Efficient disruption of small asteroids by Earth's

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Efficient disruption of small asteroids by Earth’s atmosphere P. A. Bland* & N. A. Artemieva† * Department of Earth Science and Engineering, Exhibition Road, Imperial College London, South Kensington Campus, London SW7 2AZ, UK † Institute for Dynamics of Geospheres, Russian Academy of Sciences, Leninsky Prospect 38/6, Moscow, 117939 Russia .............................................................................................................................................................................

Accurate modelling of the interaction between the atmosphere and an incoming bolide is a complex task, but crucial to determining the fraction of small asteroids that actually hit the Earth’s surface. Most semi-analytical approaches have simplified the problem by considering the impactor as a strengthless liquidlike object (‘pancake’ models1,2), but recently a more realistic model has been developed that calculates motion, aerodynamic loading and ablation for each separate particle or fragment in a disrupted impactor3,4. Here we report the results of a large number of simulations in which we use both models to develop a statistical picture of atmosphere–bolide interaction for iron and stony objects with initial diameters up to ,1 km. We show that the separated-fragments model predicts the total atmospheric disruption of much larger stony bodies than previously thought. In addition, our data set of >1,000 simulated impacts, combined with the known pre-atmospheric flux of asteroids with diameters less than 1 km5–12, elucidates the flux of small bolides at the Earth’s surface. We estimate that bodies >220 m in diameter will impact every 170,000 years. We performed 16 simulations for stony impactors (‘stones’) using the separated fragments (SF) model, and 16 for iron impactors (‘irons’), for bodies from 1 to 108 kg, repeating each simulation for a given mass .20 times to derive average impact conditions (in total, .1,000 SF model simulations were performed). ‘Pancake’ model simulations were performed over the range 1–1012 kg. When the model outputs are compared (Fig. 1), we find that ‘pancake’ and SF model estimates of total surviving material at the surface coincide tolerably well for irons, but the same is not true for stones. A ‘pancake’ model with spreading to twice the initial radius is typically chosen, which significantly overestimates impactor survivability for stones over the whole mass range (Fig. 1). SF and ‘pancake’ results only converge when we consider spreading to four times the initial radius (much larger than typically used) and only for initial masses .107 kg. The ‘pancake’ model is not capable of providing a mass- or velocity-distribution for fragmented impactors, and therefore is not relevant to modelling production of terrestrial crater fields where the size of the largest crater is related to the largest surviving fragment. At larger masses (.107 kg) this becomes less important, possibly as larger stones behave as a liquidlike ‘swarm’ of fragments. The SF simulations allow us to define the various styles of meteoroid fragmentation exhibited by differing impactor types and masses. Meteoroids that are disrupted and dispersed in the atmosphere give rise to strewn fields at the surface. For lower-mass objects, the strewn field exists as meteorite fragments, and then (with increasing mass) meteorites plus impact pits; small, well separated craters with diameters ranging from metres to tens of metres; craters whose rims overlap; and finally, single craters produced by a swarm of poorly separated fragments. The masses that define the transition from one type of disrupted meteoroid impact to another are indicated in Fig. 1. SF modelling also quantifies the very different survivability of iron and stony impactors. Over the mass range 103–107 kg, iron impactors transfer to the surface about three orders of magnitude more energy per unit area than stones: a fragmented iron impactor 288

