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Resonant Behavior of Comet Halley and the Orionid Stream
A. Sekhar
1 1,2

and D. J. Asher

1

Armagh Observatory, College Hill, Armagh BT61 9DG, United Kingdom

arXiv:1303.2928v2 [astro-ph.EP] 21 Mar 2013

2

Queen's University of Belfast, University Road, Belfast BT7 1NN , United Kingdom E-mail: asw@arm.ac.uk , asekhar01@qub.ac.uk

Received: 24 Aug 2012; Accepted: 6 Mar 2013; Meteoritics & Planetary Science

Abstract- Comet 1P/Halley has the unique distinction of having a very comprehensive set of observational records for almost every perihelion passage from 240 B.C. This has helped to constrain theoretical models pertaining to its orbital evolution. Many previous works have shown the active role of mean motion resonances in the evolution of various meteoroid streams. Here we look at how various resonances, especially the 1:6 and 2:13 mean motion resonances with Jupiter, affect comet 1P/Halley and thereby enhance the chances of meteoroid particles getting trapped in resonance, leading to meteor outbursts in some particular years. Comet Halley itself librated in the 2:13 resonance from 240 B.C. to 1700 A.D. and in the 1:6 resonance from 1404 B.C. to 690 B.C., while stream particles can survive for timescales of the order of 10,000 years and 1,000 years in the 1:6 and 2:13 resonances respectively. This determines the long term dynamical evolution and stream structure, influencing the occurrence of Orionid outbursts. Specifically we are able to correlate the occurrence of enhanced meteor phenomena seen between 1436-1440, 1933-1938 & 2006-2010 with the 1:6 resonance and meteor outbursts in 1916 & 1993 with the 2:13 resonance. Ancient as well as modern observational records agree with these theoretical simulations to a very good degree. Keywords: comet, meteor, orbit

1

Intro duction

Various contributions from ancient civilizations have helped in making a detailed observational record (Yeomans & Kiang 1981) of comet 1P/Halley for almost every perihelion passage right from 240 B.C. There are no credible observations relating to this comet before 240 B.C. Furthermore comet Halley has reliably determined (Yeomans & Kiang 1981) perihelion passage times (the first calculations done by Halley 1705 using Newton 1687) and orbital elements back till 1404 B.C., beyond which the uncertainty in the orbit starts to increase because of a significant close encounter with Earth at a distance of about 0.04 AU. 1


Historical confirmations of the annual nature of the Orionid meteor shower date back to as early as Edward Herrick's observations in 1839 (Lindblad & Porubcan 1999) and Alexander Herschel's radiant determination (Denning 1899) in 1864 (Herschel 1866). Many ancient records of meteors seen in October from the Chinese, Japanese and Korean civilisations (Imoto & Hasegawa 1958, Zhuang 1977) could also correspond to the Orionid shower. Nevertheless the association of the stream with comet Halley and explaining the differences of the Orionid shower compared to the Eta Aquariids (which have the same parent body) has been a very challenging task (McIntosh & Ha jduk 1983, McIntosh & Jones 1988) which interested many theoreticians for decades. Coincidentally it is widely believed that Sir Edmond Halley was the first (by 1688) to suggest that meteors were of cosmic origin (Williams 2011). Comet Halley might lose approximately 0.5% of its mass during every perihelion passage (Whipple 1951, Kresak 1987) which would predict its physical lifetime to be a couple of hundred revolutions or 15 kyr. The dynamical lifetime (time scale to remain on any kind of Halley type comet orbit i.e. orbital period from 20 to 200 years) of 1P/Halley is estimated to be of the order of 100,000 years (Hughes 1985, Hadjuk 1986, Steel 1987, Bailey & Emel'yanenko 1996). Bailey & Emel'yanenko (1996) showed that Halley undergoes Kozai resonance (Kozai 1979) during its long term evolution. It is reasonable to believe (see also Section 4 below) that Halley has been on an orbit comparable to its present one (with perihelion distance q < 1 AU), and outgassing particles thereby populating the Orionid stream, for a couple of tens of kyr. It is interesting to note that the zenithal hourly rates (ZHR) of Orionids are non-uniform (Miskotte 1993, Rendtel & Betlem 1993, Rendtel 2007, Trigo-Rodriguez et al. 2007, Arlt et al. 2008, Rendtel 2008, Kero et al. 2011, IMO database) with respect to each year. Many previous works have discussed the active role of mean motion resonances (MMR) in the dynamical evolution of various meteoroid streams (e.g. Asher et al. 1999, Emel'yanenko 2001, Asher & Emel'yanenko 2002, Ryabova 2003, Ryabova 2006, Jenniskens 2006, Vaubaillon et al. 2006, Jenniskens et al. 2007, Christou et al. 2008, So ja et al. 2011), and consequent year to year variations in shower activity. Our work aims to study the long term evolution of Halley and its associated stream focusing especially on past resonant behavior. We model particles ejected from the comet and try to correlate these with ancient as well as present observational records of meteor showers.

