The effects of mechanical interaction between the interstellar medium and comets

ICARUS 68, 276--283 (1986)

The Effects of Mechanical Interaction between the Interstellar Medium and Comets S. ALAN STERN Laboratory for Atmospheric and Space Physics, University of Colorado, Campus Box 392, Boulder, Colorado 80309-0392 Received August 23, 1985; revised July 21, 1986 Oort Cloud comets mechanically interact with the interstellar medium (ISM). In this report we discuss and evaluate the importance of accretion of interstellar material onto comets, the erosion of cometary surfaces by impacting interstellar grains, and the consequences of these interactions. B a s e d upon scaling analyses, we find that collisions with interstellar grains can provide a significant evolutionary mechanism for the modification of cometary surfaces and, in doing so, can also contribute an appreciable number of low-mass particulates to the ISM. © 1986AcademicPress, Inc.

other volatiles, including CO). The spectra of cometary comae (Hanner, 1984) indicate Studies of observed cometary orbits indi- that the mass ratio of dust to ice, though cate that our Solar System is surrounded by variable, is typically near 1:10. At Oort a cloud of several times 1012 comets in Cloud distances, the radiative equilibrium weakly bound solar orbits, with character- temperature of a comet with no internal istic semimajor axes of 5 x 104 AU (Weiss- heat source will be low enough (-10°K) man, 1982). Sekanina (1976) and Weissman that the surface ices will remain in the solid (1980) have made detailed studies of the phase with no significant evaporative losses various diffusion and loss mechanisms op- over time (Lebofsky, 1975). To date, the only demonstrated evoluerating in the Oort Cloud, and concluded that approximately one-half of the original tionary mechanisms important to comets in population should have been removed from the Oort Cloud are their interaction with the reservoir over time; Weissman (1982) highly energetic radiation, and the surface estimates the present-day population of this effects caused by UV ionization. In this pacloud of comets to be between 1.2 x 1012 per, we consider an additional, previously and 2.5 x 1012 comets. Of late, Weissman unrecognized, evolutionary agent: the me(1985a, 1985b), Fernandez (1980), and chanical interaction of comets with the gasClube and Napier (1982) have reported eous and solid components of the interstelstrong theoretic evidence for an additional, lar medium (ISM). The approach taken inner cloud of -1014 comets with character- here is meant to scale the effects of such a mechanism, and is not meant to satisfy the istic semimajor axes of 104 AU. Comets are agglomerations of ice, dust, future need for detailed time-dependent and rocky material with characteristic modeling of this process. masses of 1016 to 1019 g, characteristic radii of a few kilometers, and bulk densities near 1 g/cm 3 (Wyckoff, 1982). Observations sup- II. MECHANICAL INTERACTION: ACCRETION AND EROSION port Whipple's well-known dirty-iceball The motion of the Sun through the ISM model in which the cometary nucleus is will cause interstellar gas and dust to imcomposed of an admixture of H20 ice and silicate grains (probably in a clathrate with pact cometary nuclei at high velocities. I. INTRODUCTION

276 0019-1035/86 $3.00 Copyright© 1986by AcademicPress. Inc. All fightsof reproductionin any formreserved.

