trailobservations are dominated by particles with β > − .There is an apparent conflict between our interpretation of the mid-infrared images(and the in situ size distributions) and the traditional interpretation of optical images andinfrared spectra. The optical imaging and infrared spectroscopy studies generally deriveparticle sizes of order 10 µ m and consider particles only up to 100 µ m (cf. Kelley et al.2006; Lisse et al. 2004; Kolokolova et al. 2004), which all fall within the small particle population. The existence of some small particles is required to explain silicate emissionfeatures ( a < λ/ π where the silicate feature is at λ ∼ µ m). Silicate features have alsobeen correlated with the ‘super-heating’ of grains above the isothermal sphere (blackbody)temperature, due to the lower absorption efficiency of small grains in the infrared where 39 –their cooling occurs ( a < /T µ m where the grain temperature T is in K). Silicate featuresare generally not strong for Jupiter-family comets, and they can arise from a populationof grains distinct from the large particles that dominate the mass loss and produce thedebris trails. Figure 13 shows that a significant contribution to mid-infrared emission(and in particular the silicate feature) can arise from the the small particle population ifthey are significantly hotter than the large grains, even if a large particle population (inexcess of the power-law fitted to the small particles) is included. Therefore, we suspectthat previous models for coma spectra and optical scattering are sampling only the smallparticle population; the abundance of large particles such as in meteoroid streams is farlarger than would be inferred from an extrapolation of a simple power law normalized tothe small particle abundance.That large particles are produced by most comets is now beyond doubt, but thetotal mass and the distribution of large particles over comets’ orbits remains largelyunknown. The present survey only covers the near-nuclear environment, with the debristrails dominated by material from this and the previous revolution. The slow spread ofdebris trail material, and the rapid influence of gravitational perturbations, spreads debrisover a wide area. Strong perturbations by Jupiter occur every ∼ yr for Jupiter-familycomets. Comets in the most stable orbits can build up a meteoroid complex, containingmany orbits’ debris, easily recognizable from surface brightness imaging, while cometssuffering recent perturbations will have only young particles in their trails. The debrisdetected in the present survey with Spitzer was faint for most comets, <
1% of the zodiacallight surface brightness and with a width < ′′ . Such features are exceptionally difficult todetect in visible light (e.g. Ishiguro et al. 2002) and shallow, wide-area surveys (e.g. IRAS ).Deeper investigations along the orbits of comets may reveal the extent of their meteoroidcomplexes and the total mass production of large particles. 40 –The meteoroids of some comets enter the Earth’s atmosphere as meteor showers(Jenniskens 2006). Meteor showers are much more widely dispersed than the debris trails weobserved. The debris trails are actually more comparable to the meteor storms (Jenniskens2006; Kres´ak 1993). The debris trails evolve into the wider meteoroid streams and graduallyinto the sporadic meteors. The mass of meteoroid streams has been estimated from observedmeteor rates, yielding 10 − g for four well-studied streams (Hughes and McBride 1989).These masses are much larger than those we infer from most debris trails, with the lowestestimated meteoroid stream mass still an order of magnitude larger than the largestestimated debris trail mass. The well-known meteor streams are likely to arise frommeteoroids produced by the largest and longest-lived comets that cross the Earth’s orbit.Their properties provide a relatively unique, long-term view of cometary mass loss that iscomplementary to that obtained from studying debris trails.The meteoroid mass production rates measured from the present survey has a median2 kg s − per comet, with a few undetectable ones having smaller mass-loss. There are ∼ ∼
