Possible Sources of Toroidal Region in Sporadic Meteoroid Complex

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1 WDS'11 Proceedings of Contributed Papers, Part III, 13 18, ISBN MATFYZPRESS Possible Sources of Toroidal Region in Sporadic Meteoroid Complex P. Pokorný Institute of Astronomy, Charles University, Faculty of Mathematics and Physics, Prague, Czech Republic. Abstract. Recent development in a field of meteoroid radar detection achieved mainly by use of Advanced Meteor Orbit Radar (AMOR) in New Zealand and Canadian Meteor Orbit Radar (CMOR) in Canada, gives us an opportunity to study the sporadic meteoroid complex with far better precision than in the last few decades. There are six distinctive regions of sporadic meteoroids, each covered by measurements of hundred thousands of incoming dust particles. Even though the north/south apex and helion/anti-helion regions are very interesting in the context of sporadic meteoroid complex, the most secrets and mysteries are connected with the north and south toroidal regions. None of the studies came with the plausible designation of bodies which could be proved to be sources of toroidal region particles so far. Here I present a model which is suitable for search of real sources of toroidal sporadic meteoroids. This study focuses only on cometary sources while asteroids will be a subject of future work. Using analytical computation and numerical integrations I found that only 70 comets (12 periodic) could be possible sources of toroidal region of sporadic meteoroid complex. Introduction The sporadic meteoroid complex (SMC) is a part of the Earth s meteoroid complex, formed by meteoroids whose orbits evolved sufficiently from the orbit of their parent body that the direct identification with the parent body is no longer possible. Many decades of radar observation allowed researchers to identify six apparent sources or regions of meteor radiants in the SMC. In the coordinate system centered to the apex of the Earth s motion, and rotating as the Earth orbits the Sun, these apparent regions remain in the constant location. This study focuses on the latest discovered the north and south toroidal regions (Elford & Hawkins, 1964) located approximately 60 above/below the apex direction (see Figure 2). Even though, many different observations were made in the last few decades, two of them are the most complete and precise: the observations by AMOR (southern hemisphere) provide a set of corrected orbits taken over 5 years (Galligan & Baggaley, 2005) and the CMOR observations (northern hemisphere) with precise orbits (Campbell-Brown, 2008). Figure 1 shows the raw distribution of orbital elements for the north toroidal region from CMOR (the south toroidal region meteoroids have similar distribution of orbital elements). Figure 1.: Raw orbital parameter distributions for the north toroidal source from Canadian Meteor Orbit Radar (CMOR) and Harvard Meteor Radar Project (HRMP). CMOR corrected distributions are also given. Adopted from (Campbell-Brown, 2008) 13

2 POKORNÝ: TOROIDAL SPORADIC METEOROID COMPLEX Figure 2.: Raw radiant distribution of all CMOR orbits, in 2 2 bins, in heliocentric ecliptic coordinates. The north and south toroidal sources are marked by red bordered pentagons. The scale represents the number of individual radiant determinations in each bin. Adopted from (Campbell-Brown, 2008) and edited for the purpose of the study. The aim of this study is to search for the sources of toroidal SMC. Figure 1 gives us a basic insight what kind of bodies we have to investigate. The vast majority of toroidal meteoroids must reside on highly inclined heliocentric orbits (about I 70 ), which tells us that source bodies have also highly inclined orbits. The distribution of eccentricities points out to two things: 1) the toroidal SMC is not populated by meteoroids from one source, but rather from numerous sources and 2) low eccentricities are probably the result of Poynting-Robertson drag (Burns et al., 1979). The case 1) is also apparent from the temporal variations in toroidal SMC flux with several significant peaks (Campbell-Brown & Wiegert, 2009). These findings give us basic constrains on source bodies we are trying to identify. Selecting the possible sources of toroidal meteoroids The very first step was an acquisition of