INTERACTION OF COMETS WITH ISM

277

Here we calculate the effect of such colli- sions with solid grains promote erosion. We sions on dormant comets far from the Sun. calculate this effect according to The net effect of gas and grain impacts on AMgr = ~gr(a + fl)~rR2Vtss (2) cold cometary nuclei in the Oort Cloud will result in a balance between accretional where ffgr is the average mass density of mass deposition and erosional mass reinterstellar grains, a represents the ratio of moval. The impact of atoms and molecules impact-evaporated cometary mass to incionto the nucleus will largely promote mass dent-grain mass, fl represents the ratio of accretion at a rate controlled by the sticking ejected cometary-material to incident-grain factor f w h i c h describes the ratio of adhermass, and V, R, and ts~ retain their identiing to incident molecules. This mechanism ties as above. (Spitzer, 1978) is responsible for the growth To estimate the relative importance of of interstellar grains. Deposition of material erosional to accretional processes, one may onto comets by such a process when previtake the ratio of AMgr to AMgas, ously evaluated (O'Dell, 1971) was shown to not substantially increase the mass or radius of comets over time scales comparable to the age of the Solar System. As yet unstudied, however, is the effect of impacts The quantity M, which is independent of onto dormant cometary surfaces by inci- the comet's size and its velocity through dent interstellar grains; such impacts erode the ISM, represents the deposition to eromaterial from cometary surfaces in a man- sion ratio, per unit surface area. Note that ner analogous to micrometeoroid impacts M is directly related to the dustiness of the on icy satellites and rings (Haft et al., 1983; ISM, and is in course of fact a time varying Cintala, 1981; Griin et al., 1980). parameter. We next obtain appropriate valThe relative importance of accretion and ues for the variables in this equation, and deposition may be evaluated by calculating evaluate AM~s, AMgr, and M. the rate of increase of cometary mass due Considering the ratio ~/~-~ first, we find to these processes. We approximate the in- that conservative estimates place the mass tegrated change in mass due to such pro- fraction of the ISM in the form of grains to cesses by employing average values of the be -0.01, on average, within 1 kpc of the time-varying parameters. For atomic and Sun (Spitzer, 1978; Seab and Shull, 1985). molecular gas collisions with a cold come- We adopt this value. tary surface, the accretion-driven change in Now consider j~ which we estimate by cometary mass may therefore be calculated calculating the number abundance weighted by average sticking ratio for all species in the interstellar medium. Species other than hyAMga~ = fffzrR2Vtss (1) drogen represent about 10% of the ISM by number and have characteristic sticking rawhere ff is the average mass density of in- tios of - 1 (Watson and Salpeter, 1972; terstellar gas, Sis the average sticking ratio Burke and Hollenbach, 1983). Hydrogen, (i.e., the fraction of particles accreted to however, accounts for 90% of the ISM by particles incident) over all species in the number. Spitzer (1978) and Watson (1974) ISM, V is the average velocity of the comet estimate that approximately 30% of the inthrough the medium, ~rR2 represents the cident H atoms will initially adhere to the equivalent-sphere disk-projected collecting surface, however, approximately 90% of area of an "average" comet, and t~ is the those H atoms which stick will then locate exposure time. other H atoms and form H2. The subseIn contrast to molecular sticking, colli- quent rapid evaporation of H2 will thus

278

S. ALAN STERN

lower the effective hydrogen sticking ratio to -0.03 (Salpeter and Watson, 1973). Forming the weighted mean sticking ratio for all species in the ISM, we adopt f = 0.037. Concerning ix, Le Sergeant D'Hendecourt et al. (1981), Haft et al. (1983), and Gault (1973) have each found 2 < ct < 5. We conservatively adopt c~ = 2 and note that if the incident grain explodes upon impact (Hagen et al., 1979), a could attain higher values. The amorphous nature of cold cometary surface ices promotes the production of ejecta (Smoluchowski, 1981). Griin et al. (1980) follow Fujiwara et al. (1977) and Gault (1973) to find that/3 may be estimated by fl = 5.5 × 10-1°V 2

(4)

for basalt targets, where V is in cgs units. We take V = 2 × 106 cm/sec as controlled by the Sun's velocity through the ISM (Oort orbit velocities do not contribute because they are much smaller). Therefore, we obtain /3 ~ 2200. Laboratory data obtained on hard ice targets (Lange and Ahrens, 1982; M. J. Cintala, personal communication) and snow (Croft, 1982) demonstrate that for these materials, erosion will be enhanced by a factor of - 3 0 over the value derived above for basalts. Such enhanced erosion for snow and ice targets was adopted by Haft et al. (1983), who calculated the effects of erosion on Saturn's rings. To be completely conservative, however, we retain/3 ~ 2200. Inserting for the variables in (3), we find M -- 590. Therefore, erosion strongly dominates accretion. Indeed M -- 590 means essentially no ISM gas accretes before being removed by grain impacts. The finding that erosion greatly dominates accretion is significant since it had previously been reported that the only important role interstellar material had to play in the evolution of cometary surfaces is the accretion of an extremely thin veneer of

TABLE I THE EFFECTS

OF

ISM E R O S I O N

AND ACCRETION

ON

COMETARY NUCLEI Process

AMass/comet

Characteristic depth a

Accretion Erosion b

8.0 × 108g(7.1 × 10-9Mc) 6.2 × l011 g (5.5 × l0 6Mc)

