Baltic Astronomy, Vol.20, 289–296, 2011 SOME STUDIES OF

Baltic Astronomy, vol. 20, 289–296, 2011

SOME STUDIES OF TERRESTRIAL IMPACT CRATERING RATE

L. Jetsu Department of Physics, Gustaf Hällströmin katu 2a (P.O. Box 64), FI-00014 University of Helsinki, Finland; lauri.jetsu@helsinki.fi

Received: 2011 May 27; accepted: 2011 July 10

Abstract. In 1984, a 28.4 Myr periodicity was detected in the ages of terrestrial impact craters and a 26 Myr periodicity in the epochs of mass extinctions of species. Periodic comet showers from the Oort cloud seemed to cause catastrophic events linked to mass extinctions of species. Our first study revealed that the only significant detected periodicity is the “human signal” caused by the rounding of these data into integer numbers. The second study confirmed that the original 28.4 Myr periodicity detection was not significant. The third study revealed that the quality and the quantity of the currently available data would allow detection of real periodicity only if all impacts have been periodic, which cannot be the case. The detection of a periodic signal, if present, requires that more craters should be discovered and the accuracy of age estimates improved. If we sometimes will be able to find the difference between the craters caused by asteroid and comet impacts, the aperiodic component could be removed. The lunar impact craters may eventually provide the required supplementary data. Key words: solar system: Earth, impact craters, asteroids, comets, Oort cloud – Galaxy: solar neighbourhood

1. INTRODUCTION The origin of crater structures on Earth was understood only about one century ago. The meteor crater in Arizona, USA is one of the best preserved craters on Earth. The estimated age for this relatively young structure is 20 000 < t < 50 000 years and the diameter is D = 1.2 km. Barringer (1906) was the ﬁrst to argue that this particular crater, now also known as the Barringer crater, was caused by an impact of a celestial body. Although fragments of this object were found, there was a prolonged controversy over its composition (e.g., Fairchild 1930). Because the diameter of the impacting asteroid has only been about 25 m, the kinetic energy must have been enormous. A typical speed of a riﬂe bullet is 900 m s−1. However, should the Halley comet collide with the Earth, it would penetrate through the atmosphere within less than a second with a speed between 16 600 and 72 800 m s−1, depending on the angle of impact (Urey 1973). The origin of certain type of stones, namely the tektites, was still uncertain about half a century ago. Urey (1957) commented this dilemma with the following 290 L. Jetsu words:

However, the tektite problem has been, and is, one of the major puzzles to men ‘who pick up rocks and stop to think’. In a series of papers, he argued that the tektites were formed when asteroids or comets impacted on Earth (Urey 1962, 1963). Durrani (1972) estimated that the typical time span between such comet impacts is between 10 and 40 Myr. Then the next logical argument was made by Urey (1973): Some fifteen years ago, I suggested that tektites were produced by col- lision of comets with the Earth. ... I have also suggested that the geological periods were terminated by such collisions, but this was published in the Saturday Review of Literature, and no scientist except me, so far as I know, reads that magazine. This argument was quite soon confirmed by Alvarez et al. (1980), who detected the extraterrestrial iridium anomaly at the Cretaceous-Tertiary boundary. The site of this catastrophic impact has most probably been the Chicxulub Crater in Yucatan Peninsula, Mexico, having an age of t = 65 Myr and a diameter of D = 170 km (Pope at al. 1997). This event coincided with the extinction of dinosaurs and it was therefore suggested that in this particular case there was a clear connection between an impact and a mass extinction of species. Raup & Sepkoski (1984) detected a 26 Myr periodicity in the epochs of eight mass extinctions of species over the past 250 Myr. Additional evidence was later presented in Raup & Sepkoski (1986, 1988). Also in the year 1984, five papers were published in the Nature magazine that discussed the evidence for similar periodicity in the ages of terrestrial impact craters. Alvarez & Muller (1984) detected a 28.4 Myr period in the ages of eleven larger terrestrial impact craters. The idea of periodic “comet showers” from the Oort Cloud emerged. Two different theories about the mechanism that could trigger these showers were presented. The first theory was that a distant unseen solar companion “Nemesis” caused periodic disturbances to the Oort cloud (Davis et al. 1984; Whitmire & Jackson 1984). In the second theory, called the “Galactic Carousel”, the oscillation of the solar system through the galactic plane was assumed to cause similar periodic disturbances (Rampino & Stothers 1984; Schwartz & James 1984). During the next decade, more evidence for a regular periodic connection between numerous terrestrial and extraterrestrial events accumulated. For example, Clube & Napier (1996) argued that the mass extinctions of species, the termination of geological eras, the catastrophic impacts of large comets and even the terrestrial magnetic field reversals were all periodic, as well as connected to each other. The significance of these periodicities was debated for more than a decade and several arguments against periodicity were also presented. Some argued that the large errors in the estimated ages of impact craters prevented any detections of periodicity (e.g., Grieve & Pesonen 1996). Others noted that even if the comet impacts were periodic, the asteroids impacts certainly were not, and this noise would erase signatures of any periodic signal (e.g., Trefil & Raup 1987; Bailey & Stagg 1988). Some studies of terrestrial impact cratering rate 291

