1.3 Models of ablation for faint meteors
1.3.4 High-resolution, sputtering, and other models
As new constraints from high-resolution intensified video and spectral observations become available, models are beginning to investigate the wake and state of the flow around small meteoroids. Boyd (2000) employed the direct simulation Monte Carlo (DSMC) method to investigate the flow around a 1 g Leonid travelling 72 km s−1 at a height of 95 km. In DSMC, interactions between atmospheric particles, meteoric particles, and the meteoroid itself are simulated with collisions. Collisions with the meteoroid impart energy and momentum to evaporate meteoric particles and decelerate the meteoroid, respectively. Collisions between highly-energetic particles around the meteoroid form the luminous wake and the ion trail. The classical ablation equations, Eqs. (1.24), (1.25), and (1.26), are solved by direct evaluation of particle interactions and averaging over large populations or long timescales.25
Boyd’s (2000) calculations revealed that a wake of diameter ∼ 6 m formed around the modelled Leonid, matching intensified video observations of faint meteors at similar heights (Kaiser et al. 2004). The wake appeared to be in thermal equilibrium with temperatures of the order 103K. Spectral observations revealed similar temperatures around the meteor head, but also found that it was difficult to quantify the temperature of the wake, which might not be in thermal equilibrium (Boroviˇcka 1993). Simulating the ablation of a cometary meteoroid yielded a larger, higher temperature wake compared to an asteroidal meteoroid, suggesting that differences in meteor wake might indicate different compositions. This model was a promising first attempt to explain new observations, but was never followed up, perhaps due to lack of observational constraints.
Popova et al. (2000) also developed a model to investigate the properties of meteor wake at heights above 80 km. Incoming atmospheric particles are treated as a beam, attenuated by the dense wake immediately around the meteoroid. A number of approximations were made in 25This method is applicable at height ranges for small meteoroids (generallyh>90 km) where the atmospheric density is small enough such that the macroscopic behaviour is well-described by interactions between pairs of particles. At lower heights typical of brighter objects, a continuum-based fluid mechanics model is more appropriate.
the model (such as assuming spherical or cylindrical symmetry for flow around the meteoroid) making it difficult to evaluate, but preliminary wake temperature values ranging between 5000 and 10 000 K were produced, roughly matching spectral observations. The extent of the wake was found to be much smaller than in Boyd’s (2000) investigation, under 20 cm in diameter at a height of 100 km for a 1 cm Leonid at 72 km s−1, which did not agree with intensified video observations.
Vinkovi´c (2007) devised a high-resolution model based on particle collisions to investigate sputtering and the appearance of meteors at heights above 130 km. Atmospheric particles colliding with the meteoroid eject meteoric particles before the meteoroid is heated to the evaporation point. A detailed model by Rogers et al. (2005) found sputtering to be a significant source of mass loss for small (m < 10−3kg), fast meteoroids (typicallyv > 60 km s−1). These sputtered particles, all assumed to have a speed of 20 km s−1 relative to the meteoroid, then collide with atmospheric particles. The locations of the collisions are tracked with respect to the meteoroid to prepare a synthetic image analogous to an intensified video frame. The modelled shape of the meteor matched earlier high-altitude Leonid observations (Spurn´y et al. 2000) in a qualitative sense, and general trends, such as the width of the wake decreasing with decreasing height, were also reproduced. Quantitative comparisons with observations were not performed, but it is not likely that this would yield much information about the meteoroid, since there are few free parameters (such as meteoroid density, mean meteoric particle mass) in the model.
Though particle-based Monte Carlo modelling is a novel way to make use of high-resolution video observations to comment on meteoroid structure and ablation, other sophisticated models describe the contribution of meteoric material to the atmosphere (Vondrak et al. 2008) as well as the interaction between radar waves and the head plasma immediately around the meteoroid (Dyrud et al. 2008), for example. The Chemical Ablation Model (CAMOD) by Vondrak et al. (2008) quantitatively describes differential ablation of non-fragmenting meteoroids, which also includes sputtering, diffusion of material in the meteoroid, and meteoroid melting based on the
equation of state for olivine. Height distributions for meteors measured by radar head echoes were reproduced by the model, as well as general relative abundances of meteoric metals and ions (Na, K, Fe, Mg, Si) in the upper atmosphere, but the anomalous sodium to calcium ratio first commented on by McNeil et al. (1998) was not explained.
Dyrud et al. (2008) presented a two-step simulation to investigate how the meteor head echo radar cross section varied with the distribution of ions around the meteoroid and orientation between the meteor and incident radar waves. The first step generated a density distribution for the ions comprising the meteor plasma using a Monte Carlo technique called particle- in-cell (PIC), while the second step took this distribution and evaluated its interaction with incident radar waves. Varying the angle between the meteor and the radar wave did not have a significant effect on the radar cross section. Reflections from an assumed Gaussian ionisation profile varied significantly from the simulated profile, however. This suggested the importance of calculating a realistic ionisation profile when attempting to interpret observations, similar to what was found for meteor trail echoes by Jones (1995).
1.3.5
Summary of modelling
In summary:1. Single-body theory is the most basic model for meteoroid ablation, but it does not ad- equately describe the behaviour of most faint meteors. Faint meteors decelerate more rapidly than predicted, are luminous over shorter height intervals than predicted, and emit light at different rates than predicted.
2. Continuous meteoroid fragmentation and dustball theory accounts for these discrepan- cies. New high-resolution video observations suggest improvements are required for contemporary ablation theory, however.
3. Gross fragmentation is incompletely understood, as mentioned in Section 1.2. Aerody- namic crushing, rotation, and electrostatic charging have been suggested as mechanisms
for meteoroid disruption, but have not been quantitatively evaluated using observations. 4. High-resolution (and spectral) observations have allowed for more detailed modelling of
meteor wakes and the flow around faint meteors, but the field is early in its development, partially due to the lack of consistent observations.