the most complete database of known and well determined bodies (we focused on precision of Keplerian orbital elements) in the Solar System. We chose the database available on the Jet Propulsion Laboratory (JPL) Solar System Dynamics web site (see First, we make a decision about the bodies we will investigate. We have two basic groups, asteroids and comets that could be sources of incoming dust. There are over 500,000 known asteroids in the Solar System, but we simply lack of a mechanism that could create observed numbers of meteoroids. However, some asteroids may be extinct or dormant cometary nuclei and thus they could be an important source of interplanetary dust in the past. Further analysis of the asteroidal sources will be a subject of another study thus for the moment focus only on comets. As of May 2011, the database contained 3080 comets with well-determined orbital elements. The majority of the known comets cannot and also could not have contributed in the past to the north and south toroidal regions because of various restrictions caused by the characteristics of their orbital elements. We can set up two basic restrictions on possible sources of sporadic toroidal meteoroid complex: a) We need particles to accrete on the Earth constantly in time, therefore the perihelion distance of source body (comet) should be q < 1.2 AU in any period of their existence for particles to have at least theoretical possibility of accretion and b) the inclination of the source comet should be I > 50 at least at some moment in the past. The case b) is clear from Figure 1, where we see that the majority of meteoroids hit the Earth from ecliptic latitudes around 70. For application of these two restrictions we have to know the orbital history of each comet in a certain period. This period was set to 10,000 years from present to the past where this value appears to be a limit for our model (subject of further tests) because the model does not involve all non-gravitational effects (e.g. cometary activity). We perform backward integration (described in section Orbit integration) in time and observe, if our bodies fulfill given condition. However, applying a condition for Kozai oscillation (Kozai, 1962), where 1 e 2 cos I 3/5 eliminates majority of comets out. If the body is not in the Kozai oscillation mode, it is very unlikely the body reaches inclination I > 50 in the past. There are only 465 comets which satisfy the Kozai oscillation condition. 14

3 Orbit integration POKORNÝ: TOROIDAL SPORADIC METEOROID COMPLEX The orbits of all selected comets were numerically integrated with the swift rmvs3 code (Levison & Duncan, 1994). This code is a implementation of the Wisdom-Holman map (Wisdom & Holman, 1991), which can also deal with the close encounters between planets and particles. The code tracks the evolution of particle orbit around the Sun influenced by the gravitational perturbations of all eight planets (Mercury to Neptune). The particle is eliminated by three different reasons: a) particle impacts a planet, b) particle is ejected from the Solar System (a > 1000 AU) or c) particle finds itself within 0.05 AU from the Sun. The case c) can be justified in two ways: 1) the integration timestep was set to two days, which is too small to resolve orbits within the region r < 0.05 AU and 2) temperatures are too high for majority of particles to survive (considering that the particle is thermally destroyed when its temperature reaches T 1500 K and that the 100 µm dark amorphous pyroxene at distance R (in AU) from the Sun has the equilibrium temperature within 10 K of a black body equal T 280/ R K. For more information about the thermal behavior of dust particles see (Henning & Mutschke, 1997), (Moro-Martín & Malhotra, 2002) and (Kessler-Silaci et. al, 2007). For our dust particles we used the same method described above with only one difference. The radiation pressure and Poynting-Robertson drag forces were modelled in the Keplerian a kick parts of the code. The Keplerian part was modified trivially by substituting m by m (1 β), where β is the radiation pressure factor (Burns et al., 1979). Possible cometary sources of toroidal meteoroids We found that only 70 comets fulfill conditions from Section (Selecting the possible sources of toroidal meteoroids) during the past 10,000 years. However, only 