Figure 1 Results of SF and ‘pancake’ model simulations for stone and iron impactors. The SF model is described in detail elsewhere3,4. The model takes into account successive fragmentation and ablation of individual fragments, and simulates the evolution of a meteoroid consisting of a variable number of solid fragments. Early attempts were made at modelling separated fragments23,24, but most subsequent numerical approximations have taken the form of the more common ‘pancake’ model1,2. While ‘pancake’ models treat the disrupted meteoroid as a deformable continuous liquid, the SF approximation allows us to define a mass- or velocity-distribution at the surface for fragments that create craters (high final velocity) or occur as meteorites (fragments with low final velocity). The production of crater fields by small fragmented asteroids may therefore be simulated. Two types of projectile are principally considered: irons with density of 7,800 kg m23, ablation coefficient of 0.07 s2 km22 and strength of 4.4 £ 108 dyn cm22 (for 1-kg samples)3, and stones with density of 3,400 kg m23, ablation coefficient of 0.014 s2 km22, and 10 £ lower strength. The parameters for stones were chosen to define approximate upper limits on strength and density: larger stony bodies in the atmosphere, and carbonaceous bolides, may well have significantly lower strength and density. All simulations were at average asteroidal impact velocities and entry angles: 18 km s21 and 458, respectively. The figure portrays the ratio of final mass (both the combined mass of all surviving fragments .100 g, and the largest single surviving fragment) to initial mass for stone (a) and iron (b) impactors. The ‘pancake’ model results are also shown: ‘pancake model 1’ is based on spreading to twice initial radius; ‘pancake model 2’, spreading to four times initial radius. NATURE | VOL 424 | 17 JULY 2003 | www.nature.com/nature

letters to nature of 105 kg produces a similar crater field to a fragmented 108 kg stone. Even larger stony bodies of ,108–1010 kg are much less efficient at transferring energy to the surface than the equivalent iron impactor (Fig. 1). SF model simulations constrain the mass-, velocity- and size-distribution of those fragments, allowing us to derive morphologies of simulated crater fields. The SF results are in good agreement with terrestrial crater records, and also with available meteorite data. In meteorite falls, the proportion of stones decreases steadily at higher masses. Stony meteorites account for 96.6% of falls of ,10 kg, falling to 87.1% at 50–100 kg, and 72.7% at 300– 1,000 kg (extrapolating, falls .4 £ 104 kg will be ,5% stones). Small terrestrial craters are also typically associated with iron impactors. Seventeen craters with diameters ,1.5 km (impactors ,2 £ 108 kg) are associated with a given impactor type, and only

one is a stone13. In contrast, 18 craters .10 km have an inferred impactor type and 16 are stones13. This suggests that in the range ,4 £ 104 to 2 £ 108 kg, ,5% of terrestrial impactors are stones. Our data set of simulations provides us with a template for understanding the atmosphere–bolide interaction for a range of pre-entry masses and impactor types. With a knowledge of the overall flux and the ratio of irons to stones (I/S) at the upper atmosphere, we can use these data to calculate the mass flux (both combined mass of all fragments .100 g, and the largest surviving fragment) at the Earth’s surface. The I/S ratio for the upper atmosphere can be inferred from nearEarth object (NEO) and main-belt asteroid spectroscopy, meteorite composition, and impactor types in large terrestrial craters. Assuming that iron asteroids are within the X-class, spectroscopy places

Figure 2 Estimates of impact rate for both the top of the atmosphere and the Earth’s surface. Impactor flux is expressed in terms of number of events N greater than mass m per year at Earth (pre-entry mass for the upper-atmosphere data, final mass for surface flux estimates). Crater data are scaled to projectile diameter25,26, and the Hartmann and Neukum production functions (HPF and NPF) derived from the lunar mare crater record18,27 scaled to fit the upper-atmosphere data5–12,17. Earlier impact rate estimates are shown for reference20–22. Some combine surface and atmosphere flux estimates21, while others define separate estimates20. We scale SF model results for 10–103 kg bodies based on the NPF for the upper atmosphere, taking into account the decreasing proportion of stone meteorite falls of 1–103 kg. We also derive an estimate by extrapolating from fireball data for small meteorites on the ground5 to larger bodies based on the observed depletion in stone meteorite falls. The SF data and this curve are

coincident. Over the mass range 4 £ 104–1 £ 108 kg, SF model data constrain the fraction of the impactor that reaches the surface with high energy. A surface flux is estimated by scaling the upper-atmosphere flux given the ratio of irons to stones (I/S ) at the upper atmosphere and the calculated final mass derived from SF simulations. Modelling separated fragments becomes unwieldy for objects .108 kg. However, SF and ‘pancake’ model ( £ 4 spreading) estimates of final mass for initial bodies .107 kg converge (Fig. 1): our data indicate these objects occur as a closely separated liquid-like ‘swarm’ of fragments at the surface. We therefore scale the NPF for the upper atmosphere to a surface flux using ‘pancake’ model results for objects .108 kg, and a varying I/S ratio based on the depletion in craters formed by stony impactors over the crater diameter interval 1.5–20 km.