2

Resonant Motion of Comet Halley

Over the time frame during which 1P/Halley's orbit is reliably known, i.e. since 1404 B.C., our calculations show that the comet was resonant in the past: it was trapped in the 1:6 and 2:13 MMR with Jupiter from 1404 B.C. to 690 B.C. and 240 B.C. to 1700 A.D. respectively. Integrations were repeated for different values of non-gravitational parameters (Marsden et al. 1973, Marsden & Williams 2008) to ensure that this resonant pattern is not sensitive to small changes in non-gravitational forces. Fig. 1 shows the 1:6 resonant argument librating from 1404 B.C. to about 690 B.C., and Fig. 2 shows the 2:13 resonant argument librating from 240 B.C. to 1700 A.D. All the orbit integrations in this work were done using the MERCURY package (Chambers 1999) incorporating the RADAU algorithm (Everhart 1985), and including the sun and eight planets, whose orbital elements were taken from JPL Horizons (Giorgini et al. 1996). Elements for the comet were taken from Yeomans & Kiang (1981). 2


Figure 1: Evolution of 1:6 resonant argument of 1P/Halley over 6000 years from 2404 B.C. Since the comet has a retrograde orbit, the change in the definition of longitude of pericentre (Saha & Tremaine 1993, Whipple & Shelus 1993) was incorporated while computing the resonant arguments: =- where and are longitude of ascending node and argument of pericentre respectively. In order to absolutely confirm the librating versus circulating behavior of the resonant argument during the time frames mentioned above, various combinations of terms to define the resonant argument (Murray & Dermott 1999, Sections 6.7 and 8.2) according to the D'Alembert rules were verified. Mathematically the D'Alembert rule is given by Equation 2, and Equations 3 and 4 should be satisfied for Equation 2 to be valid. In the case of the p:(p+q) mean motion resonance = pj - (p + q )c + k1 c + k2 j + k3 c + k4
j

(1)

(2)

where q is the order of resonance, and denote resonant argument and mean longitude respectively, and subscripts c and j stand for the comet and Jupiter. k1 + k2 + k3 + k4 = q (3)

k3 + k4 = 0, 2, 4, ......

(4)

For the 1:6 MMR (q=5) there are 28 combinations and each of them was checked, verifying the interval 1404 to 690 B.C. shown in Fig. 1. For the 2:13 MMR (q=11) there are 182 combinations 3


Figure 2: Evolution of 2:13 resonant argument of 1P/Halley over 6000 years from 2404 B.C. of which 50 were checked, all of them verifying the result of Fig. 2. In Figures 1 and 2, is plotted for the combinations shown in Equation 5 and 6 respectively. k1 = 5, k2 = k3 = k4 = 0 k1 = 5, k2 = 4, k3 = 1, k4 = 1 (5) (6)

When the comet itself is resonant, there are more chances for the ejected meteoroid particles to get trapped in resonance which in turn would enhance the chances for meteor outbursts in future years. That is an important motivation for looking into the resonant behavior of the parent body.

3
3.1

Resonant Structures in the Orionid Stream
General Schematic

Figures 3 and 4 shows the general schematic of the geometry of resonant zones in the case of 1:6 (an =17.17 AU) and 2:13 (an =18.11 AU) resonances respectively. Here we quote a = an = the `nominal resonance location' (Murray & Dermott 1999, Section 8.4), which is the value of semi-ma jor axis corresponding to a resonant orbital period assumes the most simple case where (d/dt) (which denotes orbital precession) is zero, i.e. as implied by Kepler's third law (Kepler 1609, 1619) In a real case (d/dt) is never exactly zero, e.g. with the 1:6 resonance (resonant argument as per Equation 5): 4


Figure 3: (a,M) space for 1:6 resonance showing regions where particles undergo resonant librations, as a function of initial semi-ma jor axis and mean anomaly at the initial epoch JD 1208880.5.

