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Color diversity among Kuiper belt objects: The collisional resurfacing model revisited
Planetary and Space Science 50 (2002) 57–62
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Color diversity among Kuiper belt objects: The collisional resurfacing model revisited R. Gil-Hutton ∗ Felix Aguilar Observatory, Av. Benavidez 8175 Oeste, 5407 Marquesado, San Juan, Argentina Received 22 November 2000; received in revised form 18 April 2001; accepted 25 June 2001
Abstract A re-evaluation of the collisional resurfacing model based on up-to-date Kuiper belt objects size distribution and a more precise treatment of the cosmic-ray environment at the outer Solar System is presented. The result of the irradiation due to cosmic-rays with di2erent energies altered in a di2erent way the material of the objects, producing, under certain conditions, a thick irradiation mantle. Since the collisional resurfacing model is based in the competition between darkening by cosmic-rays and resurfacing due to impacts, the color of objects in di2erent regions of the belt could vary if the projectile populations in those regions are truncated at a di2erent radius. c 2002 Published by Elsevier Science Ltd.
1. Introduction The existence of a belt of remnant planetesimals beyond the orbit of Neptune was 8rst suggested by Edgeworth (1943) and Kuiper (1951). The so called Kuiper belt has been proposed as the source of the short-period comets (Fern=andez, 1980; Duncan et al., 1988) and the interplanetary dust (Stern, 1996). More than 200 Kuiper belt Objects (KBOs) have been found since the discovery of 1992 QB1 , the 8rst member of this class (Jewitt and Luu, 1992). It is estimated (Jewitt, 2000) that at least 100; 000 KBOs with diameters larger than 100 km move in nearly circular orbits at heliocentric distances between r ≈ 30 and 50 AU. They comprise three dynamical classes: objects in the 3 : 2 mean motion resonance with Neptune have been described as “Plutinos” (Luu and Jewitt, 1996a); those beyond about 41 AU known as “Classical Kuiper Belt Objects”; and those with a much larger semi-major axis and higher eccentricity than the previous two classes are named “Scattered Disk Objects” (Luu et al., 1997). The studies of the physical characteristics of the KBOs are based on photometry and spectroscopy in the visible and near-infrared regions, but there are very few observational studies available due to the faintness of the objects. However, the largest Centaurs, which presumably originated in the Kuiper belt, have low albedos and similar sizes, but very di2erent spectra. Chiron has neutral colors similar to C-type ∗
Fax: +54-264-4238494. E-mail address: [email protected] (R. Gil-Hutton).
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asteroids and some cometary nuclei (Hartmann et al., 1990). On the other hand, Pholus was found to have an astonishing spectrum (Fink et al., 1992) which make it one of the reddest objects in the solar system (Buie and Bus, 1992). Also, the spectra published for three KBOs (Luu and Jewitt, 1996a, b; Brown et al., 1997; Luu and Jewitt, 1998; Brown et al., 1999) are completely di2erent, implying di2erent surface composition. Many authors (Luu and Jewitt, 1996b; Green et al., 1997; Tegler and Romanishin, 1997; Jewitt et al., 1998) found a wide range of color values amongst the KBOs population and they argue for signi8cant compositional diversity. However, Tegler and Romanishin (1998) found that the Centaur and KBO population is split in two distinct groups with neutral and very red colors, respectively, but Barucci et al. (1999, 2000) do not con8rm this bimodality. The 8rst attempt to explain the observed color diversity was made by Luu and Jewitt (1996a, b). These authors proposed that the whole-disk surface colors of KBOs could be the result of the competition between the e2ects of irradiation of surface organics by cosmic-rays and the global resurfacing due to impacts. However, this 8rst model can not explain the color diversity for all current estimates of the projectile size distribution exponent (q ¿ 3; Jewitt et al., 1998; Gladman et al., 1998; Chiang and Brown, 1999) due to the high frequency of the resurfacing impacts. In this paper a re-evaluation of the collisional resurfacing model based on up-to-date KBOs size distribution and cosmic-ray environment at the Kuiper belt is presented. In the following sections the irradiation and collisional
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R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
processes at the Kuiper belt are described. In Section 4 the e2ects of the competition between them are presented, and Section 5 is devoted to the conclusions. 2. Irradiation process Kuiper belt objects are believed to possess interiors rich in abundant molecular ices (such as H2 O; NH3 ; CH4 ), commensurate with their formation in the outer regions of the solar nebula at temperatures of 40 –50 K. Laboratory experiments show that long-term irradiation of astrophysical ice mixtures results in the selective loss of hydrogen and the formation of an “irradiation mantle” of carbon residues (Moore et al., 1983; Johnson et al., 1984; Strazzulla and Johnson, 1991), and also show that as the radiation dose increases, an initially neutral-colored and high-albedo ice becomes red as the violet albedo decreases. Further irradiation gradually reduces the albedo at all wavelengths and, 8nally, the material becomes very dark, neutral in color, and spectrally featureless (Andronico et al., 1987; Thompson et al., 1987). Since the KBOs are under the e2ects of the ultraviolet solar radiation, the solar wind, and the Kux of galactic cosmic-rays, it is reasonable to expect that an irradiation mantle could be formed on their surfaces. Solar ultraviolet radiation at the heliocentric disL the Kux is ≈ tances of KBOs is weak (for 6 1500 A, −3 −2 −1 10 erg cm s ), but due to the long time scale about 3:2 × 1013 erg cm−2 could be deposited in 109 yr. Titan tholin is produced initially in this way from a mixture of gases, but the chemical processing is similar to that in ices (Khare et al., 1993). More interesting is the e2ect of solar cosmic-rays which could be very important for long irradiation time scales. For a solar wind proton (1 keV) the Kux is 2 × 104 protons cm−2 s−1 at 40 AU, while for a solar Kare proton (100 keV) the Kux is 6 × 107 protons cm−2 s−1 at 40 AU (Lanzerotti et al., 1978), but these are low energy ions and only a2ects the upper few millimeters of the surfaces. If higher energies are taken into account, the proton Kux at the maximum of the solar activity (¿ 20 MeV) is ≈ 0:2 protons cm−2 s−1 at 40 AU (McDonald et al., 1974), and the time required to polimerize, for example, 50% of CH4 is about 108 yr at ≈ 0:5 cm, 109 yr at ≈ 2:2 cm and 4:6 × 109 yr at ≈ 5 cm (Strazzulla et al., 1984). The irradiation processes described produce very red material at a Kux of ≈ 1016 protons cm−2 which becomes darker for larger Kuxes. When the Kux reaches a value of ≈ 1017 protons cm−2 a very black upper layer with a neutral color appears (Andronico et al., 1987). The time scale required to form this black layer in a KBO for 5 MeV protons and a Kux of 5:70 protons cm−2 s−1 is ≈ 6 × 108 yr. At higher energies, two successive ionization events are so distant or the speci8c energy loss is so low that cross-linking events are not important and the polymerization process does not occur in the upper layer of the body (Strazzulla, 1986).
