The dates and locations of these events are listed in Table 1, and the parent bodies of the meteor streams through which the Earth was passing at these times are listed in Table 2, along with the encounter speeds. Statistics of three is not a secure basis for reaching far-reaching conclusions, but neither can they be safely dismissed as chance, and they do raise questions about the completeness of our knowledge of the terrestrial environment. If a significant body of hazardous sub-kilometre objects does indeed reside in meteor streams like the Perseids, then their discovery with present-day or near-future technology --say to 90% completion-- would take millennia rather than years; warning times would be measured in weeks rather than decades; and approach speeds would in the region of ∼ 60 kms^-1 rather than ∼ 20 kms^-1.

We may also ask whether the flux of sub-kilometre impactors deduced from meteoroid and near-Earth object (NEO) data accumulated over ∼ 20 yr is in a steady-state or is a snapshot of a fluctuating system: if we extrapolate this short dataset to estimate hazards say at the per annum level of say 10^--3- to 10^-5-, we are making an assumption about statistical completeness which needs to be justified; otherwise we may be in the position of a novice pilot who has only encountered good weather and assumes that it will always be thus. Comets, arriving erratically and unpredictably, are generally assumed to be a global impact hazard at the 1% level (Stokes et al., 2003). Yet the three impacts above all occurred when the Earth was passing through meteor streams. There is a case to be made that the cometary contribution is significantly higher than 1% at several energy levels (Asher et al. 2005), and that assessing the current impact hazard requires an understanding of the effect of the solar system's Galactic environment on the Oort comet cloud (Napier & Asher 2009).

The object of this paper is to review the role of comets as a celestial hazard, beginning with the putative celestial disturbance of 12,900 BP (Firestone 2009), proceeding through a long-standing problem of supply and balance in the intermediate-period comet population, and thence to the statistics of large impact craters. Evidence is given for the occurrence for geologically brief epochs of multiple bombardment, separated by relatively quiet intervals. These bombardment episodes can be related to periodic disturbances of the Oort cloud by Galactic tides and massive nebulae. We appear to be in such an episode now; the implications for current hazard assessments are briefly discussed.

2 A giant comet in the Upper Paleolithic

2.1 The Zodiacal Cloud

The zodiacal cloud is a disc of interplanetary dust and meteoroids stretching perhaps 0.05 AU from the Sun out to at least 18 AU and probably beyond. Sunlight scattered from this cloud can be seen as the zodiacal light after nautical twilight and before dawn, and the thermal emission in the dust has been detected by the IRAS infrared satellite. The dust in the cloud arrives from comets, the asteroid belt, and the Edgeworth-Kuiper belt beyond. Orbital information about the small particles is obtained primarily from visible and radio meteors, which have masses generally in the range 10^-4 gm to ∼ 1 gm.

The current mass of the zodiacal cloud may be estimated in several ways: from its infrared or visible light, from particle counts in space, and from radio and visible meteors -- shooting stars. All estimates agree that the mass of the zodiacal cloud is in the region of 3-10x10¹⁹ gm. The lifetime of meteor streams is generally less than 10,000 years, since planetary perturbations and radiative effects destroy coherence, the dust particles merging into the background cloud. Over somewhat longer timescales, up to 100,000 years, the dust is collisionally destroyed or falls into the sun. Without replenishment, the zodiacal cloud would rapidly disappear.

Information about the replenishing sources comes from the optical and infrared emission. Nesvorny et al. (2009) modelled the orbital evolution of dust particles originating from asteroid and comet populations, and fitted these to IRAS mid-infrared emission from the zodiacal cloud. They found that dust from Jupiter Family comets yields ∼ 90% of the optical cross-section, asteroidal dust comprising ∼ 10%. These comets have orbital periods P <20 years and their dynamical evolution is strongly controlled by Jupiter (Di Sisto et al., 2009). Likewise Hahn et al. (2002) used Clementine observations of the cloud at optical wavelengths to estimate that at least 90% of the zodiacal cloud cross-section within one AU of the Sun was of cometary origin. A steady state mass for the zodiacal cloud as a whole requires a mass influx of order 10²⁰ gm/10⁵ yr ∼ 10¹⁵ gm yr^-1. Hughes (1996) estimated the mass input from the decay of known short-period comets to be ∼ (8.4+0.8) x 10¹² gm yr^-1, about two powers of 10 less than required. To put it another way, the zodiacal cloud is overmassive by about two powers of 10 in relation to the known, current replenishing dust sources. He concluded, as have others, that "at some time in the last 10³ to 10⁵ yr, the cloud has benefited from a large and unusual mass enhancement."

