Asteroid Showers on Earth after Family Breakup Events

ICARUS

134, 176–179 (1998) IS985946

ARTICLE NO.

NOTE Asteroid Showers on Earth after Family Breakup Events V. Zappala` and A. Cellino Astronomical Observatory of Torino, Pino Torinese (TO), Italy E-mail: [email protected]

B. J. Gladman Canadian Institue for Theoretical Astrophysics, Toronto, Canada

and S. Manley and F. Migliorini Armagh Observatory, Armagh, Northern Ireland, UK Received May 13, 1998

The fate of a fraction of the near-Earth asteroid (NEA) population is to collide with terrestrial planets. Collisional events in the main asteroid belt provide a source of NEAs. We provide the first quantitative evaluation of the numbers of impactors produced in different size ranges by some events which produced recognized asteroid families in the main belt. Following certain family-forming events large enhancements in the rate of Earth impacts likely occurred, in the form of ‘‘asteroid showers’’ lasting 2–30 Myr, capable of influencing the Earth’s biosphere. Such a shower could also be responsible of the hypothesized ‘‘lunar cataclysm’’ 4 Gyr ago. Because the number of NEAs is strongly affected by such events, the NEA population cannot always remain in a steady state.  1998

higher during the past 500 Myr compared to the past 3 Gyr (McEwen et al. 1997). With others, we have recently published a study of the fates of objects injected into orbital resonances in the asteroid belt. Such resonant objects experience rapid eccentricity increases, leading them to cross the orbits of the inner plannets (Gladman et al. 1997). In the present paper we show that the number of asteroids escaping the belt after some familyforming events rivals or exeeds that of the entire present NEA population.

Academic Press

Analysis. About 20 families are recognizable in the present asteroid belt (Zappala` et al. 1995). Several of them are sufficiently close to resonances (Gladman et al. 1997) to conclude that they could have been significant NEA sources at the time of the breakup events, estimated to have occurred hundreds of millions to billions of years ago (Farinella et al. 1996). We estimate both how many resonant fragments these families produced, and the sizes of these potential impactors. The analysis was restricted to an eight-family sample, selected because their apparent size distributions should be reliable over a wide diameter interval. For each family, we analyzed the size distribution and size–velocity relationship of its observed members to estimate the number of objects originally injected in resonant orbits for different size ranges (Table I), as described below. The numbers of fragments produced as a function of diameter D was extrapolated from the cumulative size distributions of the observed family members, which can be represented by power laws holding down to sizes corresponding to a completeness limit. This limit occurs because each family inventory is complete only above a size corresponding to an apparent magnitude sufficiently bright to ensure that all the larger members have been discovered. The cumulative size distributions are very steep down to the completeness limit for all the known families. According to recent analyses (Cellino and Zappala` 1998) these slopes should be constant down to at least D 5 5 km, by analogy with the Vesta and Flora families, which are complete to this diameter and exhibit no change in slope. Thus, an extrapolation of the presently observed size distributions down to D p1 km, not very far from the completeness limit, appears reasonable. Moreover, according to Marzari et al. (1995), the subsequent collisional evolution of the largest family members might have flattened

Introduction. The asteroid belt is presently believed to be the source of most of the meteoritic material hitting Earth and the other terrestrial planets. In particular, the near-Earth asteroids (NEAs), with an estimated population of p1500 with diameters D . 1 km (Rabinowitz et al. 1994), are believed to be asteroids that have escaped the main belt. Inter-asteroid collisions can produce fragments that reach resonant orbits, and recent numerical integrations (Farinella et al. 1994, Gladman et al. 1997) have shown that while the most common final fate of these objects is an impact with the Sun, a few percent impact a terrestrial planet. The past cratering rate on Earth can be estimated from the lunar and terrestrial cratering records (Neukum and Ivanov 1994, Grieve and Shoemaker 1994), and calculated currently for the known NEA population (Rabinowitz et al. 1994). Since these rates all agree within a factor of 2–3, a reasonable hypothesis is that the cratering rate has been constant and that the NEA population is in a steady state. Note that this excludes the first p500 Myr of the Solar System’s existence (the era of ‘‘heavy bombardment’’) and that there are claims that the cratering rate has been a factor of Q2 176 0019-1035/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved.

