1 Introduction

The interrelation between comets and meteor streams is one of the important topics in meteor science. The question is not only the identification of the parent body for a particular meteor stream, but also to the understand the physical aspects of cometary and meteor shower activities. The recent advancement of the dust trail theory that was effectively applied by Kondrat’eva and Reznikov (1985) made it possible to predict meteor shower activities precisely, and to give us the opportunity to observe even minor showers, such as the June Bootids (Kasuga et al. 2004; Jenniskens 2004), when we know their parent comet (see Watanabe 2004 for a review). It seems also possible to apply the proven successful dust trail theory to study the history of past activities of a parent comet by mapping its meteor streams. This “inverse” approach may be a good tool for studying the physical evolution of the comets in the inner solar system.

The validity of this approach was already demonstrated for the Phoenicid meteor shower and the parent object 2003WY25 (Watanabe and Sato 2005), which is thought to be a dormant fragment from comet P/Blanpain(1819 W1). The “inverse” application of the dust trail theory to this case successfully reproduced the historical outburst in 1956 (Watanabe and Sato 2005; Jenniskens and Lyytinen 2005). At the epoch of the outburst it was revealed that a bundle of the trails that had formed from the late eigteenth through the early nineteenth centuries came close to the Earth’s orbit on December 5 (Watanabe and Sato 2005). The bundle consisted of the trails formed mainly between 1743 and 1808, but especially the trails formed between 1760 and 1803 came close to the Earth’s orbit within 0.00045 AU. This indicates that the parent object was definitely active enough to eject meteoroids until early in the nineteenth century, including 1819 when this parent body was observed as an active comet. Because the parent comet was only witnessed during 1819, the strong cometary activity during this apparition, such as an outburst or fragmentation event may have caused the strong display in 1956 (Jenniskens and Lyytinen 2005). The parent object 2003 WY25 is either a dormant comet or a comet entering a dormant phase. Jewitt (2006) found an extremely faint coma around this object. The history of this object’s activity can be traced by inspecting the Phoenicid meteor shower activity, which then becomes a “fossil record” of its past activities.

2 Future Activities of Phoenicids

We carried out the calculations for future Phoenicid dust trails, and surveyed the situation of the dust trails that come close to the Earth’s orbit within 0.003 AU. We found two cases of possible Phoenicid activities expected in 2008 and 2014. The latter has better condition because of the lower ejection velocity and the concentration of five closely spaced trails (Fig. 1).

Fig. 1
figure 1

The geometrical relationship between the dust trails of the Phoenicids and Earth’s orbit in 2014

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It is clear that a bundle of the trails formed in early twentieth century will come close to the Earth’s orbit, especially the five trails from 1909 through 1930 (Fig. 1). That is, assuming the parent object was active enough to eject meteoroids in this period, the 2008 activity would be due to the just one trail formed in 1866. If we see any Phenicid meteor shower activity in 2008, we will know that the parent object 2003 WY25 was still active in the middle of the nineteenth century. When the dust trail theory will have successfully predicted both these shower activities, we will have gained confidence we could also apply the theory backwards using showers as “fossils” of the past parent body activity.

3 Relation between Cometary and Corresponding Meteor Shower Activities: October Draconids

In order to clarify the quantitative relation between cometary and the corresponding meteor shower activities we need an appropriate sample set. It has to satisfy two conditions: (1) strong meteor shower outbursts were observed and the attributed dust trails for the outbursts can be identified and (2) the parent comet was observed as an active comet at the epoch of the formation of these dust trails. It is generally difficult to find such example of meteor showers that satisfy both conditions. For example, in the case of the Leonids we can easily find out various records of the most of its meteor showers related to trails dating back to 802 AD (Asher et al. 1999) but not for the parent comet 55P/Tempel-Tuttle which was firts seen briefly in 1366, and well observed only in 1865 and had its next apparition in 1965.