12 of them are designated as periodic comets, and we restrict our analysis to these object(see Table 1). Non-periodic comets will be studied in near future. Comet name Epoch (MDJ) a (AU) e I (deg) Ω (deg) ω (deg) M 8P/Tuttle P/Pons-Brooks P/Olbers P/Herschel-Rigollet P/Machholz P/de Vico P/1999 J6 (SOHO) P/1999 R1 (SOHO) P/2001 Q6 (NEAT) P/2002 S7 (SOHO) P/2005 J1 (McNaught) P/2005 W4 (SOHO) Table 1.: Keplerian orbital elements of 12 periodic comets that satisfy conditions given in Section (Method of selection possible sources of toroidal meteoroids). The data were acquired from JPL website. In what follows, we focus on 96P/Machholz 1 which was selected as the first candidate for the study of toroidal meteoroid impacts onto the Earth (due to its lowest value of semi-major axis from enumerated comets)). Figures 3 a 4 show evolution of its inclination and eccentricity back in time, with the most notable feature being long-scale Kozai oscillations, preserving 1 e 2 cos I value. The influence on selected orbital elements is eminent: 96P/Machholz 1 in about 2,200 years evolves from low inclined orbit I 13 to high inclination around I 78. Model used for comparison with meteor radar observations The greatest challenge in all models of planetary accretion is to get as many accreted particles as it is possible using the available computer capability. One possibility is to use Öpik theory (Öpik, 1951) in the standard or more precise version. However, the assumption of an isotropic distribution of longitude of ascending node Ω and argument of periapsis ω is inapplicable in our model. For modeling the annual variations in the toroidal region meteoroids flux we simply need the true values of Ω and ω to distinguish when the accretion occurred. The swift rmvs3 code has a subroutine computing the collisions between particles and planets. When the particle impacts the Earth the code gives us heliocentric coordinates and velocities for the specific particle and planet allowing us to compute all orbital elements (a, e, I, Ω, ω, M) and also gravitationally unfocused impact speed and radiants. The radiants are expressed in the specific 15

4 POKORNÝ: TOROIDAL SPORADIC METEOROID COMPLEX Figure 3.: Inclination evolution of 96P/Machholz 1 from backward integration over 10,000 years. We can clearly see how the inclination varies with time due to the Kozai mechanism. Figure 4.: Eccentricity evolution of 96P/Machholz 1 from backward integration over 10,000 years. Variation caused by Kozai mechanism is not that significant as in the inclination. However, for the lowest inclination the eccentricity reaches value coordinate system, where latitude b is measured relative to the orbital plane of the Earth and longitude l is measured in the counter-clockwise direction along the Earth s orbit from the apex of Earth s motion. The detection efficiency of the meteor radars is mainly a function of the particle s speed and mass. The simplified detection probability can be represented by the ionization function (Wiegert et al., 2009): I(m, v) = m ( ) 3.5 v (1) g 30 km/s All meteoroids having I(m, v) I rad are taken in account in the model whereas all meteoroids having I(m, v) < I rad are considered undetectable by the radar. The parameter I r ad differs for the different radar facilities. We use data from two radars: CMOR, where I rad 1 (Campbell-Brown, 2008) and AMOR, where I rad (Galligan & Baggaley, 2005). For example, a 100 µm dust particle with v = 30 km/s and m = 10 6 g (having ρ = 2g/cm 3 ) has I(m, v) = This particle would be probably detected by AMOR, but it is clearly undetectable by CMOR. Because our target is to study toroidal meteoroids we need to select radiant thresholds. For the north toroidal region I selected meteoroids with b (45, 90 ) and l ( 45, 45 ), and for south toroidal region meteoroids with b ( 90, 45 ) and l ( 45, 45 ). These two areas are marked in Fig. 2 with red bordered pentagons. The CMOR radar cannot the southern hemisphere, therefore the south toroidal region is not populated in Fig. 2. Preliminary results for 96P/Machholz 1 From the previous sections we have a possible orbital evolution of 96P/Machholz 1 over the last 10,000 years. This gives us a opportunity to test the flux of dust particles in the Earth s atmosphere in last 10,000 years. The model creates 2500 dust particles of size 100 µm and density ρ = 2 g/m 3 in 20 years intervals covering 500 different periods of comet s lifetime. This gives us dust particles that could impact onto the Earth and populate toroidal regions. To achieve higher impact probabilities the Earth radius was scaled up to R = 50R, which is still within the Earth s Hill sphere thus the result should not significantly differ from the reality. The results are presented in 3 figures. Figure 5 shows all recorded impacts in last 10,000 years. 16