2.2 Replenishing the Cloud

Radar and visible meteor studies indicate that, when the known annual meteor showers are subtracted out, the remaining "sporadic" meteor population is in fact highly structured, the bulk of the material appearing to come from a very few bodies (Fig. 1). The helion-antihelion structure has been detected also through strong asymmetries in the arrival of meteoroids on exposed orbiting surfaces (the Long Duration Exposure Facility: McBride et al., 1995), and extends to the visible sporadic meteors (Stohl, 1986) where indeed it was first detected. Without replenishment, the structures shown in Fig. 1 will be gone on a timescale ∼ 10⁴ yr.

Fig.1. Schematic view of the sporadic meteor distribution over the sky, with annual meteor showers taken out. The Earth's apex of motion around the Sun is at the centre. The sporadic meteor system is dominated by the helion/antihelion pair, which is seasonally variable and corresponds to meteors of high eccentricity, short period and low inclination impacting on Earth at ∼ 30 kms^-1. This stream of "sporadic" meteors encompasses Comet Encke and the Taurid meteor streams, and appears to derive from an erstwhile giant progenitor comet. The meteors of the North and South apex group are small and dynamically old, and probably associated with 55P/Tempel-Tuttle which gives rise to the Leonid meteor shower. The source of the north and south toroidal stream is uncertain.

2.3 The Taurid Meteoroid Complex

Embedded in the broad HE/AH stream, and aligned with it, is a complex of closely related meteor streams collectively described as the Taurids: at least 13 radiants in the constellations Aries and Taurus have been known since the early 20th century, and others have been found since. The Taurids are split into two main branches, with radiants north and south of the ecliptic. This complex is diffuse, stretching over 120^o of the ecliptic, and is probably ∼ 10⁴ yr old, although some substructures within it appear to be younger. Also part of this system is Comet Encke, in a low-inclination, direct orbit with high eccentricity (e = 0.86) and short orbital period (P=3.3 yr). Comet Encke itself is much too small to be a prime source of the Taurid meteor streams. Numerical integrations of this complex system reveal that the division into northern and southern branches would take tens of thousands of years, and possibly 100,000 years, to develop. The main part of the current meteoroid system appears to have developed five to 20,000 years ago.

These observations are again most easily understood if the Taurid complex is the remnant of an erstwhile large comet, thrown into a short period, Earth-crossing orbit and undergoing a hierarchy of fragmentations, a common mode of disintegration of comets. Comet Encke itself may simply be a recently activated small asteroid belonging to this system.

2.4 Co-Orbiting Asteroids

Fig. 2. We select the brightest NEOs (H < 16.5), and from them cull the 15 known asteroids with semi-major axis (1.85< a < 2.7) AU, eccentricity (0.65< e < 1.0) and inclination (0<i< 14^o). These are shown as squares. Their mean =174^o+12^o, which is 13^o from Comet Encke's longitude of perihelion ∼ 161^o, marked with an asterisk. The inner arc gives the spread of the recognized Taurid meteor showers (Stohl 1986). The bottom five asteroids appear to form a separate group, which includes the large near-Earth asteroid Hephaistos.

Fig. 3. Differential precession would yield randomly distributed around 360^o, the mean difference from Encke then being 90^o as shown by the histogram. This Monte Carlo simulation (50,000 trials) indicates that the observed clustering of the Taurid Complex asteroids (marked by an arrow) essentially never arises by chance. A recent fragmentation of a large comet is inferred to be the source of these orbital correlations, on a timescale approximately 10⁴ - 10⁵ yr.

