Resonant behavior of comet Halley and the Orionid stream



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 (MMR) in the evolution of various meteoroid streams. Here, we look at how various resonances, especially the 1:6 and 2:13 MMR 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 time scales of the order of 10,000 yr and 1,000 yr 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, and 2006–2010 with the 1:6 resonance and meteor outbursts in 1916 and 1993 with the 2:13 resonance. Ancient as well as modern observational records agree with these theoretical simulations to a very good degree.


Various contributions from ancient civilizations have helped in making a detailed observational record (Yeomans and 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 and Kiang 1981) perihelion passage times (the first calculations performed 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.

Historical confirmations of the annual nature of the Orionid meteor shower date back to as early as Edward Herrick's observations in 1839 (Lindblad and 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 civilizations (Imoto and Hasegawa 1958; Zhuang 1977) could also correspond to the Orionid shower. Nevertheless, the association of the stream with comet Halley and explaining the differences in the Orionid shower compared with the Eta Aquariids (which have the same parent body) has been a very challenging task (McIntosh and Hajduk 1983; McIntosh and 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 approximately 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 yr) of 1P/Halley is estimated to be of the order of 100,000 yr (Hughes 1985; Hajduk 1986; Steel 1987; Bailey and Emel'yanenko 1996). Bailey and Emel'yanenko (1996) showed that Halley undergoes Kozai resonance (Kozai 1979) during its long-term evolution. It is reasonable to believe (see later) 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 nonuniform (Miskotte 1993; Rendtel and Betlem 1993; Rendtel 2007, 2008; Trigo-Rodríguez et al. 2007; Arlt et al. 2008; Kero et al. 2011; International Meteor Organization Records) 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 and Emel'yanenko 2002; Ryabova 2003, 2006; Jenniskens 2006; Vaubaillon et al. 2006; Jenniskens et al. 2007; Christou et al. 2008; Soja 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.

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 from 240 B.C. to 1700 A.D., respectively. Integrations were repeated for different values of nongravitational parameters (Marsden et al. 1973; Marsden and Williams 2008) to ensure that this resonant pattern is not sensitive to small changes in nongravitational forces. Figure 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.

Figure 1.

Evolution of 1:6 resonant argument of 1P/Halley over 6,000 yr from 2404 B.C.

Figure 2.

Evolution of 2:13 resonant argument of 1P/Halley over 6,000 yr from 2404 B.C.

All the orbit integrations in this work were performed using the MERCURY package (Chambers 1999) incorporating the RADAU algorithm (Everhart 1985), and including the sun and eight planets, whose present orbital elements were taken from JPL Horizons (Giorgini et al. 1996). Elements for the comet were taken from Yeomans and Kiang (1981).

As the comet has a retrograde orbit, the change in the definition of longitude of pericentre ϖ (Saha and Tremaine 1993; Whipple and Shelus 1993) was incorporated while computing the resonant arguments:

display math(1)

where Ω and ω are longitude of ascending node and argument of pericentre, respectively.

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 and 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:

display math(2)

where q is the order of resonance, σ and λ denote resonant argument and mean longitude, respectively, and subscripts c and j stand for the comet and Jupiter.

display math(3)
display math(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 of which 50 were checked, all of them verifying the result of Fig. 2. In Figs. 1 and 2, σ is plotted for the combinations shown in Equations (5) and (6), respectively.

display math(5)
display math(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.

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 (a= 17.17 AU) and 2:13 (an = 18.11 AU) resonances, respectively. Here, we quote an = the “nominal resonance location” (Murray and Dermott 1999, Section 8.4), which is the value of semimajor axis corresponding to a resonant orbital period assuming the most simple case where math formula (which denotes orbital precession) is zero, i.e., as implied by Kepler's third law (Kepler 1609, 1619).

Figure 3.

(a,M) space for 1:6 resonance showing regions where particles undergo resonant librations, as a function of initial semimajor axis and mean anomaly at the initial epoch JD 1208880.5 in 1404 B.C.

Figure 4.

(a,M) space for 2:13 resonance (cf. Fig. 3); initial epoch JD 1633920.5 in 240 B.C.

In a real case, math formula is never exactly zero, e.g., with the 1:6 resonance (resonant argument as per Equation (5)):

display math(7)

If we assume, as a time average, for resonant libration:

display math(8)

Then, from Equation (7),

display math(9)

where M denotes the mean anomaly.

