Collisions, Cosmic Radiation and the Colors of the Trojan Asteroids
aa r X i v : . [ a s t r o - ph . E P ] J un Collisions, Cosmic Radiation and the Colors of the TrojanAsteroids
M.D. Melita Instituto de Astronom´ıa y F´ısica del Espacio. Buenos Aires. Argentina. [email protected] andG. Strazzulla INAF-Osservatorio Astrofisico di Catania, Italy [email protected] andA. Bar-Nun Department of Geophysics and Planetary Sciences.Tel Aviv University,Tel Aviv,Israel. [email protected]
Received ; acceptedSubmitted to ICARUS 2 –
ABSTRACT
The Trojan asteroids orbit about the Lagrangian points of Jupiter and theresidence times about their present location are very long for most of them.If these bodies originated in the outer Solar System, they should be mainlycomposed of water ice, but, in contrast with comets, all the volatiles close to thesurface would have been lost long ago. Irrespective of the rotation period, andhence the surface temperature and ice sublimation rate, a dust layer exists alwayson the surface. We show that the timescale for resurfacing the entire surface ofthe Trojan asteroids is similar to that of the flattening of the red spectrum ofthe new dust by solar-proton irradiation. This, if the cut-off radius of the sizedistribution of the impacting objects is between 1mm and 1m and its slope is -3,for the entire size-range. Therefore, the surfaces of most Trojan asteroids shouldbe composed mainly of unirradiated dust.
Subject headings:
Trojan Asteroids. Asteroids, Surfaces. Comets. Solar System,Origin.
1. Introduction
All the Trojan asteroids orbit about the Sun at roughly the same heliocentric distanceas Jupiter, residing close to the Lagrangian stable points, leading or trailing at ∼ o fromthe planet. They are particularly interesting because of being relatively isolated, lying justbeyond the snow line , the distance at which water can exist in the form of ice. As such, itmay be expected that the bulk of the Trojans were mainly composed of ices. However, atthe moment, no water or other more volatile substances have been detected on the surfaceof a Trojan (Yang & Jewitt 2007, Emery & Brown 2003; 2004). In the case of Ennomos, anunusually hight-albedo object, the surface-content of water ice has been quantified to bebelow 10% in mass (Yang & Jewitt 2007). However the lack of detection does not implythat water ice is not there. Brunetto and Roush (2008) have in fact shown that a relativelythin (tens of microns) crust of specific refractory materials (they considered irradiatedmethane ice) can mask the presence of water ice bands in the spectrum.The Trojans have been characterized as similar to cometary nuclei or extinct comets(Jewitt and Luu 1990). Most of the objects fall into the D and P asteroid taxonomic classesand a few objects show spectra with neutral or even negative slopes in the visual range(Bendoya et al. 2004), with the majority having moderately-red surfaces (see figure 1).They have been observed to posses low albedos (Fernandez et al. 2003) of about 4% andinfrared observations indicate the presence of silicates (Cruikshank et al. 2001, Emery et al.2006) and depletion of water ice and volatiles (Emery & Brown 2003; 2004).Numerical models of the collisional evolution of the Trojan asteroids (Marzari et al.1997) are successful in explaining the present Trojan population (Jewitt et al. 2000). Thesteep slope of the Trojan size distribution at diameters larger than about 50 − et al . 2008a). This supports the hypothesis thatthe unstable objects are mainly byproducts of physical collisions, the transitional size hasbeen found to be H ≈ .
