Experimentation and simulation of meteoroid ablation
Keywords: Aeronautics and Astronautics.

Numerous satellite failures over the years have shown the various dangers posed to man made objects by the space environment. Meteoroids historically represent one of the foremost external phenomena to cause catastrophic loss of spacecrafts. With velocities between 11~km/s and 72~km/s, meteoroids with masses above 1~mg are easily capable of penetrating the hulls of satellites. Such an encounter is likely to cause irreparable mechanical damage and possibly electrical damage to the spacecraft and cause end of mission. Although these type of events happen infrequently, they are a major concern that needs to be taken into account when deploying payload in Lower Earth Orbit (LEO). In addition to presenting engineering risks to our space assets, meteoroids are the primary source of extra-terrestrial material to Earth. Meteoroid ablation deposits between 5 and 300 tons of material in our atmosphere every day. This daily input is responsible for multiple phenomena in the Mesospheric and Lower Thermospheric region (MLT) such as the creation of sporadic E layers, the creation of Noctilucent clouds, and the formation of stratospheric aerosol. A fundamental parameter to understand how meteoroids are responsible for the phenomena described above is their mass. Unfortunately, the only way we can observe meteoroids is via the plasma and light formation --- called a meteor --- they create as they descend through the atmosphere. Over the years, the scientific community has primarily employed two instruments to understand and estimate the Earth-bound meteoroid mass flux from the observation of meteors, namely radars and (CCD) cameras. Mass estimation from optical devices is based on the idea of energy conservation: the energy lost during the entry process of a meteoroid is converted to light. This relation is mediated via a parameter called the luminous efficiency, $\tau$. Radar mass (RM) relies instead on a more refined theoretical basis which, similarly to optical masses (OM), depends on an equivalent empirical value: the ionization coefficient $\beta$. The existing formulations for $\tau$ and $\beta$ have come from many different sources: theoretical models, ground experiments, \textit{in-situ} experiments, and ground observations. The results of these studies have produced a multitude of empirical values, each in partial disagreement with the others. The discrepancy between different modeling parameters then adversely affects our ability to correctly estimate a meteoroid's mass. This work aims to bridge these discrepancies in two major way: first, by cross-estimating the value of $\tau$ and $\beta$ from concurrent observation via both radar and optical device. Second, we provide a numerical framework to simulate the entire entry process and mass loss for millimeter-sized meteoroids. For the analysis on the cross calibration of $\tau$ and $\beta$ we used the Poker Flat Inchoerent Scatter Radar --- located in Fairbanks, Alaska --- in combination with an Andor camera. We found 28 common events over a period of 10 hours of observation over two nights. Our analysis shows that out of the existing $\beta-\tau$ values, the combination consisting of $\beta$ by \cite{Bronshten1983} with $\tau$ by \cite{Campbell2012} provides the more consistent results based off an error ratio metric. We conclude the study by providing an updated value of $\tau$ based off of our gathered data and the newest experimental results for $\beta$ conducted at the University of Colorado's dust accelerator facility \citep{thomas2016, deluca2017}. This new $\beta-\tau$ provides an error ratio value approximately 10\% lower than the previously computed best $\beta-\tau$ pair. For our numerical results we implemented a Direct Simulation Monte Carlo flow solver loosely coupled with an ablation routine. This coupled system allow us to provide the first full 2D simulation of the atmospheric entry of a sub-centimeter meteoroid into Earth's atmosphere. Our simulations show three important results: first, the existing zero order models make for a reasonable approximation of the mass loss for sub-millimeter objects, albeit the mass deposition profile is different between the two approximations. The small scales of the meteoroid considered, coupled with its high conductivity makes for a quasi-uniform meteoric temperature. Second, the neutral density surrounding the meteoroid significantly increases from it's background value. At the stagnation point it increases between two to three order of magnitude, depending on the initial velocity of the meteoroid, its ablation rate and the original neutral density. This density increase is due to a combination of the ablated mass and the compression of the impinging fluid. Lastly, existing zero order models under-estimate the total heat flux received by the meteoroid. Heat shielding for meteoroids in free molecular flow is negligible even when taking into account increases in neutral densities caused by the evaporated mass. Our simulations show meteoroids receive up to 95\% of the available heat flux from the flow. Shielding effects become significant as meteoroid size increases ($>