300 kg s − . The debris trail particles are all on bound orbits, very similar tothose of their parent comets—though they will gradually scatter away from their parentcomets due to their slightly different initial orbit, non-zero beta , different non-gravitationalforces due to outgassing and Yarkovsky effect, and different gravitational perturbationsby the planets. Thus debris trail particles will gradually fill the inner Solar System.Their lifetime is mostly limited by mutual collisions with other interplanetary particles(Gr¨un et al. ∼ µ m sized particles that generate the zodiacal light(Gr¨un et al. − due tomutual collisions and Poynting-Robertson drag, requiring a corresponding continuous inputto maintain the zodiacal light at constant brightness. Constancy of the zodiacal lightis not actually required, with the best observational evidence being constancy to ± REFERENCES
A’Hearn, M. F., Millis, R. L., Schleicher, D. G., Osip, D. J., and Birch, P. V. 1995. Theensemble properties of comets: Results from narrowband photometry of 85 comets,1976–1992. Icarus 118, 223–270.A’Hearn, M.F. et al. 2005. Deep Impact: Excavating Comet Tempel 1. Science 310,258-264.Anderson, J. D., Lau, E. L., Bird, M. K., Asmar, S. W., Clark, B. C., Giampieri,G., Gilliland, K. V., and P¨atzold, M. 2004. Stardust dynamic science at comet81P/Wild 2. JGR 109, E12S205.Brown, M. E., Schaller, E. L., Roe, H. G., Rabinowitz, D. L., Trujillo, C. A. 2006. DirectMeasurement of the Size of 2003 UB313 from the Hubble Space Telescope. ApJ643, L61–L63.Brown, P., Spalding, R. E., ReVelle, D. O., Tagliaferri, E., and Worden, S. P. 2002. Theflux of small near-Earth objects colliding with the Earth. Nature 420, 294–296.Brownlee, D. E. et al. 2004. Surface of Young Jupiter Family Comet 81P/Wild 2: Viewfrom the Stardust Spacecraft. Science 304, 1764-1769.Burns, J. A., Lamy, P. L., Soter, S. 1979. Radiation forces on small particles in thesolar system. Icarus 40, .1–48Chen, J., and Jewitt, D. 1994. On the rate at which comets split. Icarus 108, 265–271.Chyba, C. F., Thomas, P. J., Brookshaw, L., Sagan, C. 1990. Cometary Delivery ofOrganic Molecules to the Early Earth. Science 249, 366.Chyba, C. F., Thomas, P. J., Zahnle, K. K. 1993. The 1908 Tunguska explosion -Atmospheric disruption of a stony asteroid. Nature 361, 40. 43 –
Thomas, P. J., McKay, C. P., Chyba, C. F.
Comets and the Origin andEvolution of Life . Springer, Berlin.Delsemme, A. H. 2000. 1999 Kuiper Prize Lecture Cometary Origin of the Biosphere.Icarus 146, 313–325.Fazio, G. G., 64 colleagues 2004. The Infrared Array Camera (IRAC) for the SpitzerSpace Telescope. ApJS 154, .10–17Fulle, M. 1987. A possible Neck-Line Structure in the dust trail of Comet Halley. A&A181, L13-L14.Fulle, M. 1990. Meteoroids from short period comets. A&A 230, 220-226.Fulle, M. 1996. Dust environment and nucleus spin axis of comet P/Tempel 2 frommodels of the infrared dust tail observed by IRAS. A&A 311, 333-339.Goldstein, R., Goldstein, B. E., Balsiger, H., Coates, A. J., Curdt, W. 1991. Thecomposition and plasma signature of a large dust impact on the Giotto spacecraft.JGR 96, 13739-13747.Green, S. F., McDonnell, J. A. M., McBride, N., Colwell, M. T. S. H., Tuzzolino, A. J.,Economou, T. E., Tsou, P., Clark, B. C., Brownlee, D. E. 2004. The dust massdistribution of comet 81P/Wild 2. JGR 109, E12S04.Gr¨un, E., H. A. Zook, H. Fechtig, and R. H. Giese 1985. Collisional balance of themeteoritic complex. Icarus 62, 244–272.Hsieh, H. H., Jewitt, D. 2006. A Population of Comets in the Main Asteroid Belt.Science 312, 561–563.Hughes, D. W., McBride, N. 1989. The mass of meteoroid streams. MNRAS 240, 73–79. 44 –Ishiguro, M., Watanabe, J., Usui, F., Tanigawa, T., Kinoshita, D., Suzuki, J., Nakamura,R., Ueno, M., Mukai, T. 2002. First Detection of an Optical Dust Trail along theOrbit of 22P/Kopff. ApJ 572, L117–L121.
Jenniskens, P.
Meteor Showers and their Parent Comets . Cambridge. 802 pp.Jewitt, D., Matthews, H. 1999. Particulate Mass Loss from Comet Hale-Bopp. AJ 117,1056-1062.
Jewitt, D.
Comets II , Univ. of Arizona Press, Tucson, pp. 659-676.Jones, J. 1986. The effect of gravitational perturbations on the evolution of the Tauridmeteor stream complex. MNRAS 221, 257.