5. But the slopes of the reflectance spectra show no relation withthe size of the objects (see figure 2) or with the stability of the orbits (Melita et al . 2008a).We intend to understand why most of the Trojans are moderately red, regardless ifthey are large bodies or fragments of collisions. These asteroids are subject to impactswhich can extract fresh material from the interior and scatter it on the surface. The freshmaterial would be composed of dust and ice. After the Deep-Impact event, we note theincrease of emission of both organic compounds and water ice (Lisse et al. 2006). But, ifwater ice were deposited on the surface after an impact, it would sublimate very rapidly.Therefore, after a physical impact, a layer of unirradiated ice –which has a typically redspectral slope– is deposited in the surface. It has been suggested that terrestrial bitumensare good spectral analogues for such a dust layer (e.g. Moroz et al 2004 and referencestherein). The less energetic solar protons modifies the spectroscopic properties of thisdust, reducing its albedo and flattening the spectral slope (Moroz et al. 2004). But if thecollisional process can resurface the asteroids on a timescale which is similar, or shorter,than the timescale that flattens the spectrum, it is expected that most of the Trojans willbe observed to be red. In the following section we present a model to estimate relevanttimescales and we discuss its results in the last section. 5 –
2. Surface alteration timescales2.1. Timescale of flattening of the spectral slope by irradiation
There are a number of energetic ion populations bombarding the surfaces of smallbodies in the outer Solar System: solar wind ions, ions from solar flares, galactic cosmicrays, and the so called ”anomalous” cosmic ray component. The last component is howeverrelevant only to objects at the Pluto orbit and beyond.Solar wind is an expanding flux of fully ionized plasma that reaches, at distancesgreater than a few solar radii, an expansion speed of about 400 km s − corresponding to anenergy of ≈ ≈ protons cm − s − and it decreases with the square of the solar distance. The effects of thesolar wind ions irradiating ”red” organic bitumens (namely asphaltite and kerite) have beensimulated in the laboratory (Moroz et al 2004). The hypothesis is that terrestrial bitumensare good spectral analogues of the red organic surfaces of small objects in the Solar System(we consider Trojans in the present paper). The main result is a progressive flatteningof the red spectrum of bitumens with ion fluence. Moreover Moroz et al (2004) suggestthat the mechanism that produces the flattening is connected to the energy deposited byelastic collision of the incoming ions with the atoms in the target. This allows to extend thelaboratory results obtained with 10’s keV H + , N + , and Ar ++ to all solar wind ions. Becausein the laboratory the flattening of the asphaltite spectrum in the 0.3-0.8 micrometersspectral region has been obtained after about 0.4 × C-displacements cm − (see Morozet al, top panel in Fig 14), we need to calculate the time necessary to solar wind ions (at5 AU) to cause the accumulation of such an amount of damage on the bombarded surface.As said, solar wind ions have energy of about 1 keV/amu. Most of them are protons (96 %)and He (4 %) with traces of heavier elements. Using the TRIM code (Transport of Ionsin Matter; e.g., Ziegler et al. 1996) we calculate that the number of displaced atoms in 6 –asphaltite is about 1.5 for 1 keV protons and 20 for 4 keV alpha particles. Considering therespective abundances, we obtain an average of 2.2 C-displacements per solar wind ion (thecontribution of heavier ions can be neglected). At a distance of 5 AU from the Sun we thenexpect that an exposed surface will suffer about 10 × × C-displacementscm − sec − . Thus the time necessary to reproduce the effects observed in the laboratory is:0.4 × /9 × = 5.5 × sec i.e. about 2 × yrs.It is important to note that solar wind particle irradiation affects only a thin surfacelayer ( ≤ A ). This is however sufficient to affect the optical properties of the surface(as simulated in the laboratory), but may be easily destroyed by impact resurfacing. Asdiscussed here, such resurfacing of irradiated material probably occurs constantly.In order to produce a radiation-induced damage of deeper layers, more energetic ionsshould be considered. Solar cosmic rays are produced during solar flares. An average fluxof solar protons having an energy of 100 keV and a penetration depth of about 1 µ m hasbeen estimated to be ≈ × protons cm − yrs − (Lanzerotti et al., 1978). It is inverselyproportional both to the square of the energy and to the square of the solar distance. At 5AU the time necessary to reach the maximum C-displacements of our experiments is about2 × yrs.Galactic cosmic rays are less abundant but significantly more penetrating. In a recentreview Hudson et al. (2008, and references therein) reported the estimate of the radiationdoses for objects at different distances from the Sun (see their Table 1). It has beenfound that objects orbiting at 5-35 AU accumulate in about 10 yrs an irradiation damagesufficient to be fully chemically altered down to depth of the order of 1 meter. Althoughgalactic energetic particles transfer most of their energy through electronic loss (ionizationsand excitations), however at the end of their path they slow down and are thought toproduce, in the so called Bragg peak, the same effects meassured in the laboratory for low 7 –energy particles.In summary we have shown that the uppermost layers of an object orbiting at theJupiter distance can be weathered in about 10 yrs. If its surface is an organic materialspectrally similar to bitumens, its red sloped spectrum is flattened on that time scale.Deeper layers are weathered in longer times: at a depths of the order of 1 meter the targetis fully altered in about 10 yrs. The timescale for sublimation-mantle growth, τ M , is (Jewitt 2002): τ M = ρ Lf M dm/dt , where L is the depth of the sublimated material, ρ is the mass density of the asteroid, f M is the fraction of the solid mass that cannot be ejected by gas drag and dm/dt is the dragmass-loss rate per unit area.For a fast rotator, the effective temperature at the surface of a Trojan is ∼ o K -assuming an albedo of 0 .
