On 30 June 1908 a explosion near the Podkamennaya Tunguska River in what is now Krasnoyarsk Krai, Siberia, flattened around 80 million trees over an area of about 2150 km², and is thought to have killed at least three people. The cause of this is unclear; the most possible current explanation is that a stony meteorite with a diameter of about 100 m exploded in an airburst 5-10 km above the ground, although no debris from such an event has ever been found, which is surprising. Since the Chelyabinsk meteor impact of February 2013, when a meteor estimated to have been 20 m in size passed over the city of Chelyabinsk, creating a shockwave that caused considerable damage on the ground, before breaking up to the west of the city, it has been clear that a bolide passint through the Earth's atmosphere could cause considerable damage on the ground, even without impacting or detonating in an airburst.
In a paper published in the Monthly Nottices of the Royal Astronomical Society on 4 February 2020, Daniil Khrennikov of the Siberian Federal University, Andrei Titov of the Moscow Institute of Physics and Technology, Alexander Ershov, also of the Siberian Federal University, and of the Institute of Computational Modeling, Vladimir Pariev of the PN Lebedev Physical Institute, and Sergei Karpov, again of the Siberian Federal University, and also the LV Kirensky Institute of Physics and the Siberian State University of Science and Technology, examine the possibility of through passage of asteroid bodies across the Earth’s atmosphere, and the likelyhood that this might have caused the damage associated with the 1908 Tunguska Event.
Fallen trees in the aftermath of the 1908 Tunguska Event. Leonid Kulik.
The problem of the motion in the Earth’s atmosphere of a large bolide, capable of falling on to the surface of the planet in the form of meteorites, is now of great interest. An equally urgent concern is the study of the conditions for the passage of such bodies through the upper atmosphere, even without collision with the Earth’s surface, since the shockwaves produced by this passage have a colossal destructive effect.
Large bolides (1–10 km in size and larger) that carry the potential danger of collision with the Earth are detected by ordinary astronomical observations. The bodies of intermediate dimensions began to be registered relatively recently. Observations of such bodies and the interpretation of observational data make it possible to determine the probability of their collision with the Earth, their properties, and the characteristic features of passage through the atmosphere, as well as the consequences of fall. The clarification of these questions will enable us to assess more accurately the degree of asteroid hazard.
One of the fundamental problems of meteor physics is the determination of the pre-atmospheric mass of bolides, since the intensity of the meteor phenomenon is determined by the kinetic energy of the body when entering the atmosphere of the planet. It is known that the velocity of the bodies belonging to the Solar System at the entrance to the Earth’s atmosphere should be inside a relatively narrow range, between 11.2 and 72.8 km per second, so that the variance of the contribution of the velocitysquared factor to the kinetic energy does not exceed 50 times. At the same time, the mass of a meteor body can vary in a much wider range: from fractions of a gram (micrometeor) to tens of millions of tons or more (the Tunguska space body), that is, by 13–15 orders of magnitude.
The goal of Khrennikov et al.'s study was to evaluate the effect on the trajectory of the bolide of its passage through dense layers of the atmosphere, taking into account the acting forces, the initial velocity, and the mass and its variation during the flight, to determine the conditions for possible passage of a large bolide through the atmosphere with a minimum loss of mass without collision with the Earth’s surface. The obtained results are compared with observational data on the Tunguska space body with an estimated altitude of maximum energy release of about 10–15 km to receive evidence in favour of a new explanation of the Tunguska phenomenon, which attributes the absence of meteoritic material on the Earth’s surface near the epicentre to the through passage of the bolide across the atmosphere with a small loss of velocity.
Firstly, Khrennikov et al. imagine a model explaining the entry of a bolide into the Earth’s atmosphere with respect to a chosen X–Y coordinate system coinciding with the centre of the Earth and corotating with the rotation of the Earth. The altitude of the entry of the bolide into the atmosphere is measured from the starting value 160 km, at which the temperature of the bolide begins to increase. The angle of entry into the atmosphere relative to the local horizontal line at the altitude 160 km.is one of the most important parameters of the problem.