Among the short periodic comets, the most suitable example appropriate for our purpose is comet 21P/Giacobini-Zinner and the associated October Draconids. The outburst observed in 1998 is explained simply by the single dust trail produced in 1926. This comet was discovered in 1900 and observed as an active comet in 1926, which means that we may exploit this situation as a basis to relate apparitions of the meteors in October Draconids to activity of the parent comet. We selected two other apparitions of October Draconid meteor storms observed in 1933 and 1946. The former was attributed to two dust trails produced in 1900 and 1907, while the latter was caused by six trails from 1900 through 1933. The fM value for each trail is calculated by the dust trail theory (Asher 1999). The parameter fM is the degree of the extension of the trail, and is derived by fM = Δt 0/Δt, where Δt time needed for the trail passing of the ecliptic plain, and Δt 0 is the same but at the first return, without considering the perturbation (Asher 1999). The fM value is basically proportional to n −1, where n is the number of returns. Hence the fM is a measure of the meteoroid density within a trail, namely a large fM value indicates a strong shower; a low value corresponds to a weak meteor display. The strength of a meteor shower can be generally expected by the summation of the fM values of the attributing trails.

Figure 2 shows the relation between the observed ZHR and fM values. The observed ranges of the ZHR applied here are 10,000 ± 2,000 for 1933 storm, and 12,000 ± 3,000 for 1946 storm (Jenniskens 1995). Although we find the general trend that the observed ZHR increases with larger fM, the “estimated” line, normalized by the 1998s case, does not coincide with the 1933 and 1946 storm levels. The observed ZHR was much higher than was “estimated” by this method. The 1998 storm was caused by a single trail of 1926. Inspecting the average brightness of the parent comet during this apparition of 1926, we find that the parent comet was fainter than other decades (Vsekhsvyatskij 1964). The dust production rate should be larger if the comet was more active. In order to consider this effect, we surveyed the absolute magnitude derived from archived data, and corrected as Σ (fM × ΔQ(H10)), where Q(H10) is the dust production rate factor relative to the 1926s case. The result is shown in Fig. 3 that shows a generally better agreement between the observed and “estimated” ZHR for storms within the error of calculation, although the 1933s storm is still a little bit higher value than “estimated” line.

Fig. 2
figure 2

The relation between the ZHR and fM value. The solid line is the expected relation when normalized to the 1998 outburst. The vertical lines are the range of the observed ZHR. Both the 1946 and 1933 storms are higher than expected

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Fig. 3
figure 3

Same as Fig. 2, but the “corrected” fM value by the absolute magnitude of the parent comet. The 1933 and 1946 storm activities are well within the expected level of the 1998 activity case

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It should be noted that there are many factors that should be included in this correction. We assume the same size distribution for the dust particles, and here we neglected the effect of the dust ejection velocity. There are additional factors we should consider when trying to apply such relation to other meteor shower and parent comet relationships. The dust to gas ratio will be different among comets. Although 21P/Giacobini-Zinner has a typically average value for the dust to gas ratio, it is also famous for being a chemically peculiar type of comets known as carbon-depleted comets (A’Hearn et al. 1995). The coma of this comet is abundant in larger size grains (Lara et al. 2003). In order to establish the relation between the strength of meteor showers and cometary activities, we should obtain many samples appropriate for such purpose in the future.

4 Concluding Remarks

As shown for the Phoenicids, meteor activity may be used for studying past cometary activity of the parent comet. In order to do this, it is important to establish the quantitative relationship between cometary and meteor shower activities. We showed here a result of an effort to clarify the relationship for the October Draconids and their parent comet 21P/Giacobini-Zinner. More work needs to done on a larger set of related comet-meteor activities to improve the accuracy of applying the “inverse” dust trail theory. The predicted October Draconids activity in 2011 will be mainly due to the 1887 and 1900 trails. Unfortunately we do not have any data on the cometary brightness in 1887. Assuming the cometary activity in 1887 was similar to that in 1900, when the comet was much brighter than 1926, our method applied to the October Draconids 2011 activity predicts that the ZHR will be about 600. It will be around 200 when we neglect the cometary activity difference between 1887–1900 and 1926.

5 Historical Note

While travailing in the Indian Ocean as a member of a Japanese expedition on December 5, 1956, Prof. J. Nakamura observed the sudden appearance of a Phoenicid meteor shower. Watanabe and Sato (2005) noticed an apparent non-negligible discrepancy in the radiant point based on his observations. In 2006 we met with Prof. J. Nakamura, now retired in his home. He expressed his unfamiliarity at the time using the standard astronomical method of plotting meteors in a star chart. He had only a small-size star chart available that was inadequate to determine the precise radiant position.