6 Possible origin of the Tunguska Body

In the previous section we obtained 1090 orbits, which can be considered as possible orbits of the parent body of the Tunguska explosion.

Until now, despite the many papers on the origin of the Tunguska event, this topic is still controversial. In fact, with the exception of the considerations developed in previous sections, no theoretical work and/or observational data has yet been able to discriminate between a cometary or an asteroidal origin of the TCB. In particular, an assumed impact velocity threshold has generally been used to characterise a comet from an asteroid, and has served to qualify the orbit.

Bottke et al. (2000, 2001) have recently created a steady state model of the orbital and absolute magnitude distributions of the NEO population, which corresponds to a best fit of the debiased orbital and absolute magnitude distributions (limited to H < 18) of the observed NEO. To construct their model, the authors first numerically integrated several thousands of test particles over millions of years, initially located in or/and near the main identified NEO "intermediate sources'' (IS), namely the 3:1 mean motion resonance with Jupiter, the $\nu _6$ secular resonance, the Mars-crosser asteroids (MC), the outer main belt at semi-major axis a>2.8 AU (OB), and the Jupiter family comets (JFC). In Bottke et al. (2000), the JFC and OB components were not included in the model and they were added later in Bottke et al. (2001). As the authors note: "the term of IS is somewhat nebulous, since it can describe a single resonance replenished over time by a small body reservoir or a large zone, which acts as a clearinghouse for small bodies''. They could then estimate the real NEO absolute magnitude and orbital distributions and the relative importance of the previous four NEO source regions to one another by tracking the orbital evolution of test particles coming from each source, and characterising the orbital pathways of these bodies. Their results allow to estimate the relative probability that a body on a given orbit (a, e, i) in the NEO region comes from a particular source, and thus the evaluation of the asteroid and comet contributions to the NEO population defined respectively as near-Earth asteroids (NEA) and near-Earth comets (NEC).

However, as the authors themselves recognise, the method is not "perfect'', in particular in some regions where NEA and NEC pathways overlap. In this case, it is difficult to distinguish between NEO coming from the asteroid regions and those coming from the cometary intermediate source. This is specially the case for NEO coming from the outer part of the main belt (with a>2.8 AU) and NEO coming from JFC. In the following, we will thus add the contributions of OB and JFC to define a unique cometary origin. As a consequence our estimate will be obtained by considering the maximum possible contribution of a cometary source.

Despite the limitations of the method, and since we have a relatively large sample of possible TCB orbits (which, as noticed in Sect. 2, takes into account the large uncertainties of the observed trajectory values of the TCB), it appears interesting to estimate the probabilities of possible origins of the TCB parent body using the results of Bottke et al. (2001), which are the only strong dynamic constraints that can be used at present.

In our work, we only considered 886 orbits from a total set of 1090. We eliminated 204 bodies which have semi-major axes a > 4.2 AU. These bodies have been rejected because in the model of Bottke et al. (2001), the target region of the bodies evolving from each source is limited to $a \leq 4.2$ AU. In our sample of 886 particles, 175 ($20\%$) have, according to Table 4, geocentric velocities in the range 14-16 kms^-1, and 711 ($80\%$) have high velocities, i.e. 30-32 kms^-1. From these 886 orbits, we estimate the relative probabilities $P_{{\rm 1}} = P_{{\rm 3:1}}$, $P_{{\rm 2}} = P_{{\rm\nu_6}}$ , $P_{{\rm 3}} = P_{\rm MC}$, and $P_{{\rm 4}} = P_{{\rm OB+JFC}}$ that a particle on each of these orbits with orbital elements (a, e, i) comes from the associated intermediate sources $S_{{\rm 1}} = S_{{\rm 3:1}}$, $S_{{\rm 2}} = S_{{\rm\nu_6}}$, $S_{{\rm 3}} = S_{\rm MC}$and $S_{{\rm 4}} = S_{{\rm OB+JFC}}$. Then, assuming that the different intermediate sources do not overlap (i.e. the probability is different for each of them), we consider that a body comes from the source S_iif this source corresponds to the maximum value of the computed probabilities P_i. As shown in Table 8, 739 objects have the highest probability of originating from the asteroid belt; more precisely 40 come from the 3:1 mean motion resonance for which the greatest probability is  $P_{{\rm 1}}$, 678 particles are found to originate from the $\nu _6$secular resonance, while only 21 are found to come from the MC source.

Finally for 147 objects, the greatest probability  $P_{{\rm 4}}$ indicates a cometary origin. This means that the usual criterion used in many previous studies based on impact velocities is not sufficient to qualify the most probable origin of a meteoroid. Indeed according to these results, both asteroids and comets can collide with the Earth at high velocities. Therefore, on the basis of these estimates, for the TCB orbits considered, an asteroidal origin is more probable than a cometary one.