Schematic diagram of the motion of a bolide in the Earth’s atmosphere and the angle of entry into the atmosphere (β) at a given point relative to the X–Y coordinate system. Rₑ is the radius of the Earth. Thickness of the atmosphere is exaggerated. The trajectory of the bolide and its length within the atmosphere are indicated by the line with the arrow. Khrennikov et al.(2020).
Khrennikov et al. describe the ballistics of the bolide by a system of equations, including the equation of motion under the action of applied forces: the force of the aerodynamic drag and the gravitational force.
The contribution of the lifting force to the ballistic motion of the bolide is also neglected as Khrennikov et al.assume that its shape is close to spherical. The Coriolis and centrifugal forces in the rotating reference frame are negligible for fast-moving bolides compared to the aerodynamical forces from stratospheric winds, which they also neglect here because bolides move much faster than the wind speed.
In accordance with existing ideas, Khrennikov et al. assume the main contribution to the force of aerodynamic drag is made by the difference in pressure between the frontal and rear parts of the bolide's surface (low-pressure cavity forms near the rear surface).
Mass-loss of bolides occurs due to heating to a temperature much higher than the melting point. In Khrennikov et al.'s model the main contributor to this heating is the radiant heat transfer between the the bolide and the boundary layer of the shock wave, whose temperature reaches several thousand degrees close to the surface of the bolide. One of the most difficult problems in calculating the radiant heat transfer is the determination of the radiant heat transfer coefficient. Its magnitude is affected by the velocity of motion in the atmosphere, flight altitude, air density, temperature of the boundary layer and the nature of the processes in the boundary layer (dissociation and ionization of air molecules), the degree of blackness of the radiating and absorbing surfaces, etc.
Khrennikov et al.'s model does not involve the process of bolide fragmentation, since the initial dimensions of the bolide are taken to be quite significant (from 50 to 200 m) as well as moderate velocities, when most of the bolide remains intact, despite extreme external influences. First of all, maximum resistance to fragmentation is characteristic of iron bolidess, which is associated with the high homogeneity of their internal structure. In contrast to the iron bolidess, the internal structure of stone and ice bolidess is heterogeneous with an abundance of numerous microcracks. The results of the study of the conditions for the fragmentation of iron bolidess will be presented in the future.
Khrennikov et al. denote the mass-loss by the term ‘ablation’, which includes two processes: The first process is the low-temperature blowing off a liquid film from the bolide's surface (at a temperature about 1000°C) with the formation of small droplets. These droplets are typical for a slow fall of small bolides or their fragments at the final stage of the flight in the atmosphere. The second process is the high-temperature sublimation of material occurring when the surface temperature exceeds several thousand degrees. In this case, a mass-loss occurs in the form of vapours of single atoms and their ions. Under the conditions in consideration, Khrennikov et al.'s model includes the sublimation as a dominant process responsible for the mass-loss at high velocities (over 12 km per second).
As a typical example of Khrennikov et al's calculations, in th case of the trajectory of a spherical iron bolide with a radius of 50 m entering into the atmosphere at 20 km per second when passing through it at the entry angle 11.2° and a minimum altitude of 11 km, the perturbation of the trajectory of the SB deviates it from the initial direction by an angle of 11.25° when neglecting the aerodynamic drag effect and 16.9° when the aerodynamic drag effect is taken into account. These results demonstrate the significant effect of aerodynamic drag on the bolide trajectory.
Changes in the trajectory of SB during a through passage via the atmosphere. The bolide parameters are radius 50 m, the velocity of entry into the atmosphere is 20 kmper second, and the minimum altitude is 11 km. Khrennikov et al. (2020).
At present, there are over 100 hypotheses about the nature of the Tunguska phenomenon, among which three to four versions are predominant theories. They include the fall on to the Earth of a small asteroid measuring several dozen metres, consisting of typical asteroid materials, either metal or stone, as well as ice, which is characteristic of cometary nuclei. The most probable material of the Tunguska bolide mentioned in literature is ice. According to the available observational data, there are several variants of the direction and the trajectory length of the Tunguska bolide, from 450 to 600 km, in particular, with a propagation direction from ‘south–north’ to ‘east–west’. The value of the angle of entry into the atmosphere mentioned in literature is 30°–40°. The radius of the Tunguska bolide was estimated based on the amplitude of the shock wave recorded by the seismic stations and amounted to about 25 m. The minimum trajectory altitude of the Tunguska bolide approximately corresponded to the point of maximum energy release.