In the case of galactic cosmic-rays, the Kux has been roughly constant throughout the age of the solar system (Meyer et al., 1974) having its maximum in the energy range 10 MeV–10 GeV. The proton Kux before entering the solar cavity is JH (E) = 0:3E −1
0:2 ¡ E ¡ 1 GeV;
JH (E) = 0:3E −2
E ¿ 1 GeV;
(1) (2)
−2
−1 −1
−1
where J is given in protons cm sr s GeV (Leger et al., 1985). When these high-energy protons collide with an icy target, they penetrate very depth under the surface. Their range into an object with density ≈ 1 g cm−3 is log depth(m) = 1:28 log E(MeV) − 2:48
E ¿ 1 MeV; (3)
which is a 8t of Fig. 3 in Strazzulla (1986). For example, a proton with E ≈ 3 GeV penetrates down to a depth of ≈ 100 m. The fraction of polymerized material is R = 1 − exp(− );
(4) −2
where is the total Kuence of incoming ions (in cm ) and = 1 − 2 × 10−17 cm−2 is the cross section of the process for 5 MeV protons (Foti et al., 1984). With the Kuxes given by Eqs. (1) and (2) and after 4:5 × 109 yr, 50% of the target material is seriously altered down to 100 m. Since the Kuiper belt is inside the solar wind termination shock (which appears at ≈ 80 AU, Ziemkiewicz, 1994), the results given by Eq. (1) or (2) is larger than the expected Kux at 40 AU from the Sun. Nevertheless, the galactic cosmic-ray pressure falls from 0:33 eV cm−3 outside the shock to 0:17 eV cm−3 at 1 AU (Ziemkiewicz, 1994), so it is reasonable to assume that the true Kux at 40 AU is one half the value obtained with those equations, and 50% of the material is altered down to a depth of ≈ 10 m after 5 × 108 yr, ≈ 20 m after 109 yr, and ≈ 55 m after a time similar to the solar system age. Thus, the irradiation mantle of a KBO could be thick and less red going deep under the surface, with a dark and neutrally colored upper layer (if there is no collisional process present), formed after ≈ 109 and 6 × 108 yr, respectively. In this scenario, two di2erent collisional regimes are de8ned: a depth regime, where energetic collisions are necessary to reach the fresh ice under the mantle, and a super5cial regime, more frequent than the other, which only excavates the red material of the mantle. 3. Collisional process To investigate the e2ects of the collisional process on the irradiation mantle of a KBO it is assumed that the population size distribution follows a power-law of the form dN (¿ r) = Br −p dr, where N (¿ r) is the number of objects with radius between r and r + dr, B is a constant and p = 3:6 (Chiang and Brown, 1999). Also it is considered that the estimated population of objects with r ¿ 50 km is ≈ 100; 000 (Jewitt, 2000). Thus, the collision rate between
R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
a target with radius R and a projectile with radius r is dCr = Pi (R + r)2 dN (¿ r);
4. Resurfacing process (5)
where Pi is the intrinsic collision probability for the target. Theoretical and experimental investigations show that most of the mass displaced by a low velocity impact leaves the crater at speeds much less that the escape velocity, even for an energetic collision with a hard target (Housen et al., 1983). So, it is expected that the bulk of the ejecta resulting from low velocity impacts onto KBOs should fall to the surface, creating a layer of debris around each impact crater. Thus, the total area covered with the ejecta blanket each year is given by dSr = Pi (R + r)2 Ac dN (¿ r);
(6)
where Ac = l2 d2 =4 is the area covered with the ejecta in each collision, d is the crater diameter and l is the ratio between the radii of the ejecta area and the crater. Holsapple (1993) gives an expression for the diameter of an idealized crater as 1=3 −=3 AR 3:22rg d = 2:52r ; (7) r v2 where R and r are the target and projectile densities, respectively, g is the surface gravity of the target, v the collision velocity, and A and are constants dependent upon the mechanical properties of the target material. Holsapple (1993) uses values of A and of 0:2 and 0:65, respectively, for water ice. The shape of this idealized crater it is assumed to be √ a paraboloid of revolution with a depth=radius ratio of 1=2 2. Then, the percentage of target surface covered with the ejecta each year is r1 Sr 2 0:866 −0:434 = 56:56P l Bv ( R) r 1:566−p dr; Sr% = i R 4R2 r0 (8) −1 . The integration and the collisional time scale is Tr = Sr% limits r1 and r0 are di2erent for the two collisional regimes de8ned in the previous section. For the depth regime, r1 is equal to the radius of the largest projectile which does not shatter the target, and is given by