177

NOTE

TABLE I The Number of Injected Fragments from Eight Studied Family Breakup Events, and Resulting Number of Earth Impacts Family (resonance)

T10% (Myr)

T90% (Myr)

D (km) 1 0.3 1 0.3 2 1 0.3 2 1 0.3 2 1 0.3 2 1 0.3 2 1 0.3 5 2 1 0.3 2 1 0.3

Flora

(n6)

2

30

Vesta

(3 : 1)

1

10

Eunomia

(8 : 3)

5

15

Eunomia

(3 : 1)

1

10

Gefion

(5 : 2)

0.3

5

Dora

(5 : 2)

0.3

5

Koronis

(5 : 2)

0.3

5

Eos

(9 : 4)

110

140

Themis

(2 : 1)

10

90

N1 (impacts) 700 — 1700 — 900 25000 — 1500 85000 — 9000 180000 — 6300 100000 — 1200 10000 — 1000 17000 140000 — 3000 380000 —

(11) (1) (0) (4) (2) (135) (1) (30) (1) (14) (0) (2) (0) (1) (10) (1) (7)

N2 (impacts) 250 5000 10 190 250 2200 55000 350 7500 200000 2000 10000 260000 2300 16000 350000 600 3000 65000 1000 9000 32000 730000 16000 140000 2300000

(4) (76) (0) (0) (0) (0) (9) (1) (12) (318) (0) (2) (43) (0) (2) (50) (0) (0) (11) (0) (0) (2) (55) (0) (3) (43)

E (%) 1.5 0.20 0.015

0.20

0.02

0.02

0.02

0.007

0.0026

Note: The number of fragments larger than a diameter D reaching the nearby resonance is given for two extrapolations N1 and N2 (Fig. 1). The number of resulting Earth impacts is given in parentheses, using the impact efficiency E from that resonance. Only the N2 cautious extrapolation was continued down to 0.3 km. Of all the impacts that occur from the shower, only 10% occur before T10% , and 90% of the impacts have occurred by T90% .

the power law of the size distribution. This means that the slope at the epoch of formation might have been steeper; any estimate based on the current distribution would therefore underestimate the original number of fragments. At some unknown diameter the cumulative size distributions must become shallower, because extrapolating the observed trend usually leads to an infinite family mass. A plausible value for the power-law exponent at small sizes is 22.5, that expected for a collisionally evolved population (Dohnanyi 1971). One does not know at which size the slopes of the size distributions decrease, and so we have made two alternative extrapolations of the size distributions for D , 5 km (Fig. 1). The first estimate n1(D) extrapolates the cumulative size distribution keeping the same exponent (fitted above the completeness diameter) down to D 5 1 km. Even this extrapolation does not drastically influence the predicted diameter of the original parent body with respect to the value derived by summing up the masses of the family members larger than the completeness diameter. The second extrapolation n2(D) assumes a sudden decay to the equilibrium power-law exponent 22.5 at D 5 5 km; this pessimistic extrapolation was used down to D 5 300 m. Only asteroids ejected with sufficiently high speeds in the proper directions reach the resonances. Laboratory experiments indicate that the average ejection velocity V obeys V(r) Y r2k, where r is the fragment size and k is a constant estimated to be between 0.5 and 1.0 (Nakamura et al. 1992, Petit and Farinella 1993, Paolicchi et al. 1996). We chose the most conservative value k 5 0.5 and confirmed the reasonableness of

this estimate by analyzing histograms of the proper semimajor axes of family members in different size ranges. The families generally show a fairly symmetric profile and can be fitted by Gaussian curves. The standard deviation s of the best-fitting Gaussian increases for decreasing diameter, and the trend is in generally good agreement with a size–velocity relation corresponding to k 5 0.5 (slightly larger in some cases). Knowing the locations of the resonance borders (Morbidelli et al. 1995), the number of members originally injected into nearby resonances N1(. D) and N2(. D) (Table I) was determined after reconstructing the velocity field at the orbital anomaly where the breakup occurred (Morbidelli et al. 1995). The number N2(. D) is likely a lower limit because of the pessimistic slope, the conservative value of k, and the assumption that the observed size distribution has not already been flattened (Marzari et al. 1995). The next step is to determine the fraction of these injected bodies that struck Earth. The time scale for this delivery is almost independent of the location of injection into most resonances (Gladman et al. 1997). Recent integrations (Gladman et al. 1997) directly detect only a few impacts since most asteroids emerging from the belt are pushed into the Sun or outside Jupiter’s orbit. To improve the statistics, the numerical results were analyzed using an analytical algorithm to compute the planetary impact probabilities as a function of time. In particular, we used a new numerical approach (Manley et al. 1998) giving results in a very good agreement with more common algorithms (i.e., Wetherill 1967, Farinella and David 1992). When compared with simulations which directly recorded large numbers of impacts (Gladman et al. 1996), the

