INTRODUCTION

This work is a logical continuation of our previous studies (Guliyev et al., 2013a, 2013b), where we considered some aspects of the process of outbursts in comets. The processes of this kind are interesting and common phenomena in the physics of comets. They are also of interest for investigations of the interplanetary environment and the influence of solar activity on changes in the scale of cometary processes.

In terms of the causes of cometary outbursts, three opinions in the scientific literature dominant: outbursts occur as a result of changes in the solar radiation parameters; outbursts are induced by physical and chemical processes in the atmospheres of comets; outbursts result from impacts of meteoroids with cometary nuclei and the subsequent partial exposure of the nuclei surface. One cannot exclude that all the three operate. The studies of these processes were most completely reviewed by Hughes (1990).

Guliyev et al. (2013a, 2013b) considered some aspects of the type of impact of outbursts in comets. Let us briefly recall the content of the cited papers. If the comet briefly enters the zone of any meteoroid stream (see Fig. 1), the risk of collisions with meteoroids of this stream sharply increases. Consequently, in the vicinity of known meteor swarms, a total number of ascending and descending nodes (relative to the orbital planes of the swarms considered) of orbits of the flaring comets should be higher than a certain background value. In the cited papers, this effect was verified on the basis of the data on cometary outbursts and meteor streams. In fact, for many of the streams known, this prediction turns out to be accurate. In calculations, the critical distance ∆ of nodes from a stream was assumed to be 0.001, 0.005, 0.01, 0.05, and 0.1 AU.

figure 1

Fig. 1.

THE PROBLEM STATEMENT AND THE PURPOSE OF THE STUDY

Guliyev et al. (2013a, 2013b) determined some statistical properties related to the influence of meteoroid swarms on the active processes in comets. These properties are more relevant for studying the phenomenon of the disintegration of cometary nuclei. In that case, collisions may occur in the space covered by meteoroid swarms, but the comet may actually fall into fragments far from this zone (Guliyev, 2017). However, for cometary outbursts, this is far from being the case. Outbursts should occur immediately after the collision with a meteoroid. In this way, the outburst event in the comet and the cometary passage through the swarm zone may slightly differ in time. Consequently, in the present study, our primary purpose is to determine the epochs of the passages of a particular flaring comet through individual zones around the meteoroid swarms and to compare them to the epochs of outbursts. If the difference between them is not large (several days), we may suppose that the collision apparently induced a particular outburst in the comet. In addition, we also took into account the cases, when the comet was in the area of influence of several swarms for a short period of time.

So, there are many papers devoted to this concept, including those by one of the authors of the present study. Here, the complex analysis of the impact type of outbursts includes the time factor.

For definition of the parameters rs, rc, Δ, and Δ2: rc and rs are the heliocentric distances of the nodes of the cometary orbit and the meteorite stream in the corresponding direction, the value of Δ is varied in calculations, and Δ2 is also a varied parameter and means the MOID value for the pair of the comet and the meteorite stream.

OBSERVATIONAL DATA AND A WAY TO SOLVE THE PROBLEM

Unfortunately, no complete universal catalog of the outburst events is currently available. In the book by Andrienko and Vashchenko (1981), the data on the cometary outburst events, which occurred before 1975, are gathered. All of the subsequent data have not been systematized yet. In the present analysis, we primarily proceed from the systematized data of Andrienko and Vashchenko and some recent data on cometary outbursts.

In this analysis, as the data on meteoroid streams, we used the list confirmed by the International Astronomical Union (https://www.ta3.sk/IAUC22DB/MDC2007/ Roje/roje_lista.php?corobic_roje=0&sort_roje=0). It contains the information on more than 500 streams. However, only 112 of them are considered as finally approved. We also note that, in the calculations, we used the orbital elements of the streams provided by Kronk (2014) and Cook (1973). When we examined these lists in detail for the purpose of our study, it turned out that the elements of only 102 streams can be used in further calculations; in the remaining cases, either the orbit is hyperbolic, or some element of the orbit is uncertain.

To facilitate some of the calculations, we use a scheme, within which the elements of the cometary orbit are determined relative to the swarm plane. At the same time, when calculating the angular elements, we take the ascending node of the swarm’s orbit as a reference point. To obtain the heliocentric distances of the ascending and descending nodes of the cometary orbit relative to the stream, we use the formula

$${{r}_{{\text{c}}}} = {p \mathord{\left/ {\vphantom {p {\left( {1{\text{ }} + e\cos \left( v \right)} \right)}}} \right. \kern-0em} {\left( {1{\text{ }} + e\cos \left( v \right)} \right)}}$$

(where p and e are the parameter and the eccentricity of the cometary orbit, respectively). The heliocentric distance rs to the swarm is determined, when v = Ω and v = Ω + 180° (see Fig. 1). Further, the absolute value for the difference between these two distances is derived:

$$\Delta = \left| {{{r}_{{\text{c}}}}-{{r}_{{\text{s}}}}} \right|.$$

Evidently, their directions coincide. In the calculations, as in the papers by Guliyev et al. (2013a, 2013b), we chose the cases, for which the value of Δ does not exceed 0.1 AU. This selection significantly reduces the number of the cases of interest, within which a comet is linked to a meteoroid swarm; and, accordingly, the solution of the problem is facilitated.