04. At this temperature, the mass loss rate of perfectly absorbingwater-ice in equilibrium sublimation is approximately dm/dt ≈ − kg m − s − . To finda reliable estimation for dm/dt at T = 120 o K is quite a complicated problem and we havereached this value after much deliberation, following the comments of the reviewer. Thewater-vapor pressure in torr , P , vs. temperature, T , was calculated, using the polynomialfrom the International Critical Tables between 140 o K and 180 o K :log ( P ) = − . T + 8 . × log( T ) − . × T + 1 . × − T − . , and checked against the P vs. T in the CRC-Handbook of Chemistry and Physics andfound to agree with Sack and Baragiola (1993). The pressure at 120 o K is 1 . × − P a . 8 –Since the flux of sublimating water molecules, F , is, F = P ( T )(2 πKmT ) / , where K is Boltzmann’s constant and m the mass of the molecule. We recalculated the squareroot term in the denominator and found it to be: (2 πKmT ) / = 1 . × − kg m − s − per molecule. Hence the flux calculated from the pressure as obtained by the polynomial is: F ( T = 120 o K ) = P ( T = 120 o K )(2 πKmT ) / = 1 . × molec. m − s − = 1 . × molec. cm − s − . This flux was compared with the flux meassured by Ntesco and Bar-Nun (2005) in theirFigure 1 and we realized that the measured value at 120 o K is the background of watervapor in our vacuum chamber. Extrapolating the flux vs T plot in their Figure 1 to 120 o K leads to a flux of approximately 10 molec. cm − s − , which is 100 times larger than theone calculated by the P vs T through the polynomial, due to the very large surface areaof the amorphous ice, much larger than the area calculated by the geometric dimension ofthe substrate on which the ice was deposited. As measured by Bar-Nun et al. (1987), byAr adsorption at 120 o K , a surface area of 38 m g − was found, in good agreement withMayer and Pletzer (1986) who measured 40 m g − at 114 o K . Sack and Baragiola’ s (1993)Figure 2 data can be extrapolated to 8 × molec. cm − s − at 120 o K and shows an 8fold increase in the vapor pressure in amorphous non annealed ice, which they attribute tothe larger surface area. These authors (Figure 3)show a 7 fold increase in the flux at 135 o K with an ice thickness between 0 .
12 and 5 . µm and a 7 − o K during200 min at that temperature. Both observations point to a considerable effect in surfaceroughness. To be on the conservative side we shall adopt a flux of 5 10 molec. cm − s − or1 . − kg m − s − . It should be remembered that slight deviations from an albedo of 0 . o K shouldbe adopted?. The one obtained from Notesco and Bar-Nun’s (2005), 10 molec. cm − s − × molec. cm − s − ?. Since this massloss rate is very low, even the smallest sub-micron sized grains on the surface of the Trojanasteroids are retained, hence, for the fast rotator case, we take f M = 1.The known rotation periods of Trojans range approximately from 4 hr to 40 hr (Hartmann et al. 1988, Binzel and Sauter 1992, Melita et al. 2008b) .As one extreme case, in the fast rotator approximation, the time that it takes tosublimate a layer equal to the penetration-depth of the solar protons, roughly a 100 µm dustlayer, is only of ∼ T S ≈ o K , and the corresponding mass-loss rate dm/dt ( T S ) ≈ − kg m − s − (CRC-Handbook of Chemistry and Physics 1981-1982). Inthis case, the fraction of the solid mass that cannot be ejected by gas drag can be estimatedas (Jewitt 2002): f M = log ( a M /a c ) log ( a M /a m )where a M and a m are the maximum and the minimum grain sizes in the distributionrespectively and a c , the maximum particle-radius that is retained, given by: a c = v e ( R ) dm/dt ( T S ) G R ρ , where v e ( R ) is the escape velocity from a body of size R and G is the gravitational constant.If we take a M = 1 mm and a m = 1 µm and R = 100 km , then a c ≈ µm . We find that, for a P = 40 hr , the timescale in which an insulator-mantle of thickness L = 100 µm grows, is only τ M ( P = 40 hr ) ≈ days . To compute the timescale of the collisional resurfacing process we have adapted themodel by Gil-Hutton (2002) and incorporated the latest knowledge gained by the DeepImpact mission (see for example Richardson et al. 2007).The time to cover the entire surface of an asteroid of radius R with debris extractedfrom below the surface by the action of physical collisions, τ CR , is given by: τ CR = 1˙ S r , where ˙ S r = ˙ S/ (4 πR ) is the fraction of the