Collisional process on Comet 9/P Tempel 1: Mass loss of its dust and ice by impacts of asteroidal objects and its collisional history
© The Society of Geomagnetism and Earth, Planetary and Space Sciences, The Seismological Society of Japan 2010
Received: 4 September 2008
Accepted: 11 November 2008
Published: 7 February 2015
We have studied the collisional process on the nucleus of Comet 9/P Tempel 1 (T1) and estimated the mass loss of surface materials due to the impacts of asteroidal objects. The mass loss rate is around ∼2×105 kg yr-1, which is smaller than that of water sublimation of ∼6×109 kg yr-1. We then estimated the number density of craters formed by asteroid impacts to infer the collisional history of T1. We found that the time necessary to accumulate the crater population on T1 is as long as ∼ a few 104 years, suggesting that T1 crossed the asteroid belt region more than ∼ a few 104 years ago, though this estimated time may be reduced to several thousands of years by taking into account the influence of the sublimation process on the crater size. Alternatively, the total period of the recent orbit, in which the perihelion distance is small enough to cause significant sublimation by erasing a large number of small craters, may be less than ∼2×103 years.
Short-period comets were originally trans-Neptunian objects formed from dust and ice in the outer cold region of the primordial solar nebula. When such a comet leaves the trans-Neptunian region and approaches the Sun, volatile components of its nucleus begin to sublime and form a dust mantle on the surface. Vapor pressure of the sublimating components preferentially carries the dust having a high surface-to-mass ratio off the surface. The sublimation process also leads to chemical differentiation of a nucleus owing to preferential sublimation losses of highly volatile materials in the deeper parts of the nucleus. In addition, trapped primordial volatile gasses are released when pristine amorphous water ices just below the dust mantle crystallize to form a crystalline ice crust. Heating caused by radioactive decay might have altered even the central region of the nucleus. Therefore, primordial dust and ice would remain only local regions well below the surface and well above the center of the nucleus (e.g., Jewitt, 1992; Meech, 2000; Prialnik et al., 2004, 2008). This scenario, which is hereafter called the standard model, has turned out to describe well the nucleus of Comet 9P/Tempel 1 (T1), the target of NASA’s Deep Impact (DI) mission: (1) a low thermal inertia of its surface estimated from thermal maps of the nucleus indicates the presence of a dust mantle (A’Hearn et al., 2005); (2) the existence of large grains in a dust trail along the trajectory of the comet would result from the preferential elimination of small-sized dust during the formation of a dust mantle (Sykes and Walker, 1992; Reach et al., 2007); (3) the optical and infrared properties of dust excavated by the DI event are explained well by the existence of a dust mantle composed of compact aggregates, below which fluffy aggregates are also embedded with icy volatiles (Yamamoto et al., 2008); (4) near-infrared spectroscopic observations of volatiles excavated by the DI event revealed thermal processing of icy layers below a dust mantle (Mumma et al., 2005); (5) the sublimation rate of 6 x 1027 water molecules s-1 (∼180 kg s-1) from the T1 nucleus before the DI event implies that the top surface of several meters could have been lost simply by the sublimation process (e.g., Schleicher et al., 2006). In addition, the standard model has been supported by numerical studies on thermal evolution of the T1 nucleus: the formation of a dust mantle with chemical differentiations of the T1 nucleus (De Sanctis et al., 2007); a crystalline ice crust with a thickness of 40-240 m below a dust mantle (Bar-Nun et al., 1989).
In the above scenario, sublimation is an important process by which a comet nucleus can evolve. In addition to the sublimation process, however, impacts by asteroidal bodies may play a vital role in the evolution of the nucleus (e.g., Fern’andez, 1981). This is the most likely case for T1 because the present orbit of T1 crosses the asteroid belt region. Indeed, many crater-like features have been found on the T1 surface (Thomas et al., 2007). Thus, a study on the degree of the impact process is the key to understanding the evolution of the T1 nucleus. Furthermore, an application of crater chronology to the T1 nucleus may allow us to infer the collisional history on T1 and consequently provide us with clues about the orbital evolution of T1 in the past.