Arising from the giant comet fragmentation model, Clube & Napier (1984) proposed that dormant comets of significant size should exist in the Taurid meteor stream. At the time only three near-Earth asteroids out of 50 known at that time had orbital elements similar to that of Comet Encke, but the NEA database has since expanded enormously and the existence of such bodies can be tested afresh. Similarity between orbits, implying a common origin, is tested by comparing . The inclination i typically fluctuates by +5^o while the longitude of perihelion circulates at a few degrees per millennium (e.g. 6^o per millennium for Comet Encke). Other angular elements characterising the orbit are less suitable as they change relatively rapidly. Because moves at different rates for different orbits, there is no reason to expect correlation. Thus a test for common origin is to select NEOs with similar (a, e, i) using a standard similarity criterion which excludes , and ask whether there is significant clustering of amongst those so selected. If there is no generic connection between the asteroids, then will be randomly distributed. If there was a recent fragmentation of the bodies from a common progenitor, a clustering of is expected.

The hypothesis under test is that of these NEOs are significantly aligned with Comet Encke; the null hypothesis is that of random distribution. The 15 brightest known NEOs (absolute magnitudes H <16.5) were chosen with semimajor axes from 1.85 to 2.7 AU, eccentricities from 0.65 to 1.0, and inclinations from zero to 14^o. The magnitudes of these bright near-Earth asteroids correspond to a minimum diameter of 1-3 km depending on albedo. Discovery is almost complete in this range and observational selection effects are therefore unlikely to be important. Fig. 2 shows that the longitudes of perihelion of these objects do cluster around that of Comet Encke at ∼ 161^o.

The statistical significance of this apparent clustering was tested by randomly distributing 15 longitudes of perihelion around the circle and measuring the arithmetic mean of the deviation from of Comet Encke. Fig. 3 reveals the outcome of 50,000 trials: there were no cases where such clustering arises by chance; thus the clustering is highly significant. Fig. 3 allows us to reject the null hypothesis that the longitudes of perihelion of these asteroids are randomly distributed around 360° in favour of the hypothesis that bright NEOs whose (a,e,i) are close to that of Comet Encke also tend to have close to that of the comet. The Taurid Complex does, therefore, contain a significant concentration of large near-Earth asteroids orbiting within it. Since these asteroids precess at different rates, any initial clustering will disappear within a few hundred thousand years. Unfortunately it is not possible to backtrack these orbits to find a common with any confidence, since nongravitational forces limit the retrodictability of the dynamics. However Steel & Asher (1996) have shown that the observed spread of the Taurid asteroids over 20,000 - 30,000 years can be quantitatively accounted for by non-gravitational forces modelled on those observed in the motion of Comet Encke.

Figure 2 illustrates also that there seems to be a distinct second group of asteroids, clustered in longitude around the asteroid Hephaistos ( = 258^o) which, at ∼ 10 km diameter, is one of the largest objects in the NEO system (Steel & Asher 1994). It is possible that this group too was connected with the Encke progenitor in the more distant past.

Babadzhanov (2001) has found that most of the TC asteroids have associated weak meteor showers, again supporting a cometary provenance. However the surface reflectance properties of these NEOs are variable and it has been suggested that this argues against a common origin, cometary surface albedos generally being low, and akin to carbonaceous chondrites from the outer asteroid belt. However not enough is known about the origin of comets, especially large ones, to be confident of this. The 5 km object Phaethon, for example, has been supposed to be a recently 'activated' asteroid from the main belt because of its reflectance spectrum (Licandro et al. 2007). There is no current cometary activity, and the strength and density of the incoming meteoroids are more asteroidal than cometary in nature. On the other hand its orbit is more akin to that of a comet (e ∼ 0.86, q ∼ 0.14 AU), while spectroscopic analysis of Geminids meteors has shown that the abundances of elements such as Ca, Fe and Cr are close to those found in Perseids and Leonids of undoubtedly cometary origin (Borovicka et al., 2008). Phaethon thus appears to be an inactive cometary nucleus in spite of having "asteroidal" surface characteristics; in general, it is probably unsafe to infer the nature of an NEO simply from its surface reflectance properties, especially where surface melting at perihelion may take place.