0.0007-0.0028 cm 0.5-2 cm

OH-AM

AM

r~rRXop"

b fl = 2200.

frozen gases (O'Dell, 1971). Given a high rate of erosion, prospects for accreted ISM shielding of the cometary mantle (or for cometary surfaces acting as witness plates exposed to the ISM) seem remote (O'Dell, 1971; Greenberg, 1983). Taking ~-g~to be 0.01, ff = -3.36 x 10-27 g/cm 3 (Thomas, 1978; Spitzer, 1978; Seab and Shull, 1985), tss to be the age of the Solar System, and R = 3 × l05 cm (a conservative estimate in light of P/Halley's recently measured size and albedo), we find AMg~ = - 6 . 2 x 1011 g/comet. While this amount of eroded material is small in comparison to the cometary mass itself, it represents the removal of a p = 1 layer of depth 0.5-8 cm, when the range of porosities characteristic of ice and snow are accounted for (Swinzow, 1977; Smoluchowski and McWilliam, 1984; cf. Table I). Were the ice and snow fl's of Lange and Ahrens (1982) or Croft (1982) are taken into account, our erosion mass and depth estimates would be enhanced by a factor of -30. Erosion to such depths is important in two respects. First, it implies a lower cutoff in the size distribution o f primordial objects now residing in the Oort Cloud. Second, it admits an important mechanism for the evolution o f cometary surfaces in the Oort Cloud. We next consider this latter effect. What effect does erosion have on cometary surface evolution? Most importantly, the continual gardening and removal of newly exposed cometary surface material will obliterate the previously reported ef-

INTERACTION OF COMETS WITH ISM fects of UV radiation and ion bombardment (Watson, 1974; Whipple, 1977), since these effects penetrate to depths less than or comparable to the calculated erosive depth. Galactic cosmic ray damage, we note, can, however, extend to several meters below the surface (Shurman, 1972; Draganic and Draganic, 1984), and will not be much affected by the erosion of a centimeter-deep layer. Erosion-driven gardening and fragmentation will also produce a source of loose material, which will be prone to both electromagnetic levitation (Mendis and Flammer, 1984) and gas-dynamical drag upon approach to the Sun. Since our conservative estimate of AMgr implies a surface exposure time before erosion of ~4 × 104 year, we point out that erosion-induced surface freshness may have a direct bearing on the observed anomalous volatility of new comets (Greenberg, 1982). We further find that if the cometary surface contains both exposed rock and ice, then differential weathering effects (caused by enhanced 13 values for ice) will greatly modify the surface morphology, promoting the formation of spires, pedestal rocks, rubble accumulations, and other complex constructs. The material ejected from comets in ISM grain impacts will exhibit characteristic radii comparable to ISM grains themselves (GrOn et al., 1985; Zook, personal communication). Such ejecta particles are expected both from grain-onto-ice impact mechanics (Greenberg, 1978) and from grain-on-snow impacts (Fujiwara et al., 1977; Hrrz, personal communication). Like ISM grains themselves, the average ejected fragment will exhibit characteristic radii of - 0 . I /xm with a size distribution of radii proportional to r -3"5 (Mathis, et al., 1977). We expect these small ejecta fragments to be ice-hydrocarbon admixtures (with trace silicates) representing the photolyzed composition of cometary surfaces What is the dynamical fate of these ejected particulates? Matsuura (1976) studied the impact of meteors into ice-laden comets and calculated the characteristic

279

ejection velocity for fragments to be

voj = x / V v . / c

(5)

where C is a scaling constant 2 < C < 5, and Vcr is given by

Vor = lx/ Cp

(6)

