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Leonids 1901-2100
Introduction The Leonids are a meteor shower known for its variable activity. The years around parent comet 55P Tempel-Tuttle returns gave considerable activity enhancements, sometimes up to stormy levels. The latest perihelion of 55P was in 1998 and now it is moving to the outer areas of Solar system - its aphelion lies behind the orbit of Saturn. Significant enhancements in Leonid activity were recorded during the period 1994-2003. In 1999, 2001 and 2002 the shower gave several storms, when ZHR reached 3000-4000 (ZHR - zenithal hourly rate - the average number of shower meteors an observer can see during one hour when its radiant is directly overhead and stars to 6.5 mag. are visible). In 2003 and 2004 activity was slightly above the background level with ZHRs of 60 and 28, respectively (background activity is shown by the Leonids in their "quiet" years, it usually reaches ZHR=10-20). All main peaks of Leonid activity are traced very well with the use of meteor particles evolution modelling. Particles ejected by the comet form lengthy trails. One of the reasons is the radiation pressure force, which acts along with gravitational forces. Gravitational force depends on a particle mass, i.e. it is proportional to the third power of particle radius. The outcrying radiation pressuse is defined by the second power of particle radius. So far the influence of radiation pressure is the more the less is size of a particle. Its action is equivalent to the diminishing of gravitational constant G. So it increases the orbital period of particles, and the tinier a particle is, the more it is continuously retarded from larger particles after their ejection by the parent comet. This process therefore leads to the formation of lengthy comet trails. Meteor modelling is done through computation of orbital evolution of particles ejected by a comet with different velocities in directions tangential to the comet trajectory at the moment of perihelion. In the reality, of course, particles are ejected not only at the point of perihelion, but also during several months around it. However, comets are in perihelion part of their orbits during quite a little time comparing to their overall orbital period and main perturbations happen around their aphelions, so when comets are close to the Sun newly ejected particles move very close to them in a compact dust cloud. This is the reason we can consider that cloud as completely ejected in the point of perihelion, it doesn't virtualy influence to the results of computations. Speaking of directions in which particles are ejected we can say that, again, in the reality they are ejected far not only in tangential directions, but in all possible ones. However, ejection velocities (from 0 to 100 m/s, and the overwhelming majority of real ejections - from 0 to 20 m/s) are negligibly small comparing to the own comet velocity (from 30 to 40 km/s) near the Earth's orbit), ejected particles have only slightly changed orbits and don't "fly away in all directions". Radial part of ejection velocity defines only thickness of a trail, which usually reaches several hundreds thousands kilometers. The shape of the trail is defined by tangential part of ejection velocity. And the last. Non-gravitational forces are often not taken into consideration in meteor calculations, as is in our case. However, some of them, say, radiation pressure, can be considered indirectly. As far as this kind of force works as diminishing of gravitational constant G, this is equivalent to increase of ejection velocity which could be easily accounted in the model. So this non-gravitational force, as many others doesn't change configuration of trails, but leads to shifting of particles with different masses along them. As spoken previously, Leonid trails modelling allowed to prepare very good predictions of shower activity around the latest comet perihelion, real maximums differed from predicted ones mostly no more than on 10-15 minutes - not very much considering that computations are made for several hundreds years of particles movement. Also succesful post-predictions were done for Leonid outbursts in the past, for example, for famous storm in 1966. More serious problem is prediction of outburst intensity - how strong the maximum could be. For such predictions special empirical models were elaborated (the single way in this case) but as before for their improvment new observations are very necessary. The results the Author obtained for suggested past and future Leonid during the period 1901-2100 are presented in this paper. Predictions were done for each year in the period mentioned, and, as this work is finished in 2006, it contains "real" predictions for the years 2006-2100, while for the years 1901-2005 "postpredictions" were compiled. Also, although the models used in computations, are based after all on meteor observations of real activity in the past, I do not make comparisons for each year between my predictions and respective real Leonid activity. Computation characteristics This paper presents the results of the Leonid meteor stream simulation aimed to prediction of its meteor activity in 1901-2100. The simulation was made for the trails of past 30 revolutions and future 2 ones, i.e, beginning from the 1001 trail, and partially for the trails of 31-33, i.e. 901, 935 and 967 trails. Two future trails