The results of comparative calculations of the velocity variations of iron, stone, and ice bolides with radii 100 and 50 m along the trajectory of through passage across the atmosphere for an initial velocity of 20 km per second, suggests that stone bolides lose their velocity faster than iron bolides, and ice bolides do not survive passage through the atmosphere.
Khrennikov et al. calculated the trajectories of bolides with radii of 50 m and iron and stone compositions. Both enter the atmosphere at 160 km, reach a minium altitude of 11 km, then exit the atmosphere at 160 km agian. However, there is a considerable lengthening of trajectory of the stone bolide compared to the iron body. The iron bolide passes through the atmosphere with a minimum loss of velocity and minimum deflection due to a high initialmass, whereas the stone bolide subsequently re-enters the atmosphere due to a significant decrease in velocity. Although quite improbable, such an bolide could manifest itself as a pair of explosive phenomena in the atmosphere separated by thousands of kilometres in distance and tens of minutes in time.
Khrennikov et al. calculated the trajectories of an ice bolide with a radius of 100 m at different entry angles and changes inmass. They found that such a bolide suffered a dramatic loss of mass at angles over 11°. At angle 10°, the initial mass is preserved due to the high altitude, with the bolide remaining over 50 km above the Earth's surface.
Next Khrennikov et al. calculated the reduction of the masses of ice bolides with radii of 100, 50, and 25 m on the trajectory of collision with the surface of the Earth. The residual fractions of the mass at an initial velocity of 15 km per second were 49 per cent, 21.3 per cent, and 4.8 per cent, respectively, for radii of 100, 50, and 25 m. The length of the trajectory until the moment of the collision with the surface of the Earth is about 325 km for the initial velocity of 15 km per second. At an entry velocity of 25 km per second, for radii of 100 and 50 m, ice bolides fall with a preservation of 6 per cent and 0.000 04 per cent of the initial mass respectively. For radii of 25 m and entry velocity of 25 km per second, an ice bolide loses all its mass completely within a trajectory length of about 329 km.
Of course, the fall of a bolide with preservation of a significant part of the initial mass results in the formation of a crater with a diameter larger than 1 km. However, there are no craters near the epicentre of the Tunguska Event or in the surrounding area. The actual length of the trajectory based on the results of visual observations was estimated to be about 450–700 km, which is over 1.5 times longer than the calculated value for the ice bolide. Therefore, the hypothesis of the ice origin of the Tunguska bolide, which enters the atmosphere at an angle of 30°–40°, is hardly justified accorind to Khrennikov et al.'s model.
Moreover, the decrease in the mass of the ice bolide with an initial radius of 100 m along the trajectory at small angles of entry into the atmosphere, while preserving a significant fraction of mass is possible only at a minimum altitude above 40 km, which contradicts with the estimated minimum altitude of about 10–15 km in the Tunguska event.
Khrennikov et al.'s calculations showed that the trajectory length of the ice bolide when it passes through the atmosphere at a minimum altitude of 15.5 km and small entry angles (less than 15°) until the moment of its complete loss of mass even at a radius of 100 m is two times shorter compared to the case of the iron bolide. Thus, the through passage of the ice bolide at small entry angles with a minimum trajectory altitude 10–15 km is impossible.
For the ice bolide with a radius of 25 m, the length of the trajectory to the moment of the total loss of mass is reduced by four to five times. In addition, it was shown that a considerable part of the initial mass is preserved by iron and stone bolides with radii of 100, 50, and 25 m at an entry angle of 30°. But their fall would be accompanied by the formation of craters with a diameter larger than 1 km and a depth over 200 m.
