Fragmentation model analysis of the observed atmospheric trajectory of the Tagish Lake fireball

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1 Meteoritics & Planetary Science 42, Nr 2, (2007) Abstract available online at Fragmentation model analysis of the observed atmospheric trajectory of the Tagish Lake fireball ZdenÏk CEPLECHA Academy of Sciences of the Czech Republic, Astronomical Institute, Ond ejov, Czech Republic (Received 15 September 2006; revision accepted 22 November 2006) Abstract A recently published meteoroid fragmentation model (FM) was applied to observational data on the Tagish Lake meteoric fireball. An initial mass of 56,000 kg, derived from seismic and infrasound data by Brown et al. (2002), proved to be consistent with a very low value of intrinsic ablation coefficient of s 2 km 2. The average residual of the best fit to the observed light curve was ±0.10 stellar magnitude. The apparent ablation coefficient varied from to 1.52 s 2 km 2, with an average value of s 2 km 2 (determined by the gross fragmentation [GF] model). The FM found 33 individual fragmentation events during the penetration of the 56,000 kg initial mass of the Tagish Lake meteoroid through the atmosphere, with five of the events fragmenting more than 10% of the instantaneous mass of the main body. The largest event fragmented 88% of the mass of the main body at a height of 34.4 km. The velocity of the main body mass of 2660 kg at a height of 29.2 km (the last observed light) was 13.1 km/s. Strong fragmentation at heights lower than 29.2 km is very probable. The extreme fragmentation process of the Tagish Lake meteoroid puts its classification well outside the IIIB type in the direction of less cohesive bodies. The light curve could not be explained at all by making use of only the apparent ablation coefficient and apparent luminous efficiency. INTRODUCTION This paper applies the recently published fragmentation model (Ceplecha et al. 2005) to observational data on the atmospheric trajectory of the Tagish Lake fireball. Results are compared to older gross fragmentation model solutions. The Tagish Lake fireball reached the maximum absolute magnitude of 22 on January 11, 2000, at 16:43:43 UT. Many hundreds of meteorites of unusual types and compositions and with a very low bulk density of 1.5 Mg/m 3 were collected, as reported by Brown et al. (2000). Gross Fragmentation Model DEFINITIONS The gross fragmentation (GF) model (Ceplecha et al. 1993) makes use of height h (or distance along trajectory l) as a function of time t, and allows the determination of one fragmentation point (height), where fragmentation occurs as a sudden event stripping part of the mass of the main body in several smaller fragments. The GF model does use the light curve, and all the computed values depend only on the dynamics of the body. Meteoroid Fragmentation Model The meteorite fragmentation (FM) model (Ceplecha et al. 2005) uses both height (height curve) and light emission (light curve) as a function of time. The FM defines intrinsic and apparent values of the ablation coefficient σ and of the luminous efficiency τ. The FM is the first model to explain the long-standing conundrum of meteor physics: the difference in values of meteoroid masses (by orders of magnitude for extremely friable meteoroid types) derived from their motion (dynamic mass) and light curve (photometric mass). Application of the FM to observations requires very precise data on both light and height curves. Because of insufficient height curve data for the Tagish Lake fireball, there opportunities to apply the FM are limited. However, the application of the FM still yields interesting data on the fragmentation history of the event (Table 2) and on the intrinsic values of the ablation coefficient and of the luminous efficiency (Table 3). OBSERVATIONAL DATA Brown et al. (2002) described the sources of observational data originating from various techniques. 185 The Meteoritical Society, Printed in USA.

