On June 30, 1908, a sudden release of energy in the atmosphere above
the Tunguska region in central Siberia devastated an area of over 2100
square kilometers of forest.1 The energy release has been attributed
to a number of sources, but the most widely accepted is the sudden and
complete disruption of a large meteor well before it struck the ground.
The lack of an apparent impact crater indicates that the resulting
debris must have been quite small. Because of the remote location of
the event and the low number of human casualties, its occurrence is not
widely known, either among the general public or in the scientific
community. However, the recent entry of comet Shoemaker-Levy 9 into the
atmosphere of Jupiter has brought attention to the possibility of such a
cataclysm taking place on Earth and, therefore, has refocused interest
on Tunguska, the largest reported event of this type in modern times.
Previous studies of Tunguska have yielded widely differing interpretations as to the size, composition, velocity, and density of the body prior to its entry into the atmosphere.2,3,4 However, it is generally agreed that the object disrupted catastrophically at 6 to 10 km above the ground,5 depositing approximately 15 Mtons of energy6 in a relatively small altitude band. The atmospheric entry velocity and entry angle are not well established; experimental reconstruction of the extent and pattern of treefall suggests a value for the entry angle, gi between -10 and -60 degrees (with a most probable value of -30 degrees), while eyewitness accounts report a shallower angle of -5 to -17 degrees.2 Estimates of the atmospheric entry velocity range from under 15 km/s to over 40 km/s.2,3,4 In a comprehensive paper published in 1983, Sekanina3 interpreted the data as indicating that the body could not have been of cometary origin and was probably an Apollo-type asteroid with a diameter of 90 to 190 meters.3 More recent work by Chyba et al has suggested that the object was a stony asteroid significantly smaller than that described by Sekanina (perhaps 60 meters in diameter).2 In marked contrast, Turco et al4 concluded that the entry body was of cometary origin with an effective density of 0.002 gm/cc and a radius of 800 meters.
ATMOSPHERIC ENTRY PHYSICS
The velocity of a body in unpowered, non-lifting atmospheric flight varies according to the following equation:
where V is velocity, Cd is the coefficient of drag, A is the cross sectional area, m is the mass, g is the acceleration due to gravity, rho the ambient atmospheric density and gamma is the flight path angle (measured from horizontal with downward being negative). The change in altitude and flight path angle are given by:
where H is the altitude and R is the radius of the Earth plus the
Whatever type of object caused the Tunguska event, its passage through the atmosphere imposed enormous pressure and heat transfer loads on the body. The combination of these two effects caused the destruction of the meteor in the altitude band discussed above. Once the internal stresses induced by the pressure load exceeded the yield strength of the material, the body began to fail mechanically. The high pressure in the stagnation region and low pressure on the backside of the body resulted in a compression load, while the confining pressures on the sides were relatively low. As a result, once mechanical failure commenced, the meteor spread laterally resulting in a so-called "pancaking" effect. This increased the frontal area and caused the aerodynamic drag to go up, therefore increasing the deceleration of the body according to Eqn. 1. In Ref. 2 Chyba et al show that the increase in the radius of the body can be approximated by:
where r and rhoc are the radius and density of the body.
Aerodynamic heating of the meteor caused a high rate of material ablation resulting in a decreasing body mass. The heating was dominated by radiation from the highly compressed gas behind the bow shock and can be approximated using the Stefan-Boltzmann relation:
where qRad is the adiabatic radiative heat transfer rate and T2 is the temperature behind the shock wave (which will vary with velocity, position and shock angle). Because of radiative emission from the gas as it moves from the shock toward the body, the shock layer is non-adiabatic and it is necessary to modify the heating as given by the above equation according to a method developed by Goulard.7 For this case, Goulard's method gives approximately8,9
where qR is the non-adiabatic radiative heat transfer rate and G = qRad / ( 4 rho V3 ). These equations do not account for the presence of ablation products in the shock layer and their absorption of some fraction of the radiative heat input. The significance of this effect has been analyzed by Gupta10 and depends primarily on the ratio of the freestream mass flow rate to the mass flow rate of the ablation products (which is simply the heat transfer rate divided by the heat of ablation of the material). Since experience shows that the vast majority of the flow energy goes into heating the atmosphere rather than an entry body,8,11 the heating rate was required not to exceed fifteen percent of the total flow energy (0.075 rho V3 (10-4) W/cm2); if the rate as calculated above was in excess of this amount, it was set equal to the fifteen percent limit.
OBJECTIVES AND METHODOLOGY
The objective of this work was to determine the type(s) and size(s) of the objects which could have been responsible for the Tunguska event. The equations of motion described above were numerically integrated for a wide range of initial bolides and entry conditions, while the mass of the body was decreased according to the ablation rate. For asteroids, entry velocities from 12.5 to 20 km/s were considered (recent work indicates that this range should include the great majority of Earth-crossing asteroids), while for comets, entries were examined only at 20 km/s, an approximate lower limit for cometary entry speeds.12 The atmospheric density was calculated as a function of altitude based on curve fits of the 1976 U.S. Standard Atmosphere.13 At each time step in the trajectory, the temperature behind the shock was calculated as a function of position and shock angle by solving for the equilibrium species concentrations. (The shock angle was assumed to be 70 degrees at the body's edge.) This was used to determine the local heat transfer rate which was corrected using the technique of Goulard. Gupta's corrections for ablating surfaces were applied by curve fitting his plots of heat transfer ratio (ablating to non-ablating surface) vs mass flow ratio. The body was assumed to have a Cd of 1.2 for the nominal cases, although other values were considered. (The value of 1.7 used by Chyba et al2 is too high for irregularly shaped bodies with rounded edges such as asteroids.) Chyba's pancake model of mechanical deformation was adopted, and the increasing frontal surface area was used for both drag and heat transfer calculations. The physical characteristics of the various bolide materials are listed in Table I.
