The flux of Tunguska-sized fragments from the main asteroid belt

Planet. Space Sci., Vol. 46, NO. 213, pp. 303-309, 1998

Pergamon

0 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0032-0633/98 $19.00+0.00

PII: SOO32-0633(97)00062-7

The flux of Tunguska-sized fragments from the main asteroid belt Paolo Farinella’ and Mario Menichella2 ‘Gruppo di Meccanica Spaziale, Dipartimento di Matematica, Universit& di Pisa, Via Buonarroti 2Dipartimento di Fisica, Universitk di Pisa, Piazza Torricelli 2, 56126 Pisa, Italy Received

22 October

1996; revised 28 February

1997; accepted

1. Introduction

Although the asteroidal vs. cometary nature of the body responsible for the Tunguska catastrophe is still debated,

Correspondence to : P. Farinella

4 March

2, 56127 Pisa, Italy

1997

in the last decade it has become clear that it was a member of a vast and probably heterogeneous population of nearEarth objects in the size range from 10 to 100m. These bodies are among the least-known members of the inner Solar System, since they are too large to fall frequently onto our planet, but too small to be easily detected and studied by telescopic observations. Therefore, their nature must be inferred from sparse direct observational data, and from several indirect arguments and inferences. Possible sources for the Tunguska-like population include : asteroids, both main-belt ones and members of the near-Earth Aten-Apollo-Amor groups ; comets, coming from either the flattened Edgeworth-Kuiper belt or the isotropic Oort cloud ; the Moon and Mars, which are known to deliver meteorites to the Earth. An important, possibly dominant contribution from the main asteroid belt is suggested by the predominantly asteroidal source inferred for both the larger, km-sized near-Earth objects (Binzel et al., 1992; Menichella et al., 1996) and the smaller, l-10m sized meteoroids detected as fireballs (Ceplecha, 1988; Jopek et al., 1995) and/or collected as meteorites (Greenberg and Nolan, 1989 ; Farinella et al., 1994a). On the other hand, direct data coming from the Spacewatch Survey have indicated that the Tunguska-sized population may be overabundant with respect to a powerlaw extrapolation from larger sizes and abnormally rich in very red objects, and also that it may include a component with a peculiar, Earth-like distribution of orbits (Rabinowitz et al., 1993; Rabinowitz, 1993, 1994, 1996). Given the limited data available and the strong selection effects, these conclusions must be regarded as preliminary-but if they are confirmed by future observations and are shown to imply a different distribution of sources with respect to that inferred for km-sized near-Earth objects, there will be important consequences for the impact hazard issue, and also for our understanding of meteorites. Recent work by Rabinowitz (1997) and Rabinowitz and Wetherill (1997) suggests that, provided the main-belt size distribution has wave-like oscillations superimposed on a power law, as suggested by Campo Bagatin et al. (1994a), the main belt is sufficient to supply

304

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the observed abundance of Earth approachers throughout the observed size range, with the possible exception of the 5510% fraction of the 5-50m diameter bodies, characterized by low orbital eccentricities and semimajor axes close to 1 AU. Bottke et al. (1996) and Bottke (1996) have argued that the latter subpopulation may come from fragments of Amor asteroids, or from splitting of larger NEAs during close planetary encounters. However, more work appears to be needed on this issue, in particular because numerical integrations (Nolan and Bottke, 1996 ; Michel, 1996, personal communication) indicate that a low-eccentricity near-Earth population would be mixed with the general one by secular resonances and Earth encounters within a few Myr, implying that such a population, if real, should be fairly young and replenished by a local source. In this paper we will not deal with the complex issues related to the dynamical and collisional evolution of the near-Earth population, but will take a step backward, and will try just to quantify the flux of Tunguska-sized fragments due to impacts in the main asteroid belt, into the resonant “escape hatches” leading to Earth-crossing orbits. For this purpose, we will use a numerical model previously applied to larger objects (Menichella et al., 1996). We will show that, to an order of magnitude, the main-belt fragment source is sufficient to maintain the observed abundance of small Earth approachers. Moreover, we will show that stochastic large-scale collisions in the main asteroid belt can give rise to significant enhancements of the Tunguska-like impact flux on the Earth. We note that in this work we disregard the possibility that a significant number of small asteroid fragments are not injected directly into the resonances by collisioninduced velocity changes, but stay for some time “parked” in non-resonant orbits until a slow orbital drift due to the non-gravitational Yarkovsky mechanism causes them to fall into the resonant regions. Recent work on this mechanism (Rubincam, 1995 ; Hartmann et al., 1997 ; Farinella et al., 1997) shows that it is probably important for metersized meteoroids, whereas for bodies 100m in diameter its efficiency is critically dependent on the existence of regolith layers on their surfaces. We plan to explore this issue further in the future.

