Bolides and airbursts
The atmospheric interaction of large meteoroids provides our primary tool to characterize their population, physical and chemical properties, and dynamical evolution. In turn, this can lead to a better understanding of the diverse populations of small bodies of the Solar System. Currently, our knowledge is still quite limited, although, especially after the impact of comet D/Shoemaker-Levy 9 on Jupiter, the research efforts in this field have been intensified. In particular, in 1994 the US Department of Defense made of public domain its records on energetic bolides over a time span of about twenty years. These data indicate that, from 1975 to 1992, there were 136 airbursts of energy greater than 1 kton, but the real number was probably at least 10 times higher, because the satellite system does not cover the entire Earth surface. One of the most important question, today still open, is to understand why meteoroids break up at dynamical pressures lower than their mechanical strength. This is of paramount importance, because it allow to know whether or not a meteoroid might reach the soil. Therefore, it allows to establish a reliable criterium to assess the impact hazard.
We can however set up a reliable phenomenological model, even though we have not an efficient and quantitative theory. Specifically, as noted by Zdenek Ceplecha, it is still unknown why large meteoroids/small asteroids break up at dynamical pressures lower than their mechanical strength. For example, the Peekskill meteorite has an estimated strength close to 30 MPa, but it was found that the maximum value of fragmentation pressure was about 0.7-1.0 MPa. Why? One possible answer was recently given by Luigi Foschini, who proposed a model based on the interaction of shock waves and turbulence under unsteady conditions (see L. Foschini: "On the atmospheric fragmentation of small asteroids" Astronomy and Astrophysics 365, 2001, 612), but this is only a conceptual outline, and numerical models are necessary.
When a large meteoroid enters the Earth's atmosphere, it has a speed in the range 12-72 km/s, hence it moves at hypersonic speed (that is, with Mach number greater than about 5). Since here we are interested in the dynamics of a meteoroid large enough to reach the lower atmosphere, the fluid can be treated as a continuum. Thus, we can use current knowledge about hypersonic aerodynamics in order to understand meteoroid airbursts.
It is important to note that for large Mach numbers the linearized equations for the speed potential are not valid, so we cannot use laws holding for supersonic speeds. In hypersonic flow, Mach waves and oblique shock waves are emitted at small angles with the direction of the flow, of the order of the ratio between body thickness and length, and thus tend to follow the surface of the body. Under these conditions, the atmospheric path of a large meteoroid can be seen as a long cylinder, generating pressure waves that can detected in different ways (barographs, seismographs).
Under steady state, the small angle of Mach and oblique shock waves gives also rise to the concept of hypersonic boundary layer near the surface. In front of the meteoroid there is a bow shock, that envelopes the body. The shock is stronger on the symmetry axis, because at this point it is normal to the stream. Then, we find a zone where molecular dissociation is the main process and even closer to the body surface, we find the boundary layer, where viscous effects are dominant. As the air flows toward the rear of the meteoroid, it is reattracted to the axis, just like in a Prandtl-Meyer expansion. As a consequence, there is a rotation of the stream in the sense opposite to that of the motion (rectification); this creates an oblique shock wave, which is called wake shock. Since the pressure rise across the bow shock is huge when compared to the pressure decrease across the Prandtl-Meyer expansion, one can assume, as a reasonable approximation, that there is a vacuum in the rear of the meteoroid.
The fluid temperature increases in the boundary layer, because the speed must decrease to zero at the meteoroid surface; moreover there are heating effects due to viscous dissipation. There are also regions (like in the Prandtl-Meyer expansion) in which the presence of vacuum or near-vacuum strongly reduces heat transfer, and this contributes to the increasing body temperature. If the generation of heat increases so quickly that the loss of heat may be inadequate to achieve an equilibrium state, we may have a thermal explosion. This explosion generates pressure waves that can be detected on the ground by seismographs or barographs. It is very interesting the paper by A. Ben-Menahem: "Source parameters of the Siberian explosion on June 30, 1908 from analysis and synthesis of seismic signals at four stations" (Physics of the Earth and Planetary Interiors 11, 1975, 1), where the scientists analysed seismic and infrasound data from the Tunguska event of 1908 (see below). Note that after the Tunguska event no meteorite was recovered, so the argument the meteorites are usually cold immediately after landing does not rule out this kind of thermal explosion in this case.
It is worth noting that this picture does not take into account how does the ablation modify the hypersonic flow. This is still unknown. |