= j - 6c + 5

c

(7)

If we assume, as a time average, for resonant libration: d /dt = 0 then j - 6(c + Mc ) + 5c = where M denotes the mean anomaly. Simplifying the expression we get j - c - 6Mc = Differentiating Equation 10 on both sides with respect to time and using Equation 8, (dj /dt) - (dc /dt) - 6(dMc /dt) = 0 (11) (10) (9) (8)

From our numerical integrations we find that (dc /dt) is always positive for these resonant particles. If (dc /dt) is positive, then we require the rate of change of mean anomaly to be smaller compared to the `nominal' case, which in turn means an increase in the value of semima jor axis. 5


Figure 4: (a,M) space for 2:13 resonance (cf. Fig. 3); initial epoch JD 1633920.5

a

r eal

= an + a

(12)

Therefore the actual resonant value of semi-ma jor axis would be slightly greater than the ones given in this section. A much more comprehensive and general description about this sub ject and its application to meteor streams can be found in Emel'yanenko (2001). Integrations were done by taking 7200 particles, varying the initial a from 16.5 to 17.9 in steps of 0.014 AU for 1:6 MMR and from 17.6 AU to 18.6 AU in steps of 0.01 AU for 2:13 MMR, and initial M from 0 to 360 degrees in steps of 5 degrees, keeping all other orbital elements (namely e, i, and ) constant. The starting epochs for Fig 3 and Fig 4 are 1P/Halley's perihelion return times in 1404 B.C. and 240 B.C. respectively. All the particles were integrated for 2,000 years using the RADAU algorithm with accuracy parameter set to 10-12 . Output data were generated for every 10 years. Resonant particles were identified by employing a simple technique which looks at the overall range of the resonant arguments (for various combinations allowed by D'Alembert rules, see Section 2) of all particles during the whole integration time to check when there is no circulation. Checks on an extensive set of representative particles covering many different libration amplitudes confirm that those particles filtered by this algorithm will have librating resonant arguments which thereby confirm the presence of respective mean motion resonances. Figures 3 and 4 give a general picture of these resonances: we can visualize 6 or 13 resonant zones spaced in mean anomaly along the whole orbit, each zone consisting of individual librating particles (cf. Emel'yanenko 1988). These zones, or clouds of resonant particles, are preserved for as long as substantial numbers of particles continue to librate. Our test integrations showed that for some particular ejection epochs the 1:6 MMR is exceptionally effective in retaining the compact dust trail structures for as long as 30,000 years. However particles disperse in mean anomaly much faster (in a few thousands of years) in the case of the 2:13 resonance and do not show such high stability. Typically the rule of thumb is that the higher the order of resonance 6


Figure 5: Ascending Nodal Distance in 2007 vs Initial Semi-ma jor Axis of Meteoroids in -910.

(denoted by q, see equation 3), the lower the strength of the resonance. A necessary condition for a resonant meteor outburst is that the Earth should encounter one of these clusters of resonant particles, i.e. when the Earth misses these clusters, there is no enhancement (which is the common case in most years) in meteor activity, at least due to the MMR mechanism. Of course there are various other factors like nodal distance, solar longitude, date and time of intersection of the meteoroid with Earth, geocentric velocity etc. which play a key role in confirming the occurrence and characteristics of a meteor outburst or storm (see Section 3.2). It is possible in reality firstly that many resonant zones would only be partially filled (unlike the uniform pattern shown in Figures 3 and 4), and secondly that within a given resonant zone there is significant fine structure which could lead to enhanced meteor phenomena if Earth happens to pass exactly through the densest parts. Similar plots to Figures 3 and 4 reveal mean anomaly distributions of resonant particles in the long term (a few millennia). The cluster of particles in a single 1:6 resonant zone occupies a much longer part of the orbit (covering 5-6 years) than the equivalent for a 2:13 resonant zone (only 1-2 years). This means that for the 1:6 MMR there can be 5-6 consecutive years of enhanced meteor activity (depending on the exact parts of the resonant stream's fine structure encountered by the Earth), compared to just 1-2 years of outburst possibilities from 2:13. The 1:6 resonance is also more effective in trapping considerably larger numbers of particles compared to 2:13. Hence meteor outbursts from the 1:6 resonance would have a higher intensity than those due to the 2:13 resonance in most cases, though dependent again on the fine structure within the respective resonances. Since there is a long record of observations for Orionids (Rendtel 2008) the same pattern could be compared and justified. The maximum ZHR in 2007 was about 80 (Arlt et al. 2008) whereas in 1993 it was about 35 (Rendtel & Betlem 1993); cf. normal rates of 2 0 -2 5 . When the comet is resonant, it would remain in a single resonant zone and populate that particular zone. When the comet goes out of resonance, it would keep traversing between zones 7