Keller, H. U., Britt, D., Buratti, B. J., Thomas, N.
CometsII , Univ. of Arizona Press, Tucson, pp. 211-222.
Kelley, M. S., Reach, W. T., Lien, D. J.
Kolokolova, L., Hanner, M. S., Levasseur-Regourd, A.-Ch., Gustafson,B. A. S.
CometsII , Univ. of Arizona Press, Tucson, pp. 577-604.Kres´ak, L. 1993. Cometary dust trails and meteor storms. A&A 279, 646.
Kres´ak, L., Kres´akov´a
Symposium on the Diversity and Similarity of Comets , ESASP-278, Brussels, pp. 739–744.Kres´ak, L., Kres´akov´a 1994. Updating the catalogue of absolute magnitudes of periodiccomets. Plan. Space Sci. 42, 199-204.
Lamy, P. L., Toth, I., Fernandez, Y. R., Weaver, H. A.
Comets II , Univ. of Arizona Press, Tucson, pp. 223-264.Leinert, C., Roser, S., Buitrago, J. 1983. How to maintain the spatial distribution ofinterplanetary dust. A&A 118, 345-357.Leinert, C., Pitz, E. 1989. Zodiacal light observed by HELIOS throughout solar cycle no.21 - Stable dust and varying plasma. A&A 210, 399-402.Levison, H. F., Duncan, M. J. 1994. The long-term dynamical behavior of short-periodcomets. Icarus 108, 18–36.Levison, H. F., Duncan, M. J. 1997. From the Kuiper Belt to Jupiter-Family Comets:The Spatial Distribution of Ecliptic Comets. Icarus 127, 13–32.Lisse, C. M., M. F. A’Hearn, Y. R. Fernandez, E. Gruen, H. U. Kaufl, T. Kostiuk, D.J .Lien, D. J. Osip, S. B. Peschke, R. G. Walker 2004. A tale of two very differentcomets: ISO and MSX measurements of dust emission from 126P/IRAS (1996) and2P/Encke (1997). Icarus 171, .444–462 46 –Lowry, S. C., Weissman, P. R. 2003. CCD Observations of distance comets from Stewardand Palomar Obsevatories. Icarus 164, 492-503.Lowry, S. C., Weissman, P. R., Sykes, M. V., Reach, W. T. 2003. Observationsof Periodic Comet 2P/Encke: Physical Properties of the Nucleusand FirstVisual-Wavelength Detection of Its Dust Trail. Lunar and Planetary InstituteConference Abstracts 34, .2056–
Makovoz, D., Khan, I.
Astronomical Data Analysis Software and Systems XIV ,Astron. Soc. Pacific, San, pp. 1–5.FranciscoMarsden, B. G., Sekanina, Z. 1974. Comets and nongravitational forces. VI. Periodiccomet Encke 1786-1971. AJ 79, 413–419.
Marsden, B. G., Williams, G. V.
Catalogue of Cometary Orbits 2003: 15thEdition . Smithsonian Astrophysical Observatory, Cambridge, MA.Mazets, E. P. et al. 1987. Dust in Comet P/Halley from VEGA Observations. A&A187, 699-706.
Meech, K.J., Svoren, J.
Comets II , Univ. of Arizona Press, Tucson, pp. 317-335.McDonnell, J. A. M. et al. 1987. The dust distribution within the inner coma of cometP/Halley 1982i - Encounter by Giotto’s impact detectors. A&A 187, 719-741.McDonnell, J. A. M. et al. 1993. Dust particle impacts during the Giotto encounter withComet Grigg-Skjellerup. Nature 362, 732-734. 47 –Miville-Deschˆenes, M.-A., Lagache, G. 2005. IRIS: A New Generation of IRAS Maps.ApJS 157, 302.Napier, W. M. 2001. Temporal variation of the zodiacal dust cloud. MNRAS 321,463-470.Pansecchi, L., Fulle, M., Sedmak, G. 1987. The nature of two anomalous structuresobserved in the dust tail of Comet Bennett 1970. II - A possible Neck-LineStructure. A&A 176, 358-366.Patzold, M., Edenhofer, P., Bird, M. K., Volland, H. 1993. The Giotto encounterwith Comet P/Grigg-Skjellerup - First results from the Giotto Radio-ScienceExperiment. A&A 268, L13-L16.