2. Collisional

model and input parameters

To investigate the flux of Tunguska-sized asteroid fragments into chaotic resonant orbits pumping up their orbital eccentricities to Earth-crossing values, we have used the numerical model described in detail in Menichella et al. (1996). This model was based on previous work aimed at studying the evolution in time of a population of colliding bodies, such as the asteroids, taking into account both cratering impacts and catastrophic disruption events (Davis et al., 1989; Campo Bagatin et al., 1994a, 1994b). The overall evolving population is divided into a number of discrete size bins, which at every time step interact owing to mutual collisions ; taking into account both the collision rates and velocities typical of the main asteroid belt (Farinella and Davis, 1992 ; Bottke et al., 1994a) and the outcomes of such collisions as inferred from lab-

fragments from the main asteroid belt

oratory experiments and scaling theories (Davis et al., 1989; Petit and Farinella, 1993), the number of objects residing in all the size bins can be updated at the end of each time step. Then the procedure is repeated until an assumed initial population has evolved into the current one. Here we are interested in a specific output of the collisional evolution code, namely the number of fragments created at every time step by collisions in the whole main belt. For this purpose, we followed Menichella et al. (1996) in assuming a main-belt size distribution derived from that of known asteroids, extrapolated down to sizes z 1 m and modified in such a way to yield a quasi-stationary fragment production rate over the last z 100 Myr. Then, to estimate how many of the fragments created by collisions do fall into the resonant “escape hatches” (basically, the 3 :l mean motion Jovian resonance and the vg secular resonance in the inner asteroid belt) as a consequence of their ejection speeds from the parent asteroids, we used the results of Farinella et aZ. (1993), who estimated a “delivery efficiency” of about 2’S, i.e. that on average about 2% of the fragments created in the belt fall into the resonances. As remarked by Menichella et al. (1996), to estimate in a reliable way the fluctuations about this average yield caused by sporadic large-scale collisions close to the resonant zones of the orbital element space, the collisional code had to be partially modified, so as to take into account that collisional events involving a small fraction of the existing asteroids can supply a disproportionate fraction of “resonant fragments”. In this study, we have monitored the delivery of fragments somewhat smaller than those considered by Menichella et al. (1996), i.e. those belonging to the diameter bin ranging from 44 to 70m, in agreement with the estimated size of the Tunguska impactor. Also, we tried to explore the sensitivity of our results to some poorly known collisional response parameters, as follows. As a nominal case, we used an impact strength S, for asteroidal material at laboratory sizes (E 1Ocm) of 3 x 1O7erg cm-3, scaled up to asteroidal sizes by the strainrate scaling law of Housen and Holsapple (1990) and Housen et al. (1991)-see also Davis et al. (1994). We recall that the impact strength is defined as the projectile energy per unit of target volume required to produce catastrophic breakup of the target, with a largest fragment having half the initial mass. The S, parameter was varied by plus or minus a factor of 10, corresponding to the existing uncertainty on the composition and physical structure of asteroids. Also, as an alternative to the strainrate scaling law, we tested the simpler energy scaling relationship, which according to Davis et al. (1994) also yields a good match to the observed asteroid size distribution. Finally, we varied by plus or minus a factor of 2 (about the nominal value 0.1) the energy partitioning coefficient fKE, which gives the fraction of projectile’s kinetic energy transformed into kinetic energy of fragments. The range from 0.05 to 0.2 for fKE is consistent with the available evidence from the properties of asteroid families (Davis et al., 1989). For all the other collisional response parameters (which play a lesser role in the collisional evolution process) we made the same choices as in the “standard case” of Camp0 Bagatin et al. (1994a, 1994b).

P. Farinella and M. Menichella: Tunguska-sized

fragments from the main asteroid belt

305

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2.5e+06

2e+O6

1.5~06

1

\

0 4500

I

4520

4540

4560

4560

4600

4i20

Fig. 1. Asteroid fragment flux (in Myr-‘) to the resonances escape hatches in the main belt over a time span of 120 Myr centered at the present time. The time step is 1 Myr, and the parameter choice is the %ominal” one described in the-text

3. Results Our results are shown in Figs 1-6, which represent the number of fragments delivered to resonances per Myr as a function of time (starting at 4.5 and until 4.62 Byr after the origin of the solar system, at steps of 1 Myr). Figure 1 represents our nominal parameter choice, whereas in Figs 26 we have varied the collisional parameters, as discussed in Section 2. The results of our simulations show that the main asteroid belt on average can inject into the resonant escape hatches about one Tunguska-sized fragment per year. Varying the collisional parameters, the average flux ranges between 0.5 and 4yr-‘. Higher values are obtained for parameter choices which lead to larger fragment ejection velocities (namely, for higher values off& or S,, implying

that more impact energy is partitioned into the kinetic energy of fragments or that a larger specific energy is needed to shatter asteroids, respectively). Moreover, the figures show that large-scale stochastic collisions in the main belt can enhance this fragment flux by a factor up to 6 over intervals z 1 Myr, assuming that this corresponds to the typical dynamical timescale in the resonances. Such enhanced-flux episodes are expected to occur every several tens of Myr.

4. Discussion

and conclusions

What are the implications for the current population

of the results reported above of small Earth approachers?