Figure 6: Solar Longitude in 2007 vs Initial Semi-ma jor Axis of Meteoroids in -910.

and thereby populate different resonant zones gradually, implying that meteor outbursts could come from different zones. One of the main aims of this work is to correlate particular resonant zones to past and present meteor outbursts. Our calculations show that the outbursts during 1436-1440, 1933-1938 and 2006-2010 (Section 3.2) are from the same 1:6 resonant zone, specifically the same one in which the comet librated from 1404 B.C. to 690 B.C. Also a future meteor outburst in 2070 would occur due to the particles in the same 2:13 resonant zone which caused increased meteor activity in 1916 and 1993. Halley presumably released many meteoroids into the 2:13 resonant zone in which it librated from 240 B.C. to 1700 A.D. but most of these meteoroids do not have the precession rate required for producing Earth-intersecting orbits at the present time. Comparison with resonant zones are an excellent way to match observations with theoretical simulations. The numbers of particles trapped in other resonances close to this range of semi-ma jor axis (16.5 AU to 19 AU) were also checked. For example the percentage of particles in 1:7 (an =19.03 AU), 3:17 (an =16.53 AU), 3:19 (an =17.80 AU) and 3:20 (an =18.42 AU) resonances with Jupiter are very low compared to the 1:6 (an =17.17 AU) and 2:13 (an =18.11 AU). It should be pointed out that if particle ejection were centred around the resonant value of 1:7 MMR, then there would be substantial amounts of resonant particles which can cause outbursts, but in reality the comet is never near this resonant semi-ma jor axis in the time frames which we consider in this work. Also the ratio of particles trapped in the Saturnian resonances of 2:5 (an =17.56 AU), 3:8 (an =18.34 AU), 5:12 (an =17.09 AU), 5:13 (an =18.03 AU), 7:17 (an =17.23 AU), 7:18 (an =17.90 AU) and 8:19 (an =16.97 AU) are extremely small owing to the overpowering effect of Jupiter's gravity. Hence significant measurable enhancements in meteor activity can be ruled out from these obscure Jovian and Saturnian resonances. Even if such resonant particles encounter Earth it will be almost impossible to distinguish them because of the lack of any sizeable increase in ZHR in any year. Hence it should be understood that just the mere fact of having some resonant particles intersecting Earth does not mean an increase from normal meteor rates. The sole criterion depends on how effective that resonance mechanism is in trapping very large numbers 8


Figure 7: Difference in Nodal Passage Times in 2007 vs Initial Semi-ma jor Axis of Meteoroids in -910. of ejected particles and subsequently avoiding close encounters with other planets.

3.2

Specific Calculations

Past observations (Millman 1936, Lovell 1954, Imoto & Hasegawa 1958, Rendtel & Betlem 1993, Dubietis 2003, Rendtel 2007, Trigo-Rodriguez et al. 2007, Arlt et al. 2008, Spurny & Shrbeny 2008, Kero et al. 2011) of Orionids have shown enhanced meteor activity in some particular years. Previous interesting works (Rendtel 2007, Sato & Watanabe 2007) have highlighted the significance of 1:6 MMR in explaining the outburst in 2006. According to Sato & Watanabe (2007), the meteor outburst in 2006 was caused by 1:6 resonant particles ejected from the comet in -1265 (1266 B.C.), -1197 (1198 B.C.) and -910 (911 B.C.). All these ejection years can be directly linked to the time frame in which the comet itself was 1:6 resonant (Section 2). Hence more meteoroids became trapped in this resonance during this time frame compared to other years when the comet was not resonant. Calculations were done on similar lines to Sato & Watanabe (2007). Ejection epochs were set between 1404 B.C. and 1986 A.D. All the ejections were done by keeping the perihelion distance and other elements as constant and by varying the semi-ma jor axis and eccentricity. In this simple model, ejection was done at perihelion (M=0) in the tangential direction. Ejection velocities were set in the range -50 to +50 m/s, i.e. both behind and ahead of the comet, meaning that over all epochs collectively the initial orbital periods range from 60 to 88 years, encompassing all possible 1:6 and 2:13 resonant particles, positive ejection velocity corresponding to larger periods. Radiation pressure and Poynting-Robertson effects were not incorporated in these calculations. Because they span a range of orbital periods, test particles ejected tangentially at perihelion and moving only under gravitational perturbations are able, over the time frames we consider here, to represent the motion of all meteoroids released over the comet's perihelion arc with different 9