Prialnik, D., Benkhoff, J., Podolak, M.
Comets II , Univ. of Arizona Press, Tucson, pp. 359-387.Rabinowitz, D., Scotti, J. 1991. Periodic Comet Faye (1991n). IAU Circ. 5366, 3.Reach, W. T. 1988. Zodiacal emission. I - Dust near the earth’s orbit. ApJ 335,468–485.Reach, W. T., M. V. Sykes, D. Lien, and J. K. Davies 2000. The Formation of EnckeMeteoroids and Dust Trail. Icarus 148, 80–94.
Reach, W. T., M. S. Kelley, B. Bhattacharya
Sarugaku, Y., Ishiguro, M., Reach, W. T.
Sykes, M. V., Gr¨un, E., Reach, W. T., Jenniskens, P.
Comets II , Tucson, 677–693, pp. Univ. Ariz. Press.Sykes, M. V., L. A. Lebofsky, D. M. Hunten, and F. J. Low 1986. The discovery of dusttrails in the orbits of periodic comets. Science 232, 1115–1117.Sykes, M. V., D. J. Lien, and R. G. Walker 1990. The Tempel 2 dust trail. Icarus 86,236–247.Sykes, M. V., and R. G. Walker 1992. Cometary dust trails. I. Survey. Icarus 95,180–210.Turco, R. P., Toon, O. B., Park, C., Whitten, R. C., Pollack, J. B., Noerdlinger, P. 1982.An analysis of the physical, chemical, optical, and historical impacts of the 1908Tunguska meteor fall. Icarus 50, 1–52. 49 –Vaubaillon, J., Colas, F., Jorda, L. 2005. A new method to predict meteor showers. I.Description of the model. A&A 439, 751–760.Weismann, P. R., Lowry, S. C. 2003. The Size Distribution of Jupiter-Family CometaryNuclei. LPI 34, 2003;2003.Whipple, F. L. 1950. A comet model. I. The acceleration of Comet Encke. Astrophys. J.111, 375–394.Whipple, F. L. 1951. A comet model. II. Physical relations for comets and meteors.Astrophys. J. 113, 464–474.Whipple, F. L. 1955. A comet model. III. The zodiacal light. ApJ 121, 750–770.
Yeomans, D.
Comets: A Chronological History of Observation, Science, Myth,and Folklore . Wiley, New Tork, 485 pp.This manuscript was prepared with the AAS L A TEX macros v5.2.
Table 1. Spitzer Comet Trail Survey Summary
Comet Date UT T − T p R ∆ q e T J T pert a PA Sun PA trail F ν b dM /dt c Trail type d (hh:mm) (days) (AU) (AU) (AU) ( ◦ ) ( ◦ ) (mJy) (kg s − )2P/Encke 06/20/04 18:35 173 2.53 2.02 0.339 0.847 3.02 < < < < < < < < < < < Table 1—Continued
Comet Date UT T − T p R ∆ q e T J T pert a PA Sun PA trail F ν b dM /dt c Trail type d (hh:mm) (days) (AU) (AU) (AU) ( ◦ ) ( ◦ ) (mJy) (kg s − )108P/Ciffreo 10/05/2006 14:30 -284 2.97 2.35 1.71 0.542 2.77 < < < < < < a Year of last significant orbital perturbation b Flux within 12.5” aperture centered on nucleus c Mass production rate of trail particles assumed to have β = 10 − , ρ = 1 g cm − =leading, F=following nucleus; ‘long’ means the trail extends to the edge of the image; ‘(tail)’ means the small-particle dust tail dominates the image preventing debris traildetection; ‘intermed’ means the trail follows the β = 10 − syndyne more closely than it follows the projected orbit of the nucleus.
