Images related to the crater hypothesis




Foschini's update of the fragmentation models

In the figure: Mach numbers as a function of height for 4 different possible entry speeds. The values for the atmospheric temperature (necessary to calculate the local sound speed), are taken from the COSPAR International Reference Atmosphere 1986 (Rees 1988) for latitude 60 N in June.

The possibility that some parts of the primary TCB survived the final explosive fragmentation and reached the ground requires some changes in the atmospheric fragmentation model considered in Farinella et al. paper (2.5 Mb). Foschini [] noted that the mechanical strength follows the scaling laws. Hence, it is expected that the strength decreases as the mass increases. This also means that a fragment of the TCB has a mechanical strength greater than the initial cosmic body. Secondly, the condition of fragmentation is based on the study of unsteady flow around small asteroids/comets. In this case, the distortion of the shock wave, created during the passage in the atmosphere, interacts with the turbulence, resulting in sudden outbursts of the dynamical pressure, up to twelve times its nominal value. Therefore, even though the dynamical pressure cannot exceeds the mechanical strength, the amplification of turbulence can produce the required effect. It is worth noting that the condition for the existence of this mechanism is that the Mach number (i.e., the ratio between the speed of the cosmic body and the local sound speed) is much greater than 5 (hypersonic flow) and is changing [].
It can be seen in the figure, that the TCB suffered changing Mach numbers (hence outbursts of dynamical pressure) from the highest atmosphere down to about 20-25 km and then the Mach number was constant (thermal-mechanical stress) until about 8-10 km, where it changed again. The maximum size of the fragments, that can survive to the final airburst, strongly depends on the fractal dimensions D considered. For the range 2.50 < D < 3.00, and for an entry speed between 14 and 16 km/s, the fragment masses are ~6x10^6-7 kg, which in turn correspond to sizes between 7 and 16 m (considering stony asteroids with density of 3500 kg/m). This rough estimate is consistent with the hypothesis that one or more metre-sized fragments could have survived to the final airburst and fell to the ground.

[] Foschini L (2001) On the atmospheric fragmentation of small asteroids. Astronomy and Astrophysics 365:612621 (Section 3 and references therein)
[] Foschini L (1999) A solution for the Tunguska event. Astronomy and Astrophysics 342:L1L4


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