Among fainter NEAs observational incompleteness increases; when one reaches Tunguska size the vast majority are still undiscovered. It turns out moreover that a statistically significant alignment is presently hard to find within the current dataset. Nevertheless, Porubcan et al. (2006) and Babadzhanov et al. (2008) have demonstrated the association of identifiable filaments in the Taurid meteor orbit database with several NEOs in the hundreds of metre to 2 km size range. Some of these filaments originated 4000 - 4500 years ago, indicating that the system is still evolving.

In summary, the current zodiacal cloud is largely supplied by Jupiter family comets; but emergent new data strengthen the hypothesis that an exceptionally large comet entered the inner planetary system perhaps 50 - 100 kyr ago and has been disintegrating ever since. In the following Section the question is addressed: could this account for the postulated cosmic event at 12,900 BP?

3 Multiple Bombardment

Comet observations have revealed many cases of multiple disintegration. In late 1995, Comet 73P/Schwassmann-Wachmann 3 split into three fragments, having been seen as a single object on its previous return in 1990. On subsequent returns fresh mini-comets were seen, and by 2006 over 150 fragments had been detected (Reach et al. 2009; Ishiguro et al. 2009). At least one fragment was ∼ 300 m across and a dozen or so were in the size range of the Tunguska impactor. Comet C/1996 B2 Hyakutake split into seven sub-nuclei whose sizes seem to have been in the range of the Tunguska impactor (Desvoivres et al., 2000); Comet C/1999 S4 LINEAR disintegrated into thousands of fragments. Jenniskens (2008) considers that meteor streams originate from discrete breakup events rather than gradual sublimation of water ice. There appears to be more than one mode of disintegration, breakup at perihelion presumably due to tidal stresses being one, and `unknown' being the others. Disintegration may proceed through a route involving dormant comets (Kresak & Kresakova, 1987; Jenniskens loc. cit.). Di Sisto et al. (2009) consider that on average a Jupiter Family comet (P <20 yr) will undergo a major splitting every approximately 77 revolutions.

Generally, the separation speeds of the fragments are 1-2 ms^-1 (Sekanina, 1978), although in the case of the Kreutz sungrazers separations of approximately 5 ms^-1- may be involved. However the escape velocity from the surface of a 100 km comet is ∼ 15 ms^--1. As the bodies cascade down through smaller sizes, disruption speeds will presumably decline. Here we consider the case where a comet fragment in an Encke-like orbit disrupts at perihelion. The initial orbit is given an inclination of 6^o. The fragments are assumed to move away in random directions from the comet.

Fig. 4.Intersection of 10,000-particle meteoroid swarm with a heliocentric sphere, of 1 AU radius, viewed from the Sun. Ecliptic coordinates are used. The subfigures each represent approximately the meteoroid flux through the sphere in one week. In the example shown the storm was created by fragmentation at perihelion of a comet in an Encke-like orbit, particles being ejected in random directions at speeds up to 10 ms^-1. The scale on the horizontal axis is approximately 0.014 AU, or about 325 Earth radii. The Earth would traverse this distance right-to-left in just over a day.

Fig. 5. The reflectivity of organic particles 10^-5 cm in diameter, with refractive index m = n - ik, as a function of porosity. Particles of probable cometary origin collected from the stratosphere have porosities of 75% or more.

Figure 4 shows the projection, on a heliocentric sphere of radius 1 AU of 10,000 particles ejected at perihelion with random speeds up to V_m = 2m s^-1. These particles do not cross the sphere simultaneously, but rather move from left to right in the figure, as illustrated. For a central passage through this meteoroid swarm, the Earth will encounter typically ∼ 50 particles over a period of 1.8 days, that is ∼ 5 x 10^-3 of the ejected mass may be intercepted if the configuration is right. The target area of the stream in this case is ∼ 2.1x10^-3 square AU or about 3.7x10⁵ times that of the Earth. If the meteoroid swarm comes from the perihelion disintegration of say a 10¹⁷ gm fragment of the original comet, then the Earth would encounter 5x10¹⁴ gm of material, energetically equivalent to the impact of 10,000 Tunguska objects, over a period of two days. For higher maximum ejection speeds V_m = 15m s^-1, the number of particles intercepted is approximately 6x10^-4 but the target area presented by the ellipse is larger, about 2.8x10⁶ times that of the Earth. There is a trade-off between the intensity of bombardment from an encounter with a narrow filament of material, and the lower probability of encountering such a stream in the first place. There is thus is a clear potential for an event like that postulated at 12,900 BP, arising from the disintegration of the Upper Paleolithic comet, provided that such encounters have a reasonable probability over the active lifetime of the comet.