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letters to nature upper limits on the abundance of irons among main-belt asteroids14 (,8%) and NEOs15 (,10%). If we only consider M-class asteroids (a sub-type within the X-class), the proportions are ,5% of mainbelt asteroids16 and ,2% of NEOs15. However, it should be noted that a number of M-class asteroids show absorption features in their infrared spectra which indicate that they are not metallic, so the real number of iron asteroids may be lower. For meteorites ,10 kg, ,3% are irons, and of the craters .10 km in diameter where the impactor type is known, ,10% were formed by irons. Taking these data together, to a first approximation, we estimate 5% irons (within a factor of two) at the upper atmosphere. Over recent years, the impactor flux for the upper atmosphere has been well constrained over specific portions of the mass distribution using various techniques5–12,17. Ivanov18 showed that the NEO and main-belt asteroid mass distribution9–12, and upper-atmosphere meteoroid data6, matches the cumulative size–frequency distribution of lunar mare craters (the Neukum or Hartmann production functions—NPF or HPF). NPF and HPF curves are used in crater counting studies to date surfaces of all ages throughout the inner Solar System. Since the overall shape of the curve is likely to apply to the current impactor population at 1 AU, we fit the upper-atmosphere data with a scaled NPF and HPF (converted to projectile diameter). Over a mass range of 1–1016 kg the fit is a good one—camera network data5, recent US Department of Defense satellite data7, large NEO data9–11 and the data set of large terrestrial craters17 all fall within a factor of three of this curve (some earlier satellite data6,8 and modelled small NEO data12 lie off this curve). We now scale the NPF projectile curve for the upper-atmosphere flux to an impact rate at the Earth’s surface using data from our simulations (Fig. 2). Previous estimates for the flux at the surface and the top of the atmosphere, and the scaled NPF and HPF curves for the upper atmosphere, are shown for comparison. As noted, the terrestrial crater record is incomplete over the mass range of interest. However, if we select recent (,0.05 Myr ago) small (,1 km) impacts in Australia, an area where arid conditions limit erosion and obscuring vegetation is at a minimum, we observe a close match to our modelled flux estimate for bodies of ,105 kg (Fig. 2). For objects ,105 kg the Australia data depart from our modelled curve, but even minimal erosion would remove craters ,100 m in diameter. For bodies of 109–1012 kg, our modelled curve is essentially identical to the terrestrial crater data19. The implication is that severe atmospheric disruption of stony impactors is the cause of the departure from a primary NEO-derived flux for 1.5–20-km craters on Earth. Our simulations predict atmospheric fragmentation for much larger objects than previously thought. For stony asteroids with diameters up to several hundred metres, this means that the bulk of the energy is deposited in the atmosphere, rather than at the surface, but although similarly sized irons produce single craters, fragmentation is still an issue. The largest body we have attempted to model with the SF numerical approximation is an iron impactor with a pre-entry mass of 1010 kg. Even for a comparatively large highstrength object such as this, we find that aerodynamic loading is sufficient to disrupt the impactor (although the fragments will hit together in a confined area, and form a single complex crater of similar diameter to that which would result from the impact of a coherent projectile). In terms of defining impact rates, it is useful to separate Tunguska-like events (typically, stony objects that penetrate to the lower atmosphere before massive disruption occurs), and cratering events. Although only the latter will have a lasting surface expression, both have significance for defining the hazard to human populations. Stony bodies of .108 kg can penetrate low enough in the atmosphere before disruption to affect the surface, so the NPF/HPF fit to the upper-atmosphere data for bodies larger than 108 kg defines the approximate rate at which Tunguska-like events will occur. The 290

