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Collision with meteoroids as one of possible causes of cometary nucleus splitting
Planetary and Space Science xx (xxxx) xxxx–xxxx
Contents lists available at ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Collision with meteoroids as one of possible causes of cometary nucleus splitting Ayyub Guliyev Shamakhy Astrophysical Observatory, ANAS, Baku, Azerbaijan
A R T I C L E I N F O
A B S T R A C T
Keywords: Split comets Meteor streams
The results of the testing analysis of the dynamic parameters of 114 comets undergoing nucleus splitting are presented in the article. Some aspects of the following idea as working hypothesis are studied: disintegration of the comet nucleus happens as results of their collision with meteoroid streams also. For the verification of this working hypothesis the position of splitted comet orbits have been analyzed relative to 125 meteor streams from Kronk's list. The number of comet orbit nodes separated by 0.001, 0.005, 0.01, 0.05 and 0.1 au from known meteor streams were computed and analyzed. The orbit of each meteorite stream was replaced by a set of similar pseudo-streams for comparison. Statistical methods and simulations showed that 31 out of the 125 streams have significant predominance over pseudo streams.
1. Introduction Splitting of cometary nuclei into secondary fragments is a very interesting and common fact. According to the modern notions the cause of this phenomenon can be various external and internal factors associated with comets and the conditions of their movement (changes in the sectoral structure, solar activity, tidal influence of the Sun, rotational instability, irregular sublimation et al). Another possible mechanism of comet splitting and origin of the Kreutz, Meyer, Kracht, Marsden, and other comet groups as result of such processes has been advanced by the author of this article (Guliyev, 2010, 2016). According to this mechanism, splitting can occur due to the passage of comet nuclei (parental bodies) through meteoroid streams. In our opinion, some split comets might be formed this way. Some aspects of the collision of comets and meteoroids was considered by Matsuura (1976) and Boehnhardt (2004). In this paper we will demonstrate some new arguments for this idea. 2. Objects and purpose of the study Our list of split comets includes 114 objects (26 of them are shortperiod comets, 15- disappeared and 73 - nearly-isotropic comets). Sources of this population of comets are described in Guliyev (2016). The purpose of this investigation is to analyze the distribution of the orbits of disintegrated comets relative to the orbital planes of 125 known meteor streams, the data of which are contained in the catalog of Kronk (2014). In our earlier work (Guliyev, 2016) we have obtained a very important feature for the investigated comets. Now we state itscontent briefly. For the 114 comets we calculated the distance between the cometary node relative to the meteor streams
Δ = rc − rs relatively to the meteor streams and its number N according to the interval Δ < 0.1 au. For 125 streams N was equal to 1014. After that we have replaced the split comets to other ones (in 3 variants). It was found that after such replacements the value of N has been decreased as minimum for three time. We remind thatrc - heliocentric distances near or distant nodes of the cometary orbits, rs -heliocentric distance to a stream in the direction of the according node of the comet's orbit. Details of the used comet and meteor stream parameters are given in Fig. 1. In this work we investigate possible correlation between split comets' orbits and their nodal distances to know meteor streams. For this purpose, we will apply the method used in the work by Guliyev and Nabiyev (2015) for the study of the relationship of hyperbolic meteors with the transneptunian planetary bodies. Its meaning is to compare the frequency of comet passages through the vicinity of the real and pseudo meteor streams. At the beginning the number N of orbital nodes of comets, which underwent nuclear splitting, is calculated for the distances Δ=0.001, 0.005, 0.01, 0.05 and 0.1 au from a selected stream. For the determination of the exceed’ measure of N the selected meteor stream is exchanged by 67 pseudostreams. These streams, using for the simulation, have parameters: Ω=0°, 30°, 60°,…,330° and I =0°; 9°,49°;19°;47; 30°;41°,81; 56°,44 and 90° (elementsa,e and ω are not varied). They have been chosen in such way that the poles of the planes were at equal distances from each other. To substantiate exceed's measure of N the following parameters have been computed: n (mid-range value of the number of nodes corresponding to a selected interval of Δ), σ (standard deviation), the normalized difference t=(N -n)/σ and α - its confidence probability, respectively. According to one-side Student criteria, for α > 0.95 the
http://dx.doi.org/10.1016/j.pss.2016.11.009 Received 29 August 2016; Accepted 24 November 2016 0032-0633/ © 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Guliyev, A., Planetary and Space Science (2016), http://dx.doi.org/10.1016/j.pss.2016.11.009
Planetary and Space Science xx (xxxx) xxxx–xxxx
A. Guliyev
Fig. 1. To specification of the comet and meteor stream parameters.
value of t has to be more than 1.67 (Gmurman,1968).