52 –Table 2. Debris trail brightnes profile fits a φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)2P/Encke323 47.1 0.71 5.4 54.3 7.9 54.12 135.0248 36.1 0.81 6.2 54.5 8.0 62.44 155.6173 25.2 0.93 7.1 45.1 6.6 59.15 147.3-128 -18.6 0.78 5.9 29.4 4.3 32.35 80.6-203 -29.6 0.87 6.6 43.0 6.3 52.69 131.4-278 -40.5 0.75 5.7 42.4 6.2 44.94 111.9-353 -51.5 0.65 5.0 46.1 6.7 42.46 105.74P/Faye446 31.8 0.27 1.2 51.4 3.7 13.9 6.5295 21.1 0.24 1.1 66.1 4.7 16.0 7.79P/Tempel 1-312 -76.7 0.14 2.1 30.1 7.4 5.79 81.8-463 -113.5 0.15 2.3 50.5 12.4 10.67 150.810P/Tempel 2475 82.4 0.35 2.6 43.2 7.5 21.58 69.9
53 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)400 69.4 0.32 2.4 34.7 6.0 15.88 51.4325 56.4 0.34 2.5 32.8 5.7 15.60 50.5250 43.4 0.39 2.8 35.4 6.1 19.21 62.3175 30.4 0.39 2.9 28.3 4.9 15.41 50.0100 17.4 0.47 3.5 26.6 4.6 17.58 57.0-125 -21.7 0.62 4.6 32.0 5.6 27.94 90.5-200 -34.7 0.65 4.8 31.7 5.5 28.81 93.5-275 -47.7 0.64 4.8 28.5 4.9 25.86 83.9-350 -60.8 0.67 5.0 30.0 5.2 28.49 92.4-425 -73.8 0.70 5.2 36.9 6.4 36.45 118.0-500 -86.8 0.73 5.4 38.6 6.7 39.83 129.032P/Comas Sola-543 -53.3 0.05 0.2 18.6 1.8 1.22 0.9-992 -97.5 0.06 0.3 35.4 3.5 2.96 2.236P/Whipple b -123 -24.7 0.12 1.4 50.8 10.3 8.59 62.4-197 -39.9 0.09 1.0 34.4 6.9 4.19 30.3-273 -55.1 0.08 1.0 34.3 6.9 4.07 29.5-350 -70.7 0.08 1.0 49.7 10.0 5.87 42.5
54 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)48P/Johnson400 53.4 0.06 0.4 22.2 3.0 1.86 3.7325 43.4 0.07 0.4 35.5 4.7 3.39 6.7250 33.3 0.08 0.5 33.0 4.4 3.73 7.4175 23.3 0.09 0.6 30.3 4.0 3.86 7.7-125 -16.7 0.09 0.6 15.3 2.0 1.89 3.7-200 -26.7 0.13 0.8 24.3 3.2 4.41 8.7-275 -36.7 0.15 1.0 13.6 1.8 2.79 5.5-350 -46.7 0.13 0.9 21.5 2.9 4.03 7.9-425 -56.7 0.19 1.2 16.2 2.2 4.27 8.4-500 -66.7 0.16 1.1 15.8 2.1 3.62 7.256P/Slaughter-Burnham317 45.6 0.03 0.3 27.4 3.9 1.35 3.3-282 -40.6 0.04 0.3 27.9 4.0 1.59 3.9-432 -62.2 0.04 0.3 15.1 2.2 0.91 2.2-582 -83.7 0.05 0.4 21.8 3.1 1.61 3.9-732 -105.3 0.07 0.5 33.4 4.8 3.07 7.4-882 -126.8 0.05 0.4 27.7 4.0 2.11 5.1-1032 -148.4 0.03 0.3 15.8 2.3 0.76 1.862P/Tsuchinshan 1
55 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)148 10.1 0.07 0.3 78.0 5.3 7.78 2.265P/Gunn395 82.9 0.09 1.3 35.9 7.5 4.80 45.9320 67.1 0.14 1.9 51.4 10.8 10.00 95.3245 51.5 0.10 1.4 39.7 8.3 5.70 54.367P/Churyumov-Gerasimenko400 117.9 0.05 1.1 25.6 7.5 1.88 54.1325 95.8 0.05 1.2 30.3 8.9 2.28 65.5250 73.7 0.05 1.1 29.7 8.8 2.07 59.2175 51.6 0.07 1.5 27.4 8.1 2.73 78.6-200 -59.0 0.39 8.6 25.2 7.4 13.98 401.1-275 -81.1 0.30 6.6 27.0 8.0 11.58 332.4-350 -103.2 0.27 5.8 30.6 9.0 11.49 329.5-425 -125.3 0.22 4.8 35.7 10.5 11.03 316.8-500 -147.4 0.21 4.5 51.5 15.2 15.01 431.169P/Taylor583 57.9 0.04 0.2 13.8 1.4 0.85 0.7
56 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)357 35.5 0.04 0.2 17.0 1.7 0.97 0.871P/Clark90 19.6 0.07 0.9 20.9 4.5 2.10 20.1-60 -13.0 0.07 1.0 22.7 4.9 2.37 22.7-135 -29.3 0.08 1.1 31.1 6.8 3.47 33.3-285 -61.9 0.12 1.5 27.3 5.9 4.44 42.5-360 -78.2 0.10 1.3 28.5 6.2 4.00 38.2-435 -94.5 0.10 1.3 26.9 5.8 3.86 36.9-510 -110.8 0.11 1.5 29.6 6.4 4.77 45.5-585 -127.1 0.12 1.5 28.5 6.2 4.64 44.5-660 -143.4 0.11 1.4 32.2 7.0 4.94 47.3-735 -159.7 0.13 1.7 26.1 5.7 4.85 46.3-810 -176.0 0.10 1.4 33.3 7.2 4.91 47.278P/Gehrels 2323 31.0 0.18 1.0 19.5 1.9 4.92 3.7285 27.4 0.16 0.9 11.7 1.1 2.63 2.0135 13.0 0.18 0.9 18.7 1.8 4.64 3.588P/Howell