RESULTS AND CONCLUSIONS
Figure 1 shows a representative heat transfer pulse calculated as described above for a carbonaceous meteor compared to the pulse calculated for the same body using the method of Ref. 2 (which assumed an adiabatic shock layer at a uniform temperature of 25000 degrees Kelvin). By accounting for the non-adiabatic nature of the shock layer and the reduction of surface heating due to radiation absorption by ablation products, the current method yields much lower heating rates (and less ablative mass loss) than previous studies.2,3
Figure 2 shows the bolide velocity as a function of time for two representative carbonaceous bodies. The airburst altitude (defined here as the altitude at which a meteor has lost fifty percent of its initial kinetic energy) is plotted in Figure 3 for carbonaceous chondrites as a function of the initial body radius over a range of atmospheric entry angles. (This definition of airburst altitude yields a value which is very close to that at which the rate of energy release is a maximum.) Figure 4 shows a similar calculation for a stony asteroids. The atmospheric entry velocity in these figures is assumed to be 15 km/s. The airburst altitude was found to be only a weak function of the atmospheric entry velocity. (Since the altitude indicated in these figures is with reference to sea level, it should be realized that the average elevation in the devastated area was 500 to 1000 meters.) From these plots, it is apparent that a body of either stony or carbonaceous composition could have broken apart and deposited its energy at the appropriate altitude.
Previous studies have suggested that carbonaceous bodies would have released their energy too high in the atmosphere to have been responsible for Tunguska while comets either would have entirely ablated at altitudes in excess of 20 km or required extremely high initial masses.2,3 However, using the present model, a given bolide will airburst at a significantly lower altitude than predicted in Ref. 2 and 3. This is caused by both the lower value used for the drag coefficient and the less severe heating environment (see Fig.1). As a result, carbonaceous chondrites, which previously had been considered unlikely causes of the Tunguska event,2 become the most likely candidates. (It should be noted that Reference 14 gives slightly higher values for the density and heat of ablation of carbonaceous material; the use of these values would further serve to lower the airburst altitudes for carbonaceous bodies.) This finding is reinforced by the fact that carbonaceous bodies are the most common type of meteors to enter the Earth's atmosphere. Moreover, the present model predicts that a cometary body with a radius of 75 meters, an entry velocity of 20 km/s, and an entry angle of -45 degrees would airburst at 9.2 km. Therefore, unlike previous studies2,3 which have excluded comets as the cause of the Tunguska event, our model indicates that such an object can not be eliminated on the basis of its terminal altitude alone.
The implication of this study is that meteors do not have to be as large or dense or have as steep an atmospheric entry angle as previously believed either to reach the ground or to cause significant damage due to an airburst.
1. Gallant, R.A., Sky and Telescope, 38-43, June 1994.
2. Chyba, C.F., Thomas, P.J., and Zahnle, K.J., Nature, 361, 40-44, 1993.
3. Sekanina, Z., The Astronomical J., 88, 1382-1414, 1983.
4. Turco, R.P., Toon, O.B., Park, C., Whitten, R.C., Pollack, J.B., and Noerdlinger, P., Icarus, 50, 1-52, 1982.
5. Ben-Menahem, A., Phys. Earth and Planet. Inter., 11, 11-35, 1975.
6. Hughes, D.W., Nature, 259, 626-627, 1976.
7. Goulard, R., AIAA J., 2, 494-502, 1964.
8. Page, W.A., Compton, D.L., Borucki, W.J., Ciffone, D.L., and Cooper, D.M., AIAA Paper 68-784, 1968.
9. Tauber, M.E., J. Spacecraft and Rockets, 6, 1103-1109, 1969.
10. Gupta, R.N., Lee, K.P., Moss, J.N., and Sutton, K., J. Spacecraft and Rockets, 29, 173-181, 1994.
11. Tauber, M.E. and Sutton, K., J. Spacecraft and Rockets, 28, 40-42, 1991.
12. Chyba, C.F., Icarus, 92, 217-233, 1991.
13. U.S. Standard Atmosphere, 1976, NOAA ST 76-1562, October 1976.
14. Baldwin, B. and Scheaffer, Y., J. Geophys. Res., 76, pp. 4653-4668, 1971.
MATERIAL DENSITY (GM/CC) HEAT OF ABLATION (MJ/KG)
YIELD STRENGTH (ATM)
CARBONACEOUS 2.2 5.0 10.0
STONE 3.5 8.0 100.0
COMET 1.0 2.5 1.0