Figure 8: Ascending Nodal Distance in 2007 vs Initial Orbital Period of Meteoroids in -910.

velocities and sub ject to different radiation pressures (Kondrat'eva & Reznikov 1985, Asher & Emel'yanenko 2002). In order to confirm the correlation between theory and observations, it is vital to match the time (second half of October) when the meteoroids reach their ascending node, solar longitude (approx. 204-210 degrees) at the node and heliocentric distance of ascending node (by analyzing the difference r between heliocentric distances of Earth and ascending node of meteoroid; Earth diameter is about 0.0001 AU). These essential parameters from our simulations (Table 1) can be matched with real observations (listed in past meteor records). Each entry in Table 1 is a carefully chosen meteoroid which has the average value out of many candidate particles covering the small range of orbital periods that favors an outburst in the given year. For example, Figures 5, 6 and 7 are plots of heliocentric distance of ascending node, solar longitude and difference in time of nodal crossing of the particles from the time of observed outburst (all three parameters computed at 2007 Oct 22) versus initial semi-ma jor axis of meteoroids (ejected at -910 return). Heliocentric distance of Earth on 2007 Oct 22 was 0.995 AU. These results show that the conditions for an outburst to occur (from particles ejected in -910) at the observed time in 2007 is satisfied if initial semi-ma jor axis is around 17.22 AU, but the total suitable range in initial semi-ma jor axis and ejection velocities for meteoroids are 17.20 AU

Figure 9: Evolution of 1P/Halley's semi-ma jor axis in an integration going back in time from 240 B.C.

1 are referred to a single calendar. No observational records could be traced or identified for 1437, 1438 and 1440 though. Either there were no observations done in those years (unfavorable lunar phase is a possible explanation only in 1438) or the meteor outbursts would have been insignificant in 1437, 1438 and 1440 compared to the ones in 1436 and 1439. In our simulations we find that resonant meteoroids ejected with positive ejection velocity (higher orbital period) encountered Earth in 1436 and 1439. The ones with negative ejection velocity (smaller period) encountered Earth in 1437, 1438 and 1440. Radiation pressure (not included in our integrations) would always act in the direction which would increase the orbital perio d of meteoroids, i.e. affects the period in the same sense as positive ejection velocities. In general we expect the peak of the ejection velocity distribution is close to zero and so the largest number of particles, if affected by radiation pressure, is represented by particles having positive ejection velocites in our gravitational integration model. Radiation pressure is having a detrimental effect (with regard to causing meteor outbursts) when we calculate that negative ejection velocities are required to produce a meteor outburst in a particular year. This can explain why we find this trend in ejection velocities for resonant meteoroids reaching Earth in 1436 and 1439 which caused meteor outbursts (agreeing with past observations as shown in Imoto & Hasegawa 1958) and possibly no (or very low) activity in 1437, 1438 and 1440. We calculate that the meteor outburst in 1993 was due to 2:13 resonant meteoroids ejected around Halley's -1333, -985, -910 and -835 returns. The outburst (Miskotte 1993, Rendtel & Betlem 1993) occurred when solar longitude was between 204.7 to 204.9 degrees, a notably different time compared to other known outbursts. Our theoretical calculations match this unusually early peaking on 1993 Oct 18. Our simulations also indicate a meteor outburst in 1916 from the 2:13 resonance and there is a hint of enhanced meteor rates from past observations in 1916 (Olivier 1921) compared to the adjacent years of 1915 and 1917. For the future we predict a similar outburst (like in 1993 because favorable ejection velocities are similar in both cases) from the 2:13 resonance mechanism in 2070. 11