For an object in an orbit like that of Comet Encke, the annual collision probability with the Earth is ∼ 10^-9. However for an encounter with a meteoroid swarm with 10⁵ times the target area, the annual collision probability becomes ∼ 10^-4. An encounter of the sort postulated at 12,900 BP thus becomes likely provided that, during the disintegration history of the Taurid progenitor, one or more disintegrating fragments of significant mass are present at any given time.

The fragments from a disrupting comet tend to have size distributions ∼ d^-q with index q not very different from those expected from self-similar cascades (q = 3.5), implying that the mass tends to be concentrated in a few largest bodies (e.g. Ishiguro et al., 2009). The probability of a damaging encounter was investigated by adopting a self-similar fragmentation model, in which half the mass of a disintegrating fragment was assumed to be lost as dust, and the mass of the largest sub-fragment was taken as 0.3 times the initial mass. This yielded five sub-fragments, each of which disintegrated in self similar manner. Assume that the limiting mass for a meteoroid swarm -- generated at perihelion and intercepted at Earth -- to cause a damaging bombardment is mc = 10¹⁶ gm. A comet whose initial mass is ∼ 10²⁰ gm will yield ∼ 17,700 swarms of at least this mass in the course of its disintegration; for m_c = 10¹⁷ gm, the number of potentially damaging meteoroid swarms is ∼ 1000. Then assuming that the active lifetime of the comet is say 20,000 years, the swarm must remain as a coherent entity for 1- 20 yr for an expectation of one such encounter, depending on m_c inter alia. This requirement is modest, the more so since the orbital period of the Taurid complex bodies (∼ 3.3 yr) is close to a 7:2 mean motion resonance with Jupiter (3.39 yr), which strongly affects the orbital evolution. The effect of the resonance is to restrict the spread of dense swarms of meteoroids generated by disintegrations, so prolonging their lifetimes well beyond 20 yr (Asher & Clube, 1993; Beech et al. 2004; Dubietis & Arlt 2007).

It has been suggested by Zotkin (1969), Kresak (1978) and others that the Tunguska bolide was a fragment of Comet Encke. Asher & Steel (1998) pointed out that there is a coincidence between a reasonable estimate of the bolides's radiant and that of the β Taurids, which strike the Earth on the daytime hemisphere. The splitting from the comet could have occurred within the last 5,000-10,000 years if the semimajor axes of the orbits differed by ∼ 0.05 AU a difference easily achieved by the non-gravitational forces to which the comet is subject. The identification is not dynamically unique, since there are many more near-Earth asteroid candidates than active short-period comets (Jopek et al., 2008), but there is no known meteor stream with which one could associate any such erstwhile comet, other than the Taurid stream itself.

On this hypothesis, then, the 1908 Tunguska impactor was an outlier of the Taurid Complex. So long as bodies in asteroidal orbits are thought to comprise 99% of the impact hazard, then the impact of a small body during the Earth's passage through debris from Swift-Tuttle (Table 2) can be considered a statistical fluke (one of three). However a significant background of dark bodies in cometary orbits would make the hazard much more difficult to deal with, both from the perspectives of mapping out dangerous objects and deflecting them when they are discovered. Since for impactor diameters above one or 2 km we are dealing with the prospect of global destruction, with a significant part of humanity destroyed, it is necessary that we give the issue the most careful consideration. In the following section the case is made that dark, globally hazardous objects may in fact exist in significant numbers in Halley-type orbits.