where lp is the plastic limit of the target ice. With lp set to 107 dyn/cm z (Matsuura, 1976), we calculate Vcr = 3.16 × lO3 cm/sec, and 3.6 x 104 cm/sec < V~j < 5.6 x 104 cm/sec. This is in accordance with a conservation of impact-energy derived upper limit of Vej ~4.5 x 104 cm/sec for fl = 2200. Because the escape velocity for typical comets is on the order of 2.3 x 102 cm/sec, we conclude that the eroded material will escape the comet altogether. Because the characteristic velocity necessary for escape from the Solar System at outer Oort Cloud distances is near 1.34 x 104 c m / s e c , eroded cometary material from the outer Oort Cloud should also escape the Solar System and proceed to repopulate the ISM, even if ejected in a retrograde fashion. For erosion from the inner Oort Cloud, the characteristic solar escape requirement is - 4 . 2 x 104 cm/sec. Therefore, some of the eroded particulates derived from inner Oort Cloud comets will initially remain in bound solar orbits. Radiation pressure acceleration on these small particulates will, however, drive them from the Solar System on time scales of 105-106 years, depending upon their individual sizes, albedos, and orbit eccentricities. We therefore conclude that the eroded cometary particulates will escape into the interstellar medium on astronomically short time scales, independent of their location in the inner or outer Oort Cloud. III. THE CONTRIBUTIONOF ERODED COMETARY MATERIALTO THE ISM Because eroded cometary material will escape the Solar System, it is natural to ask whether this material makes a significant contribution to the grain mass or grain number density of the ISM. Of course, any such

280

S. ALAN STERN

estimate depends upon the assumption that all or most stars possess Oort clouds with similar integrated surface areas to that of our Sun's Oort Cloud. On the basis of cometary observations and Oort Cloud theory, the current population of kilometer-class comets orbiting the Sun is estimated to be N ~ 5 x 1013 (Weissman, 1985c; Clube and Napier, 1982); we assume smaller and larger bodies reside in the Oort Cloud as well. T o w a r d this end, we first calculate the total effective cross-sectional area available for collisions in the Oort Cloud. To make such a calculation, one integrates the ~-R 2 cross-sectional area of bodies of all sizes ranging from Rmin to Rmax, where Rmin is constrained by small particle radiationpressure driven escape, and Rmax is constrained by an escape velocity too large to permit ejecta escape (i.e., V.~ec ~> 4.5 × 104 m/sec). Accordingly, Rmin ~ 10 c m , and Rmax ~ 600 km. We conservatively assume that the number of comets o f radius R increases at the rate

dN = N(R*) -2 dR*

=

NrrR2o~Rm.~ dN JRmin (R*)2 N

as

(7)

where R* = R/Ro. This estimate is conservative because the exponent in (7) was chosen to cause the number-area product for all objects in the Oort Cloud to be flat, so that neither populations of small or large objects would bias our result. Integrating to obtain the number-area product for all objects purported to lie in the Oort Cloud, we now obtain the effective crosssectional area for the Oort Cloud Aeff

Oort Cloud of - 1.7 x 1028g over the age of the Solar System. At a yearly rate, this mass erosion from the Oort Cloud is equivalent to the gas and dust production of > 2 x 104 perihelion passages of a typical active comet! N o w the ejected cometary particulates will have finite lifetimes on the order of 5 x 108-1 x 109 years, owing to the various grain destruction mechanisms at work in interstellar space (Spitzer, 1978; Seab and Shull, 1985). Because cometary ejecta can accumulate in the ISM for only this fraction of the full span of time, only about 10% of the total comet-fragment mass should be in extant at any one time. We thereby estimate the ejecta mass resident in the ISM from the Oort Cloud at any one time to be ~ 2 × 1027 g. Taking the average distance between stars to be 1 pc, and employing ~gr to calculate the mass of grain material within such a sphere, we calculate the ratio of eroded c o m e t a r y mass to nascent ISM grain mass

(8)

where NTrR 2 represents the area contribution " k n o w n " comets in the Oort Cloud, and the integral represents a scaling factor for the full spectrum o f object sizes in the cloud. Performing this calculation, we find that Aeff = - 2 . 8 5 × 10 27 cm 2. Adopting here a conservative ice-erosion factor of three times /3 basalt (Lange and Ahrens, 1982) gives a total eroded mass from the

A~a(ot + fl)ffgrVr '19 =

~oa~-gr

(9)

where we set r to a 5 x 108 year ejectaparticle lifetime (in analogy to grain lifetimes), and D = 1 pc. It is important to recognize that ~ is independent of figs. Evaluating Eq. (9), we find "0 - 0.04. Given the conservative nature of our input parameters, we consider this value to be a notable and significant contribution to the total mass o f grains in the ISM. As cited above, experimental evidence concerning the erosion process leads us to believe the size, porosity, and p characteristics of the ejecta should be similar to those of the incident grains; therefore, a conservative estimate of the contribution of comet fragments to the ISM by n u m b e r should also be a few percent. Finally, we point out that while our model finds ~ = 4%, the true cometary contribution to the ISM may be somewhat larger. One reason for this is that comets in