 

 

Table 8: Number of TCB orbits (percentage from the 886 TCB orbits) coming distinctively from each source $S_{{\rm 1}}$, $S_{{\rm 2}}$, $S_{{\rm 3}}$ and $S_{{\rm 4}}$ according to the two criteria defined in Table 4. The number of orbits with a similar probability of coming from more than one source, according to criterium 2, are detailed in the text (see Sect. 2.3 for details) $S_{{\rm 1}}$ corresponds to the 3:1 resonance source, $S_{{\rm 2}}$ to the $\nu _6$ resonance source, while $S_{{\rm 3}}$ and $S_{{\rm 4}}$ are the MC and cometary sources, respectively.

	$S_{{\rm 1}}$	$S_{{\rm 2}}$	$S_{{\rm 3}}$	$S_{{\rm 4}}$	Criterion
Number of TCB Orbits ($\%$)	40 (4.5)	678 (76.5)	21 (2.4)	147 (16.6)	1
Number of TCB Orbits ($\%$)	31 (3.5)	528 (59.6)	11 (1.2)	147 (16.6)	2

6.1 Characteristics of TCB orbits coming from the 3:1 resonance

Of the 40 objects coming from the 3:1 mean motion resonance, 25have a semi-major axis a<2.5 AU. For 6 of these, the semi-major axis is even smaller than 2.0 AU and their inclination is relatively large, varying between  $27.3^{\circ}$ and  $28.4^{\circ}$, while the 19 orbits with a semi-major axis between 2.0 AU and 2.5 AU have an inclination which lies between  $11.3^{\circ}$and  $29.5^{\circ}$. The semi-major axis of the 15 remaining particles is $2.5 \leq a \leq 2.595$ AU and their inclination is $11.0^{\circ} \leq i \leq 24.2^{\circ}$. The eccentricities of all 40 particles are very large, the minimum value being 0.780 and the greatest being 0.862. Thus all the bodies are Apollos, defined as having a >1.0 AU, and q = a (1 - e) < 1. 0167 AU. The interval of values of the Tisserand parameter (defined as $T=a_{{\rm J}}/a + 2 \sqrt{a/a_{{\rm J}} (1-e^2)} \cos i$, where $a_{{\rm J}}$ is the semi-major axis of Jupiter) is quite large i.e. $2.72 \leq T \leq 3.38$.

6.2 Characteristics of TCB orbits coming from the $\mathsfsl{\nu_6}$ resonance

Most of the test particles in our sample, more precisely $76.5\%$(678/886 bodies), are found to come from the $\nu _6$ secular resonance. Only 81 of them have a semi-major axis larger than 2.0 AU, the largest value being a=2.397 AU. 167 objects have a semi-major axis a<1.5 AU, an eccentricity e<0.42 and an inclination $i<20^{\circ}$. The eccentricity of the remaining bodies is always larger than 0.7, their inclination being in the range $20^{\circ} \leq i \leq 38^{\circ}$. For the majority of the bodies (655/886 bodies), the Tisserand parameter is always larger than 3.0 and smaller than 5.9. Then, 23 bodies have a Tisserand parameter in the range $2.88 \leq T \leq 2.99$.

However, as for the TCB coming from the 3:1 mean motion resonance, all the TCB orbits are Apollo-like orbits.

6.3 Characteristics of TCB orbits coming from the MC source

A set of 21 particles have the greatest probability to come from the MC population. All of them have a semimajor axis smaller than 2. AU ( 1.617<a<1.9 AU). Their eccentricity is always large, in the range 0.79<e<0.84, whereas their inclination is between  $13.8^{\circ}$ and $18.0^{\circ}$. Finally, the Tisserand parameter is 3.39<T<3.88. We note that all the orbits originating in the MC source are located in a quite narrow range of orbital elements.

6.4 Characteristics of TCB orbits coming from a cometary source

A number of 147 bodies, i.e. 16.6% of the considered sample, are found to be of cometary origin according to the source model. Note that for all these bodies, the Tisserand parameter has a typical value of JFC, namely 2 < T < 3 (Kresák 1972; Carusi et al. 1987). Moreover, their eccentricities are very large, varying between 0.823 and 0.899, while only 22/147 particles have inclinations $\geq\! 20^{\circ}$ (the largest value being  $25.4^{\circ}$), the inclinations of 29 of them being even smaller than  $10^{\circ}$.