At the next stage of the analysis, for each of the couples of a comet and a meteoroid swarm, we determined the epoch, within which the comet was at a heliocentric distance rc and had ∆ < 0.05 AU. This was done on the basis of the data available on the web-site www.jpl.nasa.gov. The epoch was compared to the date of the cometary outburst event, which is given in the book by Andrienko and Vashchenko (1981). If the difference is less than 10 days, such a comet and its outburst became an object of our study.

To verify the nature of the impact of cometary outbursts, we also use two versions of the data to analyze the minimal orbit intersection distances (MOID) of the orbits of comets and meteor swarms.

RESULTS OF CALCULATIONS

The results are presented in Table 1. The data shown are restricted to the case when the parameter ∆ does not exceed 0.05 AU.

Table 1. The outbursts of comets, the corresponding meteor streams, and the values of the parameter ∆
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Twenty-four outburst events in comets satisfied the conditions accepted. In 11 cases, the comet passed through the “impact zone” when ∆ < 0.01 AU.

For 39 outbursts, the interval between the moments of the outburst event and the passage of the comet in the ∆-zone somewhat exceeded the 10-day period, while the values of ∆ were within an interval between 0.05 and 0.1 AU.

QUALITATIVE MOID-ANALYSIS OF COMETS EXHIBITING OUTBURSTS

The above analysis was mainly based on the position of the cometary orbit node and its distance from the swarm’s orbit. Because of this, to control the solution, we used the MOID-analysis. In the first approximation, this task can be solved by applying some simplifications: we may assume that the comet approaches the swarm in the direction of one of the nodes of the cometary orbit relative to the plane of motion of the swarm and that the swarm’s orbit is circular.

Then, the approximate MOID value can be calculated with the following formula:

$$\begin{gathered} \Delta _{1}^{2} = \left( {{{r}_{{\text{s}}}}^{2} + {{{\left[ {\frac{{q\left( {1 + e} \right)}}{{1 + e\cos \upsilon }}} \right]}}^{2}} - 2{{r}_{{\text{s}}}}\frac{{q\left( {1 + e} \right)}}{{1 + e\cos \upsilon }}} \right. \\ {{\left.{ \times \,\,\sqrt {1 - {{{\sin }}^{2}}i{\kern 1pt} '\,\, \times {{{\sin }}^{2}}(\omega {\kern 1pt} '\,\, - \upsilon )} } \right)}^{2}}, \\ \end{gathered} $$

where rs is the distance of the swarm in the direction of the corresponding node of the cometary orbit; q and e are the perihelion distance and the eccentricity, respectively; i' and ω' are the angular elements of the cometary orbit; and υ is the true anomaly of the comet, which varies from 0° to 360° with an interval of 1°. The latter three elements are measured with respect to the plane of the swarm, and the reference line is the line of intersection of the orbital planes of the swarm and the comet. The formula is derived from the basic transformations of spherical triangles and the requirement to find the scalar magnitude of the stream-to-comet vector in the Sun-swarm-comet triangle. It is clear that the closer the eccentricity of the chosen swarm to zero, the higher the accuracy of the above formula. For the swarms known, this condition is not always satisfied. Consequently, this approach may be considered as approximate and diagnostic.

We made calculations and analyzed the cases, for which the nearest “working” nodes of the swarm orbits were taken as a basis. From the data of calculations, we may summarize that, in 149 cases, the flaring comets pass at distances less than 0.01 AU from the considered swarms, while this distance is less than 0.001 AU in 18 cases. Within these areas, the comets may very likely collide with bodies from the swarm, which may induce outbursts. If we assume that the working nodes of the swarms are those at large distances, the pattern will differ noticeably, but not radically. In this case, the distances less than 0.01 and 0.001 AU from the swarms correspond to 221 and 10 passages of comets, respectively. The both variants of the approximate calculations show how the nature of impacts generating outbursts is promising and deserves further analysis.

MORE ACCURATE MOID-ANALYSIS OF COMETS AND METEOR STREAMS

The preliminary diagnostic analysis of the parameters ∆ and ∆1 suggests that the MOID values for the comets exhibiting outbursts can be considered more accurately with the help of generally accepted algorithms. For this, at the further stage of the study, the methods described by Gronchi (2005) and Wiśniowski and Rickman (2013) were used. The first method is more effective in calculations for almost parabolic comets, while the second one is more effective in the case of e ≠ 1.

With the algorithms described in the cited papers, we calculated the MOID values ∆2 and selected from them all of the values not exceeding 0.01 AU. The results of these calculations are presented in Table 2.

Table 2. The number of flaring comets and the meteor streams with the upper limit of ∆2
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The data in this table show that 294 values of the quantity ∆2 are within 0.01 AU, while 14 values are within 0.001 AU. The fact that the number of cases for ∆2 exceeds the total number of the comets (116) indicates that, at the moment of the outburst, some comets were in the vicinity of more than one swarm.