significance of the curvature in the NPF/HPF, and its effect on impact rate estimates at Earth, does not appear to have been recognized in some earlier studies20. Over much of the mass distribution, the NPF/HPF fit to the recent upper-atmosphere data suggest a lower flux than previous estimates20–22 (Fig. 2). For the flux at the Earth’s surface, our data suggest that impactors with largest fragment 3–5 m, capable of forming ,100-m craters, will strike the Earth every 200–400 years (.95% will be irons), larger 50-m-diameter impactors occur every 9.7 £ 104 years (,90% irons), and 220-m impactors occur every 1.7 £ 105 years (,50% irons). As we chose conservatively high values for stony bolide strength and density, and as it is entirely possible that the proportion of irons at the top of the atmosphere is ,5%, our modelled flux curve probably represents an upper limit on surface impact rate for the stated flux at the upper atmosphere. In terms of the impact hazard, these data have specific relevance for quantifying the threat posed by impact-generated tsunami. It has been shown that the peak contributors to potentially hazardous tsunami (those .5 m in height) are impactors of ,220-m diameter20. The same study derived an estimate for the frequency of impacts of 220-m bolides of 1 every 3,000–4,000 years (ref. 20). Our data suggest an impact rate ,50 £ lower. Although airburst events for stony bolides of ,200-m diameter may occur somewhat more frequently than surface impacts (,1 every 50,000–60,000 years), the rate is still low, and such events are unlikely to couple their energy efficiently enough into the ocean surface to generate large tsunami. The implication is that the hazard posed by impact-generated tsunami is lower than previously thought. This analysis is significant in redefining the asteroid impact hazard, and proposals to extend the survey of NEOs down to much smaller objects may need to have their search strategies reviewed in light of it. A Received 30 January; accepted 21 May 2003; doi:10.1038/nature01757. 1. Chyba, C. F., Thomas, P. J. & Zahnle, K. J. The 1908 Tunguska explosion: Atmospheric disruption of a stony asteroid. Nature 361, 40–44 (1993). 2. Hills, J. G. & Goda, M. P. The fragmentation of small asteroids in the atmosphere. Astron. J. 105, 1114–1144 (1993). 3. Artemieva, N. A. & Shuvalov, V. V. Motion of a fragmented meteoroid through the planetary atmosphere. J. Geophys. Res. 106, 3297–3310 (2001). 4. Shuvalov, V. V., Artemieva, N. A. & Trubetskaya, I. A. Simulating the motion of a disrupted meteoroid with allowance for evaporation. Sol. Syst. Res. 34, 49–60 (2000). 5. Halliday, I., Griffin, A. A. & Blackwell, A. T. Detailed data for 259 fireballs from the Canadian camera network and inferences concerning the influx of large meteoroids. Meteorit. Planet. Sci. 31, 185–217 (1996). 6. Nemtchinov, I. V. et al. Assessment of kinetic energy of meteoroids detected by satellite-based light sensors. Icarus 130, 259–274 (1997). 7. Brown, P., Spalding, R. E., ReVelle, D. O., Tagliaferri, E. & Worden, S. P. The flux of small near-Earth objects colliding with the Earth. Nature 420, 294–296 (2002). 8. ReVelle, D. O. Historical detection of atmospheric impacts by large bolides using acoustic-gravity waves. Ann. NY Acad. Sci. USA 822, 284–302 (1997). 9. Morbidelli, A., Jedicke, R., Bottke, W. F., Michel, P. & Tedesco, E. F. From magnitudes to diameters: The albedo distribution of near-Earth objects and the Earth collision hazard. Icarus 158, 329–343 (2002). 10. Rabinowitz, D., Helin, E., Lawrence, K. & Pravdo, S. A reduced estimate of the number of kilometresized near-Earth asteroids. Nature 403, 165–166 (2000). 11. Stuart, J. S. A near-Earth asteroid population estimate from the LINEAR survey. Science 294, 1691–1693 (2001). 12. Harris, A. W. in Proc. Asteroids, Comets, Meteors 2002 (European Space Agency, Berlin, in press). 13. Earth Impact Database khttp://www.unb.ca/passc/impactdatabase/l (accessed 20 November 2002). 14. Bus, S. J. & Binzel, R. P. Phase II of the small main-belt asteroid spectroscopic survey: A feature-based taxonomy. Icarus 158, 146–177 (2002). 15. Binzel, R. P., Lupishko, D. F., Di Martino, M., Whiteley, R. J. & Hahn, G. J. in Asteroids III (eds Bottke, W. F., Cellino, A., Paolicchi, P. & Binzel, R. P.) 255–271 (Univ. Arizona Press, Tucson, 2003). 16. Tholen, D. J. in Asteroids II (eds Binzel, R. P., Gehrels, T. & Matthews, M. S.) 1139–1150 (Univ. Arizona Press, Tucson, 1989). 17. Grieve, R. A. F. & Shoemaker, E. M. in Hazards due to Comets and Asteroids (ed. Gehrels, T.) 417–462 (Univ. Arizona Press, Tucson, 1994). 18. Ivanov, B. A., Neukum, G., Bottke, W. F. & Hartmann, W. K. in Asteroids III (eds Bottke, W. F., Cellino, A., Paolicchi, P. & Binzel, R. P.) 89–101 (Univ. Arizona Press, Tucson, 2003). 19. Hughes, D. W. A new approach to the calculation of the cratering rate of the Earth over the last 125 ^ 20 Myr. Mon. Not. R. Astron. Soc. 317, 429–437 (2000). 20. Ward, S. N. & Asphaug, E. Asteroid impact tsunami: A probabilistic hazard assessment. Icarus 145, 64–78 (2000). 21. Chapman, C. R. & Morrison, D. Impacts on the Earth by asteroids and comets: Assessing the hazard. Nature 367, 33–39 (1994). 22. Morrison, D., Chapman, C. R. & Slovic, P. in Hazards due to Comets and Asteroids (ed. Gehrels, T.) 59–91 (Univ. Arizona Press, Tucson, 1994).