4 The Mystery of the Missing Comets

The question of undetected bodies in meteor streams arises in connection with a long-standing problem of population balance, analogous to the zodiacal cloud mass balance problem, but concerned with a population of comets in orbits like those of periodic Comet Halley. These comets form a roughly spherical system, with equal numbers of prograde and retrograde orbits around the Sun, and with orbital periods P <200 yr, by convention. They have high eccentricities which brings them into the inner planetary system, say within the orbit of Mars, where they outgas and become visible. Comet Halley itself has eccentricity e=0.967, orbital inclination 162.3^o and period 75.3 yr. The mean dynamical lifetime of comets in such Halley-type (HT) orbits is less than half a million years, their usual fate being to fall into the Sun or be ejected into interstellar space. They arrive in the visibility zone from the Oort cloud, a sphere of comets extending about 50,000 AU from the Sun. About one bright comet per year arrives in the visibility zone, and 1 or 2% of these are perturbed into Halley type orbits. Conservatively, the expected num- ber of Halley-sized comets is ∼ 3000. Allowing for incompleteness of discovery, the actual number is ∼ 25. The argument is robust, depending as it does only on celestial mechanics, conservation of mass, and the observed rate of arrival of these comets into the zone of visibility (Bailey & Emel'yanenko, 1998; Biryukov, 2007). The discrepancy holds over the entire range of sizes of these comets, down to 2 km bodies.

A number of solutions to this paradox have been proposed in the literature. The comets may become dormant (Bailey & Emel'yanenko, 1998). The problem with this hypothesis is that, for albedos p ∼ 0.04, surveys should by now have detected 400 dark comets over 2 kilometres in diameter (Levison et al., 2002). However only a handful of such bodies have been detected to date. Alternatively, it has been suggested that the comets rapidly disintegrate to dust (Levison et al., 2002). This solution was accepted immediately after publication by NASA's Science Definition Team (Stokes et al., 2003) and is the basis of the assumption that the comet impact hazard is at the 1% level relative to the NEO hazard. A number of problems, however, have since emerged with this model. It requires 96% of incoming comets to disrupt on their first perihelion passage, and this is a rather extreme requirement. Comet Halley itself, for example, has certainly been observed for over 2000 years. The dust would appear as 15-30 strong annual meteor showers (Napier et al. 2004), which are not observed. And the mass balance problem is simply transferred to the dust. The Pioneer 10 dust instrument measured impacts out to 18 AU from the Sun for eight years after its launch, and the measured dust count could be modelled as a supply of ∼ 10¹⁵ gm/century from comets in Halley-type orbits (Landgraf et al., 2002). This is at least four powers of 10 less than expected if these comets disintegrate to dust (Wickramasinghe et al., 2009).

Table 3: Visual albedos for a number of surfaces. The carbonaceous aerogel albedos are for surfaces with vacuum volume fraction ∼ 0.65-0.9 similar to that observed for cometary Brownlee particles.

Fig. 5. The reflectivity of organic particles 10^-5 cm in diameter, with refractive index m = n - ik, as a function of porosity. Particles of probable cometary origin collected from the stratosphere have porosities of 75% or more.

A third possibility is that comets arising from the Oort cloud may develop extremely dark surfaces, with albedos (Napier et al., 2004). This needs organic-rich, porous surfaces, essentially carbonaceous aerogels. Such surfaces could develop if volatiles sublimed away, leaving a fairy-castle or aerogel structure, and could be many metres deep. Dust particles of probable cometary origin do indeed have this structure, with vacuum filling factors ∼ 0.75-0.95 of the required order (Fig. 5), while fireballs of cometary origin are 95% porous. Dark patches which were detected on Comet Borrelly had albedos p ∼ 0.008, and it is hard to see what else they could have been but such aerogels. While this postulate plausibly `solves' the problem of the missing comets, it cannot be said whether arriving Oort cloud comets would in fact develop such structures, and the possibility remains unverified. Some albedos of dark material are shown for comparison in Table 3.

In the absence of direct observations, whether such dormant comets exist and constitute a significant global hazard may be determined by the most direct means of all, namely counting and dating holes in the ground.