surface that is covered by material excavated bycollisions per year and ˙ S is the total area covered by collisional ejecta each year.The total area covered by ejecta per year, ˙ S , for an object of radius R is:˙ S = Z r max r min ˙ N ( r ) A E ( r ) dr, (1)where ˙ N ( r ) is the number of collisions per unit time and A E ( r ) is the area covered by theejecta produced when projectiles of radii r collide with an object of radius R , at a typicalencounter velocity v . We write A E as A E = l × A c ( R, r, v ), where A c ( R, r, v ) is the area ofthe crater produced and A c = π d , where d is the diameter of an idealized crater, and weassume the densities of the target and the impactor to be equal, i.e. ρ R = ρ r = 1 . gcm − .The volume of the crater in the gravity dominated cratering regime is estimated as(Richardson et al. 2007, Holsapple 1993): V g = K (cid:18) mρ (cid:19) (cid:18) r g ( R ) v (cid:19) − µ µ , (2) 11 –where g ( R ) is the surface gravity of the target, m is the mass of the impactor, v its impactvelocity, ρ is the density which is assumed to be equal for the target and the impactor. Thescaling constants K = 0 .
24 and µ = 41, correspond to a loosely bound material such assand, which gave a good agreement with the size of the crater produced in the Deep impactmission (Richardson et al. 2007). The diameter of the crater is easily obtained from V g = 124 πd . Now, we can write ˙ N as, ˙ N = P i ( R + r ) dN ( r ) , where P i is the intrinsic probability of collisions, as defined by Wetherill (1967), is theprobability of collision per unit time, per unit cross section and per number of collidingpairs and dN ( r ) is the number of objects with radii r . The values of P i and v , havebeen computed specifically for the Trojans by Dell’Oro et al . (1998) giving approximately6 . − km − yrs − and 5 km s − respectively.The integral on equation 1 depends critically on the limits, which must be handledcarefully. The upper limit, r max , is the maximum radii of the projectiles that do not shattera target of radius R . For the ρ R = ρ r case is, r max = R (5 βv c − − / , (Petit & Farinella 1993), where β = 10 − g erg − is a crater excavation coefficient. While r min is the cut-off radius.Finally, to compute τ C , we need an estimation of the observed distribution of sizes inthe Trojan population, which, for the smallest objects is (Jewitt et al. 2000), dN ( r ) = 1 . (cid:18) kmr (cid:19) . (3) 12 – r min , the cut-off radius The contribution of the dust phase, i.e. µm sized particles, to the modificationof the a 100 µm layer of irradiated material is negligible, since it would only producere-arrangements. For such small impactors, the cratering regime is strength-dominated.The volume of the crater produced V S can be estimated as (Richardson et al 2007, Holsapple1993): V S = K mρ (cid:18) ¯ Yρv (cid:19) − µ , where ¯ Y is the effective yield strengths of the target material. We adopt a value of¯ Y ≈ P a , as determined for comet Temple 1 and also in agreement with laboratoryexperiments (Richardson et al. 2007, Bar-Nun et al. 2007). Under the assumptions usedpreviously, the depth of this crater for an impactor of size 10 µm is 600 µm , i.e., roughly thepenetration depth of the solar protons.Moreover, micro-impacts contribute less to the resurfacing because dust is carriedaway by radiation and its size distribution is much shallower than the one corresponding tomacroscopic objects. Therefore the smallest cut-off radius that we shall assume is 1 mm ,since objects of this size are not affected by radiation. Unfortunately, there is no informationavailable on the size distribution of objects of sizes ranging between 1 mm and 100 ′ s m orbiting in the Trojan clouds. We assume that the size distribution of the smallest observedTrojans (Jewitt et al. 2000) also applies for small particles. Although this assumption mayseem extreme, there is no creation or destruction mechanism that affects the small particlesdifferently than the large objects, since none of them are affected by radiation. And theevidence of the cratering record on asteroids indicates that the slope of the size distributionof impactors is unaltered from km -sized bodies down to m -sized objects (O’Brien et al.2006).If we take l = 1, the timescale of collisional resurfacing is, neglecting overlapping, the 13 –time-span in which all the surface is covered with craters, τ C . Note that