Table 1 Statistical characteristics (number, mid-range value, standard deviation and normalized difference) of splitting comets relative to the investigated meteoroid streams.
3. Results of testing calculations
Meteor stream
Results of test calculations are given in the Table 1. Significance values for the parameter of t have been obtained in the cases of 31 from 125 meteor streams. Total number of comet passages with α > 0.95 is 107. We should note that there are the cases when the same comet passes the zone of several streams. It can be assumed that comets having Δ < 0.001 au are most interesting to investigate possible meteoroid induced splitting. In our opinion these results can be considered as an indirect argument for the studied hypothesis on the comets' disintegration. Taking into account the possible error in determining the orbital parameters of comets and meteor streams we can assume that the cases when t exceeds the value 3 (9 cases) are most promising for our investigation. The next stage of our research concerns the approximate calculation of the impact probability of the sporadic meteoroids on the split comets. To simplify the calculations in this case we assumethat such meteoroids are mainly concentrated in the asteroid belt. In other words, calculations can be applied to the vicinity of the zone having orbital parameters:
a = 2.7 au , е = 0 and I = 0°
N
n
σ
t
Δ < 0.001 au
(1)
In this case the calculations are carried out for the following values of Δ: 0.1; 0.2; 0.3; 0.4; 0.5; and 0.6 au. Because the periodic comets cross these zones more often than long-period ones, the corresponding computations are carried out independently. The resulting values of the parameter t given in the Table 2 in fact exclude randomness and point to importance of this process for the disintegration of comets. 4. Discussion We have found a new argument for the hypothesis that disintegrated comets have one important property: the frequency of passing near known meteor streams is much higher than in the case of other groups of comets. This leads to the conclusion that one of the possible causes of the fragmentation of cometary nuclei is their encounter with meteoroid streams. Furthermore also the phenomenon of comet outbursts could be related to the same process (Guliyev et al., 2013). 2
Alpha Leonids (Antihelion) June Boötids (“Pons-Winneckids”) Daytime Lambda Taurids Epsilon Geminids Coma Berenicids Geminids
1 0.09 1 0.1 1 0.03 1 0.03 1 0.12 1 0.04 Δ < 0.005 au
0.29 0.35 0.24 0.17 0.37 0.21
3.16 2.53 3.97 5.66 2.38 4.58
Alpha Hydrids Gamma Ursae Minorids Gamma Normids April Rho Cygnids Pi Puppids Corvids July Gamma Draconids July Phoenicids Alpha Pegasids
1 1 2 1 1 1 2 2 1 Δ < 0.01
0.19 0.12 0.24 0.15 0.15 0.22 0.22 0.28 0.21 au
0.43 0.33 0.5 0.36 0.4 0.42 0.45 0.55 0.48
1.85 2.7 3.56 2.37 2.13 1.85 3.91 3.15 1.66
Daytime Chi Caprocornids Alpha Capricornids Delta Aurigids Taurids
2 2 2 2 Δ < 0.05
0.43 0.61 0.3 0.45 au
0.66 0.82 0.52 0.68
2.39 1.7 3.26 2.28
Rho Geminids April Ursids Zeta Cassiopeiids Beta Equuleids Alpha Triangulids Draconids (“Giacobinids”) Chi Orionids Phoenicids Sigma Serpentids
7 2.97 7 3.09 5 2.15 6 3.3 5 2.6 6 2.33 6 2.67 7 2.18 7 2.84 Δ < 0.1 au
1.78 1.67 1.26 1.57 1.46 1.54 1.58 1.28 1.73
2.26 2.35 2.27 1.72 1.65 2.38 2.11 3.77 2.41
Psi Ursae Majorids Epsilon Pegasids December Chi and Sigma Virginids
2 13 10
0.73 2.81 2.28
1.83 1.94 1.86
0.67 7.54 5.76
Planetary and Space Science xx (xxxx) xxxx–xxxx
A. Guliyev
cometary nuclei. Last conclusion applies more short-period comets than other ones. Finally, our explanation does not contradict to other hypotheses on comets splitting. To study the phenomenon of comets split in this study have been used only the dynamic characteristics of meteorid streams. There is an urgent need to use also their physical parameters, such as the concentration of particles, the actual number of meteors zenith hour of each stream, etc. This issue could be the subject of a separate study. In addition, we plan the calculation and analysis of the values of the inclinations of cometary orbits relative to the plane of the streams. It is necessary for estimation of relative velocity of the impacts. In the case of apartness (superiority of values I > 90°) of this distribution we will have the additional argument for considered hypothesis.