5 Bombardment Episodes

Figure 6 shows the age distribution of 40 well-dated terrestrial impact craters known to epoch November 2004. All but five are dated to better than α<5 Myr. There is clearly a decline in the known craters with increasing age, presumably due to loss with time through erosion and sedimentation. There is also, amongst the larger craters, a strong tendency to cluster. Almost every crater over 20 km across occurs, not in isolation, but as part of an episode of bombardment. Six of the 40 craters are less than 5 Myr old. One of these, Kara-Kul in Tajikistan, has an age given only as an upper limit of <5 Myr. Its diameter, 50 km, corresponds to a 2.5 km diameter projectile and a megatonnage 6x10⁵, which exceeds the threshold for incinerating the planet. This current episode appears to be real and not a discovery artefact. Table 4 gives a list. Statistical scrutiny confirms their overall reality, although a `false positive' in any particular case cannot be excluded (Napier 2006).

Fig. 6. Forty terrestrial impact craters with diameters >3 km, ages <250 Myr quoted to precision better than 10 Myr. These have been culled from the Earth Impact Database (2005). The circles represent the formation dates for 12 craters over 40 km across with ages measured to precision 2.6 Myr or better. The asterisks mark out a best-fitting periodicity of 35 million years for those 12.

Table 4:Possible impact episodes. Each episode is found to include at least one crater >40 km in diameter, and these large craters appear to have a periodicity ∼ 35 Myr with phase zero, consistent with the Sun's passage through the Galactic plane ∼ 1-2 Myr ago. Debris in SW England probably from the Rochechouart crater yield an age 214+2 Myr.

The ages of the Chicxulub and Boltysh craters are identical to within their statistical errors, but as the latter amount to ∼ 0.7 Myr it has been suggested that this coincidence in time is not particularly significant (a 24 km diameter crater is formed on average every 1--3 Myr). This argument does not, however, allow for the severe incompleteness of discovery of craters of Boltysh size. For example, 9 craters are listed in the range 20--40 km diameter over the 250 million years of Table 1, that is one per 28 million years, as against an expectation that perhaps 80 - 250 such craters were formed over this period. The temporal coincidence is most easily explained if 10-30 medium-sized impact craters occurred at the KT boundary (an expectation value of 10 - 30 such craters fits the data comfortably). The dinosaurs, it seems, became extinct during a bombardment episode.

Asteroid disintegration in the main belt will send debris inwards, but to produce a shower the disintegration would have to happen close to one of the strong resonances which throw asteroids quickly inward. The Veritas asteroid family, for example, was formed by the breakup of a 140 km body only 8.3 Myr ago, but produced no asteroid shower on Earth. However it turns out that the breakup of asteroid families is too infrequent, and the arrival in Earth- crossing orbits too spread out in time, for such breakups to match the observations (Zappala et al., 1998; Napier & Asher, 2009). Disturbance of the Oort cloud by Galactic tides or molecular clouds can yield weakly periodic comet showers. There is a large and contentious literature on the subject, but several workers appear to have settled on the view that that there is a weak periodicity of ∼ 35-37 Myr amongst the largest craters, say D >40 km (Stothers, 2005; Yabushita, 2004; Wickramasinghe & Napier, 2008), but none discernible amongst the smaller craters. The break even point corresponds to the threshold for globally destructive impacts, and suggests that the contribution from Oort cloud comets, acting probably through Halley-type and other intermediaries, cannot be neglected in hazard assessments.

Dynamical modelling suggests that the Galactic tides acting in concert with molecular clouds may produce this modulation (loc. cit.). The phase of this periodicity is zero, consistent with our current passage through the plane of the Galaxy and implying that we are currently in a bombardment episode.

Levison et al. (2002) computed that, without disintegration, there would be a population of N ∼ 3 x 10⁴ dormant Halley-type comets with diameters D > 2:4 km and perihelia q 1 AU. The mean interval between impacts from a population of N isotropically distributed bodies with mean orbital period P years is ∼ ³³⁰P/N Myr. Adopting P = 60 yr, N = 30000, we find the mean interval between impacts to be ∼ 0.67 Myr between comets of at least 2.4 km diameter. For a mean impact speed ∼ 60 km s^-1 the impact energy delivered is 1.5x10⁶ Mt, about the threshold for global catastrophe. These figures indicate that dark comets, should they exist, are a significant hazard for humanity. The Oort cloud is currently disturbed since we are passing through the Galactic plane, and the long-term average impact rate, taking account of quiescent intervals between impact episodes, may easily be an order of magnitude less than this.