Khrennikov et al. did not deal with the problem of the formation of a shock wave, although when comparing the Tunguska phenomenon with the Chelyabinsk meteorite with a size of about 10 m and an altitude of maximum energy release of about 30 km, they have no reason to doubt that the body that is 10–20 times larger with an altitude of maximum energy release of 10–15 km at a velocity of 20 km per second will create a shock wave with a huge amplitude and destructive force, capable of causing tree-fall over an area exceeding 1600 km². Experimental modelling of the knock-down effect of a shock wave from the source with cylindrical geometry was performed in a 1966 study. The cylindrical source of the shock wave was modelled by a long detonating cord inclined at a certain angle to a plane planted with small sticks, which imitated trees in the Siberian forest. It was shown that the shape of the area of fallen sticks was similar to the shape of real treefall territory. However, that study did not model the dependence of the strength of the cylindrical shock wave on the height of its source above the ground. Instead, they added a point explosive at the lower end of their cord to model a presumed spherical component of the shock wave. Because rates of the mass and energy losses of the bolide that caused the Tunguska event depend strongly on its altitude above the ground a sharp increase in energy release close to the minimum altitude reached by the through passing bolide can be interpreted as an explosion creating a spherical component of the shock wave. Clearly, making a detailed prediction for the patterns of tree-fall in the framework of our hypothesis of a through-passed bolide as a cause for the Tunguska event will be an important subject of future research.
In solving the main problems in this work, Khrennikov et al. confined themselves to the need to make an upper estimate for calculating the residual mass of space body using the parameters maximising the massloss. They did not consider the problem of the mass-loss of the space body due to its fragmentation. This will be the subject of future research and the results will be published elsewhere.
Based on the obtained results, Khrennikov et al. make the following statements: (i) The conditions for the possible through passage of a large space body composed of various materials across the Earth’s atmosphere with a minimal loss of mass and without collision with the surface of the planet are established. It was shown that this corresponds to the entry angles of space body into the atmosphere of at least 11.5°. (ii) It was shown that the Tunguska space body could hardly consist of ice, since the length of the trajectory of such a body in the atmosphere before the complete loss of its mass would be less than the length of its trajectory estimated on the basis of observational data. (iii) The value of the angle of entry into the atmosphere of 30°–40° mentioned in the literature for the Tunguska space body looks unrealistic, since it corresponds to the trajectory of a fall of a body with a large residual mass and trajectory length, which is 1.5–2 times shorter than the estimated trajectory length based on the observational data. Such a fall would be accompanied by the formation of a large crater, absent near the epicentre and around. (iv) The most realistic version explaining the Tunguska phenomenon is the through passage of the iron asteroid body as the most resistible to fragmentation across the Earth’s atmosphere at a minimum altitude of 10–15 km with the length of the trajectory in the atmosphere of about 3000 km and a subsequent exit of this asteroid body into the outer space to the near-solar orbit. This version is supported by the fact that there are no remnants of this body and craters on the surface of the Earth. Within this version, Khrennikov et al. can explain optical effects associated with a strong dustiness of high layers of the atmosphere over Europe, which caused a bright glow of the night sky.
If Khrennikov et al. admit the version of the complete loss of mass of the bolide after the passage of the epicentre or close to it, then the evidence of its reality would be the presence of droplets of meteoric iron of millimetre sizes on the Earth’s surface along the trajectory of the bolide. It follows that the smaller the bolide size and its mass are, the faster it loses a velocity (the amplitude of the shock wave near the epicentre also becomes smaller). Finally, when the velocity of a diminishing bolide reduces to such an extent that its surface temperature approaches 1000°C, the sublimation ceases and the dominant mechanism of mass-loss consists of blowing off a liquid film from the surface of the body. In this case, the bolide becomes the source of a huge amount of droplets, which will be sprayed by the bolide. However, such microformations have not been found despite intensive searches around the epicentre and far beyond. The absence of iron droplets around the epicentre is explained by the high velocity of the bolide during through passage across the Earth’ s atmosphere, always over 11.2 km per second when the surface temperature exceeds several thousands of degree Celcius. The dominant mechanism of mass-loss at these temperatures is the sublimation of material in the form of single atoms, which can be found on the Earth’s surface as iron oxides, which do not differ from the same widespread iron oxides of terrestrial origin.
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