57 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)437 44.8 0.12 0.6 47.2 4.8 7.91 7.0288 29.5 0.11 0.6 27.1 2.8 4.25 3.894P/Russell 4 b -125 -20.0 0.46 3.7 22.1 3.5 14.41 43.3-275 -43.9 0.21 1.7 28.5 4.5 8.60 25.9-500 -79.8 0.09 0.7 18.3 2.9 2.23 6.7104P/Kowal 2 b -223 -39.6 0.06 0.6 31.7 5.6 2.50 12.6-373 -66.3 0.03 0.3 24.0 4.3 1.07 5.4108P/Ciffreo-403 -68.7 0.05 1.33 11.1 1.9 0.8 0.1-283 -48.2 0.05 1.20 11.1 1.9 0.7 0.1-204 -34.8 0.07 1.71 13.2 2.3 1.3 0.1111P/Helin-Roman-Crockett-170 -36.9 0.04 0.5 22.1 4.8 1.18 11.3-320 -69.5 0.05 0.7 15.8 3.4 1.10 10.7
58 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)-470 -102.0 0.05 0.6 21.9 4.8 1.43 13.6120P/Mueller 1443 67.1 0.04 0.3 13.3 2.0 0.76 2.3293 44.4 0.03 0.3 12.0 1.8 0.51 1.6143 21.6 0.02 0.2 12.3 1.9 0.37 1.1-120 -18.2 0.11 0.9 20.6 3.1 3.12 9.5-195 -29.6 0.06 0.6 13.9 2.1 1.25 3.8-270 -40.9 0.04 0.3 21.2 3.2 1.20 3.7-345 -52.3 0.08 0.7 20.2 3.1 2.39 7.3-420 -63.7 0.07 0.7 16.5 2.5 1.74 5.3123P/West-Hartley425 52.8 0.04 0.2 25.4 3.2 1.46 2.0127P/Holt-Olmstead b -127 -20.7 0.10 0.9 40.7 6.6 5.71 19.9-203 -33.0 0.06 0.5 31.6 5.1 2.59 9.1129P/Shoemaker-Levy 3
59 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)430 71.8 0.14 1.3 31.2 5.2 5.96 23.4355 59.3 0.12 1.1 32.3 5.4 5.42 21.2280 46.7 0.18 1.6 21.5 3.6 5.33 21.0205 34.2 0.16 1.5 23.4 3.9 5.39 21.1130 21.7 0.16 1.5 20.0 3.3 4.64 18.2-170 -28.4 0.37 5.77 21.9 3.7 11.52 25.23-245 -40.9 0.38 5.91 19.4 3.2 10.42 22.81-320 -53.4 0.36 5.57 19.4 3.2 9.85 21.58-395 -65.9 0.30 4.66 20.8 3.5 8.82 19.32-470 -78.5 0.25 3.90 19.9 3.3 7.06 15.45-545 -91.0 0.24 3.66 23.8 4.0 7.93 17.36-620 -103.5 0.24 3.77 27.8 4.6 9.55 20.92-695 -116.0 0.25 3.86 27.0 4.5 9.49 20.78-770 -128.5 0.23 3.63 22.9 3.8 7.59 16.63-845 -141.1 0.22 3.39 25.7 4.3 7.92 17.35-920 -153.6 0.19 3.01 27.5 4.6 7.54 16.52-995 -166.1 0.21 3.30 35.7 6.0 10.73 23.51-1070 -178.6 0.21 3.21 33.5 5.6 9.81 21.48131P/Mueller 2-318 -43.2 0.04 0.3 6.5 0.9 0.40 0.8P/2003 S2
60 –Table 2—Continued φ φ ∆ I ν τ W W ∆ F D dM /dφ ( ′′ ) (10 km) (MJy/sr) (10 − ) ( ′′ ) (10 km) (mJy/ ′ ) (10 g/deg)-183 -40.1 0.09 1.2 16.7 3.7 2.06 21.3-258 -56.6 0.04 0.5 15.5 3.4 0.82 8.4-333 -73.0 0.04 0.5 9.1 2.0 0.46 4.7-408 -89.5 0.03 0.4 17.1 3.7 0.75 7.8 a φ is the distance behind the nucleus at which the trail profile was analyzed. F D is the brightness integrated perpendicular to the trail. dM /dφ is the mass per unitprojected angle on the sky. b Profiles taken through map rotated at angle of β = 10 − syndyne rather than β = 0, to match observed orientation of trail.