Figure 10: Heliocentric distance of descending node of 1P/Halley in an integration going back in time from 240 B.C. The ejection epochs for 1:6 resonant meteoroids which caused continuous enhanced activity in 2007, 2008, 2009 and 2010 (Trigo-Rodriguez et al. 2007, Arlt et al. 2008, Kero et al. 2011, International Meteor Organization database) are also given in Table 1. These ejection years correspond to the time when the comet itself was 1:6 resonant. Hence it is obvious that a large number of meteoroids would have been trapped into this resonance during those time frames which would clearly indicate the reason for high ZHR apart from the contribution due to the inherent geometry (see Section 3.1) of these zones. Our simulations match the observed ranges (207-210 degrees) of solar longitude and outburst times (Trigo-Rodriguez et al. 2007, Arlt et al. 2008, Kero et al. 2011, IMO database) for these outburst years very well. Even though the uncertainties in semi-ma jor axis (to directly compare with theoretical values in our calculations) of observed meteoroids from these highly successful observations are quite high (which is the typical case for all meteor observations, especially when the semi-ma jor axis itself is high), the matching of outburst time frames and solar longitudes from these papers itself is a very effective way of comparing the orbital evolution of resonant meteoroids with real observations. Our results show that 1:6 resonant meteoroids ejected from the resonant comet also caused enhanced activity from 1933-1938 which match old observational records (Millman 1936, Lovell 1954). Most of these meteoroids had positive ejection velocities which is more favorable for stronger outbursts as discussed before. Fig. 8 clearly shows that meteoroids with initial orbital periods corresponding to 1:6 (around 71 years) and 2:13 (around 77 years) resonances have their ascending nodes near the orbit of the Earth. Hence it can be concluded that resonance mechanisms (specifically 1:6 and 2:13 MMR in this case) aid these particles to come near the Earth at the present epoch while the non-resonant ones precess away from the Earth's orbit. This is typical of other ejection epochs (as shown in Table 1) as well. The ascending node of Halley during its last apparition (in 1986) was 1.8 AU. One could clearly see that the number of particles trapped in 1:6 resonance is considerably larger than the number trapped in 2:13 resonance. Moreover in Fig. 5 we notice that particles having orbital periods of almost 5Pj (59.2 years), 6Pj (71.1 years) and 7Pj (83.0 years) come near 12


the Earth's orbit which agrees with earlier calculations done by Sato & Watanabe (2007). The typical ZHR for Orionids during non-outburst years is about 20 (Rendtel & Betlem 1993, Rendtel 2008, IMO records). From the recorded previous observations it is seen that the ZHR is about 60 (Rendtel 2007, Kero et al. 2011, IMO records) due to 1:6 MMR during 20062010 and about 35 (Rendtel & Betlem 1993) due to 2:13 MMR in 1993. Using these previous observations and flux, one could actually make a simplistic estimation of the mass delivered to Earth from the Orionid stream during these outburst years. According to the detailed work of Hughes and McBride 1989, the typical influx rate (at shower maximum perpendicular to the radiant) of Orionids is 1.8 в 10-18 g cm-2 s-1 which in turn (after multiplying with the incident area of Earth) predicts 7 g/s during 2006-2010 and 4 g/s during 1993. It should be made clear that enhanced ZHR could be quite different in other outburst years (in past as well as future) as it depends on the exact cross section and density distribution of resonant trails intersecting the earth. Moreover, given the high speed of Orionid meteors and the strong dependence of meteor brightness on velocity, the meteoroidal mass influx to Earth is not dominated by this level (ZHR = a few tens) of Orionid outburst.

4

Orbit of Halley b efore 1404 B.C.

Our calculations show that the orbit of Halley was substantially different from the present orbit at about 12,000 years in the past. Fig. 9 shows the time evolution of semi-ma jor axis, indicating a drastic change in the semi-ma jor axis near this time frame. A similar sudden change occurred in eccentricity, inclination and longitude of pericentre. Fig. 10 plots the time evolution of heliocentric distance of descending node, showing that close encounters with Jupiter are the reason for this drastic variation in the comet's orbit. 100 clones with orbits very similar (varying semi-ma jor axis and eccentricity minutely while keeping the perihelion distance as constant) to the comet were integrated 30,000 years backwards in time from 240 B.C. and this behavior is typical for about 95% of the clones. From these orbital integrations it is clear that any meteoroid ejection before 12,000 years in the past would not correspond to the present day Orionid meteor shower. Hence this particular time constraint can be used as a starting epoch for ejection to simulate the present day Orionid stream. It is also interesting to note that this timescale is close to the physical lifetime of the comet itself. In our test simulations, almost 80% of the clones get trapped into 1:6 and 2:13 resonances for at least a few thousand years between -12,000 and -1403. Hence it is confirmed that the phenomenon of resonance plays a vital role in the long term dynamical evolution of Halley itself which further stresses the motivation in looking into more resonant structures in the present day Orionid stream. This gives good scope for a lot of interesting further work.