rmax = R(5 v2 − 1)−1=3 ;
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The competition between cosmic-ray reddening and collisions produces a continuous modi8cation of the instantaneous color of the surface. Since both processes have typical time scales, it is possible to decide which one is most e2ective for certain range of sizes. For all the KBOs, targets and projectiles, a density of 1 g cm−3 is assumed. Mean values for the impact velocity and intrinsic collision probability were obtained using the numerical approach developed by Bottke et al. (1994), which is an algorithm based on the formulation of impact probabilities by Greenberg, 1982 (1982; see also Bottke and Greenberg, 1993). The orbital elements of 299 KBOs were considered as representative of the whole population. As test particles, ideal objects at 37; 40; 42; 45 and 50 AU were used. For these test particles the orbital elements were obtained calculating the mean values for all the objects inside an annulus centered at those semi-major axis and Sa = ± 1 AU. The results are shown in Table 1, where are listed the orbital elements of the test particles, the number of objects inside the respective annulus, the mean intrinsic collision probability and the mean collision velocity. Since the values obtained for Pi and v are similar for the 8ve regions, an average is used (Pi = 2:83 × 10−22 km−2 yr −1 and v = 1:25 km s−1 ). Since it is not possible to 8nd analytically the area covered by the ejecta blanket because it approaches in8nity when the fragment radius approaches zero, two extreme values which appear in the literature are used in the following examples. In Fig. 1 the resurfacing time for depth and super8cial regimes are shown for l = 2 (Weissman and Stern, 1994). An irradiation time scale of 109 yr was chosen and, since the mantle is ≈ 20 m wide, it is assumed that rmed = 50 m. The time needed to form the dark upper layer (6 × 108 yr) is also indicated. For rmin 6 7 m (Fig. 1a) the thick mantle does not form because the time needed to bring fresh ice to the surface is less than the irradiation time scale. On the other hand, the time needed to resurface the upper layer is always shorter than 6 × 108 yr, so the black material over the surface of the KBO does not appear and the objects are, at most, red. If objects with r ¡ 10 m, do not exist in the population, the resurfacing time grows as shown in Fig. 1b. Since rmed ¡ 10 m for KBOs with R 6 200 km the resurfacing time for both regimes are the same. Finally,
(9)
where = 1×10−8 g erg−1 is a crater excavation coeRcient and the equation is valid for R = r (Petit and Farinella, 1993). If a projectile with r ¿ rmax collide with the KBO, the process is not valid because the target is shattered. For the depth regime, the value for r0 is obtained inverting Eq. (7) to 8nd the radius of the projectile (rmed ) which makes a crater on the target with a depth enough to allow that some fresh ice is excavated. For the super8cial regime, r1 = rmed and r0 is 8xed to the radius of the smallest particle in the population, rmin .
Table 1 Mean intrinsic collision probability and mean collision velocity for Kuiper belt objects at di2erent semi-major axis a (AU)
e
i (o)
N
Pi (km−2 yr −1 )
v (km s−1 )
37.408 39.883 42.112 44.905 50.330
0.121 0.156 0.064 0.090 0.230
10.692 10.257 9.300 6.373 6.527
9 66 39 58 6
3:11 × 10−22 2:88 × 10−22 3:83 × 10−22 2:42 × 10−22 1:91 × 10−22
1.40 1.35 1.15 1.40 0.99
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R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
Fig. 2. Collisional time scale for depth and super8cial regimes for l = 10. The irradiation time scale of 109 yr and the time scale required to form a black upper layer (6 × 108 yr) are indicated. (a) Depth regime for rmin = 500 m; (b) for rmin = 1 km. The super8cial regime does not appear in any case.
Fig. 1. Collisional time scale for depth and super8cial regimes for l = 2. The irradiation time scale of 109 yr and the time scale required to form a black upper layer (6 × 108 yr) are indicated. (a) Depth and super8cial regimes for rmin = 7 m; (b) for rmin = 10 m; (c) for rmin = 50 m the super8cial regime disappear.