61 –Table 3. Mass-loss rates from visible observationsComet Q max a < Q > /Q max dM ice /dt dM/dt (K&K)(10 mol s − ) (kg s − ) (kg s − )2P/Encke 4.6 0.014 19 719P/Tempel 1 1.7 0.20 96 2.710P/Tempel 2 0.2 0.14 9.1 6.249P/Arend-Rigaux 0.18 0.074 3.8 0.862P/Tsuchinshan 1 0.26 0.12 9.4 0.467P/Chury-Ger 0.41 0.057 6.7 1.165P/Gunn 0.3 0.25 22 5.669P/Taylor 0.14 0.19 7.7 1.878P/Gehrels 2 0.025 0.17 1.2 1.688P/Howell 0.24 0.14 9.5 1.894P/Russell 4 0.11 0.23 7.5 3.2 a from A’Hearn et al. (1995), Table III last column; except for 65P/Gunn for which we scaledQ(OH) from its observed distance to perihelion dθ/dφ is the change in mean anomaly per unitdegree on the sky. 62 – 63 – 64 –Fig. 1.— Illustration of cometary debris dynamics and viewing geometry, drawn specificallyfor the conditions of the observation of 48P/Johnson. (a) In a view looking down ontothe ecliptic plane, the orbits of the observatory and comet are shown together with thevectors from comet-to-Sun and comet-to-observatory. The trajectory of particles with β = 1(radiation pressure equal to gravitational force) and β = 0 . (b) This is a blow-up of the region in panel (a) shown as a light-greysquare. The trajectories of particles with a range of β (ratio of radiation pressure to gravity)are shown as thin arcs, and the orbit of the comet as a thick line. Dashed vectors on eachsyndyne show the net direction of solar forces, which is repulsive for β > β → (c) This panel shows a view projected onto the plane of the sky,perpendicular to the observer-comet vector. The projected trajectories from panel (b) areshown; these are the zero-velocity syndynes , which serve as a guide to cometary dust anddebris. The smallest particles (largest β ) feel the most radiation pressure, and they lie closerto the antisolar direction or β = 1 syndyne. Progressively larger particles lie closer to thecomet’s projected orbit, and particles with β < − are effectively along the orbit and formthe debris trails which are the focus of the present survey. 65 – 66 –Fig. 2.— Mid-infrared images and zero-velocity syndynes for comets 2P/Encke, 9P/Tempel1, 10P/Tempel 2, 32P/Comas Sola, and 36P/Whipple. For each comet there are two panels.The upper, labeled panel shows the 24 µ m image in greyscale together with the imageorientation (celestial N and E), a scale bar showing 10 km perpendicular to the line ofsight, the projected orbit (yellow line), and color-coded syndynes that show the location ofparticles of different size emitted over the 1 yr period before observation (red, green, blue,cyan, and magenta correspond to β = 1, 10 − , 10 − − − , where β is the ratio ofradiation to gravitational force and is approximately the inverse of the particle size in µ m).For each comet, the lower panel shows the mid-infrared image alone, in a color table thatranges from black (faintest) through shades of orange to white (brightest). 67 – 68 –Fig. 3.— Mid-infrared images and zero-velocity syndynes for comets 42P/Neujmin 3,48P/Johnson, 53P/van Biesbroeck, and 49P/Arend-Rigaux. Labels and overlays are thesame as in Figure 2. The color images of 42P and 49P have been convolved with a 3-pixel(2.5 ′′ /pixel) gaussian. 69 – 70 –Fig. 4.— Mid-infrared images and zero-velocity syndynes for comets 56P/Slaughter-Burnham, 62P/Tsuchinshan 1, 65P/Gunn, 67P/Churyumov-Gerasimenko, and 78P/Gehrels2. Labels and overlays are the same as in Figure 2. For 62P, the color table runs from 37.7–41MJy sr − (linear) and the contours from 39.5–70 MJy sr − (square-root spaced). The Sunwas almost directly E of 62P at the time of observation. For 78P, the color table runs from41.1–43.6 MJy sr − (linear) and the contours from 45–100 MJy sr − (square-root spaced).The two bright splotches 1/3 of the image above and below 78P are latent images of thenucleus (which saturated the detector) and inner coma. 71 – 72 –Fig. 5.