There are several studies on the impacts of asteroids onto the T1 nucleus, the results of which strongly depend on the model of the asteroidal population (e.g., Hawkes and Eaton, 2004; Gronkowski, 2007; Yamamoto et al., 2008). For example, Hawkes and Eaton (2004) estimated the mass flux of asteroids into the T1 nucleus to range from ∼102 to 107 kg yr-1, depending on the model they used. While the previous models are based on the data of asteroids with sizes larger than ∼ 100 m, small asteroids with sizes of less than 100 m play an important role in the collisional history of the T1 nucleus. The asteroidal model by O’Brien and Greenberg (2005) or O’Brien et al. (2006) (hereafter OGR model) is a self-consistent numerical model for the main-belt and near-Earth Asteroid (NEA) populations of small asteroids. These researchers developed the model based on a wide range of observational constraints, including small crater population on NEAs (see OGR model). Michel et al. (2009) reported that the asteroid population model by Bottke et al. (2005) (hereafter BTK model) may actually be more realistic than the OGR model to explain the crater population on NEA (25143) Itokawa. We are, therefore, convinced that either the OGR model or the BTK model is the best available model for the population of small asteroids colliding with comet nuclei. On the basis of these models, we have studied collisional and sublimation processes on the T1 nucleus to assess the mass loss rate of surface materials by impacts of asteroids and to infer the collisional history of the T1 nucleus.
2. Mass Loss of Surface Materials from T1 due to Impacts of Asteroidal Objects
3. Collisional History of T1 Nucleus
3.1 Number density of craters formed by impacts of asteroids
Numerical calculations suggest that before T1 had close approaches to Jupiter ∼300–400 years ago, the perihelion of T1 may have been further than the asteroid belt region (e.g., Yeoman et al., 2005). However, this does not necessarily mean that T1 has never crossed the asteroid belt region prior to ∼400 years ago. Levison and Duncan (1997) reported that typical Jupiter-Family Comets (JFCs) change their perihelion and aphelion distances frequently after becoming JFCs. Thus, it is likely that T1 may have crossed the asteroid belt region many times in the past, forming craters corresponding to the R-plot for at least 104 years. Note that the actual duration time may be longer (or shorter) than 104 years, because we used the values of Pi and vi for the present orbit of T1 (see Table 1), which might have been smaller (or larger) than the present values.
3.2 Effects of sublimation process on crater population
As we see in Section 2, the mass loss by the sublimation process is more significant than that by impacts of asteroids. In this case, we may consider the possibility that the sublimation process erases or changes the crater population. Our question is: how would the sublimation process change the discussion in Section 3.1? We thus investigate the effect of sublimation on the crater population of the T1 surface hereafter.
We see that the observational data with Dcr ∼ 50 m is less than that by the sublimation erase model in Fig. 1. This may be explained as follows. First, water sublimation under the dust mantle may also contribute to erasing such small craters. The dust mantle layer would subside when the water ices below the dust mantle are lost by the sublimation process. During this subsidence, some of the small craters might have collapsed. Second, involved with the escape of water vapor through the dust mantle, the shape of small craters may be deformed too much to be identified as crater features. Third, large-sized dust fallen back to the surface may cover small craters. Fourth, the redistribution of re-golith by seismic-shaking induced by large impacts proposed by Richardson et al. (2005) may erase small craters. The decrease in the R value for small craters is a typical feature for the small crater population with D < ∼100 m of near-Earth asteroids, such as Eros or Itokawa, which can be explained by a smoothing effect from the redistribution of regolith by the seismic-shaking (e.g., Richardson et al., 2005; Michel et al., 2009). However, the report by Thomas et al. (2007) that T1 has higher surface slopes than other small bodies suggests a lack of the smoothing effect from the redistribution of regolith. In any case, although it is difficult to uniquely attribute the erasure of craters to one of the above-mentioned processes, some erase processes may be needed to explain the small crater population on the T1 nucleus.
