Hyperbolic meteor orbits from the catalog of 64,650 meteors observed by the multistation video meteor network located in Japan (SonotaCo 2009) have been investigated with the aim of determining the relation between the frequency of hyperbolic and interstellar meteors. The proportion of hyperbolic meteors in the data decreased significantly (from 11.58% to 3.28%) after a selection of quality orbits, which shows its dependence on the quality of observations. Initially, the hyperbolic orbits were searched for meteors unbound due to planetary perturbation. It was determined that 22 meteors from the 7489 hyperbolic orbits in the catalog (and 2 from the selection of the orbits with the highest quality) had had a close encounter with a planet, none of which, however, produced essential changes in their orbits. Similarly, the fraction of hyperbolic orbits in the data, which could be hyperbolic by reason of a meteor's interstellar origin, was determined to be at most 3.9 × 10−2. From the statistical point of view, the vast majority of hyperbolic meteors in the database have definitely been caused by inaccuracy in the velocity determination. This fact does not necessarily assume great measurement errors, since, especially near the parabolic limit, a small error in the value of the heliocentric velocity of a meteor can create an artificial hyperbolic orbit that does not really exist. The results show that the remaining 96% of meteoroids with apparent hyperbolic orbits belong to the solar system meteoroid population. This is also supported by their high abundance (about 50%) among the meteor showers.
The problem of the contribution of interstellar particles to the solar system meteoroid population has always been contentious. The substantial problem, whether meteors arriving from outside the heliosphere are present among the registered hyperbolic orbits and, if so, how great is their frequency, according to mass and velocity, has led to much research, including attempts to map the galactic sources of interstellar dust (Baggaley et al. 2007). The contribution of interstellar particles to the interplanetary meteoroid population was found to be much higher for small particles obtained from cosmic dust detectors (Grün 1993; Krüger et al. 2007), in comparison with the range of larger meteoroids obtained from radar (Weryk and Brown 2004), photographic (Hajduková 1994, 2008), and video (Hawkes and Woodworth 1997; Hajduková 2011; Musci et al. 2012) observations. While the proportion of larger interstellar meteoroid particles (m > 10−7 kg) was determined to be at most a small fraction (in the order of 10−3) of the interplanetary population (Hajduková 1994, 2008, 2011; Musci et al. 2012), the results from the Ulysses and Galileo space probes show a predominance of interstellar particles (in the mass range between 10−17 and 10−15 kg) in the outer solar system (Grün et al. 1997). Their retrograde trajectories, high impact speed, and independence from the ecliptic latitude were thought to demonstrate their interstellar origin (Grün and Landgraf 2000). However, it has to be noted that hyperbolic orbits or hyperbolic velocities do not necessarily entail interstellar particles, they rather represent the highest upper limit for their number.
The identification of interstellar meteoroids among the detected hyperbolic meteors is very demanding because, as it was shown in our previous studies (Hajduková 2008, 2011), the hyperbolicity of the majority of meteor orbits is only apparent due to inaccuracy in the velocity measurements. Furthermore, there is also a possibility of a hyperbolic meteor orbit being caused by planetary perturbations. In both cases, we deal with meteoroids which originated within our solar system and have to distinguish them from those which originated in the interstellar medium.
This paper clearly demonstrates that the number of hyperbolic meteors in the data investigated does not, in any case, represent the number of interstellar meteoroids and that a search for them involves a proper error analysis and requires an understanding of the galactic environment of the Sun, which indicates the influx of particles arriving from outside the heliosphere, according to their masses. A distribution of excess velocities of such particles arriving at the Earth should correspond to the distribution of radial velocities of close stars; and the distribution of their characteristics is expected to follow the motion of interstellar material. Moreover, a concentration of their radiants to the Sun's apex in respect to the motion of neighboring stars should be observed.
The present work is based on an analysis of precise determined meteor orbits collected in the Japanese meteor shower catalog from video observations by SonotaCo (2009). The results are discussed and compared with our previous analysis of hyperbolic meteor orbits of the photographic and radar catalogs of the IAU Meteor Data Center, as well as with the reports by the other authors mentioned above. The meteors observed continuously in the years 2007–2009 by the SonotaCo network were detected mostly up to +2 magnitude (the average absolute magnitude of detected meteors is −0.87) and 63% of them create a large set of sporadic meteors. All hyperbolic orbits from the catalog were selected for our analysis, with the aim of finding the reason for their hyperbolicity, and showing the real proportions of interstellar and perturbed meteors, and their contribution to all hyperbolic orbits.
Hyperbolic Orbits and Quality of Observations
The fact that the proportion of hyperbolic orbits in the data depends on the quality of observations and accuracy of measurements has been clearly demonstrated many times (Štohl 1971; Hajduková and Paulech 2007; Hajduková 2008, 2011), including in this study.
The 2009 version of the SonotaCo catalog contains 64,650 video-observed meteoroids, of which 7489 are hyperbolic. Indeed, the accuracy of the velocity measurements in the database depends on the geometric conditions of simultaneous observations, and so the accuracy is different for each meteor (SonotaCo 2009). The measurement errors in the database are not given. Thus, in our error analysis we took into account an additional parameter given for each meteor in the catalog—the difference in the velocity determination from different stations. The varying precision of measurements, depending on the conditions and quality of observations, causes a natural spread in the velocity distribution, which in the vicinity of the parabolic limit exceeds the difference between the heliocentric velocity of a particular meteor and the parabolic velocity, and results in apparent hyperbolic orbits. The value of the heliocentric velocity vH is very sensitive to the value of semimajor axis a, an orbital element, which is most intimately connected with the origin of the meteor particle. The derivation da = 2vHa2dvH shows that, for a large value of the semimajor axis a, even a small error in the velocity determination can change an elliptic orbit to a hyperbolic one. Hence, any error in the determination of vH near the parabolic limit can create an artificial hyperbolic population that does not really exist.
To separate high quality orbits from the SonotaCo data, multiple selective criteria were used. These included: the meteor trail had to be longer than 1 degree (because the accuracy of the velocity determination is related to the observed trail length), the duration of the trail had to be over 0.3 s, and the entire meteor trail had to be inside the field of view of at least two video meteor stations. The analysis of the qualitative aspects of the meteor orbits derived from the multistation video observation is described in more detail in the paper by Vereš and Tóth (2010). This selection created a subset of 14,763 precise video orbits, in which there are 484 hyperbolic meteors. The proportion of hyperbolic meteors in the Japanese TV catalog decreased significantly (from 11.58% to 3.28%) after the selection of quality orbits (Hajduková 2011).
In the selection of orbits with the highest quality, more than half (246) of the hyperbolic meteors were identified with the meteor showers. The presence of orbits with e > 1 and a <0 among shower data is clear evidence of errors arising, in most cases, from the velocity determination. Here, it is worth remembering a notable finding from our previous analyses (Hajduková 2008, 2011)—a dependence of the contribution of hyperbolic orbits between shower meteors on the mean heliocentric velocity of particular meteor shower (Ne>1/N = f(vH))—which supports this suggestion. The radiants of shower meteoroids with hyperbolic excesses are plotted in Fig. 1 right. A high concentration around the radiants of meteor showers with a mean velocity close to the parabolic limit is evident. Figure 1 left shows all 238 sporadic hyperbolic meteors from the data. However, the concentration of their radiants toward the Sun's apex, expected for interstellar particles, is not noticeable.
The vast majority (above 80%) of hyperbolic orbits in the catalog belong to meteors moving on retrograde orbits (in the quality subset there are 406 orbits with i > 90° from all the 484 hyperbolic orbits). This is not surprising as the errors in the measured velocity increase toward higher velocities, which belong mostly to retrograde orbits, and so they increase the proportion of hyperbolic orbits among particles moving on retrograde orbits. The distribution of the inclinations of all hyperbolic meteors is shown in Fig. 2.
Meteoroids Perturbed Due to a Close Planetary Encounter
Meteors that have hyperbolic orbits caused by planetary perturbation generally have velocities just above the parabolic limit, with hyperbolic excesses (defined as the difference between hyperbolic and parabolic heliocentric velocity) smaller than in the case of interstellar meteoroids, in most cases less than 1 km s−1. However, in a study on the gravitational slingshot effect by Wiegert (2011), it was shown that there are orbits of perturbed meteoroids, the excesses of which can reach a few km s−1 (in their model some of them exceeded 5 km s−1).
In our analysis, all of the 7489 hyperbolic meteors from the TV catalog were searched for meteoroids unbound due to a close accelerating encounter with one of the massive planets of the solar system. To follow their orbital evolution, all hyperbolic orbits were integrated backwards for 80 yrs. At this time, all meteors reached a heliocentric distance at least of 100 AU.
For the integration, the multistep procedure of Adams-Bashforth-Moulton's type, up to the 12th order with a variable step-width, developed by Shampine and Gordon (1975) and implemented by Montenbruck and Pfleger (2000), was used. In the model, the planets Mercury through Neptune were considered as perturbing bodies; Earth and Moon were treated separately. The positions of the perturbing planets were obtained from the Planetary and Lunar Ephemerides DE406, prepared by the Jet Propulsion Laboratory (Standish 1998).
The orbital evolution of the meteoroids was traced in two steps. In the first step, a backward motion of a meteoroid on Kepler's heliocentric orbit into the distance of 3 Hill's radii from Earth was calculated, because the orbital elements in SonotaCo data set refer to the orbit of each meteoroid before it came under the influence of Earth's gravity. In the second step, the above mentioned gravitational model was used and the integration was performed. On such a short passage of the orbit, it is not necessary to include the influence of nongravitational forces.
The number of close encounters in the database is very low, which is partly a consequence of the high inclinations of the orbits (about 80% of hyperbolic orbits in the data have inclinations greater than 90°), which results in only a short section of a meteor's orbit being near the ecliptic plane. From all 7489 hyperbolic orbits, 22 meteoroids (and only 2 in the quality data) encountered one of the major planets closer than 1 Hill's radius. Most close encounters occurred with Jupiter and Saturn, but one with Venus (at a distance of 0.0065 AU) was found. The hyperbolic excesses of their velocities observed at Earth are low, with an average value of 1.26 km s−1, except in 3 cases (but none of them belong to the selection of quality orbits), whose velocities exceeded the parabolic limit by 3.59, 4.64, and 4.37 km s−1. However, for none of these meteoroids did the integration procedure show essential changes in their orbits.
Some of the meteors changed their orbits from hyperbolic to elliptic during the integration process, but none was caused by a close meteoroid's encounter with a planet. The change from hyperbola to ellipse, which generally takes place behind Jupiter's, or a more distant planet's orbit, is connected with the meteoroid's motion retreating away from the Sun with respect to the barycenter of the whole solar system. In the integration process, we follow the motion of the particle in the heliocentric system, but at greater distances from the Sun, this motion is practically identical with the barycentric motion. Theoretically, precisely determined meteor orbits should be elliptic or, after a sufficient distance, should change to elliptic, while only orbits of interstellar meteors should stay hyperbolic. In the catalog investigated, there are 54 orbits (giving a proportion of only 0.007 of all hyperbolic orbits) that changed during the integrations from hyperbolic to elliptic.
An overview of hyperbolic orbits from the TV catalog is shown in Table 1 and that of the meteoroids' close encounters in Table 2.
Table 1. Hyperbolic orbits in the Japanese catalog of TV meteors from 2007 to 2009 (SonotaCo 2009) and separately those of the highest quality (Vereš and Tóth 2010)
The quality orbits
Number of all orbits Nall
The proportion of hyperbolic orbits in the database Ne>1/Nall
Number of hyperbolic orbits Ne>1
Number of hyperbolic shower meteors Nshower
Number of sporadic hyperbolic meteors Nspor
Shower meteors among the hyperbolic orbits Nshow /Ne>1
Number of hyperbolic orbits with i < 90 Ni<90
Number of hyperbolic retrograde orbits Ni>90
Retrograde orbits among the hyperbolic meteors Ni>90/Ne>1
Hyperbolic orbits changed to the ellipse Nhyp→ellipt
Their proportion to all hyperbolic orbits Nhyp→ellipt/Ne>1
Number of close meteoroid encounters with Jupiter NJupiter
Number of close meteoroid encounters with Saturn NSaturn
Number of close meteoroid encounters with Venus NVenus
The proportion of meteoroid encounters to all hyperbolic orbits
Table 2. Meteoroids that had encountered a planet within the frame of 1 Hill's sphere of a particular planet, obtained by the backwards integration performed for all hyperbolic meteors from the SonotaCo catalog (given separately for each year of observation). Their heliocentric velocities obtained at Earth and the distances of the closest encounters to a particular planet (in the parentheses next to the meteor numbers) are listed
Close meteoroid encounters from the SonotaCo database
vH (km s−1)
vH (km s−1)
vH (km s−1)
1 Hill's radii of Jupiter
14,006 (0.094 AU)
15,803 (0.164 AU)
18,980 (0.070 AU)
1 Hill's radii of Saturn
3716 (0.133 AU)
8505 (0.100 AU)
1 Hill's radii of Venus
12,484 (0.0065 AU)
Hyperbolic Velocities of Interstellar Meteoroids
The distribution of the hyperbolic excesses of heliocentric velocities of interstellar meteoroids is expected to correspond to the distribution of radial velocities of stars in the nearby solar environment. Then, for the velocity of an interstellar meteor around vi = 20 km s−1 and taking into account the equation vi2 = vH2 − vp2, with vp = 42.1 km s−1, we obtain a heliocentric velocity vH = 46.6 km s−1 of an interstellar meteor arriving at the Earth. But, considering a broad distribution of stellar velocities, in principle, all values of hyperbolic excesses ∆vH can be of interstellar origin; and thus a deep analysis of orbital and geophysical characteristics of individual cases is needed.
Among the orbits from the quality selection, the hyperbolic excesses in all cases are very low (there are no cases with the expected velocity for interstellar meteors), about one order less than required from the velocity distribution of neighboring stars. A precise search for interstellar meteoroids in the SonotaCo database was made in our previous study (Hajduková 2011). To get a comprehensive view of the problem of hyperbolic orbits, we recapitulate some of those results here. Possible interstellar meteoroids could be found in the data only within the error bars of their heliocentric velocity. The meteors with hyperbolic excesses did not show any similar orbital characteristics, which could have supported their interstellar origin. It was concluded that there is a lack of any statistical argument for the presence of interstellar meteors in the catalog. A detailed examination of the subset of the 14,763 most precisely determined orbits selected from the Japanese TV database set the frequency limit for interstellar meteoroids of masses, which correspond to the video observations to 1.3 × 10−3. This means that maximally 3.9 × 10−2 of the total number of 484 hyperbolic orbits could represent interstellar meteoroids.
Discussion and Conclusions
A total of 7489 hyperbolic meteor orbits from the catalog of 64,650 meteors observed by the multistation video meteor network located in Japan (SonotaCo 2009) were investigated, with the aim of finding the reason for their hyperbolicity and demonstrating the relation between the frequency of hyperbolic and interstellar meteors. To separate high quality orbits, important for the identification of the interstellar origin of meteors, multiple selective criteria were used and a selection of 14,763 quality orbits was created, after which the proportion of hyperbolic meteors decreased from 11.58% to 3.28%.
The data were searched for hyperbolic meteors unbound due to a close encounter with one of the major planets. Only 2 meteoroids from the orbits of the highest quality (22 from the whole catalog) had closely encountered a planet. However, the backwards integration processes did not show any considerable changes in their orbits. None of all the hyperbolic orbits from the catalog was caused by a meteoroid encountering a planet. It can be concluded that, in general, the proportion of hyperbolic meteoroids influenced by the planetary perturbation is, from the statistical point of view, minor.
Considering the result from the search for particles of interstellar origin, which set the frequency limit for interstellar particles of masses corresponding to the video observations to 1.3 × 10−3, we can conclude that maximally a fraction of 0.04 of the total number of 484 hyperbolic orbits from the subset of the 14,763 most precisely determined orbits selected from the Japanese TV database could represent interstellar meteoroids. The true hyperbolic orbits in the data set investigated seem to be negligible.
These results correspond to those of our previous studies. The analysis of photographic meteors from the most precise Harvard catalogs of the IAU Meteor Data Center set the frequency limit for interstellar meteoroids to 2 × 10−3 (Hajduková 1994). From the updated version of the photographic catalogs of the IAU MDC containing 4581 orbits, we obtained a similar upper limit (6.1 × 10−3) for the abundance of the interstellar meteoroids in the database (Hajduková 2008). In the same data, no meteors were found whose hyperbolicity was caused by planetary perturbation (Jakubík 2001). This demonstrates that the majority (about 98%) of hyperbolic orbits in the photographic catalogs of the IAU MDC are hyperbolic only due to erroneous determination of their heliocentric velocity. Similarly, analysis of the radar data of the IAU Meteor Data Center (Hajduková and Paulech 2007) led to the conclusion that only 1.4 × 10−3 of all the 39,145 meteors from Harvard radar catalog can be considered as possible interstellar meteoroids, which is only about 5% from the number of all 970 hyperbolic orbits. All the results of our studies call the occurrence of interstellar meteoroids (with the masses corresponding to the observation technique) in the vicinity of the Earth into question. They are in agreement with the recent analysis made by Musci et al. (2012), who in their optical survey found no clear evidence of interstellar meteoroids among the total number of 1739 meteors of millimeter sizes and concluded that their few identified hyperbolic meteors were most likely the result of measurement errors. They also came to the conclusion that the majority of their nominally hyperbolic events could not have been more than very slightly perturbed due to recent close planetary encounters.
In summary, we are led to conclude that, seen statistically, the vast majority of hyperbolic orbits from the Japanese TV catalog (SonotaCo 2009), even those of the highest quality, have been caused by erroneous velocity determination. This, however, does not assume great measurement errors, as near the parabolic limit a small error in the value of the heliocentric velocity of a meteor can create an artificial hyperbolic orbit that does not really exist. In the data investigated, 96% of meteoroids with orbits determined as hyperbolic definitely belong to the solar system meteoroid population. About 50% of them are shower meteors and the other half should be assigned to the interplanetary sporadic background.
This work was supported by the Slovak Scientific Grant Agency VEGA, grant No 0636/09 and by the Slovak Research and Development Agency, project No APVV-0516-10.