6.5 Discussion

It is important to stress that an overlap between the different intermediate sources is possible. In fact our criterium, i.e. a body is from a source S_i if the corresponding probability P_i is the greatest, is a crude approximation. In particular, when the difference between two source probabilities is smaller or equal to 0.1, the method used by Bottke et al. (2000, 2001) is not accurate enough to discriminate between the two sources. Thus for each orbit, which source has been defined by applying the first criterium, we have also calculated all the differences P_i - P_j and decided that it is not possible to discriminate between two sources S_i and S_j whenever P_i - P_j is smaller or equal to 0.1. This defines criterium 2 in Table 8.

From the 40 bodies whose origin was first found to be the 3:1, 9may actually come from either the 3:1 or the secular resonance $\nu _6$. Furthermore, among these 9 particles, 2 could come also from the MC source.

Considering the 678 bodies first identified coming from the S₂ source (criterium 1), it is equally possible, according to criterium 2, that 70 come from the two asteroidal sources S₂ and S₁ since their P₂ - P₁ is smaller than 0.1. For 80 other particles, we also found that P₂ - P₃ < 0.1, which indicates that they may come either from the $\nu _6$ secular resonance or the Mars-crosser source. Moreover among these 150 bodies with two potential sources, 24 bodies have P₂ - P₁, P₂ - P₃ and P₁ - P₃ smaller than 0.1. These 24 bodies may thus come either from the 3:1 or the $\nu _6$ resonances or the Mars-crosser source. Among them, 8 of the 24 bodies have a semimajor axis $a \simeq 2.4$ AU and a Tisserand parameter always smaller than 3 ( $2.89 \leq T \leq 2.98$), while the 16 remaining ones have a semi-major axis smaller than 1.6 AU and a Tisserand parameter between 3.88 and 4.05.

Thus applying criterium 2, among the 678 bodies, 528 should come from the $\nu _6$ intermediate source, 70 either from the 3:1 or the $\nu _6$ sources, 80 either from the $\nu _6$ or the Mars-crosser source. Futhermore among these latter 150 bodies, 24 may come from one of the three asteroidal sources.

Considering the 21 orbits, which according to criterium 1 originated in the Mars-crosser source, 10 bodies have P₃ - P₂ < 0.1. Thus following criterium 2, they may find their origin either in the MC source or the $\nu _6$ one. Finally, criterium 2 does not change the result with criterium 1 concerning orbits coming from the cometary source.

It is also interesting to compare our results using a more traditional distinction between NEA and NEC. In fact, NEA and NEC are traditionally classified according to the Tisserand parameter. Bodies on orbits with T < 3 are classified as comets while NEO with T > 3 are classified as asteroids. Following this classification, in our sample of 886 particles, we counted 201 ($22.7\%$) bodies on orbits with T<3 and 685 (77.3%) bodies on orbits with T>3. Therefore, this classification also indicates that the asteroidal origin is more probable than a cometary one.

However, there are some exceptions of small bodies for which this classification is not valid. Indeed, several of the comets observed actually have a Tisserand parameter greater than 3. One of them, namely 2P/Encke (with T=3.03), has a perihelion distance q <1.3 AU and a semi-major axis a<4.2 AU, i.e. has orbital properties in the range which consents the computation of source probabilities according to our previous method. We thus selected the 18 TCB orbits resembling that of 2P/Encke in our sample. These orbits have a semi-major axis in the range $1.8 \leq a \leq 2.65$ AU, an eccentricity $0.6 \leq e < 0.9$, an inclination $i \leq 15^{\circ}$ and a Tisserand parameter 3.0<T<3.3. If 2P/Encke represents well this kind of orbits, we would expect to find a greater probability of cometary origin for these similar TCB orbits. We therefore checked this possibility and have found that for 100% of these orbits, the greatest probability is given by the $\nu _6$ resonance source. Note however that in the model of Bottke et al. (2001), terrestrial planets were not included in their comet integrations. The authors suggest that their model cannot precisely determine how many extinct comets can reach Encke-type orbits. However, it is still not clear whether accounting for terrestrial planets in cometary integrations would change this result.

Nevertheless, if Encke-type orbits can be reached from the $\nu _6$ source, two explanations can be proposed. Bodies on these orbits could have an asteroidal origin (recall that this source corresponds to main belt bodies injected in the $\nu _6$ secular resonance). Another explanation is that these bodies actually have a cometary origin, and that there is a dynamic path provided by the $\nu _6$ resonance, which allows JFC to become NEC via the main asteroid belt. Such an explanation has already been proposed by Valsecchi et al. (1995) and Valsecchi (1999) concerning a possible connection of the Taurid complex to JFC via the main asteroid belt.

Therefore, even weighting our interpretation in favour of a cometary origin, i.e. assuming a cometary source for the 2P/Encke-like orbits, and using the traditional classification based on the Tisserand parameter, we find only 18+201=219 (24.7%) orbits in our sample with a cometary origin.