3.3 Possible scenario for the evolution of T1
From the above discussion, we expect the following scenario for T1. T1 might have become JFC ∼ 104–105 years ago. T1 subsequently changed the perihelion distance as well as the aphelion distance many times, which was predicted by numerical calculations for JFCs (Levison and Duncan, 1994, 1997). During this period, T1 crossed the asteroid-belt frequently to accumulate the observed crater population on the surface. Recent close approaches to Jupiter about ∼400 years ago changed the T1 perihelion to be ∼1.5 AU (Yeomans et al., 2005). During this period, the smaller crater population decreased owing to significant sublimation. We cannot rule out the possibility that T1 suffered from significant sublimation before 400 years ago, but the total duration time of such significant sublimation is most likely less than ∼2×103 years.
This scenario is based on the assumption that crater size does not change during the sublimation process. On the other hand, crater sizes may increase with time, because the sublimation process may erode the inside wall of craters, as suggested by Britt et al. (2004). From Eq. (19) with the water sublimation of Ṁs = 180 kg s-1, the retreat rate by sublimation may be ∼0.11 m yr-1. Thus, we estimate that the increase in Dcr by sublimation is ∼88 m for 400 years. In this case, the original crater sizes of Dcr = 200–300 m (with T ∼ 104 yr) might have been Dcr ∼ 100–200 m, which corresponds to T ∼ 2000–5000 years estimated from Eq. (15), i.e., T ∝ D146cr. Thus, the age that T1 crossed the asteroid belt region may be as short as several thousands of years. Nevertheless, there is currently no clear correlation between the active regions and the impact craters on T1 (see Thomas et al., 2007). If the sublimation process eroded the inside wall of craters, we would observe many active regions inside the craters. This is, however, not the case. We expect that craters formed by asteroid impacts can be eroded by the sublimation process and become bigger, but the sublimation process would be quenched immediately owing to the formation of a dust mantle on the crater wall. The increase in the crater size by sublimation may not change significantly the above scenario for T1.
We also assume that there are no ancient craters formed by impacts with the other trans-Neptunian objects before T1 entered the inner Solar System. The reasoning for this is as follows. If the observed craters were ancient craters formed in the trans-Neptunian region, a large number of impacts with trans-Neptunian objects may be expected (e.g., Stern, 1996), and the R value for T1 would be around the empirical saturation line with R ∼ 0.2. 81P/Wild 2 is an example showing that the most of crater population follow the empirical saturation line (Basilevsky and Keller, 2006). It has been suggested that the surface of 81P/Wild 2 nuclei remains very old ancient terrain, presumably dating back to the comet’s residence in the trans-Neptunian region (e.g., Brownlee et al., 2004). Furthermore, while 81P/Wild 2 has many large craters with Dcr > 400 m, there are no large craters with Dcr > 400 m, suggesting that the T1 surface is not old enough to accumulate such large craters. We conclude that resurface events over the T1 surface in the past might have erased most of ancient craters on T1.
We have studied the mass-loss rate of surface materials by impacts of asteroidal objects. The mass-loss rate by impacts of asteroidal objects is around ∼2×105 kg yr-1, which is smaller than that of the water sublimation of ∼6×109 kg yr-1. This result suggests that the mass loss of a comet nucleus is mainly due to sublimation processes, and such a significant sublimation process has lost most, if not all, of the primordial materials on the surface layers of T1. However, this does not necessarily mean that the impact is not important for the evolution of the T1 nucleus because the collision process may play a role in triggering the formation of active regions on the surface. We have then estimated the number density of craters by asteroid impacts and compared this with the observational data. We found that the time necessary to accumulate the crater population on T1 is longer than 300 years, probably ∼ a few 104 years, suggesting that T1 crossed the asteroid belt region during at least ∼104 years in the past. If the crater size increases with time owing to sublimation, this age may be as short as several thousands of years. The present sublimation rate for T1 is very significant because of the recent orbit close to the Sun. A large number of small craters would be erased by such significant sublimation processes. Comparing the number density of craters with the sublimation erase model, we estimate that the timing of T1’s entry into the recent orbit may be later than ∼2×103 years ago.
The authors thank A. M. Nakamurafor helpful comments, and D. Durda and D. O’Brien for giving valuable comments and suggestions as reviewers. This study was supported in part by T. Yoda, and Grant-in-Aid for Young Scientists (B) (20740249; 20740247).
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