τ C is larger thanthe time to cover the object with ejecta. Values of τ C for the size range of the known Trojanasteroids, are shown in figure 3 for different values of the cut-off radius r min . For a value of r min = 1 mm the object is completely covered by craters in about 700 to 1100 yrs , while for r min = 10 m , it occurs in 10 to 10 yrs .Now we estimate how the area covered by optically thick ejecta, scales with the size ofthe crater. If we assume that the optically thick ejecta is close to the edge of the crater,and is mostly originated by material close to it, then the ejection velocity from the impact, v e , scales as (Richardson et al. 2007): v e ∝ r g d . Then, for the distance travelled by the ejecta, h , is: h ∝ v e g = d , and therefore, the ratio l = (cid:18) hd/ (cid:19) is constant. To fix this constant we use the fact that the size of the crater produced incomet Temple 1 by the Deep Impact mission has a radius of approximately 30 m and thebase of the plume after the event had a radius of about 150 m (Richardson et al. 2007),hence we adopt a value for the ratio of the areas of l = 25. In figure 3 we also plot valuesof the timescale for collisional resurfacing, τ , assuming a value of l = 25. For a value of r min = 1 mm the resurfacing occurs in about 100 to 300 yrs , while for r min = 10 m , it occursin 3000 to 7000 yrs . 14 –
3. Conclusion
The surface properties of a Trojan asteroid are determined by the interplay of threedifferent mechanisms. When an impact occurs, if it is sufficiently energetic, the innermaterials of the body are exposed and scattered on the surface. Given that the site ofresidence and formation of the Trojans is the outer Solar System, water ice could beabundant, but, as shown in section 2.2, it sublimates fast from the surface, leaving a mantleof dust, most probably with a red spectroscopic slope. If this dust layer would remainunaltered for more than 10 yrs , its spectroscopic slope would turn to neutral by the actionof solar protons. But impacts occur so frequently that the irradiation mantle is disrupted.The surfaces of most Trojans are red, but some neutral objects exists, therefore, it issuggested that the irradiation resurfacing timescale is similar, but not much shorter, thanthe collisional one. The conclusion reached here is that the timescale to fill the entiresurface of the Trojan asteroids with craters is similar to that of the flattening of the redspectra by solar-proton irradiation, if the cut-off radius of the size distribution is 1 mm andits slope is − m , with the same slope, renders a collisional resurfacing-timescale in therequired range.The model presented here can be seen as an exercise to illustrate a scenario ofcollisional and radiation balance to understand the distribution of spectral slopes in theTrojan swarms. Naturally, refinements are needed to represent better reality. For example,our estimates of the collisional resurfacing timescales bear large uncertainties, mainly dueto our lack of knowledge of the size distribution of small particles around the Lagrangianpoints of the orbit of Jupiter. On the other hand, the information regarding visual spectralslopes of known dynamical-family members (Fornasier et al. 2007), indicates that mostdynamical families are remarkable uniform. With the noticeable exception of the one of 15 –Eurybathes, they are mostly moderately red, suggesting a correlation with age. Eventually,the calculations presented here could be used to understand such a potential trend.Finally, a comment on how the scenario would change if the mass-loss rate of water iceat 120 o K , based in realistic rotation rates and albedos where to be higher than estimatedhere. In this case mass loss due to sublimation would be higher and the exposed surfaceice could have been lost from the Trojans in their current orbit. A different orbit is notrequired. Acknowledgements
We are grateful for the comments of an anonymous referee, which have helped toimprove this article greatly, particularly regarding the sublimation rate of water ice.GS has been supported by Italian Space Agency contract n. I/015/07/0 (Studidi Esplorazione Sistema Solare). A.B-N acknowledges partial support by the US-IsraelBinational Science foundation. MDM acknowledges partial support by UBACyT X465.
References
Bar-Nun,A., Dror, J., Kochavi,E., Laufer, D. 1987. Amorphous water ice and its abilityto trap gases.