1

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01 4500

, 4520

4540

4560

4560

4600

4620

Fig. 2. The same as Fig. 1, but for the value of S,,, which here is assumed to be 3 x lo6 erg cmM3

306

P. Farinella

and M. Menichella:

Tunguska-sized

fragments

from the main asteroid

belt

4.5e+06

3.5e+06

I 3~~06

I 4500

4520

4540

4560

4560

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ii20

Fig. 3. The same as Fig. 1, but for the value of S,,, which here is assumed to be 3 x 10’ erg cmd3

Of course, given the flux from the main-belt source, the corresponding steady-state population would depend on the sink mechanisms and their time scales. Recent dynamical work, mainly based on long-term numerical integrations, has shown that the residence time inside both the 3 : 1 and the vg resonance is only of the order of 1 Myrafter which, most objects fall into the Sun or are ejected by Jupiter on a comet-type orbit (Farinella et aZ., 1994b ; Froeschle et al., 1995; Valsecchi et al., 1995; Morbidelli and Moons, 1995; Gladman et al., 1995, 1996; Migliorini et al., 1997). However, there is also a tail of long-lived objects which exit the resonances owing to a “lucky” planetary encounter, and typically survive up to a few tens Myr before entering a resonance again or hitting a planet.

For this latter “slow-track” population, collisional disruption is also a significant sink mechanism, especially for small objects reaching the main belt near aphelion (Farinella and Davis, 1994; Bottke et al., 1994b). If we assume that 10% of the resonant fragments get diverted into a slow track with a typical lifetime of 10 Myr (vs. 1 Myr for the “fast track”), in our nominal case the steady-state population would be about 1.9 million objects, divided almost equally between the two dynamical types. Of course, this is a very rough estimate, because in reality there is a variety of dynamical patterns and a continuous distribution of lifetimes (see, e.g. Migliorini et al., 1997) ; the quantitative results about the “exit routes” from the resonances (due to terrestrial planet pertur-

3e+06

2SetO6

2e+06

1.5e+06

500000

i!jOC 1

I

4520

4540

4560

4560

Fig. 4. The same as Fig. 1, but for the value off,,, which here is assumed peak, at about t = 4570 Myr, reaches a value of 6.2 x lo6

4600

I 4620

to be 0.05. The highest

P. Farinella and M. Menichella: Tunguska-sized

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307

4.5e+O6

4e+06

3.5e+06

3ec06

IhvL

25e+06

Pe+06

!-

I

4500

4520

4540

4560

4560

4600

4620

Fig. 5. The same as Fig. 1, but for the value off&, which here is assumed to be 0.2. The highest peak, at about t = 4520 Myr, reaches a value of 9.6 x lo6

bations), their relative importance and the subsequent evolution of such “slow-track” orbits are still limited, since they have to be based on integrations over time spans > 10Myr. However, we believe that in order of magnitude the estimates reported above are correct, especially because they are in fair agreement with the existing population of such objects, as estimated from the current observational searches (Rabinowitz, 1993). The ratio between the flux of km-sized fragments in the resonances (370 per Myr) predicted by Menichella et al. (1996) and the corresponding Earth cratering rate (2-5 per Myr, see Grieve and Shoemaker (1994)) suggests that, overall, only z 1% of the incoming fragments are going to hit the Earth. This would imply about one Tunguska-

like impact per century, in good agreement with the ratio between our estimated population of 1.9 x lo6 objects and the average lifetime vs. Earth impact of the near-Earth population (235 Myr, according to Bottke et al. (1994b)). One Tunguska-like impact per century is about a factor of 3 higher than the estimate of Shoemaker et al. (1996) based on the terrestrial and lunar cratering record, but this discrepancy is well within the error bars of both our calculations and the observational estimate. Also, we note that the Tunguska object was probably closer to the upper than to the lower limit of the size bin chosen in our model (4470 m), thus somewhat decreasing the corresponding flux. These results suggest that the asteroidal source is sufficient to maintain the observed Tunguska-sized near-

3e+06

2.5e+06

2e+O6

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500000

0 4500

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4520

4540

4660

4560

4600

!O

Fig. 6. The same as Fig. 1, but for the assumed strength scaling law. Here we used the energy scaling

law, as described in Davis et al. (1994)

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and M. Menichella:

Earth population, although other, probably minor, contributions cannot be excluded. Our model also indicates that large-scale collisions occurring in the main belt close to the resonance zones, such as those which formed many asteroid families (Morbidelli et al., 1995), can cause strong spikes in the Earth cratering rate by Tunguska-sized fragments, with increases by almost one order of magnitude occurring every several tens of Myr. It is tempting to speculate that such episodes of increased impact flux might have had significant environmental consequences.

Acknowledgements. We are grateful for useful discussions and comments to W. F. Bottke, D. R. Davis, P. Michel and D. L. Rabinowitz. P.F. acknowledges partial support from the Italian Space Agency (ASI) and the Italian Ministry for University and Scientific Research (MURST), and is grateful to the University of Bologna for supporting his participation to the “Tunguska 96” workshop.

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from the main asteroid

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