5

Main Results

We find that dust trails formed by 2:13 resonant meteoroids caused the unusual meteor outbursts on 1993 Oct 18 (Miskotte 1993, Rendtel & Betlem 1993) and 1916 Oct 17 (Olivier 1921). Meteor outbursts from 1436-1440 and 1933-1938 were due to the 1:6 resonance mechanism which matches historical observations in 1436 and 1439 (Imoto & Hasegawa 1958) and 1933-1938 (Millman 1936, Lovell 1954). Furthermore we are able to correlate the recent observations of outbursts from 13


Ejection year -1 1 9 7 -9 8 5 -9 1 0 -8 3 6 -1 2 6 5 -9 8 5 -9 1 0 -9 1 0 -9 8 5 -9 1 0 -1 2 6 5 -9 8 5 -1 3 3 3 -9 8 5 -9 8 5 -9 1 0 -1 2 6 5 -1 1 9 7 -1 2 6 5 -8 3 6 -1 1 9 7 -1 2 6 5 -1 3 3 3 -9 8 5 -9 1 0 -8 3 5 -1 2 6 5 -9 1 0 -1 3 3 3 -1 2 6 5 -1 1 9 7 -9 8 5 -9 1 0 -8 3 6 -1 3 3 3 -1 2 6 5 -1 1 9 7 -9 8 5 -9 1 0 -8 3 6 -1 3 3 3 -1 2 6 5 -9 1 0 -9 1 0

Table 1: Data Expected pea (UT) 1 4 3 6 O ct 1 3 1 4 3 6 O ct 1 4 1 4 3 7 O ct 1 4 1 4 3 8 O ct 1 4 1 4 3 9 O ct 1 4 1 4 3 9 O ct 1 5 1 4 3 9 O ct 1 6 1 4 4 0 O ct 1 3

of dust trails which k time (J2000.0) 01:44 207.551 17:40 208.212 03:00 208.344 13:30 208.522 23:54 208.698 00:00 208.702 15:03 210.324 19:17 208.258 204.771 204.990 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 8 8 8 8 8 8 8 9 8 8 8 8 4 4 4 4 7 9 7 8 8 8 8 9 0 7 8 8 8 8 8 8 .1 .1 .3 .3 .1 .7 .9 .5 .8 .9 .6 .8 .6 .7 .7 .7 .4 .4 .8 .1 .2 .4 .5 .1 .0 .4 .1 .2 .3 .2 .3 .4 7 9 2 3 2 7 8 6 9 9 7 8 6 2 7 8 5 6 5 1 5 8 1 4 5 1 1 1 6 2 0 2 0 0 1 0 0 1 2 8 0 8 5 3 2 4 4 2 2 1 8 8 2 6 3 0 0 2 4 4 7 5 2 4

caused various Orionid outbursts r Ejection Period at (AU) velocity (m/s) ejection (years) +0.0012 +13.16 71.76 +0.0027 -12.79 71.64 -0.0013 -13.60 71.95 +0.0010 -22.08 70.12 +0.0021 +11.88 70.67 -0.0001 -14.74 71.23 -0.0008 -18.07 71.01 +0.0037 -20.37 70.54 +0.0002 +0.0014 + + + + + + + + + + + + + + + + + + + + + + + 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 8 4 0 3 8 7 5 6 2 9 0 3 4 1 8 0 6 4 0 3 4 0 7 7 2 1 7 0 1 5 1 1 6 4 2 4 7 3 8 7 2 1 1 9 1 7 8 5 9 3 4 2 7 2 1 3 2 9 7 8 1 6 3 +10.64 +8.79 +15.69 -12.18 +9.13 -11.16 -16.42 -14.35 +17.35 +10.77 +17.27 -13.68 +7.00 +14.31 +31.88 +12.68 +8.98 +10.45 +11.03 -17.73 +8.60 +12.95 +11.25 -15.22 -15.81 -15.76 +6.61 +14.65 +9.30 -18.72 -17.34 -17.88 +6.30 +15.26 +9.24 +9.80 77.22 77.29 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 1 1 1 1 1 1 1 1 1 1 1 1 7 7 7 7 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 1 .5 .7 .8 .9 .8 .7 .9 .2 .9 .8 .3 .2 .7 .7 .3 .6 .4 .0 .7 .9 .3 .1 .4 .4 .2 .3 .8 .4 .1 .9 .1 .4 4 7 2 9 8 9 3 1 1 5 7 2 0 7 4 4 8 8 0 1 2 3 8 1 5 0 8 1 6 7 8 4