Physical Review B , , 2427-2435.Bar-Nun, A., Pat-El, I., Laufer, D. 2007. Comparison between the findings of DeepImpact and our experimental results on large samples of gas-laden amorphous ice. Icarus , , 2, 562-566.Beauge, C., Roig, F. 2001. A Semi-analytical Model for the Motion of the Trojan 16 –Asteroids: Proper Elements and Families. Icarus , , 2, 391-415.Bendoya.,P, Cellino, A, Di Martino, M., Saba, L. 2004. Spectroscopic observations ofJupiter Trojans. Icarus , , 2, 374-384.Binzel, R.P. and Sauter, L.M. 1992. Trojan, Hilda, and Cybele asteroids - Newlightcurve observations and analysis. Icarus , , 222-238.Brunetto, R., Roush, T.L. 2008. Impact of irradiated methane ice crusts oncompositional interpretations of TNOs. Astronomy and Astrophysics , , 879-882.CRC-Handbook of Chemistry and Physics, 1981-1982, The Chemical RubberCo.Cleveland OH.Cruikshank, D. P., Dalle Ore, C. M., Roush, T. L., Geballe, T. R., Owen, T. C., deBergh, C., Cash, M. D.; Hartmann, W. K. 2001. Constraints on the Composition of TrojanAsteroid 624 Hektor. Icarus , , Issue 2, 348-360.Dell’Oro, A., Marzari, P., Paolicchi F., Dotto, E., Vanzani, V. 1998. Trojan collisionprobability: a statistical approach. Astronomy and Astrophysics , , 272-277.Emery, J. P. , Brown, R. H. 2003. Constraints on the surface composition of Trojanasteroids from near-infrared (0.8-4.0 µ m) spectroscopy, Icarus , , 104-121.Emery, J. P. , Brown, R. H. 2004. The surface composition of Trojan asteroids:constraints set by scattering theory. Icarus , , 131-152.Emery J.P., Cruikshank D.P. , Van Cleve J. 2006. Thermal emission spectroscopy(5.2-38 µ m) of three Trojan asteroids with the Spitzer Space Telescope: Detection offine-grained silicates. Icarus , , 2, 496-512.Fern´andez, Y. R. , Sheppard, S. S. , Jewitt, D. C. 2003. The Albedo Distribution ofJovian Trojan Asteroids. The Astronomical Journal , , 1563-1574. 17 –Fornasier, S., Dotto, E., Hainaut, O., Marzari, F., Boehnhardt, H., de Luise, F.,Barucci, M. A. 2007. Visible spectroscopic and photometric survey of Jupiter Trojans:Final results on dynamical families. Icarus , 2, 622-642.Gil-Hutton, R. 2002. Color diversity among Kuiper belt objects: The collisionalresurfacing model revisited.
Planetary and Space Science , , 1, 57-62.Gosling, J.T., 2007, The Solar wind, in: Encyclopedia of the Solar System 2nd Edition,L.McFadden, P.R. Weissman, T.V. Johnson Eds, Academic Press, pp 99-116Hartmann, W. K., Binzel, R.P., Tholen, D.J., Cruikshank, D. P., Goguen, J. 1988.Trojan and Hilda asteroid light-curves. I - Anomalously elongated shapes among Trojans(and Hildas?). Icarus , , 487-498.Holsapple K.A. 1993. The scaling of impact processes in planetary sciences. Annu.Rev. Earth Planet. Sci. , , 333-374.Hudson R.L., Palumbo M.E., Strazzulla G., Moore M.H., Cooper J.F., , SturnerS.J., 2008, Laboratory studies of the chemistry of TNO surface materials, in: The SolarSystem beyond Neptune, The University of Arizona Space Science Series, M. A. Barucci,H. Boehnhardt, D. P. Cruikshank, A. Morbidelli (editors), University of Arizona Press,Tucson, pp 507-523Jewitt, D.C. 2002, From Kuiper Belt Object to Cometary Nucleus: The MissingUltrared Matter. The Astronomical Journal , , 2, 1039-1049.Jewitt, David C., Luu, Jane X. 1990. CCD spectra of asteroids. II - The Trojans asspectral analogs of cometary nuclei. Astronomical Journal , , 933-944.Jewitt, David C., Trujillo, Chadwick A., Luu, Jane X. 2000. Population and SizeDistribution of Small Jovian Trojan Asteroids. The Astronomical Journal , , 2, 18 –1140-1147.Lanzerotti L. J., Brown, W. L., Poate, C. M., Augustyniak, W. M. 1978. Low energycosmic ray erosion of ice grains in interplanetary and interstellar media. Nature ,431-433.Marzari, F., Farinella, P., Davis, D. R., Scholl, H., Campo Bagatin, A. 1997.