ADDITIONAL MATERIAL FOR THE ANALYSIS OF HOW IMPACTS CREATE COMETARY OUTBURSTS

The results of the analysis of the data collected by Andrienko and Vashchenko give grounds to investigate more recent events of outbursts within the framework of the stated problem. We analyzed the material on the light curves of various comets, which had been accumulated at the Shemakha Astrophysical Observatory (ShAO). The results of the processing of the collected series and the calculated values of the photometric quantities were reported by Churyumov et al. (2007), Guliev and Rustamova (2005), and Guliev and Poladova (2017). Recall that, in these papers, the data on 122 long-period comets are analyzed, for which 10 664 visual estimates of the brightness of comets serve as a basis. The finally derived values and the residual dispersions allow us to determine the deviations from the general light curves of comets at a level of 3σ. Naturally, we are interested only in the deviations towards the increase of the visual brightness in a certain time interval.

We selected 34 long-period comets with the values of ∆ not exceeding 0.01 AU. The results for 16 long-period comets are presented in Table 3.

Table 3. The data on outburst events in 16 long-period comets
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The analysis of the data on the parameter ∆ rounded up to the fourth digit shows that in 21 cases the corresponding distance is even less than 0.001 AU. Some comets (for example, C/1998 U3, C/2006 A1, C/2006 M4, etc.) appear in the direct vicinity of several streams during the outburst epoch.

ABOUT COMET 17P (HOLMES)

In the present paper, the main emphasis is placed on the analysis of outburst activity of long-period comets. However, among periodic comets, there are also objects, in the light curves of which these phenomena are often observed. The object 17P is a striking representative of the comets of this kind (Gronkowski and Sacharczuk, 2010). This periodic comet (the rotation period is 6.89 years) is a member of Jupiter’s family. Consequently, it may be observed almost throughout the orbit and be under constant attention of observers.

For this comet, we calculated the values of ∆2 with respect to all of the approved meteor swarms. The result has been that the comet passes very close to nine swarms at a distance of less than 0.1 AU. The list of these streams and the values of ∆2 are given in Table 4.

Table 4. The parameter ∆2 for comet 17P relative to nine meteor swarms
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Very likely, it is this circumstance that causes unusual activity of comet 17P. Its perihelion distance is greater than 2 AU, due to which the comet is less influenced by such factors like solar activity and the solar wind.

The comet has the smallest MOID value relative to the stream 61 TAH (0.00018 AU). In the calculations, we used the orbit of the comet for 1892 (the first apparition observed).

DISCUSSION AND CONCLUSIONS

The possibility that cometary outbursts may be induced by impacts was also supposed by the other authors, in particular, by Babadzhanov et al. (1991) and Gronkowski (2004). As our analysis shows, there is strong evidence that impacts are a cause. Moreover, based on our approach and the epochs calculated for the passages through specific swarms, we may predict the outbursts of comets. However, the intensity of the stream, the physical properties of the nucleus of a particular comet, and the direction of possible collisions may also be important for this prediction. The latter factor is also related to the mutual inclinations of the orbits of the comet and the swarm (Guliyev, 2017). In head-on collisions, a cometary nucleus may disintegrate rather than only an outburst may occur. It should also be noted that, when attempting to predict outbursts, it seems to be more practical to use the parameter ∆ instead of the MOID-values for comets (∆1 or ∆2).

Impacts have an indisputable advantage: they can logically and without internal contradictions explain the events of outbursts in comets at very large distances. For example, comet C/2017 K2 exhibits activity of this kind at distances of the Kuiper belt (Jewitt et al., 2021).

Our calculations show that, among the comets from the list of Andrienko and Vashchenko, object C/1947 X1-B is at greatest risk. As follows from our calculations, the number of cases, where the MOID-value for the comet is less than 0.1 AU, is 45. Moreover, it is very likely that the corresponding parent nucleus disintegrated just due to impacts. From the additional list, comet C/2006 A1 is the most interesting object in this case. For this comet the distance ∆ takes 31 values that do not exceed 0.01 AU, and ten of them are less than 0.001 AU.

We are aware of the fact that the results of the MOID analysis need to be verified for statistical validity. On the whole, we believe that the results of our work give grounds for further development of this issue. For this, first of all, the other well-known cases of cometary outbursts should be analyzed. These cases were sporadically reported in individual papers without systematization. The list compiled by Andrienko and Vashchenko (1981) may, at best (if the number of outbursts is proportional to the number of comets), contain only one-third of all the outburst events that had occurred by that time. The additional material collected at the ShAO provides independent confirmation for the type of impact causing outbursts. After the appearance of a more comprehensive and up-to-date catalog, the nature of outbursts can be revisited. Moreover, in future, the catalog of confirmed meteor swarms will certainly be enlarged. Consequently, the various natures of cometary outbursts should be further studied in more detail. We also take into account the opinion expressed by the academician M.Ya. Marov that the analysis of the problem requires additional and more rigorous estimates of the energy providing the generation of outbursts during collisions of particles with a cometary nucleus.