— Mid-infrared images and zero-velocity syndynes for comets 69P/Taylor, 71P/Clark,88P/Howell, and 94P/Russell 4. Labels and overlays are the same as in Figure 2. The colorimage of 69P was convolved with a 2-pixel radius tophat filter. 73 – 74 –Fig. 6.— Mid-infrared images and zero-velocity syndynes for comets 103P/Hartley2, 104P/Kowal 2, 111P/Helin-Roman-Crockett, 116P/Wild 4, 120P/Mueller 1, and121P/Shoemaker-Holt 2. Labels and overlays are the same as in Figure 2. 75 – 76 –Fig. 7.— Mid-infrared images and zero-velocity syndynes for comets 123P/West-Hartley,127P-Holt-Olmstead, 129P/Shoemaker-Levy 3, 131P/Mueller 2, and P/2003 S2. Labels andoverlays are the same as in Figure 2. For 131P, the images were smoothed with a 2 pixelradius tophat. 77 – 78 –Fig. 8.— Mid-infrared images and zero-velocity syndynes for comets 4P/Faye. 108P/Ciffreo,and 71P/Clark from 2006 observations. Labels and overlays are the same as in Figure 2. 79 –Fig. 9.— The separation of meteoroids from the nucleus as a function of particle age, for129P/Shoemaker-Levy 3 at the epoch and sky-plane of the Spitzer observation in 2005.Dashed lines indicate the ages of particles ejected at each of the previous two perihelionpassages. The inset shows the separation versus time for particles younger than 3 yr, atwhich time zero-ejection-velocity particles with β = 10 − would reach the edge of the Spitzer image in Figure 7. 80 –Fig. 10.— Trail optical depth versus the time of observation with respect to the periheliondate, for 30 comets. 81 –Fig. 11.— Scatter diagram of the mass loss rate required to produce the observed debristrails versus perihelion distance. 82 –Fig. 12.— Correlation of the debris trail width versus the time of observation relative toperihelion (days). 83 –Fig. 13.— Contribution of different sizes to the surface area of cometary particles, for athree-population size distribution similar to that found from the in situ observations bydust detectors on the
Stardust spacecraft in the coma of 81P/Wild 2. Particle sizes on thehorizontal axis are parameterized by β/Q pr ρ = 0 . µ m /s , where s is the particle radius, Q pr
84 –is the radiation pressure efficiency in the solar radiation field ( ∼ β < . ρ is the particle density in g cm − . The solid line shows the fractional contribution togeometric area; the dotted line shows the contribution to visible light scattering; the dashedline shows the contribution to 24 µ m emission. The dash-dot line shows the Planck-weightedcontribution to 10 µ m emission (such as the silicate feature), if the smaller grains ( β > . vs
280 K). All curves overlap for small β (i.e. on the left side of the plot); then, one by one, each effective cross section diverges fromthe geometric cross-section, with 24 µ m emission diverging at lowest β and visible scatteringdiverging at highest ββ