Table 2 The results (number, mid-range value, standard deviation and normalized difference) of calculations on ecliptic and nearly-isotropic comets relative to the vicinity of the zone (1). Δ, а.е. in plane (4)
N nср σ ecliptic comets
t
N nср σ Nearly-isotopic comets
t
0.1 0.2 0.3 0.4 0.5 0.6
4 7 9 10 12 16
5.5 6.5 7.1 7.0 6.8 8.3
5 7
2.4 1.8
0.30 0.60 1.81 2.44 3.00 3.30
0.67 0.99 1.02 1.08 1.33 1.54
1.90 3.97
1.28 1.67
Our hypothesis has a strength aspect. Statistical test method (Student-test) is applied to classify the comet nucleus splitting events due to collisions with meteor streams. As a result, the probabilities that the orbits of comets and meteoroids cross are given quantitatively. But on the other hand our idea has some weaknesses: ROSETTA and other in situ space probes show only very rare occurrence of impact surface features (craters). Even for Halley-type comets collisional effects are negligible on both the dynamical and collisional time scales as it was concluded by van der Helm and Jeffers (2012). Therefore, in most cases comet nucleus breakup is hardly caused by impact of meteoroids – but in very rare occasions impact induced splitting could perhaps be possible.". Some comets may suffer impact events - but very rare events - which can trigger the outbursts and perhaps the splitting. The cometary orbits in the inner solar system - as like meteoroids mainly the main belt asteroids can be suffered by collisions with meteoroids. During the last years there were collisional events between main belt asteroids and meteoroids, for example: P/2010 A2 (LINEAR) with comet designation but it is an asteroid unknown before collision with a meteoroid and another example is 596 Schelia. Our calculations have also shown that sporadic collisions with meteorids in the asteroid belt could lead to the disintegration of
Acknowledgements Author acknowledges organizing committee of Conference “Meteorids – 2016″ for the financial support. Also I would like acknowledge the reviewers for very helpful and valuable remarks. References Boehnhardt, H., 2004. (Comets II)In: Festou, M.C., Keller, H.U., Weaver, H.A. (Eds.), Split comets. University of Arizona Press, Tucson, 301–316. Gmurman, V.E., 1968. Fundamentals of Probability Theory and Mathematical Statistics 269P. Elsevier Publishing, NY. Guliyev A.S., 2010. Origin of short-perihelion comets. Baku, Publ. Comp. Elm, 151. Guliyev, A., 2016. Meteoroid streams and comet disintegration. In: Proceedings of the IMC, Egmond, pp. 94–95. GuliyevA.S., KokhirovaG.I., PoladovaU.D., 2013. Comet outbursts and the meteor showers.In: Proceedings of the Meteoroid conf.eds. Jopek T.J. et al. A.M. Univ. Press, pp. 263-266. Guliyev, A., Nabiyev, A., 2015. The features of sporadic hyperbolic meteors observed by television techniques in the period of 2007–2009. Planet. Sp. Sci. 118, 107–111. Kronk, Gary W., 2014. Meteor Showers 350P. Springer. Matsuura, O.T., 1976. Collision of comets with meteoroids. Icarus 27, 323–329. van den Helm, E., Jeffers, S.V., 2012. Dynamical and collisional evolution of Halley-type comets. Icarus 218, 448–458.
