Electron impact ionization in the icy Galilean satellites’ atmospheres

Abstract

Electron impact ionization is critical in producing the ionospheres on many planetary bodies and, as discussed here, is critical for interpreting spacecraft and telescopic observations of the tenuous atmospheres of the icy Galilean satellites of Jupiter (Europa, Ganymede, and Callisto), which form an interesting planetary system. Fortunately, laboratory measurements, extrapolated by theoretical models, were developed and published over a number of years by K. Becker and colleagues (see Deutsch et al. in Adv At Mol Opt Phys 57:87–155, 2009) to provide accurate electron impact ionization cross sections for atoms and molecules, which are crucial to correctly interpret these measurements. Because of their relevance for the Jovian icy satellites, we provide useful fits to the complex, semiempirical Deutsch–Märk formula for energy-dependent electron impact ionization cross sections of gas-phase water products (i.e., H$_2$O, H$_2$, O$_2$, H, O). These are then used with measurements of the thermal plasma in the Jovian magnetosphere to produce ionization rates for comparison with solar photo-ionization rates at the icy Galilean satellites.

Graphic abstract

Appendices

Appendix

A DM formula

The “modified” DM formula [20] derives the total energy-dependent electron-impact ionization cross section, $\sigma (E)$, of an atom as:

$$\begin{aligned} \sigma (E) = \sum _{n,l} \pi g_{n,l} r_{n,l}^2 \xi _{n,l} b_{n,l}^{(q)}(u) \left[ \ln (c_{n,l} u) / u \right] . \end{aligned}$$

(2)

Table 6 Various terms in the energy-dependent function $b_{n,l}^{(q)}(u) \left[ \ln (c_{n,l} u) / u \right]$ (Eqs. 2–3) for electron impact ionization cross section of H atoms

Table 7 Various terms in the energy-dependent function $b_{n,l}^{(q)}(u) \left[ \ln (c_{n,l} u) / u \right]$ (Eqs. 2–3) for electron impact ionization cross section of O atoms

Here $r_{n,l}$ is the radius of maximum radial density of and $\xi _{n,l}$ is the number of electrons in the atomic subshell characterized by quantum numbers n and l; $g_{n,l}$ is a weighting factor originally determined from a fitting procedure; $u = E / E_{n,l}$, where E is the incident energy of the electrons and $E_{n,l}$ is the ionization energy in the (n, l) subshell; and $c_{n,l}$ is a constant determined from measured cross sections for various values of n and l. Tables 4 and 5 list values for the various terms in Eq. 2 for H and O atoms, respectively. The energy-dependent function $b_{n,l}^{(q)}(u) \left[ \ln (c_{n,l} u) / u \right]$ allows the DM formula to be applied up to keV-energy regimes, with $b_{n,l}^{(q)}(u)$ written as the following:

$$\begin{aligned} b_{n,l}^{(q)}(u) = \frac{A_1 - A_2}{1 + (u / A_3)^p} + A_2, \end{aligned}$$

(3)

where $A_{1-3}$ and p are constants determined from measured cross sections for various values of n and l, and the superscript (q) refers to the number of electrons in the (n, l) subshell. Tables 6 and 7 list values for the various terms in the energy-dependent function $b_{n,l}^{(q)}(u) \left[ \ln (c_{n,l} u) / u \right]$ for H and O atoms, respectively. We refer the reader to the review by [18] for how $\sigma (E)$ of atoms are used to calculate $\sigma (E)$ of molecules composed of those atoms; i.e., how to estimate $\sigma (E)$ of H$_2$, O$_2$, and H$_2$O from $\sigma (E)$ of H and O.

B Photoionization rates

Table 8 lists the range of photoionization rates determined by [26] for a “quiet” Sun (i.e., solar minimum)—“active” Sun (i.e., solar maximum), which are then scaled to the average Jovian system’s distance from the Sun, 5.2 AU, ignoring any possible absorption with depth into the atmosphere.

Table 8 Photoionization rates at 5.2 AU