are 2031 and 2065 ones. The Author used the program created by S. Shanov and S. Dubrovsky "Comet's Dust 2.0" to calculate orbital elements of ejected meteor particles. To estimate expected ZHRs for different encounters the model built by E. Lyytinen and T. van Flandern and presented in their paper [4] was used with some Author's alterations made in order to adopt the model for ejection velocity (Vej) instead of da0 (difference in a-semimajor axis) as well as to correct fn function to consider factual Leonids activity during recent storms and outbursts. The computation considered only gravitational forces, however, the results are in the whole in good accordance with those of other researchers. The prediction includes all encounters found within interval +/-0.007 a.u. The following parts of trails were computed: the first 5 rev. trails for ejection velocities [-50;100] m/s, 6-10 rev. trails - [-30;50] m/s, 10-20 rev. trails - [-20;30], older than 20 rev. trails - [-10;20] m/s. Predictions for different years of Leonid activity are divided into decades, for each year a table with meaningful encounters with Leonid trails (i.e. giving ZHR>=1) and with time of traditional maximum based on the moment of the closest distance between the Earth and the current for decribed year orbit of the comet 55P is given. A typical sample of such table is shown in Table A1. Table А1
2000
We have to give some details for reliability and intensity. For each encounter with a trail the tables give the Author's estimations of its reliability (on 5-degree scale) and for traditional maximum - the Author's estimation of its intensity (also on 5-degree scale). The values of these estimations have the following interpretation: А. Reliability of encounters with trails: 4 - very high reliability. The enhancement will almost exactly take place, its actual maximum time should differ from predicted one up to no more than several minutes and its intensity should be quite close to the predicted value. 3 - high reliability. The enhancement will almost exactly take place, but its actual maximum time can differ from predicted one up to 15-20 minutes and its intensity can substantially, in 2-3 times, differ from the predicted value. 2 - moderate reliability. The enhancement will very likely take place, but there is small possibility of its absense. Its actual maximum time can differ from the predicted one up to many tens of minutes and its intensity can differ from the predicted value in many times. 1 - low reliability. There is substantial possibility of enhancement appearance, but its absence is also quite likely. Its actual maximum time can differ from the predicted one up to many tens of minutes and its intensity can differ from the predicted value in many times. 1 - very low reliability. The enhancement appearance is possible, but its absence is more likely. Its actual maximum time can differ from the predicted one up to many hours and its intensity can differ from the predicted value in many times. B. Expected intensity of traditional maximum 4 - very high intensity. In usual years (i.e. far from perihelion of 55P) activity should be about 25 meteor on ZHR scale or even higher. 3 - high intensity. In usual years activity should be about 20-25 meteor on ZHR scale. 2 - normal intensity. In usual years activity should be about 15-20 meteor on ZHR scale. 1 - low intensity. In usual years activity should be about 10-15 meteor on ZHR scale. 0 - very low intensity. In usual years activity should be about 5-10 meteor on ZHR scale, but almost total lack of activity is also not excluded. Intensity of traditional maximum depends on two things: 1) variations of distance between the Earth orbit and background Leonid activity due to perturbations from planets of the Solar system, and 2) periodic perihelions of the parent comet, as there is much more bachground particles in its surrondings comparing to the rest of the Leonid orbit. It should be noted, that intensity estimations for traditional maximum in prediction table are given only on the base of the first mentioned point, i.e. perihelions of 55P are not taken into considerations. So far the Author's comments to the tables are also of great importance. As it is impossible to display in tables all nuances and detales for each prediction, information given in comments has priority-driven character comparing to the data in tables. It doesn't mean that it will be in contradiction with tables (at least, not in the Author's point of view), but formal figures far not always can tell the reader how to understand prediction correcly. For example, it may be written in tables that intensity of traditional maximum is expected to be normal (estimation of intensity is equal 2), but for a year close to perihelion of the parent comet a normal intensity of traditional maximum should be several times higher than in usual years. There could be a number of such situations in different predictions. Orbit of the comet 55P in 1901-2100 Initial orbital elements of 55P, starting from perihelion of 901 and up to 1998 are taken from Nakano's site, [2]. Orbital elements for perihelions in 2031, 2065 and 2098 are generated in the program [1]. Orbital elements of 55P in the period 1901-2100, as well as values of minimal distances to the Earth orbit for these elements and relative solar longitudes are given in Table A2. Table А2
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