Simplifying the expression we get

display math(10)

Differentiating Equation (10) on both sides with respect to time and using Equation (8),

display math(11)

From our numerical integrations, we find that math formula is always positive for these resonant particles. If math formula is positive, then we require the rate of change of mean anomaly to be smaller compared with the “nominal” case, which in turn means an increase in the value of semimajor axis.

display math(12)

Therefore, the actual resonant value of semimajor axis would be slightly greater than the ones given in this section. A much more comprehensive and general description about this subject and its application to meteor streams can be found in Emel'yanenko (2001).

Integrations were performed by taking 7,200 particles, varying the initial semimajor axis 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, ω, and Ω) constant. The starting epochs for Figs. 3 and 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 yr using the RADAU algorithm with accuracy parameter set to 10−12. Output data were generated for every 10 yr. 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 previous section) 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 MMR.

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 yr. 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 (denoted by q, see Equations (2) and (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 'Specific Calculations' section). It is possible in reality first that many resonant zones would only be partially filled (unlike the uniform pattern shown in Figs. 3 and 4), and second 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 Figs. 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 yr) than the equivalent for a 2:13 resonant zone (only 1–2 yr). 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 with just 1–2 yr of outburst possibilities from 2:13. The 1:6 resonance is also more effective in trapping considerably larger numbers of particles compared with 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, although dependent again on the fine structure within the respective resonances. As 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 and Betlem 1993); cf. normal rates of 20–25.

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 and thereby populate different resonant zones gradually, implying that meteor outbursts could come from different zones. One of the main aims of this work was to correlate particular resonant zones with past and present meteor outbursts. Our calculations show that the outbursts during 1436–1440, 1933–1938, and 2006–2010 (see 'Specific Calculations' section) 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 that 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 is an excellent way to match observations with theoretical simulations.

The numbers of particles trapped in other resonances close to this range of semimajor axis (16.5–19 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 is 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 centered 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 semimajor axis in the time frames that 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 the 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 the 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 of ejected particles and subsequently avoiding close encounters with other planets.

Specific Calculations

Past observations (Millman 1936; Lovell 1954; Imoto and Hasegawa 1958; Rendtel and Betlem 1993; Dubietis 2003; Rendtel 2007; Trigo-Rodríguez et al. 2007; Arlt et al. 2008; Spurny and Shrbeny 2008; Kero et al. 2011) of Orionids have shown enhanced meteor activity in some particular years. Previous interesting works (Rendtel 2007; Sato and Watanabe 2007) have highlighted the significance of 1:6 MMR in explaining the outburst in 2006. According to Sato and 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 (see previous section). Hence, more meteoroids became trapped in this resonance during this time frame compared with other years when the comet was not resonant.

Calculations were performed on similar lines to Sato and Watanabe (2007). Ejection epochs were set between 1404 B.C. and 1986 A.D. All the ejections were performed by keeping the perihelion distance and other elements as constant and by varying the semimajor axis and eccentricity. In this simple model, ejection was performed at perihelion (M = 0) in the tangential direction. Ejection velocities were set in the range −50 to +50 m s−1, i.e., both behind and ahead of the comet, meaning that over all epochs collectively, the initial orbital periods range from 60 to 88 yr, 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 into 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 velocities and subject to different radiation pressures (Kondrat'eva and Reznikov 1985; Asher and Emel'yanenko 2002).

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 (approximately 204–210 degrees) at the node and heliocentric distance of ascending node (by analyzing the difference Δr 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).