3
Contents lists available at ScienceDirect
Planetary and Space Science journal homepage: www.elsevier.com/locate/pss
Collision with meteoroids as one of possible causes of cometary nucleus splitting Ayyub Guliyev Shamakhy Astrophysical Observatory, ANAS, Baku, Azerbaijan
A R T I C L E I N F O
A B S T R A C T
Keywords: Split comets Meteor streams
The results of the testing analysis of the dynamic parameters of 114 comets undergoing nucleus splitting are presented in the article. Some aspects of the following idea as working hypothesis are studied: disintegration of the comet nucleus happens as results of their collision with meteoroid streams also. For the verification of this working hypothesis the position of splitted comet orbits have been analyzed relative to 125 meteor streams from Kronk's list. The number of comet orbit nodes separated by 0.001, 0.005, 0.01, 0.05 and 0.1 au from known meteor streams were computed and analyzed. The orbit of each meteorite stream was replaced by a set of similar pseudo-streams for comparison. Statistical methods and simulations showed that 31 out of the 125 streams have significant predominance over pseudo streams.
1. Introduction Splitting of cometary nuclei into secondary fragments is a very interesting and common fact. According to the modern notions the cause of this phenomenon can be various external and internal factors associated with comets and the conditions of their movement (changes in the sectoral structure, solar activity, tidal influence of the Sun, rotational instability, irregular sublimation et al). Another possible mechanism of comet splitting and origin of the Kreutz, Meyer, Kracht, Marsden, and other comet groups as result of such processes has been advanced by the author of this article (Guliyev, 2010, 2016). According to this mechanism, splitting can occur due to the passage of comet nuclei (parental bodies) through meteoroid streams. In our opinion, some split comets might be formed this way. Some aspects of the collision of comets and meteoroids was considered by Matsuura (1976) and Boehnhardt (2004). In this paper we will demonstrate some new arguments for this idea. 2. Objects and purpose of the study Our list of split comets includes 114 objects (26 of them are shortperiod comets, 15- disappeared and 73 - nearly-isotropic comets). Sources of this population of comets are described in Guliyev (2016). The purpose of this investigation is to analyze the distribution of the orbits of disintegrated comets relative to the orbital planes of 125 known meteor streams, the data of which are contained in the catalog of Kronk (2014). In our earlier work (Guliyev, 2016) we have obtained a very important feature for the investigated comets. Now we state itscontent briefly. For the 114 comets we calculated the distance between the cometary node relative to the meteor streams
Δ = rc − rs relatively to the meteor streams and its number N according to the interval Δ < 0.1 au. For 125 streams N was equal to 1014. After that we have replaced the split comets to other ones (in 3 variants). It was found that after such replacements the value of N has been decreased as minimum for three time. We remind thatrc - heliocentric distances near or distant nodes of the cometary orbits, rs -heliocentric distance to a stream in the direction of the according node of the comet's orbit. Details of the used comet and meteor stream parameters are given in Fig. 1. In this work we investigate possible correlation between split comets' orbits and their nodal distances to know meteor streams. For this purpose, we will apply the method used in the work by Guliyev and Nabiyev (2015) for the study of the relationship of hyperbolic meteors with the transneptunian planetary bodies. Its meaning is to compare the frequency of comet passages through the vicinity of the real and pseudo meteor streams. At the beginning the number N of orbital nodes of comets, which underwent nuclear splitting, is calculated for the distances Δ=0.001, 0.005, 0.01, 0.05 and 0.1 au from a selected stream. For the determination of the exceed’ measure of N the selected meteor stream is exchanged by 67 pseudostreams. These streams, using for the simulation, have parameters: Ω=0°, 30°, 60°,…,330° and I =0°; 9°,49°;19°;47; 30°;41°,81; 56°,44 and 90° (elementsa,e and ω are not varied). They have been chosen in such way that the poles of the planes were at equal distances from each other. To substantiate exceed's measure of N the following parameters have been computed: n (mid-range value of the number of nodes corresponding to a selected interval of Δ), σ (standard deviation), the normalized difference t=(N -n)/σ and α - its confidence probability, respectively. According to one-side Student criteria, for α > 0.95 the
http://dx.doi.org/10.1016/j.pss.2016.11.009 Received 29 August 2016; Accepted 24 November 2016 0032-0633/ © 2016 Elsevier Ltd. All rights reserved.