INTERACTION OF COMETS WITH ISM

281

now-extinct (and hence unobserved) stellar minosity stellar systems. Grains created by systems (which increase the space density process (3) should exhibit low velocities of stellar systems of Oort Clouds over the relative to their parent star, as described in adopted value) will increase the total effec- Eqs. (5) and (6), and should promote entive area for erosion. Further still, if the hanced reddening and an IR excess. Candimass of the average Oort Cloud is propor- dates for such a search abound (Aumann, tional to the ratio of an average stellar sys- 1984), and should include Alpha PsA, Altem's mass to Msun, */ will be proportion- pha Lyra, and Beta Pic (Harper et al., 1984; ately increased. Finally, we point out that Weissman, 1984; Smith and Terrile, 1984). Still another possibility for the detection the low albedo measured for Halley, if typical, would indicate that our total effective of the comet-ISM erosion mechanism cencross-section estimate may be low by 60% ters on observations identifying the sigor more. Taken together, these effects nature of HzO mantled grains in dense inwould enhance the comet-ejecta contribu- terstellar clouds, such as p Oph (Snow, tion by a factor of - 5 , indicating that come- personal communication). The clouds contary ejecta could account for as much as taining these H20 ice mantled grains are ob20% of the ISM grain population and mass. served to display characteristic velocities of 10-20 km/sec relative to the stars imbedIV. DETECTABILITY ded within them. This poses the intriguing It may be asked whether the erosion pro- possibility that the observed H20 mantled cess described in this paper can be ob- grains are in fact eroded cometary material served, since such an observation would from imbedded extrasolar Oort Clouds. In clearly have direct relevance to both Solar this regard we note that high cometarySystem and Oort Cloud formation pro- grain production rates would be expected at cesses. In this regard, it appears that the such sites due to the increased matter denradiation signature from this process within sity within the dense clouds. our own Solar System will be quite diffuse (due to the angular sparsity of Oort comets V. CONCLUSIONS as seen from the Earth); a detailed examination of IRAS background measurements, We have called attention to the erosional however, could provide a limit on the ero- interaction between dust in the interstellar sion-fragment population at large heliocen- medium and comets in the Oort Cloud. tric distances. Were there no grain impacts, gas molecules Perhaps a better place to search for the would accrete a thin veneer on cometary comet/ISM interaction would be around surfaces. We have found, however, that other stars likely to possess comet clouds. grain impacts provide a strong erosive Because such sources appear compact mechanism, removing many hundreds of when viewed from afar, ~1014 comets un- times the mass accreted by molecular stickdergoing several times 105 collisions per ing. Because 0.5-8 cm of surface material second could be monitored simultaneously. will be eroded from any object in the Oort The possible signatures of the interaction Cloud, we conclude that primordial objects process will include (1) the Greenberg with radii less than a few centimeters will grain-explosion signature, (2) the release of not survive in the cloud to the present. light associated with grain and gas impacts The net removal of cometary surface ma(~1019 erg/sec for our Oort Cloud), and (3) terial may also be relevant to the anomaan enhanced population of small dust and lous brightness of fresh comets, since erowater mantled grains around certain stars. sion effects surface age and granularity. Emissions from processes (1) and (2) might Erosion may therefore contribute to obbest be detected around extinct or low-lu- servable thermal, morphological, and sur-

