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A computer model of the atmospheric entry of the Tunguska object

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A computer model of the atmospheric entry of the Tunguska object
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  Planet. Space Sci., Vol. 46, No. 213, 245-252, 1998 p. 0 1998 Elsevier Science Ltd All rights reserved. Printed in Great Britain 0032-0633/98 19.00+0.00 PII: S0032-0633(97)0001~7 Pergamon A computer model of the atmospheric entry of the Tunguska object James Evans Lyne,’ Michael E. Tauber2 and Richard M. Fought’ ‘Dept. of Mechanical Engineering, 414 Dougherty Building, University of Tennessee, Knoxville, TN 37996, U.S.A. ‘Aeronautics and Astronautics, Durand Building, Stanford University, Stanford, CA 94035, U.S.A. Received 2 August 1996; accepted 3 January 1997 Introduction The nature of the Tunguska object has been the topic of considerable debate for many years, with some inves- Correspondence to: J. E. Lyne tigators favoring a cometary body (Turco et aZ., 1982; Whipple, 1930 ; Hughes, 1976), others supporting an asteroidal object (Chyba et al., 1993; Sekanina, 1983; Hills and Goda, 1993), and a third group proposing much more exotic events such as the interaction of antimatter with the atmosphere (Bullough, 1995). Despite numerous authors’ beliefs that their studies had “put the matter to rest”, the controversy continues with proponents of both the asteroid and comet camps presenting their results at the Tunguska96 Workshop. Although many techniques have been applied in an attempt to determine the nature of the impactor, perhaps the most frequently used has been numerically modeling the atmospheric entry of various bolides and comparing the results with the known characteristics of the event-an airburst releasing approximately 15 Mton TNT equivalent of energy at an altitude of 6-10 km above the surface (Ben-Menahem, 1975). By this approach, it has been claimed that certain categories of objects either could be absolutely excluded or had been determined to be extremely unlikely in favor of more likely culprits. It is interesting that this approach has been used in various studies to support both a cometary body and an asteroid as the most probable impactor (Turco et al., 1982 ; Chyba et al., 1993). In performing an analysis of the entry trajectory of a moderately large meteor such as the Tunguska object, two interacting physical phenomena must be considered- mechanical fragmentation and aerothermodynamic ablation. Both processes serve to reduce the body’s initial kinetic energy. The fundamental equations describing the motion of an intact object in the atmosphere have been described elsewhere (Chyba et al., 1993 ; Lyne et al., 1995) and are given in Appendix A. A number of approaches to modeling the mechanical fragmentation process have been attempted over the last thirty years, ranging from the simple analytical technique of Chyba et al. (1993) to more sophisticated numerical models such as the hydrodynamic approach of Svetsov et al. (1995) and the smooth particle hydrodynamics (SPH) method of Thomas et al. (1994). (The analytic model of Chyba et al. is very similar to that of Hills and Goda (1993).) Comparisons of these  246 techniques have shown that Chyba’s “pancake” model produces results which agree reasonably well with those of the more complex approaches (Svetsov et al., 1995; Thomas et al., 1994). Chyba’s model assumes that the fragmentation process begins when the stagnation pres- sure is equal to twice the yield strength of the meteor material (so the pressure at the center of the body equals the yield strength), and the entire object fragments at once. The resulting debris begins to spread radially once mechanical fragmentation occurs since the confining pres- sures on the sides of the body are relatively low. The radius of the debris increases according to : d2r/dt= = CdpaV2/(2p,r) (1) where Y and pc are the radius and density of the body, V is the meteor velocity, t is time, C, is the coefficient of drag, and pa is the local atmospheric density. Ablation modeling and trajectory analysis Generally speaking, in recent meteor research, analysis of aerodynamic heating has not received as much attention as the fragmentation process, and existing ablation models have differed widely in their results. Consider, for exam- ple, the findings of recent studies by Svetsov et al. (1995) compared with those of Hills and Goda (1993). The first of these articles reviews the results of detailed studies by Biberman et al. (1978a, 1978b, 1980) on high speed radiative heating and concludes that “for large bodies above several meters in size, as the first-order approxi- mation, we can consider only mechanical processes” (and ignore aerothermal ablation altogether). On the other hand, Hills and Coda (1993) adopt the ablation equation from the well-known work of Bronshten (1983) : dmldt = 0.50Ap,V3 (2) where m is the meteor mass, A is the projected frontal area of the body (rcr2), and a is the ablation parameter which they assume to have a constant value of 1 O x lo-l2 s2 cm-2. The application of these two methods can lead to remarkably different results ; for example, Svetsov et al. 1995) determine that an ice sphere with a radius of 1OOm entering the atmosphere vertically at a velocity of 50 kms-’ does not loose half of its srcinal kinetic energy until it reaches an altitude of