2. “HUMAN” STATISTICS OF TERRESTRIAL IMPACT CRATERING RATE Our first study of the terrestrial impact crater record was presented in Jetsu (1997). Six different subsamples of craters were drawn from the database main- tained by the Geological Survey of Canada. The selection criteria for these samples were the age, the diameter and the accuracy of the age estimates. The idea was to eliminate three bias effects. Firstly, younger craters are easier to detect. Secondly, larger craters survive erosion for a longer time. Thirdly, only reasonably accurate ages should be analysed. These selection criteria were similar to those already applied in several earlier studies (e.g., Grieve & Pesonen 1996). We also analysed the sample of eleven impact craters, where Alvarez & Muller (1984) detected the 28.4 Myr periodicity and one sample of the epochs of mass extinction of species from Matsumoto & Kubotani (1996). Most of the former studies of periodicity in these data had utilised the method of Broadbent (1955, 1956) or the power spectrum method of Scargle (1982). But because these time points are circular data, there are numerous different nonparametric methods that could have been applied (see Batschelet 1981). We applied Kuiper (1960) and Swanepoel & De Beer (1990) methods, as well as the weighted versions of these methods formulated in Jetsu & Pelt (1996). These weighted versions could also utilise the additional information obtained from the accuracy of the data. The tested period interval was between 2.2 and 200 Myr. Our typical values for the best periods detected were 2.50, 3.00, 3.33, 4.00 5.00, 7.00, 10.00 and 15.00 Myr. The significance of these periodicities was extremely high, in some cases even “impossible”. Had we interpreted this finding like the periodicity detections in the previous studies, it would have seemed that impacts occur with extreme regularity and are somehow connected to million rotations of the Earth around the Sun. The real reason for detecting these periodicities was that many ages of impact craters have been rounded to multiples of 20, 10, 5, 2 and 1 Myr. This apparently periodic phenomenon was named the “human signal” and it remained significant even in the samples, where we had removed all ages which had been rounded to multiples of 5 Myr. Finally, no signs of significant real periodicity was detected in the Alvarez & Muller (1984) or Matsumoto & Kubotani (1996) data. The main conclusion of this first study was Over a decade has elapsed in redetecting the regularities of our own integer number system and then interpreting them as periodicity in the ages of impact craters.

3. SPURIOUS PERIODS IN THE TERRESTRIAL IMPACT CRATER RECORD Our second study by Jetsu & Pelt (2000) began by reanalysing the data of eleven crater ages ti from Alvarez & Muller (1984). Their main result was that the period P = 28.4 Myr had a critical level Q = 0.008. We repeated their power spectrum analysis using the formulation of Scargle (1982). The following three Monte Carlo simulations were made ∗ Case I: Select n=11 random ti between 5 Myr and 250 Myr.

Case II: Select ti,i+1 = ti+i − ti from the original ti data in random order to ∗ determine a new sample ti . 292 L. Jetsu

Fig. 1. Arbitrary examples of uni-, bi- and multimodal phase distributions. ∗ Case III: Select ti as in Case I, but four values rounded with 1, and six with 5 (and two of these made equal). The results were Q = 0.13 (Case I), Q = 0.96 (Case II) and Q = 0.23 (Case III), i.e. there was no significant periodicity in these data. This result was then confirmed with a Rayleigh test using the formulation given in the appendix of our study. Nine of the ages of eleven craters analysed by Alvarez & Muller (1984) had been revised between 1984 and 2000. The two largest revisions had been 5.2σti and 3σti , i.e., the ages and the error estimates of the original data were both unreliable. This shows that the accuracy estimates of the techniques applied in the age determination were misleading (Deutsch & Schaerer 1994). The analysis of the same data can give different results with different methods. Arbitrary examples of different types of phase distributions are given in Figure 1. The detectability of these different types of phase distributions with different methods is summarised below. Method Unimodal Bimodal Multimodal Scargle (1982) Yes No No Broadbent (1955,1956) Yes No No Rayleigh test Yes No No Kuiper (1960) Yes Yes Yes Swanepoel & De Beer (1990) Yes Yes Yes These are only some examples. Numerous other nonparametric methods for analy- Some studies of terrestrial impact cratering rate 293 sing circular data have been presented, e.g. in Batschelet (1981). One application example of these sensitivity effects was discussed in greater detail (Jetsu & Pelt 2000: Figure 3). The main conclusions of this second study were:

1. the signiﬁcance of the 28.4 Myr periodicity detected in 1984 was overes- timated and the data available in those days have also later been found unreliable;

2. the signiﬁcance estimates depend on the chosen Monte Carlo scheme and rounding (i.e., “human” signal) misleads these estimates;

3. rounding causes other spurious (i.e. unreal) periodicities and a real periodicity (if present) is therefore more diﬃcult to detect, and

4. the sensitivity of different methods to different phase distributions causes differences in the results.