1916 Oct 17 07:40 1916 Oct 17 12:57 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 3 3 3 3 3 3 3 3 3 3 9 9 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 3 3 4 4 5 5 6 6 7 7 8 8 3 3 3 3 6 6 7 7 7 7 7 7 8 8 8 9 9 0 0 0 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t t 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 2 1 2 1 1 1 2 7 8 8 8 1 3 1 2 2 2 2 3 3 0 1 1 1 1 1 2 0 0 1 1 1 0 1 0 2 2 2 0 2 0 0 0 0 0 1 0 0 0 1 0 0 1 0 1 1 2 2 0 2 2 2 2 3 5 6 6 0 3 1 2 2 0 2 2 2 3 8 0 4 9 0 1 5 4 7 5 9 1 3 2 :2 :5 :1 :2 :2 :1 :1 :2 :2 :0 :2 :2 :4 :1 :2 :4 :0 :3 :1 :2 :3 :2 :0 :1 :1 :4 :2 :0 :4 :3 :3 :2 4 2 4 8 6 6 9 8 4 2 1 4 8 4 6 0 9 8 4 8 6 1 4 2 6 0 8 7 3 6 1 4

2070 Oct 18 19:12 2070 Oct 18 19:26

204.770 204.779 14

-0.0029 +0.0003

77.41 77.56


2006-2010 (Rendtel 2007, Trigo-Rodriguez et al. 2007, Arlt et al. 2008, Kero et al. 2011, IMO database) due to 1:6 resonant meteoroids with our theoretical simulations. These correlations are very promising and give us great confidence in confirming theory with observations. Using similar techniques one could also predict similar events for the future. We foresee a meteor outburst in 2070 (due to the 2:13 resonance) similar to the 1993 outburst. Using the data (ZHR and mass flow rate) from previous observations it is also possible to roughly estimate the mass influx in outburst years (see Section 3.2). Although non-resonant particles can produce random outbursts, our calculations show that a substantial ma jority of Orionid outbursts are due to resonant structures in the meteor stream. However it must be pointed out that much older meteoroids (ejected before 1404 B.C.) may also contribute to all these outbursts (which makes further backward integrations and calculations very crucial).

6

Conclusions and Future Work

Most of the theoretical aspects of these two resonances can have very significant and interesting effects on real observations. The compact dust trails getting preserved for many 10 kyr due to 1:6 MMR hint at an exciting possibility that strong meteor outbursts could occur in the future even after the comet becomes extinct, i.e. survival times of some resonant structures could be much higher than the physical lifetime of the parent body. It is well known and obvious that understanding the history of comets is crucial to predicting meteor showers. In this work we find that Orionid outbursts in 1436-1440,1916,1933-1938, 1993 and 2006-2010 were caused by resonant particles ejected from Halley before 240 B.C., the date beyond which there are no direct observational records of the comet. As a corollary to the above point about the importance of knowing comets' histories, one could argue that non-uniform meteor rates can act as a great tool to backtrack the history of a comet beyond the time frame in which there are direct sightings of the comet itself. All of these prove how useful the comparison between meteor observations and these simulations are. In short it is an indirect confirmed observation of the comet beyond 240 B.C. Even though the Eta Aquariid shower is considerably different (McIntosh & Ha jduk 1983) from the Orionid shower in many ways, it would be worthwhile to verify whether all these resonant phenomena and enhanced activity are applicable in its case as well (CBET 944, 2007). The low number (compared to Orionids) of credible observations of Eta-Aquariids is a limitation in this regard though. Near future releases of radio results on Eta Aquariids (personal communications with Campbell-Brown and Jenniskens) would be very promising in this direction. Negative observations, comprising diminished meteor rates of Orionids in some particular years compared to adjacent years (e.g. ZHR reaching only 7 in 1900: Kronk 1988) could be as scientifically valuable as enhanced meteor phenomena which we have investigated in this work. A future careful study of such events can also be intriguing in many aspects. As the next step we plan to design an ejection model to simulate the Orionid stream beginning 12,000 years in the past and to correlate more past and present observations as accurately as possible. 15


7

Acknowledgements

The authors wish to thank both the anonymous reviewers for the helpful comments and also intend to express their gratitude to the Department of Culture, Arts and Leisure of Northern Ireland for the generous funding to pursue astronomical research at Armagh Observatory.

8

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