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letters to nature 23. Passey, Q. R. & Melosh, H. J. Effects of atmospheric breakup on crater field formation. Icarus 42, 211–233 (1980). 24. Melosh, H. J. Impact Cratering: A Geological Process (Oxford Univ. Press, Oxford, 1989). 25. Schmidt, R. M. & Housen, K. R. Some recent advances in the scaling of impact and explosion cratering. Int. J. Impact Eng. 5, 543–560 (1987). 26. Ivanov, B. A., et al. in Chronology and Evolution of Mars (ed. Kallenbach, R.) 87–104 (Kluwer, Dordrecht, 2001). 27. Hartmann, W. K. Martian cratering VI: Crater count isochrons and evidence for recent volcanism from Mars Global Surveyor. Meteorit. Planet. Sci. 34, 167–177 (1999). 28. Bland, P. A. et al. The flux of meteorites to the Earth over the last 50,000 years. Mon. Not. R. Astron. Soc. 283, 551–565 (1996).

Acknowledgements We thank B. Ivanov, W. Hartmann and P. Brown for providing cratering data, flux data, and for discussions, and B. Ivanov, H. J. Melosh, V. Shuvalov, J. Morgan, B. Pierazzo and M. Gounelle for suggestions that improved earlier drafts of this manuscript. This work benefited greatly from comments and suggestions from C. Chapman. N.A. thanks RFBR for support, and P.A.B. thanks the Royal Society for support. Competing interests statement The authors declare that they have no competing financial interests. Correspondence and requests for materials should be addressed to P.A.B. ([email protected]).

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Nanometre-scale displacement sensing using a single electron transistor Robert G. Knobel*† & Andrew N. Cleland* * Department of Physics and iQUEST, University of California, Santa Barbara, California 93106, USA .............................................................................................................................................................................