for rmin = 50 m the resurfacing time grows again (Fig. 1c), the super8cial regime does not exist any more, and any object with R ¿ 80 km has a good chance to appear as very dark, forming a thick mantle only on KBOs larger than R ≈ 250 km. This example shows clearly that changing the value of rmin also changes the behavior of the resurfacing process,
allowing to obtain di2erent results. For example in Fig. 2a, for l = 10 (Luu and Jewitt, 1996b) and rmin = 500 m, only a depth regime appears. If rmin is changed to 1 km (Fig. 2b) a result similar to that shown in Fig. 1c is obtained. The examples in Figs. 1 and 2 show that the collisional time scale changes if the projectile population is truncated at certain minimum radius. If this truncation radius is di2erent for di2erent regions of the Kuiper belt, the collisional time scale varies allowing di2erent surface colors for KBOs of the same size. Is it possible that this size truncation of the population occur? The regions of the Kuiper belt where this phenomenon might occur are those a2ected by strong mean motion resonances with Neptune. The process is similar to that proposed by Gil-Hutton and Brunini (2000) to explain the depletion of the Hildas size distribution: the small fragments created after a collision reach relative velocities suf8cient as to escape from the resonance and a truncation of the population occurs. In this scenario, the color of the KBOs is controlled by the irradiation produced by the total Kux of particles with E 6 5 MeV, and this Kux depends on the time scale of
R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
the fastest collisional process on the object. Since the Kux needed to produce very red material (≈ 1016 protons cm−2 ) is reached on a time scale of 6 × 107 yr, the reddest objects will be those with a similar collisional time scale, becoming more neutral as the collisional time scale approaches 6 × 108 yr. This is the case for Figs. 1a, b, and 2a, where a large spread in color could appear. Also, since a thick mantle is not formed for these short collisional time scales, large amounts of fresh ices could cover the surface of these objects. This could be the case for the Classical KBOs which are orbiting in a region where strong mean motion resonances do not exist and a truncation of the size distribution is diRcult. On the other hand, for collisional time scales larger than 6 × 108 yr the objects become more and more neutral as the area covered with black material grows (Figs. 1c and 2b), allowing a narrow range in color, but in this case the thick mantle is almost formed and could be dif8cult to 8nd fresh ices on top of them. This could be the case for the Plutinos, which are in 2 : 3 mean motion resonance with Neptune and their population could be truncated. It could be also the case for the Scattered Disk objects, which have extremely low collision probabilities due to their highly inclined orbits, and with very long collisional time scales also when truncation of the size distribution does not occur. Photometry and spectroscopy of Kuiper belt objects agree very well with this scenario. The Plutinos appear to have colors concentrated around (V − R) ≈ 0:5 ± 0:1, while the Classical objects are scattered in a larger range (Gil-Hutton and Licandro, 2001). On the other hand, the Classical object 1996 TO66 appears to be neutral in color and its spectrum shows strong absorptions that are characteristic of water ice (Brown et al., 1999), and 1996 TL66 , which is a member of the Scattered Disk population, also appears neutral in color but the spectra shows no evidence for absorption features (Luu and Jewitt, 1998). Finally, it is possible to 8nd a trend in the albedo. Since cosmic-ray irradiation changes the optical properties of the upper layer of material and collisions is the only way to modify the result of the irradiation, objects with longer collisional time scales will have darker surfaces and low albedos. 5. Conclusions A new evaluation of the collisional resurfacing model proposed by Luu and Jewit (1996a; b) to explain the color diversity of Kuiper belt objects has been presented. This updated version includes a more precise treatment of the e2ect of the cosmic-ray environment and new estimates of the Kuiper belt population. On this basis it is possible to conclude that: 1. The color diversity in the Kuiper belt could be explained as the competition between the color change produced by the cosmic-ray bombardment and the resurfacing due to impacts.
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2. The results of the irradiation due to di2erent types of cosmic-rays altered in a di2erent way the material present in the KBO. The solar protons a2ect only the upper layers modifying very fast the color of the material. The galactic cosmic-rays penetrate more depth and a2ect a thick layer of many meters, making necessary more energetic collisions to give fresh ices to the surface. 3. As a consequence of the previous point, two di2erent collisional regimes appear. The super8cial regime prevails over the depth regime if the projectile population is not truncated in the small end and the collisions of this tiny objects resurface the KBO with very short time scales. On the other hand, if the population is truncated the super8cial regime could disappear and the collisional process is controlled by depth impacts. 4. A thick mantle could survive in the largest KBOs because the resurfacing time scale in the depth regime for these objects is longer than the time needed to form the mantle. 5. It is possible that KBOs in di2erent regions of the belt are a2ected by projectile populations truncated at a different radius. Then, their colors and albedos could vary in function of their di2erent collisional history. Acknowledgements The author is very grateful to C. L=opez and J. Licandro for their useful comments on the manuscript. References Andronico, G., Baratta, G.A., Spinella, F., Strazzulla, G., 1987. Optical evolution of laboratory-produced organics: applications to Phoebe, Iapetus, outer belt asteroids and cometary nuclei. Astron. Astrophys. 184, 333–336. Barucci, M.A., Doressoundiram, A., Tholen, D., Fulchignoni, M., Lazzarin, M., 1999. Spectrophotometric observations of Edgeworth– Kuiper belt objects. Icarus 142, 476–481. Barucci, M.A., Romon, J., Doressoundiram, A., Tholen, D.J., 2000. Compositional surface diversity in the Trans-Neptunian objects. Astron. J. 120, 496. Bottke, W.F., Greenberg, R., 1993. Asteroidal collision probabilities. Geophys. Res. Lett. 20, 879–881. Bottke, W.F., Nolan, M.C., Greenberg, R., Kolvoord, R.A., 1994. Velocity distributions among colliding Asteroids. Icarus 107, 255–268. Brown, R.H., Cruikshank, D.P., Pendleton, Y., Weeder, G.J., 1997. Surface composition of Kuiper belt object 1993 SC. Science 276, 937–939. Brown, R.H., Cruikshank, D.P., Pendleton, Y., 1999. Water ice on Kuiper belt object 1996 TO66 . Astrophys. J. 519, L101–L104. Buie, M.W., Bus, S.J., 1992. Physical observations of (5145) Pholus. Icarus 100, 288–294. Chiang, E.I., Brown, M.E., 1999. Keck pencil-beam survey for faint Kuiper belt objects. Astron. J. 118, 1411–1422. Duncan, M., Quinn, T., Tremaine, S., 1988. Astrophys. J. 328, L69. Edgeworth, K.E., 1943. The evolution of our planetary system. J. Br. Astron. Assoc. 53, 181–188. Fern=andez, J.A., 1980. MNRAS 192, 481. Fink, U., Ho2mann, M., Grundy, W., Hicks, M., Sears, W., 1992. The steep red spectrum of 1992 AD: an asteroid covered with organic material? Icarus 97, 145–149.