6 Summary and Conclusions

The evidence that an exceptionally large (50-100 km) comet entered a short-period, Earth- crossing orbit during the upper Paleolithic, and underwent a series of disintegrations, now seems compelling. The idea is not new, but it has been strengthened by an accumulation of evidence from radar studies of the interplanetary environment, from the LDEF experiment, from numerical simulations of the Taurid complex meteoroids and 'asteroids', and from the latter's highly significant orbital clustering around Comet Encke.

The disintegration of this massive Taurid Complex progenitor over some tens of thousands of years would yield meteoroid swarms which could easily lead to brief, catastrophic episodes of multiple bombardment by sub-kilometre bolides, and it is tempting to see the event at ∼ 12,900 BP as an instance of this. Whether it actually happened is a matter for Earth scientists, but from the astronomical point of view a meteoroid swarm is a much more probable event than a 4 km comet collision.

The existence of sub-kilometre bodies in cometary streams may constitute a significant hazard not yet picked up in the NEO surveys simply because they have not been running for long enough. Two components to this are of concern and may be illustrated through the Brazilian event of 1930. If actually due to a body in the Perseid major stream, the impactor approached at ∼ 60 kms^-1. And with an orbital period of 133 years, it could not have been detected with current technology until impact was imminent, if at all. Mapping out of a small body population of dark objects in Halley-type orbits to a satisfactory level is not feasible for the foreseeable future.

That kilometre-sized bodies may exist and be a significant hazard, and be likewise undetectable, is a possibility arising from uncertainty about the nature of the fading problem. It would be good if arriving Oort cloud comets thrown into Halley-type orbits disintegrated harmlessly to dust; even better if that dust were observed. A possible resolution of the missing comets problem is that carbonaceous aerogels develop on the surfaces of long period comets when they first arrive in the planetary system. However the problem remains unsolved, although it might be of great consequence for impact hazard assessment. Mass for mass, Halley type comets have an order of magnitude more impact energy than near-Earth asteroids ( ∼ 57 km/s as against ∼ 20 km/s). Dark, dormant comets may be extremely hard to detect, and the warning time may be measured in months or weeks rather than centuries or decades. The mapping of a system of dark comets in Halley type orbits, say to 95% completion, would take a millennium or more with current technology. Such objects are difficult to detect from the ground but would be detectable at thermal wavelengths above the atmosphere, with a space-based infrared telescope operating in the 6-10 micron waveband (Cellino et al. 2004).

On longer timescales, there is evidence for bombardment episodes which appear to be too strong and sharp to be caused by asteroid fragmentation. Given the importance of large comets and the likelihood of their arrival and breakup over ∼ 100,000 years, the nature of mass extinctions -- when they occur due to such events -- is more likely to be one of a mixture of prolonged and sharp events, coupled with a series of coolings due to strong cometary dusting and multiple bombardments. Some mass extinction events, such as the Late Devonian of 374.5+2.6 Myr ago, appear to be of this character (McGhee, 1996). For others, the geophysical evidence is lacking or controversial (Kelley, 2007). While a single catastrophic impact may, depending on the target rock and the like, cause simultaneous mass extinctions on land and sea, the message generally being delivered is one of prolonged trauma, multiple bombardments and climatic upsets through dusting. The world which emerges through such a ∼ 100,000 yr episode may well be very different from that which went before. There is evidence for a periodicity amongst large, well-dated craters which appears to be well matched to the Galactic environment; and this strengthens the view that the history of the Earth is a record of its motion through the Galaxy.

Amongst all the naturally occurring hazards (Bostrom & Circovic, 2008), impacts seem to be unique in that they are unbounded. The annual risk of a global celestial catastrophe is small, but the consequences may be overwhelmingly large. A modest impact has the potential to end civilisation, a giant one might put our species into an irreversible decline, like other primate species past and present. It took over three billion years of evolution to produce the sole terrestrial species capable of understanding the universe, and we do not know whether, if we are removed, intelligence is likely to evolve again. Nor do we know whether there are other intelligent species in our Galaxy. In the event that we are alone, and are removed by some catastrophe, then our Galaxy will return to its former dumb state and may never again leave it. In that sense, the survival of this particular species of ape is a cosmic imperative.