178

` ET AL. ZAPPALA

FIG. 1. The size distribution extrapolation for the Eunomia family. Except for the few largest objects (,10), the family is well fit above the 10-km completeness limit by a power-law cumulative size distribution of D24.12. Below 10 km the observationally incomplete distribution is extrapolated by keeping the fitted distribution down to 1 km (n1), or just until 5 km after which a D22.5 distribution is used (n2).

results agreed to within a very satisfactory relative error of 30%. The impacting fraction E depends on the resonance, and ranges from 0.15 for the n6 resonance to 4 3 1026 for the 7 : 3 resonance (Table I). This provides the number (parenthesized N1 or N2 of Table I) of injected fragments that struck our planet within p100 Myr after the formation event, for both extrapolations. The number of impacts onto Venus is the same (within a factor of 2) and Mars receives a factor of 3–10 fewer impacts. Our computations indicate the duration of these ‘‘asteroid showers,’’ by providing the times after which 10% (T10%) and before which 90% (T90%) of the impacts would have occurred, starting at the family breakup event. This is because it requires some initial time for the resonance to deliver the asteroids to Earth-crossing orbits, and there is always a longlived ‘‘tail’’ after most of the objects have been destroyed by Sun grazing (see Gladman et al. 1997). The Eos family shower through the 9 : 4 resonance lasts 30 Myr, but the first impacts onto Earth would have occurred 100 Myr after the birth of the family, due to the intrinsic slowness of the 9 : 4 resonance in pumping up asteroid eccentricities. In contrast, the 3 : 1 and 5 : 2 resonances quickly produce NEAs, but also destroy them efficiently (Gladman et al. 1997), resulting in a relatively brief shower. For the first time we have a quantitative indication about the numbers of energetic terrestrial impacts (Table I) that occurred after well-defined collisonal events in the asteroid belt (although we do not know how long ago the events occurred). Similar showers would also have occurred if ancient, thus no-longer visible, families broke up near the resonances. Discussion. For D . 1 km, there are currently Q1500 NEAs (Rabinowitz et al. 1994), and about 400/Myr are estimated to be continually supplied by background collisions in the main belt (Menichella et al. 1996). Because family-creation events inject 1–100 times this number (Table I) into a resonance (even using the pessimistic estimates), effectively all of which will eventually become NEAs (Gladman et al. 1997),

the NEA population cannot remain in a steady state. The roughly constant cratering rates concluded from the lunar and terrestrial crater records (Neukum and Ivanov 1994, Grieve and Shoemaker 1994) are based on a small number of craters or lunar surfaces, and in any case the asteroid showers need not leave an obvious signature. If the cratering rate increased by a factor of 100 for only several Myr (p0.1% of the age of older post-mare lunar surfaces) this contributes only 10% of the craters accumulated on the surface, an excess below the accuracy of crater counting studies. Thus these showers would effectively be invisible given the current lunar crater record. The terrestrial crater record predominantly records only the past 200 Myr, but has the advantage that many craters are dated (Grieve and Shoemaker 1994). While the existence of clusters and periodicities in this record (and that of mass extinctions of biological species) is hotly debated (Grieve and Shoemaker 1994, Rampino and Haggerty 1994), Earth’s crater record has no obvious signature of a massive increase of impactors lasting several Myr in the past 100 Myr. The coincidence of the Chesapeake Bay and Popigai impact events Q36 Myr ago is intriguing (Bottomley et al. 1997). Depending on how pessimistic we have been in our assumptions, asteroid showers could have had moderate to drastic effects on Earth’s biosphere. White also the subject of considerable debate, the postulated impactors necessary for the hypothesized ‘‘lunar cataclysm’’ (Dalrymple and Ryder 1993) could be provided by the creation of a large family near a resonance Q4 Gyr ago. An outstanding problem in the debate over this cataclysm is the lack of a mechanism to produce an increase in the projectile population Q0.5 Gyr after the formation of the Moon (Hartmann 1975, Taylor 1992). An asteroid shower provides such a process. However, because the basin-forming impactors were p100 km, this would have requuired the breakup of an asteroid larger than Ceres, whose family, after 4 Gyr of collisional evolution, may no longer be visible. While this scenario renders the cataclysm dynamically more plausible, further lunar studies will decide the issue.