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Color diversity among Kuiper belt objects: The collisional resurfacing model revisited R. Gil-Hutton ∗ Felix Aguilar Observatory, Av. Benavidez 8175 Oeste, 5407 Marquesado, San Juan, Argentina Received 22 November 2000; received in revised form 18 April 2001; accepted 25 June 2001
Abstract A re-evaluation of the collisional resurfacing model based on up-to-date Kuiper belt objects size distribution and a more precise treatment of the cosmic-ray environment at the outer Solar System is presented. The result of the irradiation due to cosmic-rays with di2erent energies altered in a di2erent way the material of the objects, producing, under certain conditions, a thick irradiation mantle. Since the collisional resurfacing model is based in the competition between darkening by cosmic-rays and resurfacing due to impacts, the color of objects in di2erent regions of the belt could vary if the projectile populations in those regions are truncated at a di2erent radius. c 2002 Published by Elsevier Science Ltd.
1. Introduction The existence of a belt of remnant planetesimals beyond the orbit of Neptune was 8rst suggested by Edgeworth (1943) and Kuiper (1951). The so called Kuiper belt has been proposed as the source of the short-period comets (Fern=andez, 1980; Duncan et al., 1988) and the interplanetary dust (Stern, 1996). More than 200 Kuiper belt Objects (KBOs) have been found since the discovery of 1992 QB1 , the 8rst member of this class (Jewitt and Luu, 1992). It is estimated (Jewitt, 2000) that at least 100; 000 KBOs with diameters larger than 100 km move in nearly circular orbits at heliocentric distances between r ≈ 30 and 50 AU. They comprise three dynamical classes: objects in the 3 : 2 mean motion resonance with Neptune have been described as “Plutinos” (Luu and Jewitt, 1996a); those beyond about 41 AU known as “Classical Kuiper Belt Objects”; and those with a much larger semi-major axis and higher eccentricity than the previous two classes are named “Scattered Disk Objects” (Luu et al., 1997). The studies of the physical characteristics of the KBOs are based on photometry and spectroscopy in the visible and near-infrared regions, but there are very few observational studies available due to the faintness of the objects. However, the largest Centaurs, which presumably originated in the Kuiper belt, have low albedos and similar sizes, but very di2erent spectra. Chiron has neutral colors similar to C-type ∗
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c 2002 Published by Elsevier Science Ltd. 0032-0633/02/$ - see front matter PII: S 0 0 3 2 - 0 6 3 3 ( 0 1 ) 0 0 0 7 3 - 3
asteroids and some cometary nuclei (Hartmann et al., 1990). On the other hand, Pholus was found to have an astonishing spectrum (Fink et al., 1992) which make it one of the reddest objects in the solar system (Buie and Bus, 1992). Also, the spectra published for three KBOs (Luu and Jewitt, 1996a, b; Brown et al., 1997; Luu and Jewitt, 1998; Brown et al., 1999) are completely di2erent, implying di2erent surface composition. Many authors (Luu and Jewitt, 1996b; Green et al., 1997; Tegler and Romanishin, 1997; Jewitt et al., 1998) found a wide range of color values amongst the KBOs population and they argue for signi8cant compositional diversity. However, Tegler and Romanishin (1998) found that the Centaur and KBO population is split in two distinct groups with neutral and very red colors, respectively, but Barucci et al. (1999, 2000) do not con8rm this bimodality. The 8rst attempt to explain the observed color diversity was made by Luu and Jewitt (1996a, b). These authors proposed that the whole-disk surface colors of KBOs could be the result of the competition between the e2ects of irradiation of surface organics by cosmic-rays and the global resurfacing due to impacts. However, this 8rst model can not explain the color diversity for all current estimates of the projectile size distribution exponent (q ¿ 3; Jewitt et al., 1998; Gladman et al., 1998; Chiang and Brown, 1999) due to the high frequency of the resurfacing impacts. In this paper a re-evaluation of the collisional resurfacing model based on up-to-date KBOs size distribution and cosmic-ray environment at the Kuiper belt is presented. In the following sections the irradiation and collisional
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R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
processes at the Kuiper belt are described. In Section 4 the e2ects of the competition between them are presented, and Section 5 is devoted to the conclusions. 2. Irradiation process Kuiper belt objects are believed to possess interiors rich in abundant molecular ices (such as H2 O; NH3 ; CH4 ), commensurate with their formation in the outer regions of the solar nebula at temperatures of 40 –50 K. Laboratory experiments show that long-term irradiation of astrophysical ice mixtures results in the selective loss of hydrogen and the formation of an “irradiation mantle” of carbon residues (Moore et al., 1983; Johnson et al., 1984; Strazzulla and Johnson, 1991), and also show that as the radiation dose increases, an initially neutral-colored and high-albedo ice becomes red as the violet albedo decreases. Further irradiation gradually reduces the albedo at all wavelengths and, 8nally, the material becomes very dark, neutral in color, and spectrally featureless (Andronico et al., 1987; Thompson et al., 1987). Since the KBOs are under the e2ects of the ultraviolet solar radiation, the solar wind, and the Kux of galactic cosmic-rays, it is reasonable to expect that an irradiation mantle could be formed on their surfaces. Solar ultraviolet radiation at the heliocentric disL the Kux is ≈ tances of KBOs is weak (for 6 1500 A, −3 −2 −1 10 erg cm s ), but due to the long time scale about 3:2 × 1013 erg cm−2 could be deposited in 109 yr. Titan tholin is produced initially in this way from a mixture of gases, but the chemical processing is similar to that in ices (Khare et al., 1993). More interesting is the e2ect of solar cosmic-rays which could be very important for long irradiation time scales. For a solar wind proton (1 keV) the Kux is 2 × 104 protons cm−2 s−1 at 40 AU, while for a solar Kare proton (100 keV) the Kux is 6 × 107 protons cm−2 s−1 at 40 AU (Lanzerotti et al., 1978), but these are low energy ions and only a2ects the upper few millimeters of the surfaces. If higher energies are taken into account, the proton Kux at the maximum of the solar activity (¿ 20 MeV) is ≈ 0:2 protons cm−2 s−1 at 40 AU (McDonald et al., 1974), and the time required to polimerize, for example, 50% of CH4 is about 108 yr at ≈ 0:5 cm, 109 yr at ≈ 2:2 cm and 4:6 × 109 yr at ≈ 5 cm (Strazzulla et al., 1984). The irradiation processes described produce very red material at a Kux of ≈ 1016 protons cm−2 which becomes darker for larger Kuxes. When the Kux reaches a value of ≈ 1017 protons cm−2 a very black upper layer with a neutral color appears (Andronico et al., 1987). The time scale required to form this black layer in a KBO for 5 MeV protons and a Kux of 5:70 protons cm−2 s−1 is ≈ 6 × 108 yr. At higher energies, two successive ionization events are so distant or the speci8c energy loss is so low that cross-linking events are not important and the polymerization process does not occur in the upper layer of the body (Strazzulla, 1986).