Please cite this article as: Guliyev, A., Planetary and Space Science (2016), http://dx.doi.org/10.1016/j.pss.2016.11.009
Planetary and Space Science xx (xxxx) xxxx–xxxx
A. Guliyev
Fig. 1. To specification of the comet and meteor stream parameters.
value of t has to be more than 1.67 (Gmurman,1968).
Table 1 Statistical characteristics (number, mid-range value, standard deviation and normalized difference) of splitting comets relative to the investigated meteoroid streams.
3. Results of testing calculations
Meteor stream
Results of test calculations are given in the Table 1. Significance values for the parameter of t have been obtained in the cases of 31 from 125 meteor streams. Total number of comet passages with α > 0.95 is 107. We should note that there are the cases when the same comet passes the zone of several streams. It can be assumed that comets having Δ < 0.001 au are most interesting to investigate possible meteoroid induced splitting. In our opinion these results can be considered as an indirect argument for the studied hypothesis on the comets' disintegration. Taking into account the possible error in determining the orbital parameters of comets and meteor streams we can assume that the cases when t exceeds the value 3 (9 cases) are most promising for our investigation. The next stage of our research concerns the approximate calculation of the impact probability of the sporadic meteoroids on the split comets. To simplify the calculations in this case we assumethat such meteoroids are mainly concentrated in the asteroid belt. In other words, calculations can be applied to the vicinity of the zone having orbital parameters:
a = 2.7 au , е = 0 and I = 0°
N
n
σ
t
Δ < 0.001 au
(1)
In this case the calculations are carried out for the following values of Δ: 0.1; 0.2; 0.3; 0.4; 0.5; and 0.6 au. Because the periodic comets cross these zones more often than long-period ones, the corresponding computations are carried out independently. The resulting values of the parameter t given in the Table 2 in fact exclude randomness and point to importance of this process for the disintegration of comets. 4. Discussion We have found a new argument for the hypothesis that disintegrated comets have one important property: the frequency of passing near known meteor streams is much higher than in the case of other groups of comets. This leads to the conclusion that one of the possible causes of the fragmentation of cometary nuclei is their encounter with meteoroid streams. Furthermore also the phenomenon of comet outbursts could be related to the same process (Guliyev et al., 2013). 2
Alpha Leonids (Antihelion) June Boötids (“Pons-Winneckids”) Daytime Lambda Taurids Epsilon Geminids Coma Berenicids Geminids
1 0.09 1 0.1 1 0.03 1 0.03 1 0.12 1 0.04 Δ < 0.005 au
0.29 0.35 0.24 0.17 0.37 0.21
3.16 2.53 3.97 5.66 2.38 4.58
Alpha Hydrids Gamma Ursae Minorids Gamma Normids April Rho Cygnids Pi Puppids Corvids July Gamma Draconids July Phoenicids Alpha Pegasids
1 1 2 1 1 1 2 2 1 Δ < 0.01
0.19 0.12 0.24 0.15 0.15 0.22 0.22 0.28 0.21 au
0.43 0.33 0.5 0.36 0.4 0.42 0.45 0.55 0.48
1.85 2.7 3.56 2.37 2.13 1.85 3.91 3.15 1.66
Daytime Chi Caprocornids Alpha Capricornids Delta Aurigids Taurids
2 2 2 2 Δ < 0.05
0.43 0.61 0.3 0.45 au
0.66 0.82 0.52 0.68
2.39 1.7 3.26 2.28
Rho Geminids April Ursids Zeta Cassiopeiids Beta Equuleids Alpha Triangulids Draconids (“Giacobinids”) Chi Orionids Phoenicids Sigma Serpentids
7 2.97 7 3.09 5 2.15 6 3.3 5 2.6 6 2.33 6 2.67 7 2.18 7 2.84 Δ < 0.1 au
1.78 1.67 1.26 1.57 1.46 1.54 1.58 1.28 1.73
2.26 2.35 2.27 1.72 1.65 2.38 2.11 3.77 2.41
Psi Ursae Majorids Epsilon Pegasids December Chi and Sigma Virginids
2 13 10
0.73 2.81 2.28
1.83 1.94 1.86
0.67 7.54 5.76
Planetary and Space Science xx (xxxx) xxxx–xxxx
A. Guliyev
cometary nuclei. Last conclusion applies more short-period comets than other ones. Finally, our explanation does not contradict to other hypotheses on comets splitting. To study the phenomenon of comets split in this study have been used only the dynamic characteristics of meteorid streams. There is an urgent need to use also their physical parameters, such as the concentration of particles, the actual number of meteors zenith hour of each stream, etc. This issue could be the subject of a separate study. In addition, we plan the calculation and analysis of the values of the inclinations of cometary orbits relative to the plane of the streams. It is necessary for estimation of relative velocity of the impacts. In the case of apartness (superiority of values I > 90°) of this distribution we will have the additional argument for considered hypothesis.