approximately 3 km. In this model, no material is lost to thermal ablation, but about 20% of the srcinal mass is lost to mechanical processes. The same body is predicted to have lost half its kinetic energy by the time it reaches an altitude of 22 km in the study by Hills and Goda (1993), with the entire meteor eventually being consumed by aerothermal ablation. The work of Chyba et al. (1993) applied yet another method to determine the rate of heat transfer to the sur- face of a meteor. Their technique was based on calculating the radiative flux from the gases of the shock layer using the Stefan-Boltzmann equation : qR = ‘7 T2j4 3) where the gas temperature, T2 s assumed to be uniform throughout the shock layer and at a constant value of J. E. Lyne et al.: Atmospheric entry of the Tunguska object 25 000 K. Moreover, the heating rate is required not to exceed 10% of the total flow energy (this is equivalent to limiting the heat transfer coefficient to 0.1). The great disparity between the studies of Svetsov et al. (1995) and Hills and Goda (1993) illustrates that the ablation models of various investigators have not agreed nearly as well as the mechanical fragmentation models. Although it is certainly not as critical as the fragmentation process, aerthermodynamic ablation can play a significant role in determining the trajectory of meteors the size of the Tunguska object, particularly if they are of icy com- position and, as a result, fragment relatively high in the atmosphere and have a low heat of ablation. (Of course, for meteors with large initial radii, the relative importance of thermal ablation decreases rapidly and becomes neg- ligible for kilometer-sized objects.) Unfortunately, accurate calculation of the aerodynamic heating and the rate of ablative mass loss is extremely difficult, since it requires a knowledge of the temperature distribution in the shock layer, the chemical composition of the meteor, and the degree to which the ablation prod- ucts block radiative heat transfer to the body. Moreover, for many entries, the shock layer conditions exceed the limits of existing tabulations for the properties of high temperature gases. The most sophisticated studies of the ablation process on meteors have been performed for relatively small bodies which were assumed not to frag- ment (Biberman et al., 1980; Fay et al, 1964), and these studies have not been adequately coupled with models of mechanical fragmentation. This coupling is critical since, as the object disrupts, its frontal surface area (which is exposed to the hot gases of the shock layer) grows sig- nificantly, and the rate of heat input to the fragmented meteor increases greatly. We previously reported on the development of a com- putational model which provides a more detailed analysis of the aerothermodynamics of meteor entry than has been performed in most earlier studies (Lyne and Tauber, 1995 ; Lyne et al., 1995). The model (which is described in more detail in Appendix A) determines the temperature dis- tribution immediately downstream of the shock as a func- tion of time during the meteor’s trajectory (Fig. I), assuming that the gas is in thermodynamic equilibrium. The temperature distribution is then used to calculate the heating distribution over the bolide’s surface (Fig. 2). The meteor’s mechanical fragmentation and the radius of the resulting debris is determined using the analytic approach of Chyba et al. (1993). An adaptation of the technique developed by Goulard (1964) is applied to account for radiative energy loss from the shock layer gases and the resulting reduction in gas temperatures and moderation of surface heating. Data from previous studies on silicon dioxide heat shields are used to account for the reduction in surface heating due to radiation blockage by ablation products. (These particular heat shield studies were used since the material composition is reasonably similar to what would be expected for many stony meteors.) Our calculations using this model indicated that the ablation rates determined by Chyba et al. (1993) and Sekanina (1983) were probably excessive. Partly as a result of our less severe calculated radiative heating rates, we found that a given meteor tends to plunge lower into the atmo- sphere before its energy is dissipated than had previously  J. E. Lyne et al.: Atmospheric entry of the Tunguska object 247 ENTRY VELOCITY = 19 KM/S BODY DENSITY = 1.0 GM/CC ENTRY ANGLE = 45 DEGREES 5000 BODY RADIUS = 35 METERS DRAG COEFFICIENT = 1.2 00 0 ‘IO 20 30 40 50 60 70 80 90 BODY POSITION (DEGREES) ‘. Fig. 1. Shock layer temperature distribution around the nose of a meteor. 