Table 1. Data of dust trails which caused various Orionid outbursts
Ejection yearExpected peak time (UT)Solar longitude (J2000.0)r (AU)Ejection velocity (m s−1)Period at ejection (years)
−11971436 Oct 13 01:44207.551+0.0012+13.1671.76
−9851436 Oct 14 17:40208.212+0.0027−12.7971.64
−9101437 Oct 14 03:00208.344−0.0013−13.671.95
−8361438 Oct 14 13:30208.522+0.0010−22.0870.12
−12651439 Oct 14 23:54208.698+0.0021+11.8870.67
−9851439 Oct 15 00:00208.702−0.0001−14.7471.23
−9101439 Oct 16 15:03210.324−0.0008−18.0771.01
−9101440 Oct 13 19:17208.258+0.0037−20.3770.54
−9851916 Oct 17 07:40204.771+0.0002+10.6477.22
−9101916 Oct 17 12:57204.990+0.0014+8.7977.29
−12651933 Oct 21 02:24208.170+0.0011+15.6971.54
−9851933 Oct 21 02:52208.190+0.0086−12.1871.77
−13331934 Oct 21 12:14208.321+0.0044+9.1371.82
−9851934 Oct 21 12:28208.330+0.0002−11.1671.99
−9851935 Oct 21 13:26208.120+0.0034−16.4271.88
−9101935 Oct 22 05:16208.771+0.0087−14.3571.79
−12651936 Oct 21 16:19208.982−0.0073+17.3571.93
−11971936 Oct 22 06:28209.568+0.0058+10.7771.21
−12651937 Oct 21 20:24208.890+0.0067+17.2771.91
−8361937 Oct 21 23:02208.998+0.0022−13.6871.85
−11971938 Oct 21 21:21208.675−0.0091+7.0071.37
−12651938 Oct 22 02:24208.883+0.0001+14.3171.22
−13331993 Oct 17 22:48204.662+0.0039+31.8877.70
−9851993 Oct 18 00:14204.724+0.0041+12.6877.77
−9101993 Oct 18 02:26204.774−0.0017+8.9877.34
−8351993 Oct 18 02:40204.782+0.0088+10.4577.64
−12652006 Oct 21 02:09207.452+0.0005+11.0370.48
−9102006 Oct 23 03:38209.461−0.0069−17.7371.08
−13332007 Oct 21 18:14207.858+0.0043+8.6071.70
−12652007 Oct 22 00:28208.118−0.0004+12.9570.91
−11972007 Oct 22 04:36208.252+0.0032+11.2571.32
−9852007 Oct 22 09:21208.486+0.0047−15.2271.13
−9102007 Oct 22 10:04208.513+0.0002−15.8171.48
−8362007 Oct 23 01:12209.140−0.0071−15.7671.41
−13332008 Oct 23 05:16210.050+0.0073+6.6171.25
−12652008 Oct 20 14:40207.412+0.0022+14.6571.30
−11972008 Oct 21 07:28208.114−0.0019+9.3070.88
−9852009 Oct 21 15:07208.214+0.0077−18.7270.41
−9102009 Oct 21 19:43208.367−0.0008−17.3471.16
−8362010 Oct 21 21:36208.225−0.0011−17.8870.97
−13332010 Oct 21 23:31208.302+0.0056+6.3071.18
−12652010 Oct 22 02:24208.424+0.0013+15.2671.44
−9102070 Oct 18 19:12204.770−0.0029+9.2477.41
−9102070 Oct 18 19:26204.779+0.0003+9.8077.56

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, Figs. 5-7 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 October 22) versus initial semimajor axis of meteoroids (ejected at −910 return). Heliocentric distance of Earth on 2007 October 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 are satisfied if initial semimajor axis is around 17.22 AU, but the total suitable range in initial semimajor axis and ejection velocities for meteoroids are 17.20 AU < a < 17.25 AU and −16.53 m s−1 < v < −15.05 m s−1, respectively. The plots are similar for other ejection epoch/outburst year pairs as well.

Figure 5.

Ascending nodal distance in 2007 versus initial semimajor axis of meteoroids in −910.

Figure 6.

Solar longitude in 2007 versus initial semimajor axis of meteoroids in −910.

Figure 7.

Difference in nodal passage times in 2007 versus initial semimajor axis of meteoroids in −910.

Our simulations indicate meteor outbursts from 1436 to 1440 A.D. due to 1:6 resonant meteoroids, which were ejected around Halley's −1265, −1197, −985, −910, and −836 returns (details in Table 1). The initial orbital periods of ejected meteoroids, which lead to all five outbursts show that most of them had almost 6 times the Jovian period. There are also historical observational records, which show heightened activity, indicating hundreds of bright meteors, in 1436 and 1439 (Imoto and Hasegawa 1958) and match our theoretical simulations well. We converted the dates from Julian calendar to proleptic Gregorian calendar in order that all dates in Table 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 performed 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 with the ones in 1436 and 1439. In our simulations, we find that resonant meteoroids ejected with positive ejection velocity (higher orbital period) encountered the Earth in 1436 and 1439. The ones with negative ejection velocity (smaller period) encountered the Earth in 1437, 1438, and 1440. Radiation pressure (not included in our integrations) would always act in the direction that would increase the orbital period 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 velocities 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 and 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 and Betlem 1993) occurred when solar longitude was between 204.7° and 204.9°, a notably different time compared with other known outbursts. Our theoretical calculations match this unusually early peaking on 1993 October 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 the past observations in 1916 (Olivier 1921) compared with 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.