4. DETECTION OF REAL PERIODICITY IN THE TERRESTRIAL IMPACT CRATER RECORDS: QUANTITY AND QUALITY REQUIREMENTS Our third study concentrated on the quantity (number of crater ages) and quality (accuracy of these ages) requirements for the data that would allow detection of real periodicity (Lyytinen et al. 2009). Another aim was to test, what is the rounding limit that would still allow reliable detection of periodicity. It was assumed that the simulated data contained a periodic component (e.g. comet impacts) and an aperiodic component (e.g. asteroid impacts). The tested cases were S = 0 (no aperiodic impacts), S = 1/3 (one third aperiodic impacts) and S = 2/3 (two thirds aperiodic impacts). The alternatives for the accuracy of the data σP were 5, 10, 20 and 30% in units of the simulated periodicity. The tested sample sizes were n = 10, 25, 50, 75, 100 and 200. The effect of erosion was estimated from the real data and this effect was then implemented into the simulations. The probability density functions and the respective cumulative distribution functions were solved for every combination of S, σP and n. One example of these functions is shown in Figure 2 for the case S = 2/3 and σP = 20%. The probability density function is shown in the left panel of this figure. The aperiodic part is denoted with a continuous line, the periodic part with a dotted line and their sum with a dashed line. The right hand panel shows the respective cumulative distribution functions. For every simulated case, we determined the probability that the real, i.e. the simulated, periodicity was detected with a fixed preassigned significance level. The probability for detecting an unreal, i.e. a wrong, periodicity was also determined. The aim of this study was to determine the quantity (n) and quality (σP ) that would allow certain detection of real periodicity, if such a phenomenon were actually present in the ages of impact craters. The results were: • if all impacts have been periodic (S = 0), detection is possible for some combinations, e.g. with σP = 0.05 and n ≥ 25; • if one third of all impacts are aperiodic (S = 1/3), detection requires quality and quantity combinations like σP = 0.05 and n ≥ 75; 294 L. Jetsu

Fig. 2. Panel (a): probability density function; panel (b): cumulative distribution function (see text in Sect. 4).

• if two thirds of all impacts are aperiodic (S = 2/3), detection is impossible even with σP = 0.05 and n = 200, and • if the data are rounded with σP ≤ 0.1, detection of periodicity is possible for some combinations, like σP = 0.05 and n ≥ 75. The main conclusion of this third study was

“Reliable” detection of “real” periodicity from the currently available terrestrial impact crater data is impossible – unless all impacts have been due to periodic comet showers.

5. CONCLUSIONS The idea of a periodic signal literally buried in the ground of the Earth was presented in the year 1984. The possibilities for detecting such a signal in the currently available terrestrial impact crater record were buried in the three studies discussed here. It is certain that some (unknown) fraction of terrestrial craters have been caused by aperiodic asteroid impacts. Hence the signal, if present, has also been buried in the “noise” and the amplitude of this signal decreases for older craters due to erosion. Yet, evidence for periodicity has been reported quite recently (e.g., Chang & Moon 2005; Stothers 2006). The next generations may solve this controversy by pursuing at least four diﬀerent approaches that support each other: Quantity. Enlarge the sample, i.e. increase n by identifying new craters.

Quality. Determine the ages more accurately, i.e. decrease σti by developing the applied age estimation techniques. Some studies of terrestrial impact cratering rate 295

Remove noise. Develop criteria for separating between comet and asteroid impacts. Perhaps it will be possible to utilise the composition of the impacting body to achieve this. Or perhaps this information can sometimes be deduced from the crater morphology or the characteristics of impact debris. Lunar craters. Due to the absence of erosion, the Moon preserves an un- contaminated impact crater record, the relative impact rate having been the same as on the Earth. Perhaps the ages of lunar craters can sometimes be used to supplement the record of terrestrial crater ages.

ACKNOWLEDGMENTS. The use of SAO/NASA Astrophysics Data System (ADS) is acknowledged. I also wish to acknowledge the prolonged co-operation of Jaan Pelt from Tartu Observatory (Estonia) with several astronomers from Helsinki Observatory (Finland).

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