282

S. ALAN STERN

face scattering properties of new comets entering the Solar System. We have also found that material eroded from cometary surfaces will escape both the comet and the Solar System. Scaling analysis indicates that the fractional number and mass contribution of particles returned to the medium by cometary erosion can be significant. At least - 4 % and perhaps as much as 20% of the total ISM grain population can be attributed to this mechanism. Such a source of ISM grains has not been previously recognized, and may display observable traits. Concluding, our analysis indicates that comets serve as a temporary sink for some fraction of the ISM which is first lost through the processes of nebular collapse and planetesimal/cometesimal accretion and then is returned to interstellar space by impacts of cometary surfaces with the grainy constituents of the ISM. Dust to dust. This brings to mind the possibility of a closed loop feedback between Solar System/comet formation, and the interstellar medium. Such a mechanism could serve to address some of the difficulties imposed by shock-destruction effects with respect to the apparent dearth of grain nuclei (Seab and Shull, 1985). For the future, we recommend additional laboratory studies of extremely low-mass impacts into icy/snowy surfaces at Vre~- 20 km/sec, searches to determine the extent of extrasolar Oort clouds, and detailed timedependent modeling of mechanical interactions between the ISM and comets as a function of the varying conditions imposed by ISM shocks and other density fluctuations. ACKNOWLEDGMENTS I take this opportunity to thank William McClintock, Gary Thomas, and Theodore Snow of the University of Colorado at Boulder, and Larry Trafton of the University of Texas at Austin for generous comments. Productive discussions with Paul Weissman and Gene Shoemaker, and the support of Charles Barth are also appreciatively recognized. Ann Alfaro's assistance in the preparation of this manuscript is gratefully acknowledged.

REFERENCES AUMANN, H. H. (1984). IRAS observations of nearby main-sequence dwarfs. Bull. Amer. Astron. Soc. 16, 483. BURKE, J. R., AND D. J. HOLLENBAEH (19830. The gas-grain interaction in the interstellar medium: Thermal accommodation and trapping. Astrophys. J. 265, 223-234. CINTALA, M. J. (1981). Meteoroid impact into shortperiod comet nuclei. Nature 291, 134-136. CLtmE, S. V. M., AND W. M. NAPIER (1982). Comet capture from molecular clouds: A dynamical constraint on star and planet formation. Mon. Not. R. Astron. Soc. 208~ 575-588. CROFT, S. K. (1982). Impacts on ice and snow: Implications for crater scaling on icy satellites. Lunar Planet. Sci. Xlll, 135-205. DRAGANIC, I. G., AND E. D. DRAGANIC (1984). Some radiation-chemical aspects of chemistry in cometary nucleii. Icarus 60, 464-475. FECHTIG, H. (1982). Cometary dust in the Solar System. In Comets (L. L. Wilkening, Ed.), pp. 370382. Univ. of Arizona, Press, Tucson. FERNANDEZ, J. A. (1980). On the existence of a comet belt beyond Neptune. Mon. Not. R. Astron. Soc. 192, 481-491. FUJIWARA, A., G. KAMIMOTO, AND A. TSUKAMOTO (1977). Destruction of basaltic bodies by high velocity impact. Icarus 31, 227-288. GAOLT, D. E. (1973). Displaced mass, depth, diameter, and effects of oblique trajectories for impact craters formed in dense crystalline rocks. The Moon 6, 32-44. GREENBERG, J. M. (1978). Interstellar dust. In Cosmic: Dust (J. A. M. McDonnell, Ed.), pp. 187-294. New York: Wiley and Sons. GREENaERG, J. M. (1982). What are comets made of? A model based on interstellar grains. In Comets (L. L. Wilkening, Ed.), pp. 131-164. Univ. of Arizona Press, Tucson. GREENBERG, J. M. (1983). A fine mist of very small comet dust particles. Adv. Space Res. 4(9), 211212. GREENBERG, R., et al. (1978). The accretion of planets from planetesimals. In Protostars and Planets (T. Gehrels, Ed.), pp. 599-623. Univ. of Arizona Press, Tucson. GRON, E., et al. (1980). A model of the origin of the Jovian ring. Icarus 44, 326-338. GRON, E., et al. (1985). Collisional balance of the meteoric complex. Icarus 62, 244-272. HAFF, P. K., et al. (1983). Ring and plasma: The enigma of Enceladus. Icarus 56, 426-438. HAGEN, W., et al. (1979). Interstellar molecule formation in grain mantles: The laboratory analog experiments, results, and implications. Astrophys. Space Sci. 65, 215-240. HANNER, M.S. (1984). Comet cernis: Icy grains at last? Astrophys. J. 272, L75-L78.