The ejection epochs for 1:6 resonant meteoroids, which caused continuous enhanced activity in 2007, 2008, 2009, and 2010 (Trigo-Rodríguez et al. 2007; Arlt et al. 2008; Kero et al. 2011; IMO Records) 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 (cf. Fig. 3) of these zones. Our simulations match the observed ranges (207–210°) of solar longitude and outburst times (Trigo-Rodríguez et al. 2007; Arlt et al. 2008; Kero et al. 2011; IMO Records) for these outburst years very well. Even though the uncertainties in semimajor 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 semimajor 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 an enhanced activity from 1933 to 1938, which match old observational records (Millman 1936; Lovell 1954). Most of these meteoroids had positive ejection velocities, which are more favorable for stronger outbursts as discussed above.

Figure 8 clearly shows that meteoroids with initial orbital periods corresponding to 1:6 (around 71 yr) and 2:13 (around 77 yr) resonances have their present 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 nonresonant 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. 8, we notice that particles having orbital periods of almost 5Pj(59.2 yr), 6 Pj (71.1 yr), and 7 Pj (83.0 yr) come near the Earth's orbit, which agrees with earlier calculations performed by Sato and Watanabe (2007).

Figure 8.

Ascending nodal distance in 2007 versus initial orbital period of meteoroids in −910.

The typical ZHR for Orionids during nonoutburst years is about 20 (Rendtel and 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 2006–2010 and about 35 (Rendtel and 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 the 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 × 10−18 g cm−2 s−1, which in turn (after multiplying with the incident area of Earth) predicts 7 g s−1 during 2006–2010 and 4 g s−1 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.

Orbit of Halley Before 1404 B.C

Our calculations show that the orbit of Halley was substantially different from the present orbit at about 12,000 yr in the past. Figure 9 shows the time evolution of semimajor axis, indicating a drastic change near this time frame. A similar sudden change occurred in eccentricity, inclination, and longitude of pericentre. Figure 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. One hundred clones with orbits very similar (varying semimajor axis and eccentricity minutely while keeping the perihelion distance as constant) to the comet were integrated 30,000 yr backwards in time from 240 B.C. and this behavior is typical for about 95% of the clones.

Figure 9.

Evolution of 1P/Halley's semimajor axis in an integration going back in time from 240 B.C.

Figure 10.

Heliocentric distance of descending node of 1P/Halley in an integration going back in time from 240 B.C.

From these orbital integrations, it is clear that any meteoroid ejection before 12,000 yr 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 time scale 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.

Main Results

We find that dust trails formed by 2:13 resonant meteoroids caused the unusual meteor outbursts on 1993 October 18 (Miskotte 1993; Rendtel and Betlem 1993) and 1916 October 17 (Olivier 1921). Meteor outbursts from 1436 to 1440 and from 1933 to 1938 were due to the 1:6 resonance mechanism, which matches historical observations in 1436 and 1439 (Imoto and Hasegawa 1958) and 1933–1938 (Millman 1936; Lovell 1954). Furthermore, we are able to correlate the recent observations of outbursts from 2006 to 2010 (Rendtel 2007; Trigo-Rodríguez et al. 2007; Arlt et al. 2008; Kero et al. 2011; IMO Records) 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 the 'Specific Calculations' section).

Although nonresonant particles can produce random outbursts, our calculations show that a substantial majority 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 any of these outbursts (which makes further backward integrations and calculations very crucial).

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 this point about the importance of knowing comets' histories, one could argue that nonuniform 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 comparisons 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 and Hajduk 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 (Central Bureau for Electronic Telegrams 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 (Campbell-Brown and Jenniskens, personal communications) 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 seven in 1,900: 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 yr in the past and to correlate more past and present observations as accurately as possible.


The authors thank both the anonymous reviewers for their helpful comments, and also 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.

Editorial Handling

Dr. Dina Prialnik