It has been a long-standing goal to detect the effects of quantum mechanics on a macroscopic mechanical oscillator1–3. Position measurements of an oscillator are ultimately limited by quantum mechanics, where ‘zero-point motion’ fluctuations in the quantum ground state combine with the uncertainty relation to yield a lower limit on the measured average displacement. Development of a position transducer, integrated with a mechanical resonator, that can approach this limit could have important applications in the detection of very weak forces, for example in magnetic resonance force microsopy4 and a variety of other precision experiments5–7. One implementation that might allow near quantum-limited sensitivity is to use a single electron transistor (SET) as a displacement sensor8–11: the exquisite charge sensitivity of the SET at cryogenic temperatures is exploited to measure motion by capacitively coupling it to the mechanical resonator. Here we present the experimental realization of such a device, yielding an unequalled displacement sensitivity of 2 3 10215 m Hz21/2 for a 116-MHz mechanical oscillator at a temperature of 30 mK—a sensitivity roughly a factor of 100 larger than the quantum limit for this oscillator. A classical simple harmonic oscillator, in equilibrium with its environment at temperature T, will have an average total energy k BT. The position of the oscillator fluctuates continuously, with a root mean square displacement amplitude dx ¼ ðkB T=mq20 Þ1=2 for an oscillator of mass m and resonant frequency f 0 ¼ q 0/2p. This classical displacement amplitude can be made arbitrarily small by reducing the temperature. One implication of quantum mechanics, however, is that the quantized nature of the oscillator energy yields an intrinsic fluctuation amplitude, the ‘zero-point motion’ dxzp ¼ ðh=2mq0 Þ1=2 . This is achieved for temperatures T well below the energy quantum, T ,, T Q ; h q0 =kB : A second implication † Present address: Department of Physics, Queen’s University, Kingston, Ontario K7L 3N6, Canada.

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of quantum mechanics is that the instrument used to measure the position of the oscillator will necessarily perturb it, further limiting the possible measurement resolution, as quantified by the Heisenberg uncertainty principle. A continuous measurement of the average position of an oscillator, using a quantum-limited pffiffi amplifier, is thus limited to 2 times the zero-point motion, or dxmeas * ðh=mq0 Þ1=2 : We note that ‘back-action evading’ techniques have in principle unlimited measurement precision, although these yield less information and are still subject to zero-point fluctuations if the measurement is slower than the oscillator relaxation time1,12. A 1-GHz nanomechanical flexural resonator was recently demonstrated13. This resonator would have T Q ¼ 50 mK, so when operated on a dilution refrigerator at 10 mK, the inequality T ,, T Q could be reached. A resonator with similar dimensions would be a candidate for detecting the transition from classical to quantum noise, because the small mass gives a relatively large zero-point displacement noise, dxzp < 2 £ 10214 m: In terms of the spectral displacement noise density, this corresponds to S1=2 x ¼ 5 £ 10218 m Hz21=2 on resonance, fairly small due to the relatively low quality factor Q < 500. Techniques to measure the displacement of large-scale resonators, such as optical interferometry or electrical parametric transducers1,14,15, can achieve better displacement noise limits than this, but the larger mass of the resonator makes reaching the quantum limit more difficult. Such techniques do not scale well to nanomechanical resonators, and other techniques more applicable to these size scales16,17 are unlikely to approach quantum-limited sensitivity. The single electron transistor provides a possible system in which sufficient sensitivity can be achieved. The single-electron transistor (SET) consists of a conducting island separated from leads by low-capacitance, high-resistance tunnel junctions. The current through the SET is modulated by the charge induced on its gate electrode, with a period e, the charge of one electron. The SET is the most sensitive electrometer18,19, with a demonstrated sensitivity below 1025 e Hz21/2. The motion of a nanomechanical resonator may be detected by capacitively coupling the gate of the SET to a metal electrode placed on the resonator, and biasing the electrode at a constant voltage V beam (see Fig. 1). The capacitance C between the SET and the beam then has a coupled charge q ¼ V beamC. As the beam vibrates in the x direction, in the

Figure 1 The device used in the experiment. a, Scanning electron micrograph of the device, showing the doubly clamped GaAs beam, and the aluminum electrodes (coloured) forming the single electron transistor and beam electrode. Scale bar, 1 mm. The Al/AlOx /Al tunnel junctions have approximately 50 £ 50 nm2 overlap. b, A schematic of the mechanical and electrical operation of the device. 291