REFERENCES Bottomley, R., R. Grieve, D. York, and V. Masaltis 1997. The age of the Popigai impact event and its relation to events at the Eocene/Oligocene boundary. Nature 388, 365–368. Cellino, A., and V. Zappala` 1998. Structure and inventory of the asteroid main belt population. In Asteroids, Comets, Meteors 1996 (A. C. Levasseur-Regourd and M. Fulchignoni, Eds.), in press. Dalrymple, G., and G. Ryder 1993. J. Geophys. Res. 98, 13085–. Dohnanyi, J. S. 1971. Fragmentation and distribution of asteroids. In Physical studies of minor planets (T. Gehrels, Ed.), pp. 263–295. NASA SP-267, Washington, DC. Farinella, P., and D. R. Davis 1992. Collision rates and impact velocities in the main asteroid belt. Icarus 97, 111–123. Farinella, P., Ch. Froeschle´, C. Froeschle´, R. Gonczi, G. Hahn, A. Morbidelli, and G. Valsecchi 1994. Asteroids falling into the Sun. Nature 371, 314–317. Farinella, P., D. R. Davis, and F. Marzari 1996. Asteroid families, old and young, In Completing the Inventory of the Solar System (T. W. Rettig and J. M. Hahn, Eds.), ASP Conf. Series, Vol. 107, pp. 45–56. San Francisco. Gladman, B. J., J. A. Burns, M. Duncan, P. Lee, and H. F. Levison 1996. The exchange of impact ejecta between terrestrial planets. Science 271, 1387–1392. Gladman, B. J., F. Migliorini, A. Morbidelli, V. Zappala`, P. Michel, A. Cellino, Ch. Froeschle´, H. F. Levison, M. Bayley, and M. Duncan 1997. Dynamical lifetimes of objects injected into asteroid belt resonances. Science 277, 197–201. Grieve, R. A. F., and E. M. Shoemaker 1994. The record of past impacts

NOTE on Earth. In Hazards Due to Comets and Asteroids (T. Gehrels, Ed.), pp. 417–462. Univ. Arizona Press, Tucson. Hartmann, W. K. 1975. Lunar ‘‘cataclysm’’: A misconception? Icarus 24, 181–187. Manely, S., Migliorini, F., and M. Bailey 1998. An algorithm for determining collision probabilities between small Solar System bodies. Submitted for publication. Marzari, F., D. R. Davis, and V. Vanzani 1995. Collisional evolution of asteroid families. Icarus 113, 168–187. McEwen, A. S., J. M. Moore, and E. M. Shoemaker 1997. The phanerozoic impact cratering rate: Evidence from the farside of the Moon. J. Geophys. Res. 102, 9231–9242. Menichella, M., P. Paolicchi, and P. Farinella 1996. The main belt as a source of near-Earth asteroids. Earth Moon Planets 72, 133–149. Morbidelli, A., V. Zappala`, M. Moons, A. Cellino, and R. Gonczi 1995. Asteroid families close to mean-motion resonances: dynamical effects and physical implications. Icarus 118, 132–154. Nakamura, A., K. Suguiyama, and A. Fujiwara 1992. Velocity and spin of fragments from impact disruptions. Icarus 100, 127–135. Neukum, G., and B. A. Ivanov 1994. Crater size distributions and impact probabilities on Earth from lunar, terrestrial-planet, and asteroid cra-

179

tering data. In Hazards Due to Comets and Asteroids (T. Gehrels, Ed.), pp. 359–416. Univ. Arizona Press, Tucson. Paolicchi, P., A. Verlicchi, and A. Cellino 1996. An improved semiempirical model of catastrophic iimpact processes. I. Theory and laboratory experiments. Icarus 121, 126–157. Petit, J. M., and P. Farinella 1993. Modelling the outcomes of highvelocity impacts between Solar System bodies. Celest. Mech. Dynam. Astron. 57, 1–28. Rabinowitz, D., E. Bowell, E. M. Shoemaker, and K. Muinonen 1994. The population of Earth-crossing asteroids. In Hazards Due to Comets and Asteroids (T. Gehrels, Ed.), pp. 285–312). Univ. Arizona Press, Tucson. Rampino, M. R., and B. M. Haggerty 1994, extraterrestrial impacts and mass extinctions of life. In Hazards Due to Comets and Asteroids (T. Gehrels, Ed.), pp. 827–858. Univ. Arizona Press, Tucson. Taylor, S. R. 1992. Solar System Evolution. Cambridge Univ. Press, New York. Wetherill, G. W. 1967. Collisions in the asteroid belt. J. Geophys. Res. 72, 2429–2444. Zappala`, V., P. Bendjoya, A. Cellino, P. Farinella, and C. Froeschle´ 1995. Asteroid families: Search of a 12,487 asteroid sample using two different clustering techniques. Icarus 116, 291–314.