Table 2 The results (number, mid-range value, standard deviation and normalized difference) of calculations on ecliptic and nearly-isotropic comets relative to the vicinity of the zone (1). Δ, а.е. in plane (4)
N nср σ ecliptic comets
t
N nср σ Nearly-isotopic comets
t
0.1 0.2 0.3 0.4 0.5 0.6
4 7 9 10 12 16
5.5 6.5 7.1 7.0 6.8 8.3
5 7
2.4 1.8
0.30 0.60 1.81 2.44 3.00 3.30
0.67 0.99 1.02 1.08 1.33 1.54
1.90 3.97
1.28 1.67
Our hypothesis has a strength aspect. Statistical test method (Student-test) is applied to classify the comet nucleus splitting events due to collisions with meteor streams. As a result, the probabilities that the orbits of comets and meteoroids cross are given quantitatively. But on the other hand our idea has some weaknesses: ROSETTA and other in situ space probes show only very rare occurrence of impact surface features (craters). Even for Halley-type comets collisional effects are negligible on both the dynamical and collisional time scales as it was concluded by van der Helm and Jeffers (2012). Therefore, in most cases comet nucleus breakup is hardly caused by impact of meteoroids – but in very rare occasions impact induced splitting could perhaps be possible.". Some comets may suffer impact events - but very rare events - which can trigger the outbursts and perhaps the splitting. The cometary orbits in the inner solar system - as like meteoroids mainly the main belt asteroids can be suffered by collisions with meteoroids. During the last years there were collisional events between main belt asteroids and meteoroids, for example: P/2010 A2 (LINEAR) with comet designation but it is an asteroid unknown before collision with a meteoroid and another example is 596 Schelia. Our calculations have also shown that sporadic collisions with meteorids in the asteroid belt could lead to the disintegration of
Acknowledgements Author acknowledges organizing committee of Conference “Meteorids – 2016″ for the financial support. Also I would like acknowledge the reviewers for very helpful and valuable remarks. References Boehnhardt, H., 2004. (Comets II)In: Festou, M.C., Keller, H.U., Weaver, H.A. (Eds.), Split comets. University of Arizona Press, Tucson, 301–316. Gmurman, V.E., 1968. Fundamentals of Probability Theory and Mathematical Statistics 269P. Elsevier Publishing, NY. Guliyev A.S., 2010. Origin of short-perihelion comets. Baku, Publ. Comp. Elm, 151. Guliyev, A., 2016. Meteoroid streams and comet disintegration. In: Proceedings of the IMC, Egmond, pp. 94–95. GuliyevA.S., KokhirovaG.I., PoladovaU.D., 2013. Comet outbursts and the meteor showers.In: Proceedings of the Meteoroid conf.eds. Jopek T.J. et al. A.M. Univ. Press, pp. 263-266. Guliyev, A., Nabiyev, A., 2015. The features of sporadic hyperbolic meteors observed by television techniques in the period of 2007–2009. Planet. Sp. Sci. 118, 107–111. Kronk, Gary W., 2014. Meteor Showers 350P. Springer. Matsuura, O.T., 1976. Collision of comets with meteoroids. Icarus 27, 323–329. van den Helm, E., Jeffers, S.V., 2012. Dynamical and collisional evolution of Halley-type comets. Icarus 218, 448–458.
3