In the case of galactic cosmic-rays, the Kux has been roughly constant throughout the age of the solar system (Meyer et al., 1974) having its maximum in the energy range 10 MeV–10 GeV. The proton Kux before entering the solar cavity is JH (E) = 0:3E −1
0:2 ¡ E ¡ 1 GeV;
JH (E) = 0:3E −2
E ¿ 1 GeV;
(1) (2)
−2
−1 −1
−1
where J is given in protons cm sr s GeV (Leger et al., 1985). When these high-energy protons collide with an icy target, they penetrate very depth under the surface. Their range into an object with density ≈ 1 g cm−3 is log depth(m) = 1:28 log E(MeV) − 2:48
E ¿ 1 MeV; (3)
which is a 8t of Fig. 3 in Strazzulla (1986). For example, a proton with E ≈ 3 GeV penetrates down to a depth of ≈ 100 m. The fraction of polymerized material is R = 1 − exp(− );
(4) −2
where is the total Kuence of incoming ions (in cm ) and = 1 − 2 × 10−17 cm−2 is the cross section of the process for 5 MeV protons (Foti et al., 1984). With the Kuxes given by Eqs. (1) and (2) and after 4:5 × 109 yr, 50% of the target material is seriously altered down to 100 m. Since the Kuiper belt is inside the solar wind termination shock (which appears at ≈ 80 AU, Ziemkiewicz, 1994), the results given by Eq. (1) or (2) is larger than the expected Kux at 40 AU from the Sun. Nevertheless, the galactic cosmic-ray pressure falls from 0:33 eV cm−3 outside the shock to 0:17 eV cm−3 at 1 AU (Ziemkiewicz, 1994), so it is reasonable to assume that the true Kux at 40 AU is one half the value obtained with those equations, and 50% of the material is altered down to a depth of ≈ 10 m after 5 × 108 yr, ≈ 20 m after 109 yr, and ≈ 55 m after a time similar to the solar system age. Thus, the irradiation mantle of a KBO could be thick and less red going deep under the surface, with a dark and neutrally colored upper layer (if there is no collisional process present), formed after ≈ 109 and 6 × 108 yr, respectively. In this scenario, two di2erent collisional regimes are de8ned: a depth regime, where energetic collisions are necessary to reach the fresh ice under the mantle, and a super5cial regime, more frequent than the other, which only excavates the red material of the mantle. 3. Collisional process To investigate the e2ects of the collisional process on the irradiation mantle of a KBO it is assumed that the population size distribution follows a power-law of the form dN (¿ r) = Br −p dr, where N (¿ r) is the number of objects with radius between r and r + dr, B is a constant and p = 3:6 (Chiang and Brown, 1999). Also it is considered that the estimated population of objects with r ¿ 50 km is ≈ 100; 000 (Jewitt, 2000). Thus, the collision rate between
R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
a target with radius R and a projectile with radius r is dCr = Pi (R + r)2 dN (¿ r);
4. Resurfacing process (5)
where Pi is the intrinsic collision probability for the target. Theoretical and experimental investigations show that most of the mass displaced by a low velocity impact leaves the crater at speeds much less that the escape velocity, even for an energetic collision with a hard target (Housen et al., 1983). So, it is expected that the bulk of the ejecta resulting from low velocity impacts onto KBOs should fall to the surface, creating a layer of debris around each impact crater. Thus, the total area covered with the ejecta blanket each year is given by dSr = Pi (R + r)2 Ac dN (¿ r);
(6)
where Ac = l2 d2 =4 is the area covered with the ejecta in each collision, d is the crater diameter and l is the ratio between the radii of the ejecta area and the crater. Holsapple (1993) gives an expression for the diameter of an idealized crater as 1=3 −=3 AR 3:22rg d = 2:52r ; (7) r v2 where R and r are the target and projectile densities, respectively, g is the surface gravity of the target, v the collision velocity, and A and are constants dependent upon the mechanical properties of the target material. Holsapple (1993) uses values of A and of 0:2 and 0:65, respectively, for water ice. The shape of this idealized crater it is assumed to be √ a paraboloid of revolution with a depth=radius ratio of 1=2 2. Then, the percentage of target surface covered with the ejecta each year is r1 Sr 2 0:866 −0:434 = 56:56P l Bv ( R) r 1:566−p dr; Sr% = i R 4R2 r0 (8) −1 . The integration and the collisional time scale is Tr = Sr% limits r1 and r0 are di2erent for the two collisional regimes de8ned in the previous section. For the depth regime, r1 is equal to the radius of the largest projectile which does not shatter the target, and is given by
rmax = R(5 v2 − 1)−1=3 ;
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The competition between cosmic-ray reddening and collisions produces a continuous modi8cation of the instantaneous color of the surface. Since both processes have typical time scales, it is possible to decide which one is most e2ective for certain range of sizes. For all the KBOs, targets and projectiles, a density of 1 g cm−3 is assumed. Mean values for the impact velocity and intrinsic collision probability were obtained using the numerical approach developed by Bottke et al. (1994), which is an algorithm based on the formulation of impact probabilities by Greenberg, 1982 (1982; see also Bottke and Greenberg, 1993). The orbital elements of 299 KBOs were considered as representative of the whole population. As test particles, ideal objects at 37; 40; 42; 45 and 50 AU were used. For these test particles the orbital elements were obtained calculating the mean values for all the objects inside an annulus centered at those semi-major axis and Sa = ± 1 AU. The results are shown in Table 1, where are listed the orbital elements of the test particles, the number of objects inside the respective annulus, the mean intrinsic collision probability and the mean collision velocity. Since the values obtained for Pi and v are similar for the 8ve regions, an average is used (Pi = 2:83 × 10−22 km−2 yr −1 and v = 1:25 km s−1 ). Since it is not possible to 8nd analytically the area covered by the ejecta blanket because it approaches in8nity when the fragment radius approaches zero, two extreme values which appear in the literature are used in the following examples. In Fig. 1 the resurfacing time for depth and super8cial regimes are shown for l = 2 (Weissman and Stern, 1994). An irradiation time scale of 109 yr was chosen and, since the mantle is ≈ 20 m wide, it is assumed that rmed = 50 m. The time needed to form the dark upper layer (6 × 108 yr) is also indicated. For rmin 6 7 m (Fig. 1a) the thick mantle does not form because the time needed to bring fresh ice to the surface is less than the irradiation time scale. On the other hand, the time needed to resurface the upper layer is always shorter than 6 × 108 yr, so the black material over the surface of the KBO does not appear and the objects are, at most, red. If objects with r ¡ 10 m, do not exist in the population, the resurfacing time grows as shown in Fig. 1b. Since rmed ¡ 10 m for KBOs with R 6 200 km the resurfacing time for both regimes are the same. Finally,
(9)
where = 1×10−8 g erg−1 is a crater excavation coeRcient and the equation is valid for R = r (Petit and Farinella, 1993). If a projectile with r ¿ rmax collide with the KBO, the process is not valid because the target is shattered. For the depth regime, the value for r0 is obtained inverting Eq. (7) to 8nd the radius of the projectile (rmed ) which makes a crater on the target with a depth enough to allow that some fresh ice is excavated. For the super8cial regime, r1 = rmed and r0 is 8xed to the radius of the smallest particle in the population, rmin .
Table 1 Mean intrinsic collision probability and mean collision velocity for Kuiper belt objects at di2erent semi-major axis a (AU)
e
i (o)
N
Pi (km−2 yr −1 )
v (km s−1 )
37.408 39.883 42.112 44.905 50.330
0.121 0.156 0.064 0.090 0.230
10.692 10.257 9.300 6.373 6.527
9 66 39 58 6
3:11 × 10−22 2:88 × 10−22 3:83 × 10−22 2:42 × 10−22 1:91 × 10−22
1.40 1.35 1.15 1.40 0.99
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R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
Fig. 2. Collisional time scale for depth and super8cial regimes for l = 10. The irradiation time scale of 109 yr and the time scale required to form a black upper layer (6 × 108 yr) are indicated. (a) Depth regime for rmin = 500 m; (b) for rmin = 1 km. The super8cial regime does not appear in any case.
Fig. 1. Collisional time scale for depth and super8cial regimes for l = 2. The irradiation time scale of 109 yr and the time scale required to form a black upper layer (6 × 108 yr) are indicated. (a) Depth and super8cial regimes for rmin = 7 m; (b) for rmin = 10 m; (c) for rmin = 50 m the super8cial regime disappear.
for rmin = 50 m the resurfacing time grows again (Fig. 1c), the super8cial regime does not exist any more, and any object with R ¿ 80 km has a good chance to appear as very dark, forming a thick mantle only on KBOs larger than R ≈ 250 km. This example shows clearly that changing the value of rmin also changes the behavior of the resurfacing process,
allowing to obtain di2erent results. For example in Fig. 2a, for l = 10 (Luu and Jewitt, 1996b) and rmin = 500 m, only a depth regime appears. If rmin is changed to 1 km (Fig. 2b) a result similar to that shown in Fig. 1c is obtained. The examples in Figs. 1 and 2 show that the collisional time scale changes if the projectile population is truncated at certain minimum radius. If this truncation radius is di2erent for di2erent regions of the Kuiper belt, the collisional time scale varies allowing di2erent surface colors for KBOs of the same size. Is it possible that this size truncation of the population occur? The regions of the Kuiper belt where this phenomenon might occur are those a2ected by strong mean motion resonances with Neptune. The process is similar to that proposed by Gil-Hutton and Brunini (2000) to explain the depletion of the Hildas size distribution: the small fragments created after a collision reach relative velocities suf8cient as to escape from the resonance and a truncation of the population occurs. In this scenario, the color of the KBOs is controlled by the irradiation produced by the total Kux of particles with E 6 5 MeV, and this Kux depends on the time scale of
R. Gil-Hutton / Planetary and Space Science 50 (2002) 57–62
the fastest collisional process on the object. Since the Kux needed to produce very red material (≈ 1016 protons cm−2 ) is reached on a time scale of 6 × 107 yr, the reddest objects will be those with a similar collisional time scale, becoming more neutral as the collisional time scale approaches 6 × 108 yr. This is the case for Figs. 1a, b, and 2a, where a large spread in color could appear. Also, since a thick mantle is not formed for these short collisional time scales, large amounts of fresh ices could cover the surface of these objects. This could be the case for the Classical KBOs which are orbiting in a region where strong mean motion resonances do not exist and a truncation of the size distribution is diRcult. On the other hand, for collisional time scales larger than 6 × 108 yr the objects become more and more neutral as the area covered with black material grows (Figs. 1c and 2b), allowing a narrow range in color, but in this case the thick mantle is almost formed and could be dif8cult to 8nd fresh ices on top of them. This could be the case for the Plutinos, which are in 2 : 3 mean motion resonance with Neptune and their population could be truncated. It could be also the case for the Scattered Disk objects, which have extremely low collision probabilities due to their highly inclined orbits, and with very long collisional time scales also when truncation of the size distribution does not occur. Photometry and spectroscopy of Kuiper belt objects agree very well with this scenario. The Plutinos appear to have colors concentrated around (V − R) ≈ 0:5 ± 0:1, while the Classical objects are scattered in a larger range (Gil-Hutton and Licandro, 2001). On the other hand, the Classical object 1996 TO66 appears to be neutral in color and its spectrum shows strong absorptions that are characteristic of water ice (Brown et al., 1999), and 1996 TL66 , which is a member of the Scattered Disk population, also appears neutral in color but the spectra shows no evidence for absorption features (Luu and Jewitt, 1998). Finally, it is possible to 8nd a trend in the albedo. Since cosmic-ray irradiation changes the optical properties of the upper layer of material and collisions is the only way to modify the result of the irradiation, objects with longer collisional time scales will have darker surfaces and low albedos. 5. Conclusions A new evaluation of the collisional resurfacing model proposed by Luu and Jewit (1996a; b) to explain the color diversity of Kuiper belt objects has been presented. This updated version includes a more precise treatment of the e2ect of the cosmic-ray environment and new estimates of the Kuiper belt population. On this basis it is possible to conclude that: 1. The color diversity in the Kuiper belt could be explained as the competition between the color change produced by the cosmic-ray bombardment and the resurfacing due to impacts.
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2. The results of the irradiation due to di2erent types of cosmic-rays altered in a di2erent way the material present in the KBO. The solar protons a2ect only the upper layers modifying very fast the color of the material. The galactic cosmic-rays penetrate more depth and a2ect a thick layer of many meters, making necessary more energetic collisions to give fresh ices to the surface. 3. As a consequence of the previous point, two di2erent collisional regimes appear. The super8cial regime prevails over the depth regime if the projectile population is not truncated in the small end and the collisions of this tiny objects resurface the KBO with very short time scales. On the other hand, if the population is truncated the super8cial regime could disappear and the collisional process is controlled by depth impacts. 4. A thick mantle could survive in the largest KBOs because the resurfacing time scale in the depth regime for these objects is longer than the time needed to form the mantle. 5. It is possible that KBOs in di2erent regions of the belt are a2ected by projectile populations truncated at a different radius. Then, their colors and albedos could vary in function of their di2erent collisional history. Acknowledgements The author is very grateful to C. L=opez and J. Licandro for their useful comments on the manuscript. References Andronico, G., Baratta, G.A., Spinella, F., Strazzulla, G., 1987. Optical evolution of laboratory-produced organics: applications to Phoebe, Iapetus, outer belt asteroids and cometary nuclei. Astron. Astrophys. 184, 333–336. Barucci, M.A., Doressoundiram, A., Tholen, D., Fulchignoni, M., Lazzarin, M., 1999. Spectrophotometric observations of Edgeworth– Kuiper belt objects. Icarus 142, 476–481. Barucci, M.A., Romon, J., Doressoundiram, A., Tholen, D.J., 2000. Compositional surface diversity in the Trans-Neptunian objects. Astron. J. 120, 496. Bottke, W.F., Greenberg, R., 1993. Asteroidal collision probabilities. Geophys. Res. Lett. 20, 879–881. Bottke, W.F., Nolan, M.C., Greenberg, R., Kolvoord, R.A., 1994. Velocity distributions among colliding Asteroids. Icarus 107, 255–268. Brown, R.H., Cruikshank, D.P., Pendleton, Y., Weeder, G.J., 1997. Surface composition of Kuiper belt object 1993 SC. Science 276, 937–939. Brown, R.H., Cruikshank, D.P., Pendleton, Y., 1999. Water ice on Kuiper belt object 1996 TO66 . Astrophys. J. 519, L101–L104. Buie, M.W., Bus, S.J., 1992. Physical observations of (5145) Pholus. Icarus 100, 288–294. Chiang, E.I., Brown, M.E., 1999. Keck pencil-beam survey for faint Kuiper belt objects. Astron. J. 118, 1411–1422. Duncan, M., Quinn, T., Tremaine, S., 1988. Astrophys. J. 328, L69. Edgeworth, K.E., 1943. The evolution of our planetary system. J. Br. Astron. Assoc. 53, 181–188. Fern=andez, J.A., 1980. MNRAS 192, 481. Fink, U., Ho2mann, M., Grundy, W., Hicks, M., Sears, W., 1992. The steep red spectrum of 1992 AD: an asteroid covered with organic material? Icarus 97, 145–149.
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