2 186 Z. Ceplecha Table 1. Intrinsic σ (s 2 km 2 ) Initial mass m B (kg) , , , ,000 ReVelle (personal communication) provided detailed data on the calibrated light curve to perform the FM analysis. Detailed data on the height curve are not available. The approximate heights used in Brown et al. (2000; Figs. 1 and 2) and provided by ReVelle are only schematic values represented as a linear function of time neglecting the Earth s curvature. However, they are based on a zenith distance of the radiant z R = 72.2 at a height h = 37.6 km. This I kept as the only valid definition of the height curve, h = h(t), and I did not use those schematic values of h originally provided by ReVelle. I shifted the relative time of the light curve (corresponding to Figs. 1 and 2 in Brown et al. 2000) by adding 10 s. This was done deliberately to have t = 0 at the beginning of FM integration. Thus: t (this study) = t (Brown et al. 2002) + 10 s My relative timing starts at 16:43:33 UT. The initial mass of 56,000 kg was derived in Brown et al. (2002) using infrasound and seismic observations. The initial velocity was derived in the same paper as v = 15.8 ± 0.6 km/s. FM APPLIED TO THE LIGHT CURVE Due to the lack of enough precise data on height as function of time, the opportunities for applying FM to the Tagish Lake fireball are limited. First, it is impossible to determine the initial mass without having dynamical data. Second, it is impossible to determine a value for the intrinsic ablation coefficient solely from the light curve. Third, the same is true for the shape-density coefficient K, which can be chosen in a rather large range. Fourth, K and σ have to be assumed constant; any assumption of the variability of these coefficients with time would be superfluous due to absence of a precisely observed height curve. When beginning to apply FM to the Tagish Lake data, I used K = 0.9 c.g.s. and intrinsic σ = I was not able to receive any observational check on K because of the lack of precise data on h = h(t). However, trying to model the light curve with K = 0.4 or 1.5 resulted in less precise fits. Using the intrinsic σ larger than required an unreasonably large initial mass. I started the integrations at h B = km, where t B = 0 and z B = This value is derived from the originally observed value of 72.2 at a height of 37.6 km (Brown et al. 2002), taking into account the Earth s curvature. I took the initial velocity from Brown et al. (2002) as v B = 15.8 km/s. The initial mass with σ = s 2 km 2 resulted as m B = 270,000 kg (±10,000 kg), Table 2. h f (km) Δm (%) dt f (s) dt u (s) an unrealistic value with respect to seismic and infrasound data. The small standard deviation represents fixed K and σ (i.e., standard deviations of K and σ are taken as zero by definition). The fit of the light curve was very good and the standard deviation for one observed value of magnitude was ε M = ±0.11 magnitude (the precision of the photometric observations was included). I also confirmed that changing K to smaller values made almost no change to the fit; the initial mass remained the same 270,000 kg with K = 0.7 c.g.s. However, changing intrinsic σ makes a large change in the resulting value of the initial mass. Using fits just for the main flares on the light curve as a very good approximation; I derived the dependence of initial mass, m B, on the intrinsic σ as given in Table 1. With respect to the initial mass of 56,000 kg (Brown et al. 2002), Table 1 points to a very low value of the intrinsic σ somewhere in vicinity of s 2 km 2. This is the lowest value among all fireballs to which the FM has been applied thus far.

3 Fragmentation model analysis of the observed atmospheric trajectory of the Tagish Lake fireball 187 Table 3. FM solution GF solution Apparent σ (s 2 km 2 ) Oscillating (see Fig. 8) Intrinsic σ (s 2 km 2 ) Unknown Initial mass (kg) 56,000 (assumed) 53,000 Main fragmentation height 34.4 km 34.7 km Amount of fragmented mass 88% 81% at the main fragmentation height Mass (kg) at the main fragmentation height: Before fragmentation 31,900 32,700 After fragmentation Velocity at the km/s km/s fragmentation height Deceleration: Before the main 0.43 km/s 0.42 km/s fragmentation After the main 0.88 km/s 0.73 km/s fragmentation Terminal mass at h E = 29.2 km 2660 kg 1800 kg Fig. 1. The Tagish Lake fireball observed and FM-computed light curve (M = absolute magnitudes for 100 km distance). FM Applied to the Light Curve on the Assumption that the Initial Mass is Equal to 56,000 kg The solution presented in Table 2 and Figs. 1 8 was derived with K = 0.7 c.g.s. This implies that ΓA = 0.917, i.e., a rather symmetric shape is assumed this way (K = 0.9 assumes rather a flat shape with ΓA = 1.18, where Γ is the drag coefficient). ΓA was derived from K and the measured bulk density of the meteorites, which is quite low, i.e., ρ M = 1.5 Mg/m 3. I assumed the initial mass of 56,000 kg as derived from the infrasound and seismic data. The heights were determined from a geometrical condition that the zenith distance of the radiant is 72.2 at a height of 37.6 km. The integration started at h B = km, where t B = 0 and z B = The initial velocity was taken as 15.8 km/s. The initial mass of 56,000 kg can be modeled by fitting the light curve with constant intrinsic σ = s 2 km 2. The fit of the light curve is again very good and the standard deviation for one observed value of magnitude is ε M = ±0.10 magnitude (the precision of the photometric observations is covered). The fit to the light curve is presented in Fig. 1 and the distribution of the fit residuals with time is presented in Fig. 2. Table 2 contains all FM-revealed fragmentation points. h f is the height of a fragmentation point (start of the flare), Δ m is mass loss at this height in a form of fragments expressed in percent of the main body, dt f is duration of the flare, and dt u is the time of increasing brightness. The terminal velocity is still very high (v E = 13.1 km/s) at the terminal height defined as the last observed light (h E = 29.2 km). Fragmentation that was not observed optically almost certainly followed beyond the terminal height. The Fig. 2. Residuals of stellar magnitudes observed and FM-computed light curve. terminal mass of the main body at the terminal height is m E = 2660 kg, but the mass remaining after the unobserved fragmentation should be much less. Apparent values of the ablation coefficient σ and of the luminous efficiency τ are compared with the their intrinsic values in Figs. 7 and 8. The maximum value of apparent σ is 1.52 s 2 km 2 and the maximum value of apparent τ is 17,000% (i.e., 170 times the maximum physically possible value!). This is due to the extremely large fragmentation process of the Tagish Lake body (it is outside the regular classification, well outside IIIB in the direction of less cohesive bodies). An explanation of the Tagish Lake light curve based solely on the apparent ablation coefficient and apparent luminous efficiency is completely impossible, while the FM explains the light curve extremely

