The Tunguska Event

J.E. Lyne
Assistant Professor, Aerospace Engineering
The University of Tennessee

Michael Tauber
Consulting Professor, Aeronautics and Astronautics
Stanford University

Dear Sir:

It is generally accepted that the Tunguska event resulted from the catastrophic disruption of a large meteor high above the ground. Previous studies have yielded diverse interpretations as to the meteor's size, composition, velocity, and density before its arrival.1-3 Nevertheless, there is consensus that the disruption occurred 6 to 10 km above the ground,4 depositing approximately 15 Mtons of energy in a narrow altitude band. In a comprehensive analysis, Sekanina concluded that the body was not a comet, but rather an Apollo-type asteroid 90-190 meters across.2 More recent work has suggested that the object was a stony asteroid perhaps 60 meters in diameter.1 In contrast, Turco et al3 concluded that the meteor was of cometary origin with an effective density of 0.003 gm/cm3 and a diameter of 1200 meters.

The atmospheric trajectory of a meteor is influenced by mass loss due to ablation and fragmentation caused by enormous aerodynamic loads. The equations of motion for such a body have been described elsewhere.1,2 An essential aspect of modeling the entry involves accurately calculating the radiation-dominated aerodynamic heating. This can be approximated using the Stefan-Boltzmann relation:

qRad = 5.67 ( T2 / 1000 )4   W/cm2      (1)

where qRad is the adiabatic radiative heat transfer rate, and T2 is the temperature behind the shock wave (a function of velocity, altitude, and shock angle). However, because of radiative emission from the shock layer, the flow is non-adiabatic. This effect can be accounted for following Goulard,6,7

qR = qRad / ( 1 + 3.33 G0.7 )      (2)

where qR is the non-adiabatic radiative heat transfer rate and G = 4 qRad / ( rho V3 ). Moreover, ablation products in the shock layer will absorb some fraction of the radiation before it reaches the body. The significance of this effect has been analyzed by Gupta8 and depends primarily on the ratio of the freestream and ablation product mass flow rates.

The objective here was to determine the type(s) and size(s) of the objects which could have caused the Tunguska event. The equations of motion were numerically integrated for a wide range of bolides and entry conditions, while the body's mass was decreased according to the ablation rate. For asteroids, entry velocities from 12.5 to 20 km/s were considered, while for comets, entries were examined at the approximate lower limit of 20 km/s.9 At each time step, the temperature distribution behind the shock was calculated by solving for the equilibrium species concentrations. These temperatures were used to determine the local heating rates which were corrected for non-adiabatic effects and radiative blockage using the techniques of Goulard and Gupta.6,8 The drag coefficient, Cd, of 1.2 which was assumed for the nominal case corresponds to a blunted ellipsoid. (The value of 1.7 used in Ref. 1 is appropriate for a flat-faced, sharp-edged cylindrical body with its axis aligned with the flow. A naturally occuring meteor would have rounded edges, particularly after even a brief period of atmospheric passage; this rounding decreases the Cd substantially.) Chyba's model of mechanical deformation was adopted, and the physical characteristics of the bolide materials were based on Ref. 1.

Figure 1 shows a heat transfer pulse calculated as described above for a carbonaceous meteor and, also for the same body using the method of Ref. 1 (which assumed a uniform, constant shock layer temperature of 25000 K). Our calculations yield temperatures which for most cases are below 20000 K in the stagnation region and rapidly decrease towards the edge of the body because of the smaller shock angle. As a result of these lower temperatures and our analysis of the non-adiabatic effects and radiation absorption, the current method yields much lower heating rates than hose calculated in Ref. 1 and 2.

While previous studies suggest that carbonaceous bodies probably would have released their energy too high in the atmosphere to have been responsible for Tunguska, the present study, because of the more realistic, lower drag coefficient and the less severe calculated heating loads, indicates that a given meteor would airburst at a significantly lower altitude than previously believed.1,2 As a result, carbonaceous chondrites 50-100 meters in diameter are found to airburst in the 6-10 km range characteristic of the Tunguska object. Therefore, since these are the most common type of meteor to enter the Earth's atmosphere, they must be considered the most probable cause of the Tunguska event.

References

  1. Chyba, C.F., Thomas, P.J., and Zahnle, K.J., Nature, 361, 40-44, 1993.
  2. Sekanina, Z., The Astronomical J., 88, 1382-1414, 1983.
  3. Turco, R.P., Toon, O.B., Park, C., Whitten, R.C., Pollack, J.B., and Noerdlinger, P., Icarus, 50, 1-52, 1982.
  4. Ben-Menahem, A., Phys. Earth and Planet. Inter., 11, 11-35, 1975.
  5. Hughes, D.W., Nature, 259, 626-627, 1976.
  6. Goulard, R., AIAA J., 2, 494-502, 1964.
  7. Tauber, M.E., J. Spacecraft and Rockets, 6, 1103-1109, 1969.
  8. Gupta, R.N., Lee, K.P., Moss, J.N., and Sutton, K., J. Spacecraft and Rockets, 29, 173-181, 1992.
  9. Chyba, C.F., Icarus, 92, 217-233, 1991.

Figure legends

Figure 1. Heat transfer rate vs time for a carbonaceous body.