INTERACTION

OF COMETS WITH ISM

HARPER, D. A., et al. (1984). The nature of the material surrounding Vega. Astrophys. J. Astrophys. Space Sci. 65, 215-240. KAPLAN, S. A. AND PIKELNER, S. B. (1978). The Interstellar Medium, pp. 210-224. Harvard Univ. Press, Cambridge, Mass. LANGE, M. A., AND T. J. AHRENS (1982). Impact cratering in ice and ice-silicate targets: An experimental assessment. Lunar Planet Sci. XIII, 415-416. LEBOFSKY,L. A. (1975). Stability of frosts in the Solar System. Icarus 25, 205-217. LE SERGEANT D’HENDECOURT, L. B., AND PH. L. LAMY (1981). Collisional processes among interplanetary dust grains: An unlikely origin for the p meteoroids. Icarus 47, 270-281. MATHIS, M., et al. (1977). Astrophys. J. 217,425-537. MATSUURA,0. T. (1976). Collision of comets with meteoroids. Icarus 27, 323-329. MENDIS, D. A., AND K. R. FLAMMER(1984). The multiple modes of interaction of the solar wind with a comet as it approaches the Sun. Earth, Moon, Planets, 301-311. O’DELL, C. R. (1971). A new model for cometary nuclei. Icarus 19, 137-146. SALPETER, E. E., AND W. D. WATSON(1973). Abundances of interstellar molecules and their formation on grain surfaces. Interstellar Dust and Related Topics (J. M. Greenberg and H. C. van De Hulst, Eds.), pp. 363-368. Reidel, Dordrecht. SEAB, C. G., AND J. M. SHULL (1985). Shock processing of interstellar grains. In NASA Conference Pub. 2403 (J. A. Nuth and R. E. Stencel, Eds.), pp. 3754. SEKANINA, Z. (1976). A probability of encounter with interstellar comets and the likelihood of their existence. Icarus 27, 123-133. SHUL’MAN, L. M. (1972). The evolution of cometary nuclei. In The Motion Evolution of Orbits and Origin of Comets (G. A. Chebotarev et al., Eds.), pp. 271-276. Reidel, Dordrecht. SMITH, B. A., AND R. J. TERRILE (1984). A circumstellar disk around Beta Pictoris. Science 226, 14211424. SMOLUCHOWSKI,R. (1981). Erosion of particles in

283

planetary rings & interplanetary space. In Reports on the Planetary Geology and Geophysics 1980, pp. 1060-1061. SMOLUCHOWSKI, R., AND A. MCWILLIAM (1984). Structure of ices on satellites. Icarus 58, 282-287. SPITZER, L., JR. (1978). Physical Processes in the Interstellar Medium. Wiley-Interscience, New York. SWINZOW, G. K. (1977). The impact of projectiles into snows. Proc. Fuse. Ammunition. Environmental Sym. (Batelle Mem. Institute). THOMAS,G. E. (1978). The interstellar medium and its influence on the interplanetary environment. Ann. Rev. Earth Planet. Sci. 6, 173-264. WATSON,W. D. (1974). Physical processes for the formation and destruction of interstellar molecules. In Atomic and Molecular Physics and the Interstellar Mutter (R. Balian et al., Eds.), pp, 177-320. NorthHolland, Oxford. WATSON, W. D., AND E. E. SALPETER(1972). Molecule formation on interstellar grains. Astrophys. J. 174, 321-340. WEISSMAN, P. R. (1980). Stellar perturbations of the cometary cloud. Nature 288, 242-243. WEISSMAN, P. R. (1982). Dynamical history of the Oort Cloud. In Comets (L. L. Wilkening, Ed.), pp. 637-658. Univ. of Arizona Press, Tucson. WEISSMAN, P. R. (1984). The Vega particulate shell: Comets or Asteroids? Science, 224, 987-989. WEISSMAN,P. R. (1985a). Cometary dynamics. Space Sci. Rev. 41, 299-349. WEISSMAN,P. R. (1985b). The Oort cloud in transition. In Asteroids, Comets, and Meteors II (C.-I. Lagerkvist, B. A., Lindblad, H. Lundstedt, and H. Rickman, Eds.),.pp. 197-206. Uppsala Univ. WEISSMAN,P. R. (198%). The Oort cloud and the Galaxy: Dynamical interactions. To be published in The Galaxy and the Solar System. WHIPPLE, F. L. (1977). The constitution of cometary nuclei. In Comets, Asteroids, and Meteorites (A. H. Delsemme, Ed.), pp. 25-34. Univ. of Toledo, Toledo, Ohio. WYCOFF, S. (1982). Overview of comet observations. In Comets (L. L. Wilkening, Ed.), pp. 3-55. Univ. of Arizona Press, Tucson.