4 188 Z. Ceplecha Fig. 3. The height curve (height as function of time) of the main body of the Tagish Lake meteoroid. Fig. 4. The velocity computed from the FM as function of height for the main body of the Tagish Lake meteoroid. Fig. 5. Deceleration as function of height computed from the FM and GF model for the main body of the Tagish Lake meteoroid. well. This means that most of the mass-loss was produced by fragmentation. The following ablation of fragments is responsible for most of the emitted light. The FM (Ceplecha et al. 2005) proved that such a situation existed for all 14 examined events and this is exactly what explains the longstanding conundrum of meteor physics, namely, the difference by orders of magnitude of dynamically and photometrically determined meteoroid mass. GF MODEL AVERAGE VALUE OF THE APPARENT ABLATION COEFFICIENT ReVelle (personal communication) proposed an interesting check on the FM results. Though it is a purely mathematical check (because the observed height curve is missing), this check is capable of computing the average Fig. 6. Mass as function of height computed from the FM and GF model for the main body of the Tagish Lake meteoroid. apparent σ corresponding to the FM solution. Making a usual arithmetic average does not make much sense due to very large changes of σ. One can apply the GF model to the results from the FM. The GF model is capable of revealing just one fragmentation point inside an examined interval. However, the main FM-revealed fragmentation is 88% of the mass of the main body at a height of 34.4 km (Table 2) and forms the most decisive fragmentation on the entire trajectory. The other smaller fragmentations are all caused by less than 17% mass of the main body. The following results nicely verified that the GF solutions (based on dynamics only) are surprisingly good, if high-precision data for the height curve are available. In this respect, the FM-computed data on h = h(t) and l = l(t) are extremely good observations because they are exact theoretical values. I took h = h(t) and l = l(t) (where l is the distance along the trajectory) from the FM

5 Fragmentation model analysis of the observed atmospheric trajectory of the Tagish Lake fireball 189 Fig. 7. The intrinsic and apparent luminous efficiency as a function of height computed from the FM and applied to the Tagish Lake fireball data. solution as input values into the GF code. The corresponding mathematical procedure is described in Ceplecha et al. (1998, pp ). The results are in Table 3 and comparisons with the FM results are in Figs. 5, 6, and 8. The GF model proved to be a good way of averaging the apparent σ, which oscillates widely (see Fig. 8). The GF model also proved to be a powerful means for finding the fragmentation height, when one fragmentation event represents by far the largest massloss on the entire trajectory. The resulting average value of apparent σ would classify the Tagish Lake fireball as type II. This is in contrast with extreme fragmentation, which corresponds to bodies more fragile than type IIIB. This contrast is evidently caused by many fragmentation events, as demonstrated by the light curve and presented in detail in Table 2. Acknowledgments My special thanks are due to D. O. ReVelle and P. Brown for sending me detailed observational data making this work possible, and also for their patience in clarifying with me all the tiny details and meanings of observational data values and interpretations. This enabled upgrading the results of Brown et. al. (2002) based on the GF model. This work was done as a part of AV0Z project of the Astronomical Institute of the Academy of Sciences of the Czech Republic. I thank both the anonymous Fig. 8. The intrinsic and apparent ablation coefficient as function of height computed from the FM and GF model for the main body of the Tagish Lake meteoroid. reviewers for their useful comments, which helped to improve the paper. Editorial Handling Dr. Donald Brownlee REFERENCES Brown P. G., Hildebrand A. R., Zolensky M. E., Grady M., Clayton R. N., Mayeda T. K., Tagliaferri E., Spalding R., MacRae N. D., Hoffman E. L., Mittlefehldt D. W., Wacker J. F., Bird I. A., Campbell M. D., Carpenter R., Gingerich H., Glatiotis M., Greiner E., Mazur M. J., McCausland P. J. A., Plotkin H., and Mazur T. R The fall, recovery, orbit, and composition of the Tagish Lake meteorite: A new type of carbonaceous chondrite. Science 290: Brown P. G., ReVelle D. O., Tagliaferri E., and Hildebrand A. R An entry model for the Tagish Lake fireball using seismic, satellite and infrasound records. Meteoritics & Planetary Science 37: Ceplecha. Z. and ReVelle D. O Fragmentation model of meteoroid motion, mass loss, and radiation in the atmosphere. Meteoritics & Planetary Science 40: Ceplecha Z., Spurný P., BoroviËka J., and Keclíková J Atmospheric fragmentation of meteoroids. Astronomy and Astrophysics 279: Ceplecha Z., BoroviËka J., Elford W. G., ReVelle D. O., Hawkes R. L., PorubËan V., and Šimek M Meteor phenomena and bodies. Space Science Reviews 84: