Velocity distribution function of Na released by photons from planetary surfaces
Introduction
Since the advent of space exploration and ground-based observations that made possible the detection of, for instance, the tenuous Na and K atmospheres of Mercury and the Moon, several studies and experiments have been carried out on lunar mineral grains and simulant materials (e.g. (Keller and McKay, 1993)). Some studies have focused on investigating the most relevant desorption processes for alkalis (e.g. (Ageev et al., 1998; Wilde et al., 1999; Yakshinskiy and Madey, 2000; Yakshinskiy and Madey, 2004; Madey et al., 1998)) to better understand the interaction between the surface and the exosphere of the planetary body under study.
Neutral sodium in the exospheres of the Moon and Mercury is one of the most studied alkali metals since it is relatively easy to observe from the Earth, but for several decades there has been controversy concerning the processes promoting it into the atmosphere. One of the few experimental results in the laboratory studying the sodium release processes happening on Mercury's surface are the experiments by (Yakshinskiy and Madey, 2000, 2004). These authors studied the desorption induced by electronic transitions (DIET) of Na adsorbed on model mineral surfaces and lunar basalt samples. In particular, they measured velocity distribution functions (VDF) of Na released via ESD from SiO2 surfaces and found it to be “clearly non-thermal” with respect to the surface temperature, similar to that of a 1200 K Maxwellian but with a higher-energy tail. The VDF of ESD from a lunar basalt sample was found to have a smaller offset in speed compared to that of SiO2, with a peak around 0.8 km s−1 instead of 1 km s−1 (Yakshinskiy and Madey, 2004). Since ESD is a charge transfer process leading to electronic excitations similar to PSD, with comparable cross sections and an identical excitation threshold of 4–5 eV (Yakshinskiy and Madey, 2000), the VDF distributions of released sodium are quite similar, so that ESD measurements can be substituted for the effects of UV photons. Since then, people have interpreted these VDFs using either thermal (Maxwellian) or non-thermal distributions. In previous studies a Maxwell- Boltzmann velocity distribution has been assumed with temperatures in the range: 1200–1500 K (e.g. (Sarantos et al., 1968; Killen et al., 2009; Leblanc et al., 2003; Killen et al., 2007)).
In other studies, non-thermal high-energy tail distributions have been assumed, for instance the energy distribution function (EDF) used by (Johnson et al., 2002) for ESD from icy surfaces, which was later used and modified by (Wurz et al., 2010) to model PSD of volatiles to determine the Na and K density profiles in the exosphere of Mercury. This modified version was also used by (Schmidt et al., 1029) and (Mura et al., 2009) to determine the escape rates of PSD process in Mercury's exosphere, and by (Tenishev et al., 2013) and (Sprague et al., 2012) to model lunar Na exosphere. A summary of previous works using different EDFs and arriving at different temperatures of the released Na atoms by PSD or ESD is shown in Table 1.
Hitherto we use the measurement results reported by (Yakshinskiy and Madey, 2000, 2004), more specifically, the reported VDFs for neutral Na from SiO2 substrates and from lunar basalt samples. We examine the fitness of some distributions functions, namely the Maxwell-Boltzmann, the empirical energy distribution proposed by (Wurz et al., 2010) for released volatiles from Mercury's surface via PSD (named here after “E-PSD”) which is based on the one used by (Johnson et al., 2002) for icy surfaces, and the Weibull distribution. Using the Graphical Residual Analysis (GRA), we determine which of the these distributions is statistically more adequate to explain the measurements and we discuss their physical validity.
The way the energy is imparted to a photodesorbed atom from Mercury's surface (or similar planetary surfaces) is not through a thermal process, but rather by single electronic excitations. Choosing an appropriate model of the EDF/VDF of the atoms released is important to properly interpret Na measurements in planetary exospheres, which are often assumed to have temperatures way above the surface temperature (see review by (Killen et al., 2007) or the work by (Cassidy et al., 2015), for instance). This work aims to clarify the implications of assuming either thermal or non-thermal energy distributions of atoms released by PSD and ESD from planetary surfaces not protected by an atmosphere, like the majority of the planetary objects of the solar system.
In Section 2 we give a general physical description of ESD and PSD processes, and in Section 3 we describe the results from experiments by (Yakshinskiy and Madey, 2000, 2004). The measurements reported from these experiments are used for the statistical analysis in Section 4, where we present the mathematical description of the different probability distribution functions used to fit these measurements. We briefly describe in Section 4.4 the GRA we used to test the model distribution described in the previous section. In Section 5 we show the results of the fitting and the GRA, we discuss the physical interpretations in Section 6, and we conclude in Section 7.
Section snippets
Desorption induced by electronic transitions (DIET)
DIET phenomenon refers to both the electron-stimulated desorption (ESD) and the photon-stimulated desorption (PSD). Desorption of atoms on the surface occurs when the surface is bombarded by electrons or by photons with sufficient energy to induce transitions to repulsive electronic states of the atom. The released particles are supra-thermal because the absorbed UV photon has energies way in excess compared to thermal energies of the surface, which leads to the excitation of an anti-bonding
Experiments
(Yakshinskiy and Madey, 2000, 2004) studied the desorption induced by electronic transitions (DIET) of Na adsorbed on amorphous, stoichiometric SiO2 films and on a lunar basalt sample. Experiments included ESD and PSD as release processes. Reported measurements were done with a different coverage and different substrate temperature: ML of Na adsorbed at 250 K on SiO2 films (Yakshinskiy and Madey, 2000), and ML of Na adsorbed at 100 K on a lunar basalt sample (Yakshinskiy and Madey,
Velocity distribution functions
To mathematically best describe the published laboratory measurements (Yakshinskiy and Madey, 2000, 2004) and planetary observations (e.g. (Cassidy et al., 2015)) we seek a VDF that has a characteristic energy significantly higher than what corresponds to the surface temperature and that tails towards higher speeds. The second goal of the seeked model distribution function is a parametrization that allows for its applications at other surface temperatures than the measured ones, in particular
Results
In Section 4 we provided the mathematical description of three different model distributions and then searched for the best parameter combination to fit the measured VDFs under consideration. The different fits obtained are presented in this section in the main plots in Fig. 2. How well the model distributions used so far fit the measurements is qualitatively estimated by virtue of the GRA. The results of the GRA are shown in the bottom part of each panel in Fig. 2; the plots of residuals are
Discussion
In this work we test the statistical adequacy of three model distributions: the Maxwell-Boltzmann and two non-Maxwellian by means of the Graphical Residual Analysis. In this section we discuss which one we consider is physically more valid.
Concerning the results for the M-B fits: we find that the measured VDFs of released Na atoms are too narrow compared to the M-B fits suggested by (Yakshinskiy and Madey, 2004) and as noted by other authors before. A considerably better fit with M-B is only
Conclusions
Motivated by an ongoing debate whether or not ESD and PSD produce non-thermal EDF/VDF of the desorbed atoms in planetary exospheres, we compare the often-used model distributions previously proposed to fit the available observations. We use all the available measurements reported by (Yakshinskiy and Madey, 2000, 2004), who studied the ESD and PSD of Na adsorbed on SiO2 films and lunar basalt samples. They reported suprathermal Na atoms with peak speeds of and m s−1, which were
Acknowledgments
We thank the Swiss National Science Foundation (200020_172488) for supporting this work. The data used are listed in the references and included in the supplementary material.
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