0” corresponds to the stagnation point, and 90” corresponds to the shoulder. Time represents seconds after entry been believed. Therefore, carbonaceous chondrites, which had been considered unlikely candidates for the Tunguska object (Chyba et al. 1993) become quite plausible (Fig. 3). Perhaps just as significantly, our work again raised the possibility that a comet could have produced the Tun- guska event; icy bodies of reasonable size were found to have their terminal flare at approximately the correct altitude if they entered the atmosphere steeply enough (Fig. 4). For example, a body with an initial radius of 40m and a kinetic energy of 31.6 Mton entering at an angle of 80” produces an airburst at an altitude of 10 km, while a 16 Mton, 32m radius comet entering vertically airbursts at 12.4 km. It should be noted that the present model predicts a cometary airburst at approximately the correct altitude only for cases in which the body enters the atmosphere more steeply than is typically advocated for Tunguska (Sekanina, 1983) Disparities between the ablation models used in various studies can lead to significant differences between the tra- jectories predicted for a given meteor. This is illustrated in Figs 5-7 which show calculated trajectory charac- teristics for a cometary object entering the atmosphere at 19 km s-l. To isolate the influence of the heating model, mechanical fragmentation was calculated in all cases using \ COEFFICIENT OF DRAG * 1.2 500 * 6.0 SEC 0 10 20 30 40 50 60 70 80 90 BODY POSITION (DEGREES) Fig. 2. Heating distribution around the nose of an icy meteor near the time of peak intensity. 0” corresponds to the stagnation-point, and 90” corresponds to the shoulder. Times represent seconds after entry  248 J. E. Lyne et al.: Atmospheric entry of the Tunguska object \ ENTRY VELOCITY = 15 KM/S DENSITY = 2.2 GM/CC COEFFICIENT DF DRAG = 1.2 bo s of Tunguska airbursi 0, - I * I - , ., ., . 0 20 40 60 80 100 1 INlTAIL BODY RADIUS (M) Fig. 3. Airburst altitude vs. body radius for a carbonaceous chondrite 0 the technique of Chyba et al. (1993) (equation (1)). The entry speed of 19 kms-’ was chosen since this is the approximate upper limit for the method used to perform the heating calculations in the present study (see Appendix A). Although this value is lower than that used by most other authors, a recent paper by Chyba (1991) indicates that approximately 25% of short-period comets enter at or below this speed. The “no ablation” case corresponds to the model of Svetsov et al. (1995). (However, it should be recognized that their study primarily examined the entry of an ice sphere with a radius of 100 m, and it is not entirely clear if they believe ablation can be ignored for objects of the size considered here.) Figure 5 shows the predicted trajectory for a cometary object (density = 1 gcmW3, compressive yield streng- th = 1 x 1 O6 dyn cm-‘) with an initial radius of 45 m and entry angle of 45”. The only difference between the four curves is the ablation model used for the calculations. Figure 6 illustrates the airburst altitude (defined here as the altitude at which the kinetic energy is reduced to half its srcinal value) as a function of initial radius for a cometary object entering at an angle of 60” ; the separate curves again correspond to calculations performed using the different ablation models. Figure 7 shows the per- centage of a cometary object which is consumed by ther- mal ablation during its trajectory. It should be pointed out that the surface area to which the heating pulse was applied was the projected frontal area for the curves marked “Chyba et al.” and “Hills and Goda” as was the case in their papers. For the method of this paper (marked “present study”) the heating pulse was applied to a hemi- spherical nose. Therefore, the disparity between calculated 20 I ENTRY VELOCITY = 19 KM/SEC DENSITY = 1 GM/CC \ COEFFICIENT of DRAG = 1.2 80 Approximate altitude bounds of Tunguska airbunt 0 I I I I 20 30 40 50 60 INITIAL BODY RADIUS (M) Fig 4 Airburst altitude vs. body radius for a comet 70  J. E. Lyne et al.: Atmospheric entry of the Tunguska object 249 60 ENTRY VELOCITY = 19 KM/S ENTRY ANGLE = 45 DEGREES RADIUS = 45 METERS DENSlTY = 1 GM/CC DRAG COEFFICIENT = 1.2 ABLATION MODEL - Chyba et al. (1993) - Hills Goda (1993) --t- Present study -d-- No ablation 0 10 20 30 ALTITUDE (KM) Fig. 5. Calculated cometary trajectories. The separate curves correspond to different ablation models. The mechanical fragmentation model of Chyba et al. (1993) is used for all calculations heating rates is even greater than is reflected is Fig. 7. (It is interesting to note that the detailed study by Biberman et al. 1980) suggests that even the heating rates calculated by the current technique may be too high ; this is largely due to differences between the methods of the present study and Biberman’s work in modeling the radiation blockage due to ablation products.) onclusions It is apparent that the choice of ablation model can have a substantial impact on the predicted trajectory of a can- didate Tunguska object and may lead to erroneous con- clusions regarding the nature or composition of the orig- inal meteor. This is particularly true for icy bodies which fragment high in the atmosphere and have a relatively low heat of ablation. This finding has some bearing the current debate as to whether a comet could have caused the Tun- guska event. Clearly, studies which attempt to use a tra- jectory analysis to determine the nature of the srcinal body must model both the mechanical fragmentation pro- cess and the aerothermal ablation with reasonable accu- racy in order to draw reliable conclusions. Our model indicates that both asteroidal objects (hard stone or softer carbonaceous chondrites) and cometary bodies could 20 ; 1 ; I ? ENTRY ‘VELOCITY = 19 KM/S I I ENTRY ANGLE = 60 DEGREES- DRAG COEFFICIENT = 1.2 1 I + Present P----- No ablation 30 40 SO 60 70 80 INITIAL RADIUS (M) Fig. 6. Predicted airburst attitude vs. initial body radius for a comet. The separate curves correspond to different ablation models. The mechanical fragmentation model of Chyba et al. (1993) is used for all calculations
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