Icarus , , 1, 39-49.Lisse, C. M., VanCleve, J., Adams, A. C., A’Hearn, M. F., Fernndez, Y. R., Farnham,T. L., Armus, L., Grillmair, C. J., Ingalls, J., Belton, M. J. S., Groussin, O., McFadden, L.A., Meech, K. J., Schultz, P. H., Clark, B. C., Feaga, L. M., Sunshine, J. M. 2006. SpitzerSpectral Observations of the Deep Impact Ejecta. Science , , 5787, 635-640.Mayer,E., and Pelzer,R., 1986. Astrophysical implications of amorphous ice - Amicroporous solid. Nature , , 298-301.Melita, M.D., Licandro, J., Jones, D., Wiliams, I.P. 2008a. Physical properties andorbital stability of the Trojan asteroids. Icarus , , 2, 686-697.Melita, M.D., Duffard, R., Williams I.P., Jones, D.C., Licandro, J., Ortiz J.L. 2008b.Lightcurves of 21 Trojan Asteroids. A & A , Submitted.Moroz, L. V., Baratta, G., Strazzulla,G. , Starukhina,L. V., Dotto, E., Barucci, . M.A.,Arnold, G., Distefano, E., 2004. Optical alteration of complex organics induced by ionirradiation: I. Laboratory experiments suggest unusual space weathering trend.
Icarus ,214-228Notesco, G., Bar-Nun, A., Owen, T. 2003. Gas trapping in water ice at very lowdeposition rates and implications for comets.
Icarus , , 1, 183-189.O’Brien, D.P., Greenberg, R., Richardson, J.E. 2006. Craters on asteroids: Reconciling 19 –diverse impact records with a common impacting population. Icarus , , 1, 79-92.Petit, J.M. , Farinella, P. 1993. Modelling the outcomes of high-velocity impactsbetween small solar system bodies. Celestial Mechanics and Dynamical Astronomy , , 1-2,1-28.Richardson, J.E., Melosh, H.J., Lisse, C.M., Carcich, B. 2007. A ballistics analysis ofthe Deep Impact ejecta plume: Determining Comet Tempel 1’s gravity, mass, and density. Icarus , , 2, 357-390.Sack, N.J. and Baragiola, R.A., 1993. Sublimation of vapor-deposited water ice below170 K, and its dependence on growth conditions. Phys. Rev. B , , 9973 9978.Yang, B, Jewitt, D. 2007. Spectroscopic Search for Water Ice on Jovian TrojanAsteroids. The Astronomical Journal , , 1, 223-228.Wetherill, G. W. 1967. Collisions in the asteroid belt. J. Geophys. Res. , , 2429-2444.Ziegler, J. F., Biersack, J. P., and Littmark, U., 1996. The Stopping and Range of Ionsin Solids, Pergamon Press, New York. 20 – N u m be r S’ (%/1000A)
Fig. 1.— Histogram of the slopes of visual reflection spectra normalized at 6000˚ A for theTrojan asteroids. The sources of this data can be found in Melita et al. 2008. 21 –
50 100 150 200 -2 0 2 4 6 8 10 12 14 16 D ( . ) ( k m ) S’ (%/1000A)
Fig. 2.— Slopes of visual reflection spectra normalized at 6000˚ A vs. D(0.04), the physicaldiameter, assuming an albedo of 0.04, for the Trojan asteroids. Data taken form Melita etal. 2008. 22 – τ C (yr) Target Radius (km) r min = 1mmr min = 1cmr min = 10cmr min = 1mr min = 10m1 1001000100001000001e+0610 100 τ (yr) Target Radius (km) r min = 1mmr min = 1cmr min = 10cmr min = 1mr min = 10m1 Fig. 3.— Left: Timescale in which the whole body is covered with craters, τ C , as a functionof the radius of the target, for the size range of the known Trojan asteroids. Right: Timescaleof collisional resurfacing, assuming a value of l = 25, ττ