5 POKORNÝ: TOROIDAL SPORADIC METEOROID COMPLEX Figure 5.: The distribution of impact speeds, selected orbital elements and radiant distribution for dust particles released from 96P/Machholz 1 in 20 years intervals. The toroidal regions are less populated than helion and anti-helion regions. The ionization cut-off I rad > 0.01 is applied here. Figure 6.: The same as in Figure 5 but now for all impacts recorded in last 400 years. No accreted particles population the toroidal regions were identified. Figure 7.: The same as in Figure 5 but now for all particles populating toroidal regions in the last 10,000 years. The toroidal regions are populated but the incidence is much lower compared to helion and anti-helion regions. Figure 5 cover 10,000 years timespan so the today flux can be different. Figure 6 shows us impacts recorded in last 400 years where no single impact in toroidal regions was recorded. These preliminary results show us that it is possible to say, it is very unlikely that 96P/Machholz 1 is one of the sources of toroidal SMC (however, further analysis needs to be done). At last the figure 7 shows all recorded impacts from toroidal regions. Inclination and impact speed are similar to expectations from Figure 1, however, semi-major axis and eccentricity is completely different. It is important to say, that these result are only preliminary and more are to come. 17

6 Conclusions POKORNÝ: TOROIDAL SPORADIC METEOROID COMPLEX We found that only 12 periodic and 58 non-periodic comets fulfilled adopted constrains for possible sources of toroidal region meteoroids (see Table 1). Further analysis of 96P/Machholz 1 comet showed us that it is very unlikely to be one of the sources of today toroidal SMC. From dust particles of 100 µm size no single particle populating toroidal regions accreted onto the Earth in the last 400 years. In the future work, we plan to analyze more precisely all 12 periodic comets and consider particles of different size. Acknowledgments. The author thanks D. Vokrouhlický and D. Nesvorný for their invaluable help. References Burns, J. A., Lamy, P. L. and Soter, S., Radiation forces on small particles in the solar system, Icarus, 1-48, Campbell-Brown, M. D., High resolution radiant distribution and orbits of sporadic radar meteoroids, Icarus, , Campbell-Brown, M. D. and Wiegert, P., Seasonal variations in the north toroidal sporadic meteor source, Meteoritics & Planetary Science, , Elford, W. G. and Hawkins, G. S., Meteor echo rates and the flux of sporadic meteors, Harvard Radio Meteor Project Res. Rep., no.9, Galligan, D. P. and Baggaley, W. J., The radiant distribution of AMOR radar meteors, Monthly Notices of the Royal Astronomical Society, , Henning, T. and Mutschke, H., Low-temperature infrared properties of cosmic dust analogues, Astronomy and Astrophysics, , Kessler-Silacci, J. E., Dullemond, C. P., Augereau, J.-C., Merín, B., Geers, V. C., van Dishoeck, E. F., Evans, N. J., II, Blake, G. A. and Brown, J., Probing Protoplanetary Disks with Silicate Emission: Where Is the Silicate Emission Zone?, The Astrophysical Journal, , Kozai, Y., Secular perturbations of asteroids with high inclination and eccentricity, Astronomical Journal, , Levison, H. F. and Duncan, M. J., The long-term dynamical behavior of short-period comets, Icarus, 18-36, Moro-Martín, A. and Malhotra, R., A Study of the Dynamics of Dust from the Kuiper Belt: Spatial Distribution and Spectral Energy Distribution, Astronomical Journal, , Öpik, E., J., Collision probability with the planets and the distribution of planetary matter, Proceedings of the Royal Irish Academy, section A, , Wiegert, P., Vaubaillon, J. and Campbell-Brown, M., A dynamical model of the sporadic meteoroid complex, Icarus, , Wisdom, J. and Holman, M., Symplectic maps for the n-body problem, Astronomical Journal, ,